Higher Worksheets GCSE Syllabus Worksheets. Grades 1 to 9. Grade 1. Grade 6. Grade 2. Grade 7. Grade 8. Grade 3. Grade 4. Grade 9.

Transcription

1 05 GCSE Syllabus Worksheets Higher Worksheets Grades to 9 Grade Grade Grade Grade 4 Grade 6 Grade 7 Grade 8 Grade 9 Grade 5 Instructions for use Clicking on something like this Grade 4 will take you to the Grade 4 clip numbers and titles. Clicking on something like this Compound Units will take you to Worksheet 4. Clicking on something like this MathsWatch Clip 4 Grade 4 questions will take you back to the contents page.

2 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Place Value Ordering Integers Ordering Decimals Reading Scales Simple Mathematical Notation Interpreting Real-Life Tables Introduction to Algebraic Conventions Coordinates Simple Geometric Definitions Polygons Symmetries Tessellations and Congruent Shapes Names of Angles The Probability Scale Tally Charts and Bar Charts Pictograms

3 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Adding Integers and Decimals Subtracting Integers and Decimals Multiplying Integers Dividing Integers Inverse Operations Money Questions Negatives in Real Life Introduction to Fractions Equivalent Fractions Simplifying Fractions Half-Way Values Factors, Multiples and Primes Introduction to Powers/Indices Multiply and Divide by Powers of Rounding to the Nearest 0, 00 etc Rounding to Decimal Places Simplifying - Addition and Subtraction Simplifying - Multiplication Simplifying - Division A/B Function Machines Generating a Sequence - Term to Term Introduction to Ratio Using Ratio for Recipe Questions Introduction to Percentages Value for Money Introduction to Proportion Grade continued

4 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Properties of Solids Nets Angles on a Line and at a Point Measuring and Drawing Angles Drawing a Triangle Using a Protractor Reflections Rotations Translations Plans and Elevations A/B/C/D Perimeters Area of a Rectangle Area of a Triangle Area of a Parallelogram Area of a Trapezium Frequency Trees Listing Outcomes Calculating Probabilities Mutually Exclusive Events Two-Way Tables Averages and the Range Data - Discrete and Continuous Vertical Line Charts Frequency Tables and Diagrams

5 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Multiplying Decimals Dividing Decimals Four Rules of Negatives Listing Strategies Comparing Fractions Adding and Subtracting Fractions Finding a Fraction of an Amount Multiplying Fractions Dividing Fractions BODMAS/BIDMAS Reciprocals Calculator Questions Product of Primes Highest Common Factor (HCF) Lowest Common Multiple (LCM) A/B Squares, Cubes and Roots Working with Indices Standard Form Decimals and Fractions Fractions, Percentages, Decimals Percentage of an Amount (Calc.) Percentage of an Amount (Non-Calc.) Change to a Percentage (Calc.) Change to a Percentage (Non-Calc) A/B Rounding to Significant Figures Estimating Answers Using Place Value Grade continued

6 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Expanding Brackets Simple Factorisation Substitution Straight Line Graphs A/B/C The Gradient of a Line Drawing Quadratic Graphs A/B/C/D/E Sketching Functions Solving Equations Using Flowcharts Subject of a Formula Using Flowcharts Generate a Sequence from the nth Term Finding the nth Term A/B/C Special Sequences Exchanging Money Sharing Using Ratio Ratios, Fractions and Graphs Increase/Decrease by a Percentage Percentage Change Reverse Percentage Problems Simple Interest Grade continued

7 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade Foundation and Higher Metric Conversions Problems on Coordinate Axes Surface Area of a Prism A/B Volume of a Cuboid Circle Definitions Area of a Circle Circumference of a Circle A/B/C Volume of a Prism A/B Angles and Parallel Lines A/B/C Angles in a Triangle Properties of Special Triangles Angle Sum of Polygons A/B Bearings A/B Experimental Probabilities Possibility Spaces Venn Diagrams Representing Data Scatter Diagrams Averages From a Table A/B/C/D

8 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 4 Foundation and Higher Index Notation A/B Introduction to Bounds Midpoint of a Line on a Graph Expanding and Simplifying Brackets A/B Solving Equations Rearranging Simple Formulae Forming Formulae and Equations A/B/C Inequalities on a Number Line Solving Linear Inequalities A/B Simultaneous Equations Graphically Fibonacci Sequences Compound Units A/B Distance-Time Graphs Similar Shapes A/B/C Bisecting an Angle Constructing Perpendiculars Drawing a Triangle Using Compasses Enlargements Tangents, Arcs, Sectors and Segments Pythagoras Theorem A/B/C Simple Tree Diagrams A/B/C Sampling Populations Time Series

9 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 5 Foundation and Higher Negative Indices Error Intervals Mathematical Reasoning Factorising and Solving Quadratics The Difference of Two Squares Finding the Equation of a Straight Line A/B Roots and Turning Points of Quadratics Cubic and Reciprocal Graphs Simultaneous Equations Algebraically Geometric Progressions Compound Interest and Depreciation Loci A/B/C Congruent Triangles A/B Sectors of a Circle Trigonometry A/B/C/D/E Spheres Pyramids Cones A/B/C Frustums Exact Trigonometric Values Introduction to Vectors Harder Tree Diagrams A/B/C Stratified Sampling A/B

10 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 6 Higher Recurring Decimals to Fractions Product of Three Binomials Iteration - Trial and Improvement Iterative Processes Enlargement - Negative Scale Factor Combinations of Transformations Circle Theorems Proof of Circle Theorems Probability Using Venn Diagrams Cumulative Frequency Boxplots A/B/C/D/E F/G/H/I/J A/B/C/D/E/F A/B/C/D/E/F A/B/C/D

11 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 7 Higher Fractional Indices Recurring Decimals - Proof Rearranging Difficult Formulae Solving Quadratics with the Formula Factorising Hard Quadratics Algebraic Proof Exponential Functions Trigonometric Graphs A/B Transformation of Functions Equation of a Circle Regions Direct and Inverse Proportion A/B Similarity - Area and Volume The Sine Rule The Cosine Rule Area of a Triangle Using Sine And and Or Probability Questions Histograms A/B/C/D/E A/B/C/D E/F/G/H

12 Take me to... Grade Grade Grade Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 8 Grade 9 Higher Upper and Lower Bounds A/B/C Surds A/B/C Perpendicular Lines Completing the Square Algebraic Fractions A/B Simultaneous Equations with a Quadratic Solving Quadratic Inequalities Finding the nth Term of a Quadratic Inverse Functions Composite Functions Velocity-Time Graphs Pythagoras in D Trigonometry in D Vectors A/B/C/D/E

13 MathsWatch Clip Grade questions Place Value ) a) Write the number forty five thousand, two hundred and seventy three in figures. b) Write the number five thousand, one hundred and three in figures. c) Write the number three hundred thousand, seven hundred and ninety one in figures. d) Write the number two and a half million in figures. e) Write the number one and three quarter million in figures. ) Write the following numbers in words a) 50 b) 50 c) d) e) ) a) Write down the value of the 7 in the number 75. b) Write down the value of the 6 in the number c) Write down the value of the in the number d) Write down the value of the 5 in the number e) Write down the value of the in the number ) What is the value of the digit 7 in 8.47? Choose, and circle, the correct answer from the following: Page

14 MathsWatch Clip Grade questions Ordering Integers Put these numbers in order, starting with the smallest: ) 74, 57, 8, 8, 6 ) 9, 84,, 8, 4 ) 76, 0,, 40, 7 4),, 7, 0, 5),,, 5, 7 6) 4, 6, 0, 6, 7) 05, 005, 05, 55, ) 8, 6, 4, 65, 4 Page

15 MathsWatch Clip Grade questions Ordering Decimals ) Put these amounts of money in order, starting with the smallest: a) 4.50,.8, 4.05,.99,.54 b).5,.4,.4,.04,.99 c) 5.8, 4.8,.99, 46.0, 46.0 ) Circle the smallest number: 0., 0.09, 0.99, 0.5, 0. ) Put these numbers in order, starting with the smallest:.0,.45,.4,.006,.405 4) Put these numbers in order, starting with the smallest: 0.76, 0.668, 0.608, 0.099, ) Put these numbers in order, starting with the smallest: 5.004, 4.889, 4.099, 5.00, Page

16 MathsWatch Clip 4 Grade questions Reading Scales ) Estimate the reading on each of these scales: a) b) c) kg kg kg d) 0 e) 00 f) kg kg kg ) This scale shows degrees Centigrade. C a) What temperature is the arrow pointing to? b) Draw an arrow which points to -7 C. ) This is a diagram for converting between gallons and litres. Gallons Litres Use the diagram to convert a) gallons to litres. b) 4.5 gallons to litres. c) 6 litres to gallons. Page 4

17 MathsWatch Clip 5 Grade questions Simple Mathematical Notation ) For each mathematical sign, below, write a brief description of the sign. The first one has already been done. a) < less than b) c) > d) e) = ) Insert one of the two symbols < or > to make the following statements true: a) b) c) d) e)? ? 8 ) You must be at least.6 m tall to ride on a rollercoaster at Romy Park. Circle the correct description of this out of the following: Height <.6 m Height <.6 m Height =.6 m Height >.6 m Height >.6 m Page 5

18 MathsWatch Clip 6 Grade questions Interpreting Real-Life Tables ) Calculate the difference in hours and minutes between 9.0 am and.45 pm. ) Calculate the difference in hours and minutes between 5 and 5. ) The table shows the distances in kilometres between some cities in the USA. San Francisco New York Miami Los Angeles Chicago a) Write down the distance between San Francisco and Miami. One of the cities in the table is 454 km from Los Angeles. b) Write down the name of this city. c) Write down the name of the city which is furthest from Chicago. 4) Here is part of a train timetable Manchester Stockport Macclesfield Stoke Stafford Euston a) Tim catches the train from Manchester. At what time should he expect to arrive at Euston? b) Jenny arrives at the Stockport train station at (i) How long should she expect to wait for a train to Stoke? (ii) How long should her train journey take? c) Sarah needs to travel to Euston from Macclesfield. She has to arrive at Euston before What is the departure time of the latest train she can catch to get there on time? Page 6

19 MathsWatch Clip 7 Grade questions Introduction to Algebraic Conventions ) Write the following in their simplest forms using algebraic notation: a) r 5 b) c 4 c) x + x + x + x d) e ) Write the following using algebraic notation: a) I think of a number and multiply it by 4. b) I think of a number, multiply it by 6 and then add 5. c) I think of a number, triple it and then subtract 7. ) Write the following using algebraic notation: a) I think of a number, add and then multiply the result by. b) I think of a number, subtract 6 and then divide the result by. 4) Write the following using algebraic notation: a) I think of a number, add 9, multiply the result by 4 and then divide everything by. b) I think of a number, take away 5, divide the result by and then multiply the result by. Page 7

20 MathsWatch Clip 8 Grade questions y Coordinates ) Write down the coordinates of the points A to H B A C E 4 D F H O G x ) a) Write down the coordinates of: (i) A (ii) B b) Write down the coordinates of the midpoint of the line AB. y B A ) Using the pair of axes, a) Plot the points A(, 0), B(4, 0), C(5, ) and D(, ). b) Join the points in order, to form a shape and name the shape. M is the midpoint of the line segment AC. c) Find the coordinates of M. O y 5 4 x 4) Using the same pair of axes, a) Plot the points R(-, -), S(, ) and T(-, ). b) Join R to S and S to T. RSTU is a kite. c) Write the coordinates of point U O x -5 Page 8

21 MathsWatch Clip 9 Grade questions Simple Geometric Definitions ) Write one or two short sentences which say what the special features are of the triangles listed, below. The first one has been done for you. a) An equilateral triangle All the sides are the same length. All three angles are 60 b) A right-angled triangle c) A scalene triangle d) An isosceles triangle ) Next to each of the quadrilaterals, write down its special name. a) b) c) d) Page 9

22 MathsWatch Clip 0 Grade questions Polygons ) Next to each of the shapes, write down its name. a) b) ) a) What is the name given to a 0-sided shape? b) What is the name given to an 8-sided shape? ) To be a regular polygon the shape must have equal and equal. Fill in the blanks. 4) What are the names of these regular polygons? a) b) Page 0

23 MathsWatch Clip Grade questions Symmetries ) Draw all the lines of symmetry on the triangle and the rectangle. ) What is the order of rotational symmetry of the two shapes below? S ) The diagram below, shows part of a shape. P The shape has rotational symmetry of order 4 about point P. Complete the shape. 4) On each of the shapes below, draw one plane of symmetry. Page

24 MathsWatch Clip Grade questions Tessellations and Congruent Shapes ) Show how this shape will tessellate. You must draw six more shapes. ) Two of these shapes are congruent. Which are they? a) b) c) d) e) Page

25 MathsWatch Clip Grade questions Names of Angles ) Write the name of each angle, below. a) b) c) d) ) Draw a triangle which contains: a) Three acute angles. b) One obtuse angle and two acute angles. c) A right angle. Page

26 MathsWatch Clip 4 Grade questions The Probability Scale ) a) On the probability scale below, mark with a cross ( ) the probability that it will snow in Birmingham in July. 0 b) On the probability scale below, mark with a cross ( ) the probability that it will rain in Wales next year. 0 c) On the probability scale below, mark with a cross ( ) the probability that you will get a tail when you flip a fair coin. 0 d) On the probability scale below, mark with a cross ( ) the probability that you will get a number bigger than 4 when you roll an ordinary dice. 0 ) 4 jelly babies are in a bag. are red, is green and is black. Without looking in the bag, a jelly baby is taken out. a) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green. 0 b) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green or black. 0 c) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is red or black. 0 Page 4

27 MathsWatch Clip 5 Grade questions Tally Charts and Bar Charts ) Here is a list of coins in Yvonne's purse. 5p 0p p 50p Coin Tally Frequency 0p 5p 50p p 5p 5p p 5p p 5p 5p p Complete the table for this information. ) Tim made a note of how many minutes he spent on the internet over the period of a week. His results are as follows: Monday Tuesday 0 mins 0 mins Wednesday 60 mins Thursday Friday Saturday Sunday 40 mins 0 mins 50 mins 40 mins Draw a bar chart to show this information. Page 5

28 MathsWatch Clip 6 Grade questions Pictograms ) The pictogram shows the number of watches sold by a shop in January, February and March. January February March April May Key represents 4 watches. a) How many watches were sold in January? b) How many more watches were sold in March than in February? 9 watches were sold in April. 4 watches were sold in May. c) Use this information to complete the pictogram. ) The pictogram shows the number of DVDs borrowed from a shop on Monday and Tuesday. Monday Tuesday Wednesday Thursday Key represents 0 DVDs. a) How many DVDs were borrowed on (i) Monday? (ii) Tuesday? On Wednesday, 50 DVDs were borrowed. On Thursday, 5 DVDs were borrowed. b) Show this information in the pictogram. Page 6

29 MathsWatch Clip 7 Grade questions Adding Integers and Decimals ) a) 4 b) 5 7 c) ) a) 6 7 b) 9 8 c) ) a) b) c) ) There were two exhibitions at the NEC one Sunday. 86 people went to one of the exhibitions and 47 people went to the other exhibition. How many people went to the NEC, in total, on the Sunday? 5) a).6 +. b) c) ) a) +.5 b) c) Page 7

30 MathsWatch Clip 8 Grade questions Subtracting Integers and Decimals ) a) b) 7 4 c) ) a) b) 7 7 c) ) a) b) 6 8 c) ) There were two films showing at a cinema one Saturday. One of the films was shown in a large room and the other was in a smaller room. The film in the larger room was watched by a total of 56 people. The film in the smaller room was watched by 67 people. How many more people saw the film in the larger room? 5) a) b) Page 8

31 MathsWatch Clip 9 Grade questions Multiplying Integers ) Work out a) 8 b) 5 7 c) 6 4 d) 64 4 e) 6 4 f) 8 59 g) h) 48 4 i) ) MathsWatch Travel has 6 coaches. Each of these coaches can carry 5 passengers. How many passengers in total can all the coaches carry? ) MathsWatch Tours has a plane that will carry 47 passengers. To fly from Manchester to Lyon, each passenger pays 65 Work out the total amount that the passengers pay. 4) A Science textbook costs. Mr Jones buys a class set of 4 books. How much do they cost him? 5) A graphical calculator costs 8. How much would 4 calculators cost? Page 9

32 MathsWatch Clip 0 Grade questions Dividing Integers ) Work out a) 5 5 d) 77 9 g) 75 4 b) e) 7 6 h) 5 0 c) f) 5 i) 8 ) A box can hold 9 books. Work out how many boxes will be needed to hold 646 books. ) The distance from Glasgow to Paris is 90 km. A flight from Glasgow to Paris lasts hours. Given that Average speed = Distance Time Work out the average speed of the aeroplane in km/h. 4) Pencils cost 5p each. Mr Smith spends 5 on pencils. Work out the number of pencils he gets. 5) Yesterday, Gino was paid 9.6 for delivering pizzas. He is paid 5p for each pizza he delivers. Work out how many pizzas Gino delivered yesterday. 6) Emma sold 8 teddy bears for a total of 5 She sold each teddy bear for the same price. Work out the price at which Emma sold each teddy bear. 7) Canal boat for hire for 4 days Work out the cost per day of hiring the canal boat. 8) A teacher has 59 to spend on books. Each book costs 6 How many books can the teacher buy? 9) John delivers large wooden crates with his van. The weight of each crate is 68 kg. The greatest weight the van can hold is 980 kg. Work out the greatest number of crates that the van can hold. Page 0

33 MathsWatch Clip Grade questions Inverse Operations ) a) Which operation is the inverse of add? b) Which operation is the inverse of divide? ) Use inverse operations to complete the second equation each time. a) + 6 = 8? = b) 8? = 5 + = 8 ) Use inverse operations to complete the second equation each time. a) 4 = 8 = 4 b) 60 = 5 = 60 4) Use inverse operations to complete the second equation each time. a) 9 + = = 9 b) 46? = = 46 5) Use inverse operations to complete the second equation each time. a) 8 7 = 4 = 8 b) 6 = 48 = Page

34 MathsWatch Clip Grade questions Money Questions ) Tony buys 4 kg of potatoes at.60 per kilogram and kg of onions at.80 per kilogram. She pays with a 0 note. How much change should she receive? ) Bags of sweets.50 per bag Buy, get free How many bags of sweets can you buy for 9? ) Cinema Prices Adult Child Family ticket ( adults and children a) adult and 7 children went to the cinema. How much did they pay altogether? b) adults and children went to the cinema and bought a family ticket. How much did they save altogether? Page

35 MathsWatch Clip Grade questions Negatives in Real Life ) At midnight, the temperature was -7 C. By 7am the next morning, the temperature had increased by 6 C. a) Work out the temperature at 7am the next morning. At midday, the temperature was C. b) Work out the difference between the temperature at midday and the temperature at midnight. c) Work out the temperature which is halfway between -7 C and C. ) The table below gives the temperature recorded on 5th December in 7 cities across the world. City Edinburgh London New York Moscow Paris Rome Cairo Temperature -6 C 0 C -5 C - C C 5 C 8 C a) Which city recorded the lowest temperature? b) What is the difference in temperature between New York and Paris? c) What is the difference in temperature between Cairo and Edinburgh? d) The temperature in Madrid was 9 C lower than in Rome. What was the temperature in Madrid? e) The temperature in Mexico City was 6 C higher than in New York. What was the temperature in Mexico City? ) The table shows the temperature on the surface of each of five planets. Planet Temperature Venus 0 C Jupiter -50 C Saturn -80 C Neptune -0 C Pluto -0 C a) Work out the difference in temperature between Jupiter and Pluto. b) Work out the difference in temperature between Venus and Saturn. c) Which planet has a temperature 0 C lower than Saturn? The temperature on Mars is 90 C higher than the temperature on Jupiter. d) Work out the temperature on Mars. Page

36 MathsWatch Clip 4 Grade questions Introduction to Fractions ) What fraction of each of the following shapes is shaded? a) b) c) d) e) f) ) Shade the given fraction in the following grids ) Which of these fractions is the smallest? or (use the grids to help) 9 Page 4

37 MathsWatch Clip 5 Grade questions Equivalent Fractions ) Each of the grids below has a fraction written at the side of it. a) Shade the grids to show these fractions b) What do you notice about how many little squares are shaded in each grid? ) Each of the grids below has a fraction written at the side of it. a) Shade the grids to show these fractions b) What do you notice about how many little squares are shaded in each grid? ) Find the missing values in these equivalent fractions. = = = 4 4) Find the missing values in these equivalent fractions = = = 0 5) How do you know that is not equivalent to 5? 7 56 Page 5

38 MathsWatch Clip 6 Grade questions Simplification of Fractions ) Write the following fractions in their simplest forms a) b) c) d) e) f) g) ) Write the following fractions in their simplest forms a) b) c) d) e) f) g) Page 6

39 MathsWatch Clip 7 Grade questions Half-Way Values ) Write down the number which is in the middle of: a) and 9 b) and 8 c) and d) 7 and e) 7 and 08 f) and 00 g) 6 and ) Write down the number which is in the middle of: a).4 and 6.8 b) 5.9 and.5 c) -5 and 7.8 ) a) 7 is in the middle of and which other number? b) 6 is in the middle of 9 and which other number? c).4 is in the middle of. and which other number? Page 7

40 MathsWatch Clip 8 Grade questions Factors, Multiples and Primes ) Write the factors of a) 6 b) 6 c) 8 d) 0 ) In a pupil s book the factors of are listed as 4 5 The above list contains a mistake. Cross it out from the list and replace it with the correct number. ) The factors of 0 and 40 are listed 0:,,, 5, 6, 0, 5, 0 40:,, 4, 5, 8, 0, 0, 40 Write the common factors of 0 and 40 (the numbers that are factors of 0 and 40). 4) Write the first four multiples of a) b) 5 c) 0 d) 5 5) In a pupil s book the first 7 multiples of 8 are listed as The above list contains mistakes. Cross them out and replace them with the correct numbers. 6) The first five multiples of 4 and 0 are listed 4: 4, 8,, 6, 0 0: 0, 0, 0, 40, 50 From the two lists above, write the common multiple of 4 and 0. 7) List the first five prime numbers 8) Using just this list of numbers: find the following: a) The prime numbers b) The factors of 8 c) The multiples of Page 8

41 MathsWatch Clip 9 Grade questions Introduction to Powers/Indices ) Write the following using indices: eg. = 4 a) d) b) e).6.6 c) f) ) Write each of the following as a single power: eg =5 6 a) 6 6 d) 5 5 b) e) 9 c) f) ) Write each of the following as a single power: eg = 7 a) d) b) e) 6 c) 7 f) ) Write each of the following as a single power: 7 eg = = a) b) ) Match together cards with the same answer Page 9

42 MathsWatch Clip 0 Grade questions Multiply and Divide by Powers of 0 ) Multiply the following numbers by 0, 00 and 000: e.g ) Divide the following numbers by 0, 00 and 000: e.g ) Work out the following: 00 = 65 0 = 7 0 = 59 0 = =. 000 = 4 00 = = = = = = Page 0

43 MathsWatch Clip Grade questions Rounding to the Nearest 0, 00, etc ) Round these numbers to the nearest 0: a) 6 b) 6 c) 75 d) e) 797 f) 5 84 g) h) 758 ) Round these numbers to the nearest 00: a) 78 b) c) 549 d) 450 e) 8 f) 4 57 g) 9 9 h) 7 65 ) Round these numbers to the nearest 000: a) 850 b) 455 c) 0 d) e) f) g) 90 h) 8 90 Page

44 MathsWatch Clip Grade questions Rounding to Decimal Places ) Round the following numbers to decimal place a).68 b) c) 0.76 ) Round the following numbers to decimal places a) b) 4.7 c) ) Round the following numbers to decimal place a) b) c) ) Round the following numbers to decimal places a) b) 8.99 c) ) Work out the answer to and give your answer correct to decimal places. 6) Work out the answer to and give your answer correct to decimal place. 7) Work out the answer to 4.74 giving your answer correct to decimal places. 8) Find the answer to 7. giving your answer correct to decimal place. Page

45 MathsWatch Clip Grade questions Simplifying - Addition and Subtraction ) Simplify the following a) x + x b) x + x c) 5t t d) 7y 6y e) x + x + x f) g g + 6g g) x 7x + 8x h) y y y + 6y ) Simplify the following a) xy + xy b) 5xy xy c) 4x y + x y d) xy xy e) x y + 4x y x y f) 6a bc 4 + 5a bc 4 a bc 4 ) Simplify the following a) x + y + x + y b) x + y + x + 4y c) a + 4b a + b d) x + 4y x y e) 6x y + x + 5y f) 4x y x 5y g) t + 4u + t 7u h) xy + t xy 4t Page

46 MathsWatch Clip 4 Grade questions Simplifying - Multiplication ) Simplify the following a) x x b) x x x x x c) y y y ) Simplify the following a) x x 4 b) x x 5 c) y y d) x x x 4 e) y y y 4 ) Simplify the following a) x x b) 4x x c) t t d) 4y y e) x x x 4) Simplify the following a) x y b) x y c) 5r s t d) 6x y z 5) Simplify the following a) x y b) 4x y x c) xy xy d) 6xy x y y e) x y 5x 4 y f) tu t u 4tu Page 4

47 MathsWatch Clip 5 Grade questions Simplifying - Division ) Simplify the following a) x 5 x b) y 4 y c) g 8 g 5 d) y 4 y e) x x ) Simplify the following a) 6x 4 x b) y 5 y c) 0g 7 g 5 ) Simplify the following a) b) c) x 6 x x 9 x 4 6x 8 x 6 4) Simplify the following a) b) c) x 6 x x 4 x x 4 x x (x + 5) 5 (x + 5) 5) Simplify the following a) 0x 6 5x b) c) 4x 7 x 8x x 4x Page 5 A

48 MathsWatch Clip /4/5 Grade questions Simplifying ) a) Simplify 4p 6q b) Simplify d d d d c) Simplify t 9 t 4 8) a) Simplify a + 5c a + c b) Simplify x x 4 c) Simplify 4x y 4 5xy ) a) Simplify 4a + c a + c b) Simplify x 6c x + c 9) Simplify 6x + 8y + x 0y 0) a) Simplify x x x x b) Simplify x y ) a) Simplify 5xt + xt 4xt b) Simplify 4x + y x + 4y c) Simplify m m m ) a) Simplify pq + pq b) Simplify 5x + y x 4y d) Simplify n t ) a) Simplify 6a + 5b b + a 4) Simplify x 4x 5 y 4 b) Simplify x 4 + x 4 5) Simplify 4x + y x + 6y ) a) Simplify x + y + x + y + x b) Simplify t + t + t 6) a) Simplify t 4 t 5 4) a) Simplify a a b) Simplify a a a b) Simplify x y 4xy xy 7) a) Simplify x 6 x b) Simplify 0x y 4 xy 5) a) Simplify d + e d + 4e b) Simplify x x c) Simplify 5t + 8d t d d) Simplify (x + ) (x + ) Page 5 B

49 MathsWatch Clip 6 Grade questions Function Machines ) Complete the table for the function machine. 5 + In 4 7 Out 48 7 ) Complete the table for the function machine. 4 7 In - x Out 7 ) Complete the table for the function machine. + 6 In - 0 x Out 66 Page 6

50 MathsWatch Clip 7 Grade questions Generating a Sequence - Term to Term ) Write the first 5 terms of each of these sequences. a) Start at and add 6. b) Start at 4 and subtract. c) Start at 4 and subtract 7. d) Start at and multiply by. e) Start at 64 and divide by. f) Start at 600 and divide by 0. ) Find the term to term rule for each of these sequences. a) 4, 7, 0,, 6 b) 5,,, 9, 7 c), -, -8, -, -8 d) 7, 4, 8, 56, e) 00, 0,, 0., 0.0 Page 7

51 MathsWatch Clip 8 Grade questions Introduction to Ratio ) Write the following ratios in their simplest form: a) 6 : 9 b) 0 : 5 c) 7 : d) 4 : 4 e) : 40 f) 4 : : 8 g) 8 : 6 : 9 ) Write the missing value in these equivalent ratios: a) : 5 = : b) 4 : 9 = : 7 c) : 7 = 6 : 4 ) The ratio of girls to boys in a class is 4 : 5. What fraction of the class are girls? 4) A model of a plane is made using a scale of : 5. a) If the real length of the plane is 0 m, what is the length of the model? b) If the wings of the model are. m long, what is the actual length of the wings on the plane? Page 8

52 MathsWatch Clip 9 Grade questions Using Ratio for Recipe Questions ) Here are the ingredients needed to make 8 pancakes. James makes 4 pancakes. Pancakes Ingredients to make 8 pancakes 50 ml milk egg 40 g flour 5 g butter a) Work out how much milk he needs. Kate makes pancakes. b) Work out how much flour she needs. ) Here are the ingredients for making fish pie for 6 people. Fish pie for 6 people 80 g flour 40 g fish 80 g butter 4 eggs 80 ml milk Jill makes a fish pie for people. a) Work out how much flour she needs. Tim makes a fish pie for 5 people. b) Work out how much milk he needs. ) Here are the ingredients for making pineapple sorbet for 6 people. Pineapple sorbet for 6 people 800 g of pineapple 4 egg whites ½ lemon 00 g caster sugar Trevor makes pineapple sorbet for 8 people. a) Work out how much caster sugar he uses. Sid makes a pineapple sorbet. He uses lemons. b) Work out how many people he makes pineapple sorbet for. Page 9

53 MathsWatch Clip 40 Grade questions Introduction to Percentages ) What percentage of this grid is shaded? ) What percentage of this grid is shaded? ) a) What percentage of this grid is shaded? b) How many more squares should be shaded to make 80% of the grid shaded? 4) What percentage of this grid is shaded? Page 40

54 MathsWatch Clip 4 Grade questions Value for Money ) Which of the following offer better value for money? Working must be shown a) 00ml of toothpaste for 50p or 400ml of toothpaste for 90p b) 600g of bananas for 70p or 00g of bananas for p c) litres of paint for.60 or 5 litres of paint for.50 d) 60 teabags for.6 or 40 teabags for 0.96 ) Which of these is the best buy? 0 exercise books for exercise books for 7.80 ) Hamza needs to buy litres of paint. At the shop he gets two choices: 500ml for.55 or litre for a) Work out which of these would be the best buy for Hamza. b) How much does he save if he buys the best buy rather than the worst buy? You must show all your working. 4) Honey pots are sold in two sizes. A small pot costs 45p and weighs 450g. A large pot costs 80p and weighs 850g. Which pot of honey is better value for money? You must show all your working. Page 4

55 MathsWatch Clip 4 Grade questions Introduction to Proportion ) 8 bananas cost 4 Work out the cost of 5 bananas. ) Emily bought 4 identical pairs of socks for.60 Work out the cost of 9 pairs of these socks. ) The price of 6 chocolates is 7.0 Work out the cost of 8 chocolates. 4) Theresa bought 5 theatre tickets for 60 Work out the cost of 9 theatre tickets. 5) Jenny buys 4 folders. The total cost of these 4 folders is 6.40 Work out the total cost of 7 of these folders. 6) The cost of 5 litres of petrol is Work out the cost of 0 litres of petrol. 7) maths books cost 7.47 Work out the cost of 5 of these. 8) person can cut a large area of grass in 5 hours. How long would it take people to cut the grass? 9) 5 people take hours to build a wall. How long would it take people to build the wall? 0) 9 people can paint a bridge in 5 hours. How long would it take people to paint the bridge? Page 4

56 MathsWatch Clip 4 Grade questions Properties of Solids ) Draw a sketch of each of the following solids: a) A cube. b) A cylinder. ) Write down the mathematical name of each of these -D shapes. a) b) c) ) Look at this solid. a) What is its name? b) How many vertices does it have? c) How many edges are there? d) How many faces does it have? 4) This is a picture of a pentagonal prism. a) How many faces does it have? b) How many edges does it have? c) How many vertices does it have? Page 4

57 MathsWatch Clip 44 Grade questions Nets ) Sketch nets of these solids. a) b) ) On squared paper draw accurate nets of these solids. a) Cube b) Cuboid 4 cm 5 cm 4 cm 4 cm 8 cm 6 cm c) Right-angled triangular prism d) Triangular prism 5 cm cm 5 cm 4 cm 8 cm 7 cm 7 cm cm ) The two nets, below, are folded to make cubes. Two other vertices will meet at the the dot, A. Mark them with As. One other vertex will meet the dot B. Mark it with B. a) A b) B Page 44

58 MathsWatch Clip 45 Grade questions Angles on a Line and at a Point ) Work out the values of the unknown angles. 6 b 5 a 80 c d 5 5 ) Work out the values of the unknown angles. 0 5 x y Page 45

59 MathsWatch Clip 46 Grade questions Measuring and Drawing Angles ) Measure the following angles: a b d c e f ) Draw the following angles: a) Angle ABC = 60 b) Angle PQR = 7 c) Angle XYZ = 75 X Q P B A Y Page 46

60 MathsWatch Clip 47 Grade questions Drawing a Triangle Using a Protractor ) The diagram shows a sketch of triangle ABC. B Diagram NOT accurately drawn 7.4 cm A 8.5 cm 8 C BC = 7.4 cm AC = 8.5 cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on your diagram. ) The diagram shows a sketch of triangle PQR. Q Diagram NOT accurately drawn 7. cm P 9 cm 7 R Make an accurate drawing of triangle PQR. Page 47

61 MathsWatch Clip 48 Grade questions Reflections y = -x y 5 ) a) Reflect triangle T in the x axis. Label your new triangle U. b) Reflect triangle T in the line with equation y = -x. Label your new triangle V. 4 T O x y ) a) Describe fully the single transformation which maps triangle T to triangle U. T 4 b) Describe fully the single transformation which maps triangle T to triangle V O 4 5 x - - U - V -4-5 Page 48

62 MathsWatch Clip 49 Grade questions Rotations ) a) Rotate triangle T 90 anti-clockwise about the point (0, 0). Label your new triangle U. b) Rotate triangle T 80 about the point (, 0). Label your new triangle V. y 5 4 T O x y ) Describe fully the single transformation which maps triangle T to triangle U. 5 4 T U O x Page 49

63 MathsWatch Clip 50 Grade questions Translations ) -4 a) Translate triangle T by vector and label it U. b) Translate triangle T by vector - and label it V. y T O x - - ) a) Describe fully the single transformation which maps triangle A to triangle B. b) Describe fully the single transformation which maps triangle A to triangle C. y A B O x - - C Page 50

64 MathsWatch Clip 5 Grade questions Plans and Elevations ) The diagram shows a prism drawn on an isometric grid. Front a) On the grid below, draw the front elevation of the prism from the direction marked by the arrow. b) On the grid below draw a plan of the prism. Page 5 A

65 MathsWatch Clip 5 Grade questions Plans and Elevations ) Here is the plan and front elevation of a prism. The front elevation shows the cross section of the prism. Plan Front Elevation On the grid below, draw the side elevation of the prism. Page 5 B

66 MathsWatch Clip 5 Grade questions Plans and Elevations ) The diagram shows a solid prism made from centimetre cubes. a) On the centimetre square grid, draw the front elevation of the solid prism from the direction shown by the arrow. b) On the centimetre square grid below, draw the plan of the solid prism. Page 5 C

67 MathsWatch Clip 5 Grade questions Plans and Elevations ) The diagram shows a solid prism. cm cm cm 4 cm a) On the grid below, draw the front elevation of the prism from the direction of the arrow. b) On the grid below, draw the plan of the prism. Page 5 D

68 MathsWatch Clip 5 Grade questions Perimeters ) Find the perimeters of the following two shapes. a) b) 5 cm 9 cm 6 cm cm cm ) The length of a rectangle is 9 cm. The total perimeter is 0 cm. Calculate the length of the width of the rectangle. ) Work out the perimeter of this L shape. 5 cm 9 cm 4) This shape is made by cutting out an equilateral triangle from a square. 8 cm Two of these shapes are then put together to make this shape. Work out the perimeter of this new shape. Page 5

69 MathsWatch Clip 5 Grade questions Area of a Rectangle ) Find the areas of these two rectangles. a) 9 cm b) 4.5 cm 6 cm 8 cm ) Find the size of the missing sides in these two rectangles. a) b)? Area = 96 cm Area = 5 cm? cm 6.5 cm ) Find the area of the shaded section. 6 cm cm 9 cm 7 cm 4) Find the area of the L shape. 9 cm 8 cm cm 0 cm Page 5

70 MathsWatch Clip 54 Grade questions Area of a Triangle ) Find the areas of the following two triangles. a) b) 5 cm 6 cm 8 cm 9 cm ) Find the missing lengths. a) b)? Area = 5 cm Area = 84 cm cm 6 cm? ) ABCD is a square. PQRS is a square. A Q B P R C S cm 9 cm D Find the area of the shaded square, PQRS. Page 54

71 MathsWatch Clip 55 Grade questions Area of a Parallelogram ) Find the area of each of these parallelograms. a) b) 7 cm cm 0 cm 6.5 cm ) Find the missing lengths in these two parallelograms. a) b)? Area = 6 cm cm Area = 95 cm 4 cm? Page 55

72 MathsWatch Clip 56 Grade questions Area of a Trapezium ) Find the area of this trapezium. 4 cm 6 cm 8 cm ) The diagram shows a field. 70 m 86 m 88 m Work out the area of the field. ) In the trapezium, a = 6.6 cm, b = 8.4 cm and h =.6 cm. a h Work out the area of the trapezium. b 4) In the trapezium below, the area is 45 cm. a = 5 cm and b = 0 cm. Calculate the height, h, of the trapezium. a h b Page 56

73 MathsWatch Clip 57 Grade questions Frequency Trees 00 people underwent an operation at a hospital. Before the operation, based on their medical notes, it was predicted whether each person would make a full recovery or not. It was predicted that 85 people would make a full recovery. It was later found that 6 of the people expected to fully recover, didn t. Altogether, 87 people made a full recovery. Complete the frequency tree. Full recovery Full recovery Not a full recovery 00 Not a full recovery Full recovery Not a full recovery Page 57

74 MathsWatch Clip 58 Grade questions Listing Outcomes ) List all the outcomes if two coins are flipped. ) a) How many possible outcomes are there if three coins are flipped? b) List them all - the first one has been done for you: H H H ) a) How many possible outcomes are there if two six-sided dice are rolled? b) List them all. 4) a) How many possible outcomes are there if a coin is flipped and a dice is rolled? b) List them all. 5) a) How many possible outcomes are there if two coins are flipped and a dice is rolled? b) List them all. 6) How many possible outcomes are there if 6 coins are flipped? 7) If Carly has each fingernail painted at a salon and can choose between red, blue and green for each nail, how many different combinations are there for her to choose from? Page 58

75 MathsWatch Clip 59 Grade questions Calculating Probabilities ) A box contains grey counters and white counters. A counter is taken from the box at random. What is the probability of choosing a white counter? ) There are blue counters, 5 red counters and 7 green counters in a bag. A counter is taken from the bag at random. a) What is the probability that a green counter will be chosen? b) What is the probability that a blue or red counter will be chosen? ) In a class there are 0 boys and 5 girls. A teacher chooses a student at random from the class. Eric says that the probability a boy will be chosen is 0.5 because a student can be either a boy or a girl. Jenny says that Eric is wrong. Decide who is correct - Eric or Jenny - giving reasons for your answer. 4) Spinner A has numbers to 4 on it. Spinner B has numbers to on it. Both spinners are spun and the numbers on each are added together to give a score. What is the probability that the score will be a) 7? b) or 4? Page 59

76 MathsWatch Clip 60 Grade questions Mutually Exclusive Events ) If the probability of passing a driving test is 0.54, what is the probability of failing it? ) The probability that a football team will win their next game is. The probability they will lose is. What is the probability the game will be a draw? ) On the school dinner menu there is only ever one of four options. Some of the options are more likely to be on the menu than others. The table shows the options available on any day, together with three of the probabilities. Food Curry Sausages Fish Casserole Probability a) Work out the probability of the dinner option being Fish. b) Which option is most likely? c) Work out the probability that it is a Curry or Sausages on any particular day. d) Work out the probability that it is not Casserole. 4) Julie buys a book every week. Her favourite types are Novel, Drama, Biography and Romance. The table shows the probability that Julie chooses a particular type of book. Type of book Novel Drama Biography Romance Probability x x a) Work out the probability that she will choose a Novel or a Drama. b) Work out the probability that she will choose a Biography or a Romance. The probability that she will choose a Biography is the same as the probability she will choose a Romance. c) Work out the probability that she will choose a Biography. Page 60

77 MathsWatch Clip 6 Grade questions Two-Way Tables ) Billy has been carrying out a survey. He asked 00 people the type of water they like to drink (still, sparkling or both). Here are part of his results: Still Sparkling Both Total Male 6 5 Female 0 0 Total 6 00 a) Complete the two-way table. b) How many males were in the survey? c) How many females drink only still water? d) How many people drink only sparkling water? ) 90 students each study one of three languages. The two-way table shows some information about these students. French German Spanish Total Female Male 7 Total of the 90 students are male. 9 of the 50 male students study Spanish. a) Complete the two-way table. b) How many females study French? c) How many people study Spanish? ) Karen asks 00 students if they like milk, plain or white chocolates best. 6 of the students are girls. 9 of these girls like milk chocolates best. 6 boys like white chocolates best. 8 out of the 4 students who like plain chocolates best are girls. Work out the number of students who like milk chocolates the best. Page 6

78 MathsWatch Clip 6 Grade questions Averages and the Range ) Kaya made a list of his homework marks a) Write down the mode of Kaya s marks. b) Work out his mean homework mark. ) Lydia rolled an 8-sided dice ten times. Here are her scores a) Work out Lydia s median score. b) Work out the mean of her scores. ) In a two-week period, a train was this many minutes late each day: a) What was the mean average number of minutes late? b) What was the median average number of minutes late? 4) Two small Year 0 classes, Set A and Set B, sat the same Science test. Set A had these scores for the test: 6%, 7%, 48%, 95%, 46%, 8%, 77%, 6%, 7% Set B had these scores: 58%, 6%, 85%, 6%, 59% 8%, 90%, 84%, 75%, 48% How much bigger was Set B s mean average score than Set A s mean average score? Give your answer correct to decimal place. 5) A rugby team played six games. The mean score for the six games is 5 The rugby team played one more game. The mean score for all seven games is 6 Work out the number of points the team scored in the seventh game. Page 6

79 MathsWatch Clip 6 Grade questions Data - Discrete and Continuous ) Out of the following types of data, decide which is continuous and which is discrete: The lengths of some roads. The number of cats eyes on a one mile stretch of road. The time it takes twenty students to complete an English essay. The number of pages in twenty students English essays. The weights of sacks of potatoes. The number of potatoes in some sacks of potatoes. The depth of water as the tide comes in and goes out. The number of crackers in some packets of biscuits. The weight of the crackers in some packs of bicuits. ) Write a short statement which explains what continuous data is. ) Write a short statement which explains what discrete data is. Page 6

80 MathsWatch Clip 64 Grade questions Vertical Line Charts ) The line chart shows the test scores of pupils in class 0A. Frequency Test score (out of 0) a) How many pupils sat the test in class 0A? b) What was the modal test score? c) What was the median test score? ) The line chart shows the number of goals scored by a football team in their last 6 games. Frequency Number of goals scored a) How many goals did they score altogether? b) What was the median number of goals scored? Page 64

81 MathsWatch Clip 65 Grade questions Frequency Tables and Diagrams ) A class of pupils is asked to solve a puzzle. The frequency table below shows the times taken by the pupils to solve the puzzle. Time (t ) in min Frequency 0 < t 5 5 < t < t < t < t 5 5 Draw a frequency diagram to show this information. Page 65

82 MathsWatch Clip 66 Grade questions Multiplying Decimals ) Work out a) 6 0. b) c) d) e) f).5 0. ) A box contains 7 books, each weighing.5 kg. Work out the total weight of the box. ) Jim takes boxes out of his van. The weight of each box is 5.5 kg. Work out the total weight of the boxes. 4) Tim has a job which pays 6.85 per hour. If he works for 4 hours, one week, how much does he earn? 5) Sue has a part-time job and the hourly pay is 7.50 per hour. How much does she earn if she works for 8.5 hours, one week? 6) Fencing costs.5 per metre. How much does.5 m cost? Page 66

83 MathsWatch Clip 67 Grade questions Dividing Decimals ) Work out a) 9 0. b) 6 0. c) 0.4 d) e) 0. f) 5 0. ) Work out a) b) c) d) e) f) ) John takes boxes out of his van. The total weight of the boxes is 4.9 kg The weight of each box is 0.7 kg Work out the number of boxes in John s van. 4) Mr Rogers bought a bag of elastic bands for 6 Each elastic band costs p. Work out the number of elastic bands in the bag. Page 67

84 MathsWatch Clip 68 Grade questions Four Rules of Negatives ) Work out the following: a) 7 b) 4 6 c) 8 d) 0 4 ) Work out the following: a) - + b) c) d) -9 + ) Work out the following: a) - b) -4 5 c) -7 8 d) - 4) Work out the following: a) 6 - b) - -5 c) -9 - d) - 5) Work out the following: a) - 4 b) 5 - c) -4-5 d) -6-6) Work out the following: a) -4 b) -0 - c) -5 d) Page 68

85 MathsWatch Clip 69 Grade questions Listing Strategies ) A restaurant has the simple menu, as shown. Meg chooses a starter, a main course and a dessert. List all the possible combinations that Meg could choose. Starter Soup Melon Main Course Chicken Steak Vegetarian Dessert Ice Cream Trifle ) 4 7 a) Make a list of all the two-digit numbers that can be made with these three cards. b) Make a list of all the three-digit numbers that can be made with these three cards. ) Phil has three different coins. He has: a coin a coin a 50p coin a) If he chooses exactly two coins, what amounts of money can he make? b) If he chooses one or two coins, what amounts of money can he make? c) If he chooses one, two or three coins, what amounts of money can he make? Page 69

86 MathsWatch Clip 70 Grade questions Comparing Fractions ) Put these fractions in order of size, smallest to largest. Show your working for each question. a) b) c) 5 8 ) Put these fractions in order of size, smallest to largest. Show your working for each question. a) 4 8 b) 5 4 c) ) Put these fractions in order of size, smallest to largest. Show your working for each question. a) b) c) ) Ben spent his pocket money this way: on magazines on chocolates on games Order the items Ben bought by value, largest first. Show all your working. Page 70

87 MathsWatch Clip 7 Grade questions Adding and Subtracting Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: a) b) ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) ) Work out the following: 5) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) ) Ted received his pocket money on Friday. He spent of his pocket money on games. 5 He spent of his pocket money on magazines. 0 What fraction of his pocket money did he have left? a) b) c) d) ) Maisie buys a bag of flour. She uses 4 to bake a cake and to make a loaf. 5 a) What fraction of the bag of flour was used? b) What fraction of the bag of flour is left? 9) Work out the total length of this shape. Give your answer as a mixed number. 4 inches inches Page 7

88 MathsWatch Clip 7 Grade questions Finding a Fraction of an Amount ) Work out these amounts. a) 4 of 0 b) of 60 kg c) 8 4 d) 50 e) 9 of 80 cm f) g) 60 4 h) 5 8 of 48 i) ) There are 600 apples on a tree and there are maggots in 5 of them. How many apples have maggots in them? ) Liz and Lee are travelling in a car from Glasgow to Poole (770 km). At midday they had already travelled 5 7 of the total distance. What distance, in km, had they travelled by midday? 4) A digital camera that cost 49 was sold on ebay for 7 of the original price. What was the selling price? 5) Yesterday Thomas travelled a total of 75 miles. He travelled 5 of this distance in the morning. How many miles did he travel during the rest of the day? 6) Debra received her 5 pocket money on Saturday. She spent of her pocket money on magazines. She spent 5 of her pocket money on a necklace. How much of the 5 did she have left? Page 7

89 MathsWatch Clip 7 Grade questions Multiplying Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: a) b) c) 5 7 d) ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) 7 5 Page 7

90 MathsWatch Clip 74 Grade questions Dividing Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: a) 5 4 b) 7 5 c) 4 9 d) ) Work out the following: a) b) c) d) ) Work out the following: a) b) c) d) Page 74

91 MathsWatch Clip 75 Grade questions BODMAS/BIDMAS ) ) ) 5 4 4) 48 (4 ) 5) 7 ( + 6) 6) ) (9 + ) + 5 8) 4 ( + 4) 6 9) ) ) ) ) ) ) ) 4 7 7) 0 0 ( 5+ 4) 8) Page 75

92 MathsWatch Clip 76 Grade questions Reciprocals ) Write down the reciprocal of a) 8 b) c) d) ) Write down the reciprocal of a) b) c) d) ) Write down the reciprocal of a) 0. b) 0.5 c) 0. 4) Why can t we have a reciprocal of 0? Page 76

93 MathsWatch Clip 77 Grade questions Calculator Questions ) Use your calculator to work out Write down all the figures on your calculator display. ) Use your calculator to work out Write down all the figures on your calculator display. ) Work out Write down all the figures on your calculator display. 4) Use your calculator to work out the value of Write down all the digits from your calculator. Give your answer as a decimal. 5) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal. 6) Use your calculator to work out Write down all the figures on your calculator display. You must give your answer as a decimal. 7) Use a calculator to work out Write down all the figures on your calculator display. Page 77

94 MathsWatch Clip 78 Grade questions Product of Primes ) List the first seven prime numbers. ) Express the following numbers as the product of their prime factors: a) b) 0 c) 0 d) 4 ) Express the following numbers as the product of their prime factors: a) 64 b) 00 c) 50 4) Express the following numbers as the product of their prime factors: a) 75 b) 9 c) 5 5) The number 96 can be written as m n, where m and n are prime numbers. Find the value of m and the value of n. 6) The number 75 can be written as 5 x y, where x and y are prime numbers. Find the value of x and the value of y. Page 78

95 MathsWatch Clip 79 Grade questions Highest Common Factor (HCF) ) Find the Highest Common Factor of 6 and 4. ) Find the Highest Common Factor of and 8. ) Find the Highest Common Factor of 60 and 50. 4) Find the Highest Common Factor of 96 and 08. 5) (i) Write 4 and 6 as products of their prime factors. (ii) Work out the Highest Common Factor of 4 and 6. Page 79

96 MathsWatch Clip 80 Grade questions Lowest Common Multiple (LCM) ) Find the Lowest Common Multiple of 0 and 60. ) Find the Lowest Common Multiple of 8 and 7. ) Find the Lowest Common Multiple of 70 and 40. 4) Find the Lowest Common Multiple of 5 and 55. 5) (i) Write 4 and 6 as products of their prime factors. (ii) Work out the Lowest Common Multiple of 4 and 6. Page 80 A

97 MathsWatch Clip 78/79/80 Grade questions Product of Primes/HCF/LCM ) a) Express 84 as a product of its prime factors. b) Find the Highest Common Factor (HCF) of 84 and 5. ) Express 7 as the product of its prime factors. ) Express 80 as the product of its prime factors. 4) a) Express 66 as a product of its prime factors. b) Express as a product of its prime factors. 5) Express 5 as a product of its prime factors. 6) Find the Lowest Common Multiple (LCM) of 4 and 6. 7) a) Write 56 as a product of its prime factors. b) Find the Highest Common Factor (HCF) of 56 and 4. 8) a) Express 45 as a product of its prime factors. b) Find the Highest Common Factor (HCF) of 45 and 0. 9) a) Find the Highest Common Factor (HCF) of 4 and 0. b) Find the Lowest Common Multiple (LCM) of 4, 5 and 6. Page 80 B

98 MathsWatch Clip 8 Grade questions Squares, Cubes and Roots ) What is the value of 5? ) What is the value of 8? ) These are the first five square numbers:, 4, 9, 6, 5 a) What is the sixth square number? b) What is the 0th square number? 4) Which square number lies between 60 and 70? 5) What is the value of? 6) What is the value of 4? 7) Work out + + 8) Work out 5 9) Work out 49 0) Work out the value of ) Match together cards with the same answer Page 8

99 MathsWatch Clip 8 Grade questions Working with Indices ) Evaluate the following: a) b) c) 0 4 ) Evaluate the following: a) 8 b) 6 4 c) 5 6 ) Find the value of a) 4 + b) 5 c) + + 4) Find the value of a) b) 4 5 c) 9 6 5) Find the value of Page 8

100 MathsWatch Clip 8 Grade questions Standard Form ) Change the following to normal (or ordinary) numbers. a) c) e) b) d) 9. 0 f) ) Change the following to normal (or ordinary) numbers. a) c) e) b) d) f) ) Change the following to standard form. a) 60 c) e) 00 b) d) f) ) Change the following to standard form. a) 0.07 c) e) b) d) f) ) Work out the following, giving your answer in standard form. a) d) g) b) e) h) c) f) i) Page 8

101 MathsWatch Clip 84 Grade questions Decimals and Fractions Write the following fractions as decimals ) 0 ) 7 0 ) ) 5) 4 6) 5 7) 7 0 8) 9) 8 0) 5 8 Page 84

102 MathsWatch Clip 85 Grade questions Fractions, Percentages, Decimals ) Write the following fractions as decimals and percentages: eg. 0 a) = 0 b) = 5 c) = 5 d) = 4 e) = 4 f) = g) = % ) Fill in the blanks in the table below: Fraction Decimal Percentage % 5% % Page 85

103 MathsWatch Clip 86 Grade questions Percentage of an Amount with a Calculator ) Work out: a) % of 40 b) 64% of 080 c) 6% of 800 d) 98% of ) Work out: a) 7.5% of 58 b) 0% of 5.40 c) 6.7% of 000 d) 7.5% of ) A computer costs 406 plus VAT at 0%. Work out the total cost of the computer. 4) A car is usually priced at 9800 but now has a discount of 8%. What is the new price of the car? 5) 9500 people attend a festival and % of them are children. How many children are at the festival? 6) 65% of a car, by weight, is steel and iron. If a car weighs 00 kg, what is the weight of steel and iron in the car? 7) Tony earns 7800 per year and receives a.8% pay rise. How much does he now earn? Page 86

104 MathsWatch Clip 87 Grade questions Percentage of an Amount without a Calculator ) Work out: a) 0% of 70 b) 0% of 6800 c) 0% of 9 d) 0% of 6 ) Work out: a) 0% of 60 b) 0% of 90 c) 5% of 800 d) 5% of 68 ) Work out: a) 5% of 80 b) 90% of 60 c) 7.5% of 600 d) 7.5% of 850 4) Work out: a) 5% of 4.60 b) 40% of.80 c) 7.5% of.0 d) 97.5% of 4 5) The normal price of a jacket is 54. In a sale, the price is reduced by 0% What is the sale price? 6) A football costs 4 plus 0% VAT. How much is the football? Page 87

105 MathsWatch Clip 88 Grade questions Change to a Percentage with a Calculator ) Write the following as percentages, giving all your answers to decimal place. a) out of 4 b) 6 out of 85 c) out of 5 d) 50 out of 45 ) Sarah sat a Science test and got a score of 64 marks out of possible marks. What was her mark as a percentage? Give your answer to decimal place. ) In a class of students, 8 of them are boys. What percentage of the class are boys? Give your answer to decimal place. 4) In a French class there are girls and 6 boys. What percentage of the class are girls? Give your answer to decimal place. 5) A new car usually costs Henry gets a discount of 000. What is the discount as a percentage of the usual cost? Give your answer to decimal place. 6) Write out 48 as a percentage of 600. Give your answer to decimal place. 7) In a wood there are 00 oak trees, 650 silver birch trees and 400 wild cherry trees. What percentage of the trees are oak trees? 8) In England in 00 there were 6880 deaths caused by cancer. Of these deaths, 7500 were caused by smoking. What percentage of deaths due to cancer were caused by smoking? Give your answer to decimal place. Page 88

106 MathsWatch Clip 89 Grade questions Change to a Percentage without a Calculator ) Write the following as percentages. a) out of 50 b) 5 out of 5 c) 8 out of 0 d) out of 0 e) 4 out of 5 f) out of 40 g) out of 80 h) 640 out of 800 i) 6 out of 60 ) Tim got 7 out of 0 in a French test. Write 7 out of 0 as a percentage. ) Write 9 as a percentage of 5 4) Work out 4 as a percentage of 40 5) A baker burnt loaves out of the 00 loaves he baked. What percentage of the 00 loaves did he burn? 6) What is 80 as a percentage of 400? 7) What is as a percentage of 40? 8) If there are 9 girls and boys in a class, what percentage of the class are girls? Page 89 A

107 MathsWatch Clip 86/87/88/89 Grade questions Percentages ) Find the following to the nearest penny: a) % of 670 b) % of 580 c) 48% of 64 d) % of 7.50 e) 87% of 44 f) 5.7% of 7000 g).8% of 980 h) 4% of 6.4 i) 48.6% of 97.6 j) 78.4% of.8 k) 4.5% of l) 0.57% of ) Change the following to percentages, giving all answers to decimal place: a) 6 out of 8 b) 8 out of 7 c) 4 out of 8 d) 4 out of 96 e) 7 out of 40 f) 4 out of 659 g) 87 out of 90 h) 4.7 out of i) 6.9 out of 79 j) 4.8 out of.6 k) 65.8 out of 0.7 5) A shop gives a discount of 0% on a magazine that usually sells for.80. Work out the discount in pence. 6) A television costs 596 plus VAT at 7.5%. Work out the cost of the television including VAT. 7) Peter has 8 trees in his garden. 6 of the trees are pear trees. What percentage of the trees in his garden are pear trees? ) Find the following: a) 0% of 700 b) 0% of 400 c) 0% of 50 d) 0% of 50 e) 0% of 68 f) 0% of 46 g) 0% of 6.50 h) 0% of.0 i) 0% of 600 j) 0% of 900 k) 60% of 800 l) 0% of 650 m) 40% of 0 n) 5% of 00 o) 5% of 60 p) 65% of 000 q) 45% of 64 r) 85% of 96 s) 7.5% of 800 t) 7.5% of 40 u) 7.5% of ) Change the following to percentages: a) 46 out of 00 b) 8 out of 50 c) 7 out of 5 d) out of 5 e) 9 out of 0 f) 6 out of 0 g) 7 out of 0 h) 9.5 out of 0 i) 0 out of 40 j) 6 out of 40 k) 0 out of 40 l) out of 40 m) 8 out of 80 n) out of 80 o) 60 out of 80 p) out of 5 q) 4 out of 5 r) 5 out of 75 s) 4 out of 75 t) 0 out of 75 8) Jane scored 7 out of 4 in a Maths test and 9 out of 6 in a Science test. What were her percentages in both subjects to decimal place? 9) 0) ) In class 9A there are 7 girls and 8 boys. What percentage of the class are girls? A shop decides to reduce all the prices by 5%. The original price of a pair of trainers was 70. How much are they after the reduction? VAT at 7.5% is added to the price of a car. Before the VAT is added it cost How much does it cost with the VAT? Page 89 B

108 MathsWatch Clip 90 Grade questions Rounding to Significant Figures ) Round the following numbers to significant figure: a) 48 b) 78 c) 5608 d) 5 e) 999 f) ) Round the following numbers to significant figures: a) 846 b) 647 c) 55 d) e) 89 7 f) ) Round the following numbers to significant figures: a) 9 49 b) 64 8 c) 058 d) 89 5 e) 7 76 f) ) Round the following numbers to significant figure: a) b) c) d) ) Round the following numbers to significant figures: a) b) c) d) ) Round the following numbers to significant figures: a) b) c) d) ) Round the following numbers to significant figures: a) b) c).59 4) Work out the following and give your answer to significant figures: a) 6 48 b) c) ) Work out the following and give your answer to significant figures: a) b) c) Page 90

109 MathsWatch Clip 9 Grade questions Estimating Answers ) Work out an estimate for ) Work out an estimate for ) Work out an estimate for ) Work out an estimate for ) Work out an estimate for Page 9

110 MathsWatch Clip 9 Grade questions Using Place Value ) Using the information that write down the value of a) 47 4 b) c) = 59.8 ) Using the information that write down the value of a) b) c) = 555 ) Using the information that write down the value of a) 70 4 b) = 708 4) Using the information that write down the value of a) 7 56 b) c) = 5. 5) Using the information that write down the value of a) b) c) = 565 Page 9

111 MathsWatch Clip 9 Grade questions Expanding Brackets ) Expand these brackets a) (x + ) b) (x + 4) c) 5(p q) d) 4(x + y ) e) 6(r r ) ) Expand these brackets a) x(x ) b) x(x + 5) c) p(p 7q) d) y(y + 6y ) e) x(r + r ) ) Expand these brackets a) x(x 5) b) 4x(x + ) c) 5p(4p q) d) y(y + 4x ) e) x(x + r ) 4) Expand these brackets a) x(x ) b) x(x + ) c) 5p (4p ) d) y (y + 4y) e) xy(x + y ) Page 9

112 MathsWatch Clip 94 Grade questions Simple Factorisation ) Factorise a) x + 4 b) y + 0 c) x + d) x 6 e) 5x 5 ) Factorise a) p + 7p b) x + 4x c) y y d) p 5p e) x + x ) Factorise a) x + 6x b) y 8y c) 5p + 0p d) 7c c e) 6x + 9x 4) Factorise a) x 4xy b) t + 0tu c) 6x 8xy d) x y + 9xy Page 94

113 MathsWatch Clip 95 Grade questions Substitution ) y = 5x a) Work out the value of y when x = b) Work out the value of y when x = - ) y = x + 7 a) Work out the value of y when x = 4 b) Work out the value of y when x = - ) y = x + 4t x = 6 t = Work out the value of y. 9) v = u + 5as u = 6 a =.5 s = 9 0) Work out the value of v. y = p qx p = -0 q = x = -5 Work out the value of y. 4) y = a b a = 4 b = - Work out the value of y. ) v = u + as u = 6 a =.5 s = 9 Work out the value of v. 5) v = a + 5b a = 6 b = - Work out the value of v. 6) y = x a) Work out the value of y when x = 6 b) Work out the value of y when x = -4 7) y = x a) Work out the value of y when x = 5 b) Work out the value of y when x = - ) ) v = u + as u = a = 9.8 s = Work out the value of v. Give your answer correct to decimal place s = ut + 0.5at a = 9.8 t = 5 u = 7 Work out the value of s. 8) y = x + x a) Work out the value of y when x = b) Work out the value of y when x = -4 Page 95

114 MathsWatch Clip 96 Grade questions Straight Line Graphs ) a) Complete the table of values for y = 4x x y y b) On the grid, draw the graph of y = 4x, for values of x from - to. c) Use the graph to find the value of y when x =.5 d) Use the graph to find the value of x when y = O x ) a) Complete the table of values for y = x + x y 0 b) On the grid, draw the graph of y = x +. y O x Page 96 A

115 MathsWatch Clip 96 Grade questions ) On the grid, draw the graph of y = x 4 Straight Line Graphs y O x ) a) Complete the table of values for x + y = 6 x y b) On the grid, draw the graph of x + y = 6 y O - x - c) Find the gradient of the graph of x + y = 6. Page 96 B

116 MathsWatch Clip 96 Grade questions Straight Line Graphs ) a) Complete the table of values for y = x 5 y x y b) Using the axes on the right draw the graph of y = x c) Use your graph to work out the value of y when x =.5 4 d) Use your graph to work out the value of x when y = O 4 x - ) a) Complete the table of values for y = x x y - - b) Using the axes on the right, again, draw the graph of y = x -4-5 ) a) Complete the table of values for y = ½x b) Draw the graph of y = ½x x y 0 y - O 4 x - - c) Use your graph to find the value of y when x =.5 Page 96 C

117 MathsWatch Clip 97 Grade questions The Gradient of a Line ) Find the gradient of lines A, B, C and D. 6 y A B C 6 y 4 D O - x O - x ) The graph shows how Meg cycles at a constant speed for 60 minutes. Distance (km) O Time (minutes) a) Find the gradient of the line. b) What does the gradient show? Page 97

118 MathsWatch Clip 98 Grade questions Drawing Quadratic Graphs ) Complete the table of values for y = x 4x + x y On the grid, draw the graph of y = x 4x y - O x - - Page 98 A

119 MathsWatch Clip 98 Grade questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y b) On the grid, draw the graph of y = x x y O 4 - x c) Use your graph to estimate the values of x when y = - Page 98 B

120 MathsWatch Clip 98 Grade questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x + x 4 x y b) On the grid, draw the graph of y = x + x 4 y O - x Page 98 C

121 MathsWatch Clip 98 Grade questions Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y b) On the grid, draw the graph of y = x x for values of x from - to y O x c) Use the graph to find the value of y when x = -.5 d) Use the graph to find the values of x when y = 4-5 ) a) Complete the table of values for y = x x x y 8 0 b) On the grid, draw the graph of y = x x for values of x from - to y O x c) (i) On the same axes draw the straight line y =.5 (ii) Write down the values of x for which x x =.5-5 Page 98 D

122 MathsWatch Clip 98 Grade questions Drawing Quadratic Graphs ) The diagram shows the graph of y = x 5x y O x a) Use the graph to find estimates for the solutions of (i) x 5x = 0 (ii) x 5x = 6 b) Use the graph to find estimates for the solutions of the simultaneous equations y = x 5x y = x 4 Page 98 E

123 MathsWatch Clip 99 Grade questions Sketching Functions ) a) Sketch the graph of y = x 4 on the axes, showing clearly where it crosses the y-axis. b) Sketch the graph of y = -x + on the axes, showing clearly where it crosses the y-axis. y O x ) a) Sketch the graph of y = x + on the axes, showing clearly where it crosses the y-axis. b) Sketch the graph of y = -x on the axes, showing clearly where it crosses the y-axis. y O x Page 99

124 MathsWatch Clip 00 Grade questions Solving Equations Using Flowcharts ) Solve the following equations. a) x 7 = b) 5x + = 4 ) Solve the following equations. a) x 5 + = 7 b) x 6 =.5 ) Solve the following equations. a) (4x ) = 46 b) 6(x + 7) = 48 4) Solve the following equations. a) x ( 7 + ) = 6 b) 5x ( ) = 8 Page 00

125 MathsWatch Clip 0 Grade questions Subject of a Formula Using Flowcharts ) Make x the subject of the formula w = 5x + ) Make x the subject of the formula y = x 6 ) Make x the subject of the formula w = y + x 5 4) Make the subject of the formula a = (b + t) + 5) Make x the subject of the formula y = 5 + x 6) Make the subject of the formula w = x + t 7) Make n the subject of the formula m = n p 8) Make q the subject of the formula (5q + ) = c Page 0

126 MathsWatch Clip 0 Grade questions Generate a Sequence from the nth Term ) The nth term of a number sequence is n + 5 Write down the first three terms of the sequence. ) The nth term of a number sequence is n Write down the first four terms of the sequence. ) The nth term of a number sequence is n + Write down the first four terms of the sequence. 4) The nth term of a number sequence is 5n 7 Write down the first four terms of the sequence. 5) The nth term of a number sequence is n Write down the first three terms of the sequence. 6) The nth term of a number sequence is n + Write down the first three terms of the sequence. 7) The nth term of a number sequence is n a) Find the third term of this sequence. b) Find the fifth term of this sequence. 8) The nth term of a number sequence is n + n a) Find the third term of this sequence. b) Find the fifth term of this sequence. Page 0

127 MathsWatch Clip 0 Grade questions Finding the nth Term ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. 4) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. 5) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. Page 0 A

128 MathsWatch Clip 0/0 Grade questions The nth Term ) Here are the first four terms of an arithmetic sequence Find an expression, in terms of n, for the nth term of the sequence. ) The nth term of a number sequence is n + Write down the first three terms of the sequence. ) Here are the first five terms of an arithmetic sequence. 7 7 a) Find, in terms of n, an expression for the nth term of this sequence. b) An expression for the nth term of another sequence is n (i) Find the third term of this sequence. (ii) Find the fifth term of this sequence. 4) The nth term of a sequence is n (i) (ii) Find the 4th term of the sequence. Is the number 400 a term of the sequence? Give reasons for your answer. Page 0 B

129 MathsWatch Clip 0/0 Grade questions The nth Term ) The nth term of a number sequence is given by 4n + a) Work out the first two terms of the number sequence. Here are the first four terms of another number sequence b) Find, in terms of n, an expression for the nth term of this number sequence. ) Here is a number pattern. Line Number a) Complete Line Number 4 of the pattern. b) Complete Line Number 0 of the pattern. c) Use the number pattern to find the answer to Page 0 C

130 MathsWatch Clip 04 Grade questions Special Sequences ) What is the term to term rule for each sequence, below? a), 4, 6, 64, 56 b) 6,, 4, 48, 96 c) 80, 40, 0, 0, 5 d) 48,,, 0.75, ) a) What is the special name for this sequence?, 4, 9, 6, 5 b) What would be the 0th term of the sequence? c) What is the nth term of the sequence? ) By comparing the following sequences with the sequence of square numbers, find the nth term for each one. a) 4, 7,, 9, 8 b) -,, 7, 4, c),, 7, 48, 75 4) a) What is the special name for this sequence?,, 6, 0, 5 b) What would be the 8th term of the sequence? c) What is the nth term of the sequence? d) Use the nth term to work out the st term of the sequence. Page 04

131 MathsWatch Clip 05 Grade questions Exchanging Money ) Lance goes on holiday to France. The exchange rate is =.5 Euros. He changes 50 into Euros. a) How many Euros should he get? In France, Lance buys a digital camera for 5 Euros. b) Work out the cost of the camera in pounds. ) Whilst on holiday in Spain, Gemma bought a pair of sunglasses for 77 Euros. In England, an identical pair of sunglasses costs The exchange rate is =.40 Euros. In which country were the glasses the cheapest, and by how much? Show all your working. ) Luke buys a pair of trainers in Switzerland. He can pay either 86 Swiss Francs or 56 Euros. The exchange rates are: =.0 Swiss Francs =.40 Euros Which currency should he choose to get the best price, and how much would he save? Give your answer in pounds ( ). 4) The exchange rate in London is =.4 The exchange rate in Paris is = 0.86 Tony wants to change some pounds into euros. In which of these cities would Tony get the most euros? All working must be shown. Page 05

132 MathsWatch Clip 06 Grade questions Sharing Using Ratio ) Tom and Julie share 48 in the ratio 5 : Work out how much more money Tom gets than Julie gets. ) Ben and Sue share 60 in the ratio : Work out how much each person gets. ) A box contains milk chocolates and plain chocolates only. The number of milk chocolates to the number of plain chocolates is in the ratio : There are 4 milk chocolates. Work out the total number of chocolates. 4) Andy, Ben and Claire share 54 Ben gets three times as much money as Andy. Claire gets twice as much money as Ben. How much money does Claire get? 5) There are some marbles in a bag. 8 of the marbles are blue. of the marbles are red. a) Write down the ratio of the number of blue marbles to the number of red marbles. Give your ratio in its simplest form. There are some apples and pears in a box. The total number of apples and pears is 54. The ratio of the number of apples to the number of pears is : 5 b) Work out the number of pears in the box. 6) A piece of string is 80 cm long. Jim cuts it into three pieces in the ratio : : 4 Work out the length of the longest piece. 7) Sally is years old. Tammy is years old. Danny is 0 years old. Sally, Tammy and Danny share 8 in the ratio of their ages. Tammy gives a third of her share to her mother. How much should Tammy now have? Page 06

133 MathsWatch Clip 07 Grade questions Ratios, Fractions and Graphs ) In a box of chocolates, the ratio of plain chocolates to milk chocolates is : 5. a) What fraction of the chocolates are plain ones? b) What fraction of the chocolates are milk ones? ) If the ratio of x : y is : 7, which of the following statements are correct? a) x is of (x + y) 7 b) x is of (x + y) 0 c) y is 7 of x 0 d) y is 7 of (x + y) 0 ) Pounds can be converted to kilograms using the ratio : 5. a) Use the squares, below, to draw a conversion graph to illustrate this. b) Convert 4 pounds to kilograms. c) Convert 4 kilograms to pounds. Page 07

134 MathsWatch Clip 08 Grade questions Increase/Decrease by a Percentage ) Increase: a) 500 by 0% c) 80 by 5% b) 0 by 0% d) 75 by 0% ) Decrease: a) 400 by 0% c) 40 by 5% b) 80 by 0% d) 5 by 0% ) The price of a laptop is increased by 5%. The old price of the laptop was 00. Work out the new price. 4) The price of a 6800 car is reduced by 0%. What is the new price? 5) Increase: a) 65 by % c) 600 by 7.5% b) 0 by % d) 70 by 7.5% 6) Decrease: a) 4 by 5% c) 5 by 8.5% b) 79 by % d) 8900 by 8% 7) The price of a mobile phone is plus VAT. VAT is charged at a rate of 7.5%. What is the total price of the mobile phone? 8) In a sale, normal prices are reduced by 7%. The normal price of a camera is 89. Work out the sale price of the camera. 9) A car dealer offers a discount of 0% off the normal price of a car, for cash. Peter intends to buy a car which usually costs He intends to pay by cash. Work out how much he will pay. 0) A month ago, John weighed 97.5 kg. He now weighs 4.5% more. Work out how much John now weighs. Give your answer to decimal place. Page 08

135 MathsWatch Clip 09 Grade questions Percentage Change ) A car dealer is comparing his sales over the past two years. In 006, he sold 75 cars. In 007, he sold 96 cars. Work out the percentage increase in the number of cars sold. ) In September 005, the number of pupils attending MathsWatch College was 5. In September 006, the number of pupils attending MathsWatch College was 04. Work out the percentage decrease in the number of pupils attending MathsWatch College. ) The usual price of a shirt is.50 In a sale, the shirt is reduced to 9.5 What is the percentage reduction? 4) Olivia opened an account with 750 at the MathsWatch Bank. After one year, the bank paid her interest. She then had 795 in her account. Work out, as a percentage, MathsWatch Bank s interest rate. 5) Keith buys a house for and sells it two years later for What is his percentage profit? Give your answer to significant figures. 6) Shelley bought some items at a car boot sale and then sold them on ebay. Work out the percentage profit or loss she made on each of these items. a) Trainers bought for 5, sold for 0 b) DVD recorder bought for 4, sold for c) Gold necklace bought for 90, sold for 78.0 d) A DVD collection bought for 0, sold for 8.60 Page 09

136 MathsWatch Clip 0 Grade questions Reverse Percentage Problems ) In a sale, normal prices are reduced by 0%. The sale price of a shirt is 6 Calculate the normal price of the shirt. ) A car dealer offers a discount of 5% off the normal price of a car for cash. Emma pays 60 cash for a car. Calculate the normal price of the car. ) In a sale, normal prices are reduced by %. The sale price of a DVD recorder is Calculate the normal price of the DVD recorder. 4) A salesman gets a basic wage of 60 per week plus a commision of 0% of the sales he makes that week. In one week his total wage was 640 Work out the value of the sales he made that week. 5) Jason opened an account at MathsWatch Bank. MathsWatch Bank s interest rate was 4%. After one year, the bank paid him interest. The total amount in his account was then 976 Work out the amount with which Jason opened his account. 6) Jonathan s weekly pay this year is 960. This is 0% more than his weekly pay last year. Tess says This means Jonathan s weekly pay last year was 768. Tess is wrong. a) Explain why b) Work out Jonathan s weekly pay last year. 7) The price of all rail season tickets to London increased by 4%. a) The price of a rail season ticket from Oxford to London increased by.40 Work out the price before this increase. b) After the increase, the price of a rail season ticket from Newport to London was 9.80 Work out the price before this increase. Page 0

137 MathsWatch Clip Grade questions Simple Interest ) Meg has 00 in her savings account. The account pays 5% simple interest per year. How much interest will she earn in 4 years? ) Dan has 4000 in his savings account. This account pays % interest per year. How much interest will he earn in 6 years? ) Chris borrows 6000 at a simple interest rate of 0% per year. He pays the money back after 4 years. How much does he pay back in total? 4) Lisa borrows 000 at a simple interest rate of.5% per year. She pays the money back after years. How much does she pay back in total? 5) Kate borrows 000 at a simple interest rate of 6% per year. She pays the money back after months. How much does she pay back in total? 6) Neil invested 8000 in a savings account for years. He earned 640 simple interest over the two years. What was the interest rate? Page

138 MathsWatch Clip Grade questions Metric Conversions ) Change 9 m into cm ) How many square metres are there in 5 square kilometres? ) Change 4 cm into mm 4) Convert 6.5 m into mm 5) Change m into cm 6) How many cubic millimetres are there in cubic centimetres? 7) Change 7 m into mm 8) A tiler wants to tile a rectangular wall which measures 4 m by.5 m. Each tile measures 6 cm by 0 cm. How many tiles will he need for the wall? Tile 0 cm.5 m 6 cm 4 m 9) A carpet-fitter is laying carpet tiles on a rectangular floor which measures 7.5 m by 4.5 m. Each carpet tile measures 50 cm by 50 cm. How many carpet tiles will he need for the floor? Carpet tile 4.5 m 50 cm 50 cm 7.5 m Page

139 MathsWatch Clip Grade questions Problems on Coordinate Axes ) The points A (, 0), B (, 4) and C (-, ) are three corners of a parallelogram. What are the coordinates of the 4th corner? y O x ) The diagram shows vertices of a parallelogram. Write down the coordinates of all the possibilities for the 4th vertex. y O x Page

140 MathsWatch Clip 4 Grade questions Surface Area of a Prism - Cuboids ) A cube has sides of length 5 cm. Find the total surface area of the cube. 5 cm 5 cm 5 cm ) A cuboid has sides of length 0 cm, 6cm and 7 cm. Find the total surface area of the cuboid. 6 cm 0 cm 7 cm ) A cuboid has sides of length cm, 4.5cm and 6 cm. Find the total surface area of the cuboid. 4.5 cm cm 6 cm Page 4 A

141 MathsWatch Clip 4 Grade questions Surface Area of a Prism - Triangular Prisms ) Find the surface area of this triangular prism. cm 5 cm 4 cm 6 cm ) Find the surface area of this triangular prism. cm cm cm 0 cm 5 cm ) With the aid of Pythagoras Theorem, find the surface area of this triangular prism. Give your answer correct to significant figures. 9. cm 4.6 cm. cm Page 4 B

142 MathsWatch Clip 5 Grade questions Volume of a Cuboid ) Find the volume of this cuboid. 5 cm 0 cm 6 cm ) Find the volume of this cuboid. 0.8 m.7 m. m ) The volume of this cuboid is 480 cm. Find the length of the side marked x. 6 cm x 8 cm 4) Boxes A and B are both cuboids. How many of box B could be packed into box A? 50 cm 60 cm A 0 cm 5 cm B 0 cm 80 cm Page 5

143 MathsWatch Clip 6 Grade questions Circle Definitions ) In the circle, write the correct names for line A, B and C. A B C ) What is the special name given to the perimeter of a circle? Page 6

144 MathsWatch Clip 7 Grade questions Area of a Circle ) Find the areas of the following shapes. a) b) c) cm 7m 8cm ) Work out the areas of the following shapes. a) mm b) 0cm ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the area of the top of the table. b) Work out the area of the base of the table. 4) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 7 cm. Calculate the area of the shape. Give your answer correct to significant figures. cm 7 cm Page 7

145 MathsWatch Clip 8 Grade questions Circumference of a Circle ) Find the circumference of the following shapes. a) b) c) cm 5 m 8 cm ) Work out the perimeter of the following shapes. a) mm b) 0 cm ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the circumference of the top of the table. Let be.4 b) Work out the circumference of the base of the table. Let be.4 4) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 5 cm. Calculate the perimeter of the shape. Give your answer correct to significant figures. cm 5 cm Page 8 A

146 MathsWatch Clip 7/8 Grade questions Area and Circumference of a Circle ) A circle has a radius of 5 cm. A square has sides of length cm. 5 cm cm cm Work out the difference between the area of the circle and the area of the square if you take to be. ) Here is a tile in the shape of a semi-circle. 9 cm The diameter of the semi-circle is 9 cm. Work out the perimeter of the tile. Give your answer correct to two decimal places. ) A circle has a radius of 7 cm. 7 cm Work out the area of the circle. Give your answer correct to three significant figures. 4) A circle has a diameter of 4 cm. 4 cm Work out the circumference of the circle. Give your answer correct to three significant figures. Page 8 B

147 MathsWatch Clip 7/8 Grade questions Area and Circumference of a Circle ) The radius of a circle is 0 cm. 0 cm Work out the area of this circle. ) The diagram shows a circular pond with a path around it. 6 m m The pond has a radius of 6 m. The path has a width of m. Work out the area of the path. Give your answer correct to significant figures. ) The diagram shows a CD which has a radius of 6 cm. a) Work out the circumference of the CD. Give your answer correct to significant figures. 6 cm CDs of this size are cut from rectangular sheets of plastic. Each sheet is metre long and 50 cm wide. b) Work out the greatest number of CDs which can be cut from one rectangular sheet. Page 8 C

148 MathsWatch Clip 9 Grade questions Volume of a Prism ) The diagram shows a cuboid. Work out the volume of the cuboid. 50 cm 5 cm 0 cm ) Calculate the volume of this triangular prism. 4 cm 5 cm cm 9 cm ) An ice hockey puck is in the shape of a cylinder with a radius of.8 cm and a thickness of.5 cm..5 cm Work out the volume of the puck. Give your answer correct to significant figures..8 cm 4) A cuboid has: a volume of 80cm a length of 5 cm a width of cm Work out the height of the cuboid. 5) Work out the maximum number of boxes which can fit in the carton. 50 cm Box 0 cm 00 cm Carton 80 cm 0 cm 00 cm Page 9 A

149 MathsWatch Clip 9 Grade questions Volume of a Prism ) Work out the volume of the prism. cm 4 cm 5 cm 0 cm ) A solid cylinder has a radius of 5 cm and a height of 0 cm. 0 cm Work out the volume of the cylinder. Give your answer correct to significant figures. 5 cm ) 8 cm 6 cm 0 cm cm The diagram shows a solid prism made from metal. The cross-section of the prism is a trapezium. Find the volume of the prism. You must state your units. Page 9 B

150 MathsWatch Clip 0 Grade questions Angles and Parallel Lines ) Line PQ is parallel to line RS. If angle PQR is equal to 6 a) What is the size of angle QRS? b) Give a reason for your answer. P 6 Q R S ) Line DCE is parallel to line AB a) Find the size of angle ABC b) Find the size of angle DCA c) Calculate the size of angle ACB D C E A 68 B ) a) Find the size of angle DBF b) Find the size of angle HGC D E C 6 54 F B G H Page 0 A

151 MathsWatch Clip 0 Grade questions Angles and Parallel Lines ) A B C y D AB is parallel to CD. (i) Write down the value of y. (ii) Give a reason for your answer. ) Q 80 S y O x P 0 R PQ is parallel to RS. OSQ and ORP are straight lines. a) (i) Write down the value of x. (ii) Give a reason for your answer. b) Work out the value of y. Page 0 B

152 MathsWatch Clip 0 Grade questions Angles and Parallel Lines ) 45 5 a (i) Write down the size of the angle marked a. (ii) Give a reason for your answer. L ) A y N B ANB is parallel to CMD. LNM is a straight line. Angle LMD = 67 (i) Work out the size of the angle marked y. (ii) Give reasons for your answer. C M 67 D ) D C A B 46 E ABCD is a rhombus. BCE is an isosceles triangle. ABE is a straight line. Work out the size of angle DCA. Page 0 C

153 MathsWatch Clip Grade questions Angles in a Triangle ) Work out the size of angle a a ) Work out the size of angle b. 9 4 b ) Work out the size of angle c c 4) Work out the size of angle d. d 5 40 Page

154 MathsWatch Clip Grade questions Properties of Special Triangles ) ABC is a triangle. a) Find the size of angle A. C 60 Diagram NOT accurately drawn b) Triangle ABC is equilateral. Explain why. A 60 B ) BCD is a triangle. ABC is a straight line. Angle CBD = 70. BD = CD. a) (i) Work out the value of x. D y Diagram NOT accurately drawn (ii) Give a reason for your answer. x 70 A B C b) (i) Work out the value of y. (ii) Give reasons for your answer. ) The diagram shows a 5-sided shape. All the sides of the shape are equal in length. a) (i) Find the value of x. (ii) Give a reason for your answer. y x b) (i) Work out the value of y. (ii) Explain your answer. Page

155 MathsWatch Clip Grade questions Angle Sum of Polygons ) a) Work out the size of an exterior angle of a regular hexagon. b) Work out the size of an interior angle of a regular hexagon. ) a) Name the regular polygon, above. b) Work out the size of an exterior angle and of an interior angle for this polygon. ) The size of each exterior angle of a regular polygon is 40. Work out the number of sides of the regular polygon. 4) The size of each interior angle of a regular polygon is 0. Work out the number of sides of the regular polygon. Page A

156 MathsWatch Clip Grade questions Angle Sum of Polygons ) The diagram shows a regular hexagon and a square. Calculate the size of the angle a. a ) x The diagram shows a regular octagon and a regular hexagon. Work out the size of angle x. ) ABCDE and PQRSE are regular pentagons. AES is an equilateral triangle. Work out the size of angle DEP. D P C Q E B R A S Page B

157 MathsWatch Clip 4 Grade questions Bearings ) The diagram shows the position of two telephone masts, A and B, on a map. N a) Measure the bearing of B from A. N B Another mast C is on a bearing of 60 from B. On the map, C is 4 cm from B. b) Mark the position of C with a cross and label it C. A ) The diagram shows the positions of two boats, P and Q. N N Q P The bearing of a boat R from boat P is 050 The bearing of boat R from boat Q is 0 In the space above, draw an accurate diagram to show the position of boat R. Mark the position of boat R with a cross ( ). Label it R. Page 4 A

158 MathsWatch Clip 4 Grade questions Bearings ) School B is due east of school A. C is another school. The bearing of C from A is 065. The bearing of C from B is. Complete the scale drawing below. Mark with a cross the position of C. N A B ) In the diagram, point A marks the position of Middlewitch. The position of Middlemarch is to be marked on the diagram as point B On the diagram, mark with a cross the position of B given that: B is on a bearing of 0 from A and B is 5 cm from A N A ) Work out the bearing of a) B from P b) P from A N A 64 8 Diagram NOT P accurately drawn. B Page 4 B

159 MathsWatch Clip 5 Grade questions Experimental Probabilities ) Ahmad does a statistical experiment. He throws a dice 600 times. He scores one, 00 times. Is the dice fair? Explain your answer ) Chris has a biased coin. The probability that the biased coin will land on a tail is 0. Chris is going to flip the coin 50 times. Work out an estimate for the number of times the coin will land on a tail. ) On a biased dice, the probability of getting a six is. The dice is rolled 00 times. Work out an estimate for the number of times the dice will land on a six. 4) On a biased dice, the probability of getting a three is 0.5 The dice is rolled 50 times. Work out an estimate for the number of times the dice will land on a three. 5) Jenny throws a biased dice 00 times. The table shows her results. Score Frequency a) She throws the dice once more. Find an estimate for the probability that she will get a four. b) If the dice is rolled 50 times, how many times would you expect to get a five? Page 5

160 MathsWatch Clip 6 Grade questions Possibility Spaces ) Two dice are rolled and their scores are multiplied together. a) Complete the possibility space to show all the possible results. Second dice First dice b) What is the probability of getting a result that is an even number? ) Suppose there are three cards: A black card that is black on both sides, A white card that is white on both sides, A mixed card that is black on one side and white on the other side. All the cards are placed into a hat and one is taken out at random. It is placed on a table and the side facing up is black. What is the probability that the other side of the card is also black? Page 6

161 MathsWatch Clip 7 Grade questions Venn Diagrams ) The Venn diagram shows the number of students studying one or more of the sciences Chemistry, Biology and Physics. Chemistry 8 4 Biology 5 Physics 6 a) How many students are represented in this Venn diagram? b) How many students are studying exactly two sciences? c) What is the probability that a student chosen at random is not studying Physics? ) There are student who study languages. All study at least one of Spanish, French or German. 4 study all three languages. 9 study Spanish and French. 7 study French and German. 6 study Spanish and German. 7 study only French and 5 study only German. Complete the Venn diagram to show this information. Spanish French German Page 7

162 MathsWatch Clip 8 Grade questions Representing Data ) Patrick asked some of his colleagues which was their favourite holiday destination. The table shows the results. City Frequency Alicante 8 Paris 7 Ibiza 5 St Lucia Biarritz 9 Draw a pie chart to illustrate the information. ) Brian asked 60 people which region their favourite rugby team came from. The table shows the results. Region Frequency Southern England 9 London Midlands 6 Northern England Total 60 Draw a pie chart to illustrate the information. ) The stem and leaf diagram, below, shows information about the times, in minutes, it takes a group of people to eat their breakfast Key: 0 represents 0 minutes. a) How many people are in the group? b) How many people spend 5 minutes or more eating their breakfast? c) Find the median time that it took to eat breakfast. Page 8

163 MathsWatch Clip 9 Grade questions Scatter Diagrams ) The scatter graph shows some information about the marks of six students. It shows each student s marks in Maths and Science. 40 The table below shows the marks for four more students. Maths Science a) On the scatter graph, plot the information from the table. b) Draw a line of best fit. c) Describe the correlation between the marks in Maths and the marks in Science. Science Another student has a mark of 8 in Science. d) Use the line of best fit to estimate the mark in Maths of this student Maths ) The table below shows the average daily number of hours sleep of 0 children. Age (years) Number of hours sleep The first five results have been plotted on the scatter diagram. 6 a) Plot the next five points. b) Draw a line of best fit. c) Describe the relationship between the age of the children and their number of hours sleep per day. d) Use your scatter graph to estimate the number of hours sleep for a year old child. Number of hours sleep Age (years) Page 9 A

164 MathsWatch Clip 9 Grade questions Scatter Diagrams ) Sue did an experiment to study the times, in minutes, it took cm ice cubes to melt at different temperatures. Some information about her results is given in the scatter graph. 0 0 Time (Minutes) Temperature ( C) The table shows the results from two more experiments. Temperature ( C) 5 55 Time (Minutes) 5 a) On the scatter graph, plot the results from the table. b) Describe the relationship between the temperature and the time it takes a cm ice cube to melt. c) Find an estimate for the time it takes a cm ice cube to melt when the temperature is 5 C. Sue s data cannot be used to predict how long it will take a cm ice cube to melt when the temperature is 00 C. d) Explain why. Page 9 B

165 MathsWatch Clip 9 Grade questions Scatter Diagrams ) Henry reads eight books. For each book he recorded the number of pages and the time he took to read it. The scatter graph shows information about his results. 0 8 Time (hours) Number of pages a) Describe the relationship between the number of pages in a book and the time Henry takes to read it. Henry reads another book. The book has 50 pages. b) Estimate the time it takes Henry to read it. Page 9 C

166 MathsWatch Clip 9 Grade questions Scatter Diagrams ) Mr Jones sells umbrellas. The scatter graph shows some information about the number of umbrellas he sold and the rainfall, in cm, each month last year Number of umbrellas Rainfall in cm In January of this year, the rainfall was 6. cm. During January, Mr Jones sold umbrellas. a) Show this information on the scatter graph. b) What type of correlation does this scatter graph show? In February of this year, Mr Jones sold 40 umbrellas. c) Estimate the rainfall for February. Page 9 D

167 MathsWatch Clip 0 Grade questions Averages From a Table ) The number of pens in each pupil s pencil case in a classroom has been counted. The results are displayed in a table. Number of pens a) Work out the total number of pens in the classroom. b) Write down the modal number of pens in a pencil case. c) Work out the mean number of pens in a pencil case. Number of pupils d) Work out the range of the number of pens in a pencil case. ) Thomas is analysing the local football team. He records the number of goals scored in each football match in the past twelve months. Thomas said that the mode is 7 Thomas is wrong. a) Explain why. b) Calculate the mean number of goals scored. Goals scored Frequency ) Sindy recorded the time, in minutes, that her train was late over 00 days. Information about these times is shown in the table. Time (t minutes) 0 < t < 6 6 < t < < t < 8 8 < t < 4 4 < t < 0 Frequency Calculate an estimate for the mean time that her train was late. Give your answer to decimal place. Page 0

168 MathsWatch Clip Grade 4 questions Index Notation ) Write as a power of 8 a) b) ) Write as a power of a) 9 b) 0 ) Simplify a) k 5 k b) x 4 x c) k k 6 d) (k 8 ) 4) Simplify eg. (xy ) 4 = xy xy xy xy = 6x 4 y a) (xy 5 ) b) (x y ) c) (4xy 4 ) d) (xy ) 4 5) x y = 0 and x y = Work out the value of x and the value of y. 6) 5 x 5 y = 5 and 5 x 5 y = 5 6 Work out the value of x and the value of y. 7) a = x, b = y Express in terms of a and b a) x + y b) x c) y d) x + y Page A

169 MathsWatch Clip Grade 4 questions Index Notation ) a) Simplify d d d d b) Simplify t t c) Simplify m 5 m ) a) Simplify (x ) b) Simplify x 4x 5 y 4 ) a) Simplify t 4 t 5 b) Simplify x 8 x 5 c) Simplify (c 4 ) 4) a) Simplify x 6 x b) Simplify x 8 x c) Simplify (t) d) Simplify x y 4x 5 y 4 5) a) Simplify x x 4 b) Simplify t 7 t c) Simplify 4x y 4 xy 6) a) Simplify x x x x b) Simplify x y Page B

170 MathsWatch Clip Grade 4 questions Introduction to Bounds ) A silver necklace has a mass of grams, correct to the nearest gram. a) Write down the least possible mass of the necklace. b) Write down the greatest possible mass of the necklace. ) Each of these measurements was made correct to one decimal place. Write the maximum and minimum possible measurement in each case. a) 4.6 cm b) 0.8 kg c).5 litres d) 5.0 km/h e) 0. s f) 6. m g) 6.7 m/s h) 0. g ) Each side of a regular octagon has a length of 0.6 cm, correct to the nearest millimetre. a) Write down the least possible length of each side. b) Write down the greatest possible length of each side. c) Write down the greatest possible perimeter of the octagon. 4) A girl has a pen that is of length cm, measured to the nearest centimetre. Her pencil case has a diagonal of length.5 cm, measured to the nearest millimetre. Explain why it might not be possible for her to fit the pen in the pencil case. 5) A square has sides of length 7 cm, correct to the nearest centimetre. a) Calculate the lower bound for the perimeter of the square. b) Calculate the upper bound for the area of the square. Page

171 MathsWatch Clip Grade 4 questions Midpoint of a Line on a Graph ) Find the midpoint of A and B where A has coordinates (-, 5) and B has coordinates (4, -) y O x - ) Find the midpoint of A and B where A has coordinates (, 0) and B has coordinates (8, 6). ) Find the midpoint of A and B where A has coordinates (-4, -) and B has coordinates (, 4). 4) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (7, 5). 5) Find the midpoint of A and B where A has coordinates (, -5) and B has coordinates (7, 4). 6) Find the midpoint of A and B where A has coordinates (-7, -4) and B has coordinates (-, -). 7) The midpoint of A and B is at (, ). The coordinates of A are (-, 4). Work out the coordinates of B. 8) The midpoint of A and B is at (.5,.5). The coordinates of A are (, 5). Work out the coordinates of B. Page

172 MathsWatch Clip 4 Grade 4 questions Expanding and Simplifying Brackets ) Expand these brackets a) (x + ) b) (x + 4) c) 5(p q) d) 4(x + y ) e) 6(r r ) 5) Expand and simplify a) (x + y) + (x + y) b) (x + y) + (5x + y) c) 5(x + y) + (x + y) d) (c + d) + (c + d) e) 4(p + q) + (p + q) ) Expand these brackets a) x(x ) b) x(x + 5) c) p(p 7q) d) y(y + 6y ) e) x(r + r ) 6) Expand and simplify a) (x + y) + (x y) b) 5(x + y) + (x y) c) 4(x y) + (x + y) d) 6(c d) + (c d) e) (5p q) + (p q) ) Expand these brackets a) x(x 5) b) 4x(x + ) c) 5p(4p q) d) y(y + 4x ) e) x(x + r ) 7) Expand and simplify a) (x + y) (x y) b) 5(x y) (x y) c) 7(x y) (x + y) d) 6(x y) (x + y) e) (5p q) (p q) 4) Expand these brackets a) x(x ) b) x(x + ) c) 5p (4p ) d) y (y + 4y) e) xy(x + y ) Page 4 A

173 MathsWatch Clip 4 Grade 4 questions Expanding and Simplifying Brackets ) Expand and simplify a) (x + )(x + ) b) (x + 5)(x + ) c) (x + )(x + 4) d) (x + 6)(x + 4) e) (x + 5)(x + 7) 4) Expand and simplify a) (x 7)(x + ) b) (p 6)(p + 4) c) (e )(e 7) d) (x + 8)(x + ) e) (x 5)(x 5) ) Expand and simplify a) (x + 5)(x ) b) (x 7)(x + ) c) (x )(x + ) d) (x + 4)(x ) e) (x 5)(x + 5) 5) Expand and simplify a) (x + )(x + ) b) (p 4)(p + 5) c) (e )(e 4) d) (4x 6)(x + ) e) (x )(x + ) ) Expand and simplify a) (x )(x 4) b) (x )(x 6) c) (x )(x ) d) (x 7)(x ) e) (x 4)(x 5) 6) Expand and simplify a) (x + y)(x + y) b) (p q)(4p + 5q) c) (4e f )(e f ) d) (6x y)(6x + y) e) (x y)(x 5y) Page 4 B

174 MathsWatch Clip 5 Grade 4 questions Solving Equations ) Solve x = 7 7) Solve (x + ) = x + 9 ) Solve x + = 4 8) Solve x 7 = (x 4) ) Solve 5x 7 = 9) Solve 5(x + ) = (x + 6) 4) Solve 4x + 7 = 9 0) Solve 4(y + ) = ( y) 5) Solve x + x + x + x = 0 ) Solve 7 x = (x + ) 6) Solve x + x = 4 7) Solve (x + ) = 8 8) Solve (x 4) = 9) Solve 5(t ) = 0 ) Solve ) Solve 4) Solve 5) Solve x = 5 x 5 = 6 x = 4 5x = 5 0) Solve (x + 5) = 6 6) Solve x = ) Solve x + 7 = x + 7) Solve x + 5 = 7 ) Solve 5y = y + 0 ) Solve x + = 5x 0 4) Solve p = p 5) Solve d + 5 = 0 d 6) Solve 4 e = e 8 8) Solve 9) Solve 0) Solve ) Solve ) Solve x + 4 5x x + x 4 4x + 5 = = 4 = x + 4 = x = x Page 5

175 MathsWatch Clip 6 Grade 4 questions Rearranging Simple Formulae ) Make c the subject of the formula. a = b + cd ) Make t the subject of the formula. u = v + t ) Make n the subject of the formula. M = n + 5 4) Make z the subject of the formula. x = y + z 5) r = 5s + t a) Make t the subject of the formula. b) Make s the subject of the formula. 6) Rearrange y = x + to make x the subject. 7) Rearrange y = x+ to make x the subject. 8) Rearrange y = x+ to make x the subject. Page 6

176 MathsWatch Clip 7 Grade 4 questions Forming Formulae and Equations ) The width of a rectangle is x centimetres. The length of the rectangle is (x + 5) centimetres. x + 5 x a) Find an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form. The perimeter of the rectangle is 8 centimetres. b) Work out the length of the rectangle. ) x + 80 x + 0 x + 0 Diagram NOT accurately drawn x The sizes of the angles, in degrees, of the quadrilateral are x + 0 x x + 80 x + 0 a) Use this information to write down an equation in terms of x. b) Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral. ) Sarah buys 6 cups and 6 mugs A cup costs x A mug costs (x + ) a) Write down an expression, in terms of x, for the total cost, in pounds, of 6 cups and 6 mugs. b) If the total cost of 6 cups and 6 mugs is 48, write an equation in terms of x. c) Solve your equation to find the cost of a cup and the cost of a mug. Page 7A

177 MathsWatch Clip 7 Grade 4 questions Forming Formulae and Equations ) x + 9 x 4 In the diagram, all measurements are in centimetres. The lengths of the sides are x + 9 x 4 4x + 6 4x + 6 a) Find an expression, in terms of x, for the perimeter of the triangle. Give your expression in its simplest form. The perimeter of the triangle is 9 cm. b) Find the value of x. ) The diagram shows a right-angled triangle and a rectangle. 5 cm 7 cm x cm 8 cm cm The area of the right-angled triangle is equal to the area of the rectangle. Find the value of x. Page 7 B

178 MathsWatch Clip 7 Grade 4 questions Forming Formulae and Equations ) A shop sells small boxes and large boxes for storing CDs. A small box stores x CDs. A large box stores y CDs. Emma buys 8 small boxes and 5 large boxes. Emma can store a total of T CDs in these boxes. Write down a formula for T in terms of x and y. ) Batteries are sold in packets and boxes. Each packet contains 4 batteries. Each box contains 0 batteries. Tony buys p packets of batteries and b boxes of batteries. Tony buys a total of N batteries. Write down a formula for N in terms of p and b. ) Compasses cost c pence each. Rulers cost r pence each. Write down an expression for the total cost, in pence, of compasses and 4 rulers. 4) P x + 50 ABC is a straight line. Angle APB = x + 50 Angle PAB = x 0 Angle PBC = y x 0 A B C y a) Show that y = x + 40 Give reasons for each stage of your working. b) Given that y equals 45 degrees (i) Work out the value of x. (ii) Work out the size of the largest angle in triangle APB. Page 7 C

179 MathsWatch Clip 8 Grade 4 questions Inequalities on a Number Line ) Represent this inequality on the number line - < x < ) Represent this inequality on the number line - < x < ) Write down the inequality shown ) Write down the inequality shown ) If y is an integer, write down all the possible values of - < y < 5 6) If x is an integer, write down all the possible values of -9 < x < -5 Page 8

180 MathsWatch Clip 9 Grade 4 questions Solving Linear Inequalities ) Solve a) x > 5 b) 7y + 0 c) x d) 5+ x > 7 e) 8< 5p f) y + 5 g) x 5 h) 6x 5> x + i) p 9< 6 p j) 5 y < y 0 ) a) Solve the inequality z + > 7 b) Write down the smallest integer value of z which satisfies the inequality z + > 7 ) 5x + y < 0 x and y are both integers. Write down two possible pairs of values that satisfy this inequality. x =..., y =... and x =..., y =... Page 9A

181 MathsWatch Clip 5/9 Grade 4 questions Solving Equations and Linear Inequalities ) Solve the inequality 6x < 9 ) Solve 4x + = x + ) a) Solve the inequality t + < t + b) If t = 7 find a value of t 4) Solve (x + ) = 8 5) Solve the inequality 6y > y + 0 6) Solve 4(x ) = 5x + 7 7) h = 5t + Work out the value of t when h = 48 8) Solve (p 4) = p + 9) Solve the equation 4x + = 9 0) Solve 9 x = x + 5 ) Solve x 0 = x + 0 ) Solve the inequality x > x + 7 ) Solve the inequality x < 0 Page 9 B

182 MathsWatch Clip 40 Grade 4 questions Simultaneous Equations Graphically ) On the axes below, the graphs of y = x + and y = 6 x have been drawn. Use the graphs to solve the simultaneous equations y = x + and y = 6 x 8 7 y y = x + 6 y = 6 x 5 4 O x ) On the axes below draw the graphs of y = x + and y = 7 x Use your graphs to solve the simultaneous equations y = x + and y = 7 x y O x Page 40

183 MathsWatch Clip 4 Grade 4 questions Fibonacci Sequences ) Write down the next two terms of the Fibonacci sequence that begins,,,, 5, 8,,... ) If the first three Fibonacci numbers are x =, x =, x =, what is the least value of n for which x >60? n ) If the first three Fibonacci numbers are x =, x =, x =, what is the value of n for which x + x = 89? n n+ 4) If the first three Fibonacci numbers are x =, x =, x =, what is the value of n for which x + x + x = 68? n n+ n+ 5) If the first three Fibonacci numbers are x =, x =, x =, what is the value of n for which x + x = 44? n n 6) If the first three Fibonacci numbers are x =, x =, x =, what is the least value of n for which x n+ x n =.69 correct to three decimal places? Page 4

184 MathsWatch Clip 4 Grade 4 questions Compound Units ) Jane runs 00 metres in.4 seconds. Work out Jane s average speed in metres per second. Give your answer correct to decimal place. ) A car travels at a steady speed and takes five hours to travel 0 miles. Work out the average speed of the car in miles per hour. ) A plane flies 440 miles at a speed of 40 mph. How long does it take? 4) A marathon runner runs at 7.6 mph for three and a half hours. How many miles has he run? 5) A car takes 5 minutes to travel 4 miles. Find its speed in mph. 6) A cyclist takes 0 minutes to travel.4 miles. Calculate the average speed in mph. 7) An ice hockey puck has a volume of cm. It is made out of rubber with a density of.5 grams per cm. Work out the mass of the ice hockey puck. 8) An apple has a mass of 60 g and a volume of 00 cm. Find its density in g/cm. 9) A steel ball has a volume of 500 cm. The density of the ball is 95 g/cm. Find the mass of the ball in kg. 0) The mass of a bar of chocolate is 800 g. The density of the chocolate is 9 g/cm. What is the volume of the bar of chocolate? Page 4A

185 MathsWatch Clip 4 Grade 4 questions Compound Units ) Tony went on holiday to Miami. He travelled from London by plane. The distance from London to Miami is 70 km. The plane journey took 8 hours. Calculate the average speed of the plane. ) A solid cylinder has a radius of 4 cm and a height of 0 cm. 0 cm 4 cm a) Work out the volume of the cylinder. Give your answer correct to significant figures. The cylinder is made of wood. The density of the wood is 0.7 grams per cm b) Work out the mass of the cylinder. Give your answer correct to significant figures. ) 8 cm 6 cm 0 cm cm The diagram shows a solid prism made from metal. The cross-section of the prism is a trapezium. The parallel sides of the trapezium are 8 cm and cm. The height of the trapezium is 6 cm. The length of the prism is 0 cm. The density of the metal is 4 g/cm. Calculate the mass of the prism. Give your answer in kilograms. Page 4 B

186 MathsWatch Clip 4 Grade 4 questions Distance-Time Graphs 5 ) Sarah travelled 0 km from home to her friend s house. She stayed at her friend s house for some time before returning home. Here is the travel graph for part of Sarah s journey. 0 Distance from home (km) Time of day a) At what time did Sarah leave home? b) How far was Sarah from home at 0 0? Sarah left her friend s house at 0 to return home. c) Work out the time in minutes Sarah spent at her friend s house. Sarah returned home at a steady speed. She arrived home at 50 d) Complete the travel graph. e) Work out Sarah s average speed on her journey from her home to her friend s house. Give your answer in kilometres per hour. f) Work out Sarah s average speed on her journey home from her friend s house. Give your answer in kilometres per hour. Page 4

187 MathsWatch Clip 44 Grade 4 questions Similar Shapes ) B 05 6 cm 8 A 0 cm D C P Q 05 8 cm 5 cm S R ABCD and PQRS are mathematically similar. a) Find the length of PQ. b) Find the length of AD. Q ) B 5 cm 4 cm A C 6 cm P 9 cm R Triangles ABC and PQR are mathematically similar. Angle A = angle P. Angle B = angle Q. Angle C = angle R. AC = 6 cm. BC = 4 cm. PR = 9 cm. PQ = 5 cm a) Work out the length of QR. b) Work out the length of AB. Page 44A

188 MathsWatch Clip 44 Grade 4 questions Similar Shapes ) A 5 cm B.5 cm C Triangle ABC is similar to triangle ADE. AC = 5 cm. CE = 6 cm. BC =.5 cm. 6 cm Work out the length of DE. D E ) ABC and AED are straight lines. EB is parallel to DC. Angle ACD = 90 A AB = 0 cm BC = 5 cm EB = 6 cm 0 cm a) Work out the length of DC. b) Work out the area of the trapezium EBCD. E 6 cm B 5 cm D C Page 44 B

189 MathsWatch Clip 44 Grade 4 questions Similar Shapes ) The diagram shows two quadrilaterals that are mathematically similar. B P 8 cm Q A cm S 4 cm R D 4 cm C a) Calculate the length of AB b) Calculate the length of PS ) SV is parallel to TU. RST and RVU are straight lines. RS = 9 cm, ST = cm, TU = 7 cm, RV = 6 cm Calculate the length of VU. R 9 cm 6 cm cm S V T 7cm U ) BE is parallel to CD. ABC and AED are straight lines. AB = 4 cm, BC = 6 cm, BE = 5 cm, AE = 4.4 cm a) Calculate the length of CD. A b) Calculate the length of ED. 4 cm 4.4 cm B E 6 cm 5 cm C D Page 44 C

190 MathsWatch Clip 45 Grade 4 questions Bisecting an Angle ) Using ruler and compasses, bisect angle ABC. A B C ) The diagram below shows the plan of a park. The border of the park is shown by the quadrilateral RSTUV S T U V R There are two paths in the park. One is labelled TR and the other TV A man walks in the park so that he is always the same distance from both paths. Using ruler and compasses show exactly where the man can walk. Page 45

191 MathsWatch Clip 46 Grade 4 questions Constructing Perpendiculars ) Use ruler and compasses to bisect the line segment AB. You must show all construction lines. B A ) Use ruler and compasses to construct the perpendicular to the line segment CD that passes through the point P. You must show all construction lines. C P D Page 46

192 MathsWatch Clip 47 Grade 4 questions Drawing a Triangle Using Compasses ) The diagram shows a sketch of triangle ABC. B Diagram NOT accurately drawn 7.4 cm A 8.5 cm 8 C BC = 7.4 cm AC = 8.5 cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on your diagram. ) Use ruler and compasses to construct an equilateral triangle with sides of length 6 centimetres. You must show all construction lines. ) The diagram shows a sketch of triangle PQR. Q Diagram NOT accurately drawn 0.5 cm 7. cm P 9 cm R a) Use ruler and compasses to make an accurate drawing of triangle PQR. b) Measure angle P. Page 47

193 MathsWatch Clip 48 Grade 4 questions Enlargements ) a) Enlarge triangle T by scale factor using point (-5, ) as the centre of enlargement. Label your new triangle U. b) Enlarge triangle V by scale factor a half using the point (-, -) as the centre of enlargement. Label your new triangle W. y 5 4 T O x - - V -4-5 ) Describe fully the single transformation which maps triangle S to triangle T. y S T O x Page 48

194 MathsWatch Clip 49 Grade 4 questions Tangents, Arcs, Sectors and Segments Tangent Radius Minor sector Minor segment Arc Diameter Chord Circumference On the diagram, mark on all of the words from the box in an appropriate place. Page 49

195 MathsWatch Clip 50 Grade 4 questions Pythagoras Theorem ) Find the length of side a. Give your answer to decimal place. cm a 4 cm ) Find the length of side b. Give your answer to decimal place. b 5 cm 8 cm ) Find the length of side c. Give your answer to decimal place. 0 cm cm c 4) Find the length of side d. Give your answer to decimal place. d 8 cm 5 cm 5) Find the length of the diagonal of this rectangle. Give your answer to decimal place. 9 cm 6 cm Page 50 A

196 MathsWatch Clip 50 Grade 4 questions Pythagoras Theorem ) Find the length of side AC. Give your answer to decimal place. A 4) Below is a picture of a doorway. Find the size of the diagonal of the doorway. Give your answer to decimal place. cm.m 0.8m B 7cm ) Find the length of side QR Give your answer to decimal place. Q 4.8cm P C 5) In the sketch of the rectangular field, below, James wants to walk from B to D. A B 60m R 7.6cm D 50m Which of the following routes is shorter and by how much? From B to C to D or straight across the field from B to D. Give your answer to the nearest metre. C ) Find the length of side SU Give your answer to decimal place. T 4cm cm S 6) Fiona keeps her pencils in a cylindrical beaker as shown below. The beaker has a diameter of 8cm and a height of 7cm. Will a pencil of length 9cm fit in the beaker without poking out of the top? All workings must be shown. U Page 50 B

197 MathsWatch Clip 50 Grade 4 questions Pythagoras Theorem ) Points P and Q have coordinates (, 4) and (5, ). Calculate the shortest distance between P and Q. Give your answer correct to decimal place. 6 y 5 4 P Q O x ) Points A and B have coordinates (-4, ) and (, -). Calculate the shortest distance between A and B. Give your answer correct to decimal place. 5 y A O x - B Page 50 C

198 MathsWatch Clip 5 Grade 4 questions Simple Tree Diagrams ) Jim and Sue each take a driving test. The probability that Jim will pass the driving test is 0.7 The probability that Sue will pass the driving test is 0.6 a) Complete the probability tree diagram. Jim Sue 0.6 Pass 0.7 Pass Fail 0.6 Pass Fail Fail b) Work out the probability that both Jim and Sue will pass the driving test. c) Work out the probability that only one of them will pass the driving test. ) Terri has 7 pens in a box. of the pens are blue. 5 of the pens are red. Terri takes at random a pen from the box and writes down its colour. Terri puts the pen back in the box. Then Terri takes at random a second pen from the box and writes down its colour. a) Complete the probability tree diagram. st pen nd pen..... Blue Blue Red..... Red..... Blue..... Red b) Work out the probability that Terri takes exactly one pen of each colour from the box. Page 5 A

199 MathsWatch Clip 5 Grade 4 questions Simple Tree Diagrams ) Tim puts red counters and 4 blue counters in a bag. He takes at random a counter from the bag. He writes down the colour of the counter. He puts the counter in the bag again. He then takes at random a second counter from the bag. a) Complete the probability tree diagram. st counter 7 nd counter Red 7 Red Blue Blue Red Blue b) Work out the probability that Tim takes two red counters. ) In a game of chess, a player can either win, lose or draw. The probability that Jane wins any game of chess is 0. The probability that Jane draws any game of chess is 0. Jane plays games of chess. st game nd game a) Complete the probability tree diagram Win Win..... Draw Lose..... Win 0. Draw..... Draw Lose Win Lose..... Draw b) Work out the probability that Jane will win both games Lose Page 5 B

200 MathsWatch Clip 5 Grade 4 questions Simple Tree Diagrams ) Lucy throws a biased dice twice. Complete the probability tree diagram to show the outcomes. Label clearly the branches of the tree diagram. st Throw nd Throw 6 Six... Not Six ) A bag contains 0 coloured balls. 7 of the balls are blue and of the balls are green. Nathan is going to take a ball, replace it, and then take a second ball. a) Complete the tree diagram.... st Ball nd Ball... Blue Blue... Green... Green Blue Green b) Work out the probability that Nathan will take two blue balls. c) Work out the probability that Nathan will take one of each coloured balls. d) Work out the probability that Nathan will take two balls of the same colour. Page 5 C

201 MathsWatch Clip 5 Grade 4 questions Sampling Populations ) In a school there were 800 students who regularly had a school dinner. The Headteacher of the school wanted to know whether the students liked the dinners. a) What is the main advantage of asking a sample of the students whether they like school dinners rather than asking all of them? b) The Headteacher asked 00 KS students whether they liked the dinners and 40 of them said they did. Use this information to estimate how many of the 800 students liked school dinners. c) In finding your answer to part b), what assumption have you made? d) What could be done to make your estimate more accurate? ) A park-keeper wanted to know how many fish there were in the park pond. He went to the pond early one morning and used his fishing rod to catch 0 fish. The bait he used was maggots. Then, he marked each of the fish with a white dot on their tail and released them. A week later, he used his fishing rod and maggots to catch another 0 fish. He found that 4 of these 0 fish had the white dot on their tails. a) Use this information to estimate how many fish there are in the pond. b) In finding your estimate, what assumption have you made? Page 5

202 MathsWatch Clip 5 Grade 4 questions Time Series The table on the right shows the sales figures for a manufacturing company over the course of 5 years. a) Complete the time series graph to show this information. b) What is the range of the sales figures? c) Comment on the trend over the course of 5 years. Year Sales ( M) Sales in M Year Page 5

203 MathsWatch Clip 54 Grade 5 questions Negative Indices ) Find the value of: - a) - b) - c) 5-4 d) 0 ) Find the value of: - - a) b) 0 - c) d) 8 ) Write these numbers in order of size. Start with the smallest x 4) If =, find the value of x. Page 54

204 MathsWatch Clip 55 Grade 5 questions Error Intervals ) A number, x, rounded to decimal place is 4.7 Write down the error interval for x. ) A number, y, rounded to decimal places is.6 Write down the error interval for y. ) A number, x, rounded to significant figure is 400. Write down the error interval for x. 4) A number, y, rounded to significant figures is Write down the error interval for y. ` 5) A number, x, rounded to significant figures is 400. Write down the error interval for x. Page 55

205 MathsWatch Clip 56 Grade 5 questions Mathematical Reasoning ) Meg says, The sum of three prime numbers is always odd. Write an example to show that Meg is incorrect. ) Mike says. If you cube a prime number, the result will always be odd. Give an example to show that Mike is wrong. ) Explain why an odd number plus another odd number plus an even number is always even. 4) P is an odd number. Q is an even number. Explain why P + Q is always odd. 5) P is an odd number. Q is an even number. Tim says that P + Q is always a prime number. Explain why Tim is wrong. Page 56

206 MathsWatch Clip 57 Grade 5 questions Factorising and Solving Quadratics ) Factorise and solve the following equations: a) x + 5x + 6 = 0 b) x + 9x + 0 = 0 c) x + x 6 = 0 d) x + 5x 4 = 0 e) x 6x + 8 = 0 f) x x 8 = 0 g) x + 7x + = 0 h) 6x + x + = 0 i) x + x 0 = 0 j) x 4x + 6 = 0 ) Lucy said that - is the only solution of x that satisfies the equation x + x + = 0 Was Lucy correct? Show working to justify your answer ) Ben said that -5 is the only solution of x that satisfies the equation x + 0x + 5 = 0 Was Ben correct? Show working to justify your answer Page 57

207 MathsWatch Clip 58 Grade 5 questions The Difference of Two Squares ) Factorise a) x 6 c) y 9 e) x 4 b) a b d) x f) x 9 ) Factorise a) x 4y c) 9x 6y e) 4x 5y b) 9a b d) 4 x y f) x 9 y ) Simplify a) y 4 5 y+ y + 5 b) 4x x + x c) x + 8x 9x 4 d) 5a 6b 0ab 8b 4) Solve a) 4x 6 = 0 c) 49x = b) 5x = d) 9x 9 = 7 Page 58

208 MathsWatch Clip 59 Grade 5 questions Finding the Equation of a Straight Line ) Find the equations of lines A, B and C on the axes below 8 y C A B O x ) Find the equations of lines A, B and C on the axes below y C B 6 A O x Page 59A

209 MathsWatch Clip 59 Grade 5 questions Finding the Equation of a Straight Line ) Find the equation of line A on the grid below. y A O x - - ) A straight line passes through points (0, 4) and (, ). What is its equation? ) A straight line passes through points (0, 7) and (, -). What is its equation? 4) A straight line is parallel to y = x and goes through (, 8). What is its equation? 5) A straight line is parallel to y = x + 5 and goes through (5, 6). What is its equation? 6) A is the point (-, ). B is the point (, 6). C is the point (0, -). Find the equation of the line which passes through C and is parallel to AB. A (-, ) C (0, -) B (, 6) Page 59B

210 MathsWatch Clip 60 Grade 5 questions Roots and Turning Points of Quadratics ) The graph of y = x x is shown. Write down the coordinates of: a) The turning point of the curve. b) The roots of the equation x x = 0 c) The intersection of the curve with the y-axis y O x Page 60

211 MathsWatch Clip 6 Grade 5 questions ) a) Complete this table of values for y = x + x 4 x y 4 0 b) On the grid, draw the graph of y = x + x 4 c) Use the graph to find the value of x when y = ) a) Complete this table of values for y = x + x Cubic and Reciprocal Graphs 8 y O y x x 0 8 y 0 4 b) On the grid, draw the graph of y = x + x c) Use the graph to find the value of x when y = O x -4 ) Sketch the graph of y = + x -8 - Page 6

212 MathsWatch Clip 6 Grade 5 questions Simultaneous Equations Algebraically ) Solve 4x + y = 6 5x y = ) Solve 4x + y = 9 x 5y = 7 ) Solve x + 5y = x + y = 8 4) Solve x + 4y = 5 4x y = 5) Solve a + b = 4a 5b = 0 6) Solve 5x + y = 4 x + 4y = 9 7) Solve 6x y = x + y = - 8) Solve a b = 4 4a + b = 9) Solve 5x + 4y = 5 x + 7y = 9 0) Solve 6x 4y = 9 x + y = 6 Page 6

213 MathsWatch Clip 6 Grade 5 questions Geometric Progressions ) The st term of a geometric progression is 5 and the common ratio is. a) Write down the first four terms of the progression. b) What is the 0th term of the progression? ) The st term of a geometric progression is and the common ratio is 4. a) Write down the first four terms of the progression. b) What is the 7th term of the progression? ) The st and rd terms of a geometric progression are 7 and 6. a) What is the common ratio of the progression? b) Write down the first four terms. c) Work out the 5th term of the progression. 4) The 5th term of a geometric progression is 664. The 6th term of the progression is What is the st term of the progression? 5) The first four terms of a geometric progression are 875, 75, 75, 5,... a) What is the common ratio of the progression? b) Work out the 8th term of the progression. 6) The third term of a geometric progression is 9. The 4th term of the progression is 48. What is the st term of the progression? Page 6

214 MathsWatch Clip 64 Grade 5 questions Compound Interest and Depreciation ) Henry places 6000 in an account which pays 4.6% compound interest each year. Calculate the amount in his account after years. ) Sarah puts 8600 in a bank. The bank pays compound interest of.8% per year. Calculate the amount Sarah has in her account after 4 years. ) Mary deposits 0000 in an account which pays 5.6% compound interest per year. How much will Mary have in her account after 5 years? 4) Susan places 7900 in an account which pays.4% compound interest per year. How much interest does she earn in years? 5) Harry puts money into an account which pays 6% compound interest per year. If he puts 000 in the account for 5 years how much interest will he earn altogether? 6) Laura buys a new car for The annual rate of depreciation is %. How much is the car worth after years? 7) The rate of depreciation of a particular brand of computer is 65% per year. If the cost of the computer when new is 650 how much is it worth after years? 8) Sharon pays 500 for a secondhand car. The annual rate of depreciation of the car is 4% How much will it be worth four years after she has bought it? 9) Dave places 7000 in an account which pays 4% compound interest per year. How many years will it take before he has 9.69 in the bank? 0) A new motorbike costs The annual rate of depreciation is 8% per year. After how many years will it be worth ? Page 64

215 MathsWatch Clip 65 Grade 5 questions Loci ) A B D C ABCD is a rectangle. Shade the set of points inside the rectangle which are both more than 4 centimetres from the point D and more than centimetre from the line AB. ) Two radio transmitters, A and B, are situated as below. B A Transmitter A broadcasts signals which can be heard up to km from A. Transmitter B broadcasts signals which can be heard up to 6 km from B. Shade in the area in which radio signals can be heard from both transmitters. Use a scale of cm = km. Page 65A

216 MathsWatch Clip 65 Grade 5 questions Loci ) Draw the locus of all points which are equidistant from the lines AB and AC. B A C ) Draw the locus of all points which are equidistant from the points A and B. A x x B Page 65 B

217 MathsWatch Clip 65 Grade 5 questions Loci ) Draw the locus of all points that are exactly cm from the line PQ. P Q ) Draw the locus of all points that are exactly 4 cm from the rectangle ABCD A B D C Page 65 C

218 MathsWatch Clip 66 Grade 5 questions Congruent Triangles ) ABCD is a quadrilateral. A B D AB is parallel to DC. DA is parallel to CB. C Prove that triangle ABD is congruent to triangle CDB. ) P Q T S R PQRS is a square. PTS and SUR are equilateral triangles. U a) Prove that triangle USP is congruent to triangle TSR. X is the point such that RUXT is a parallelogram. b) Prove that UP = UX Page 66 A

219 MathsWatch Clip 66 Grade 5 questions ) Congruent Triangles A P Q B The diagram shows a triangle ABC. PQRB is a parallelogram where P is the midpoint of AB, Q is the midpoint of AC, and R is the midpoint of BC. R C Prove that triangle APQ and triangle QRC are congruent. You must give reasons for each stage of your proof. ) A B D C ABC is an equilateral triangle. D lies on BC. AD is perpendicular to BC. a) Prove that triangle ADC is congruent to triangle ADB. b) Hence, prove that BD = AB Page 66 B

220 MathsWatch Clip 67 Grade 5 questions Sectors of a Circle ) This sector of a circle has radius 6 cm. 5 6 cm a) Find the area of the sector. b) Find the perimeter of the sector. ) A quadrant of a circle is shown. 0 cm 0 cm Work out the area of the shaded section. ) The diagram shows a sector of a circle. 0 The arc length is 47.6 cm. Work out the radius. Page 67

221 MathsWatch Clip 68 Grade 5 questions Trigonometry A ) ABC is a right-angled triangle. AB = 50 cm. Angle ABC = 4 50 cm Work out the length of BC. Give your answer correct to decimal place. B 4 C A ) ABC is a right-angled triangle. AB = cm. Angle BCA = 0 cm Work out the length of AC. Give your answer correct to decimal place. B 0 C A ) ABC is a right-angled triangle. AC = 6 cm. Angle CAB = cm Work out the length of BC. Give your answer correct to decimal place. B C A 4) ABC is a right-angled triangle. AB = cm. AC = cm. cm x cm Work out the size of angle x. Give your answer correct to decimal place. B C A 5) ABC is a right-angled triangle. AB = 8 cm. AC = 7 cm. 8 cm 7 cm Work out the size of angle ABC. Give your answer correct to decimal place. B C Page 68A

222 MathsWatch Clip 68 Grade 5 questions Trigonometry ) PQR is a right-angled triangle. PR = cm. QR = 4.5 cm Angle PRQ = 90 Q 4.5 cm Work out the value of x. Give your answer correct to decimal place. P x cm R ) AC = 4 cm. Angle ABC = 90 Angle ACB = 4 A 4 cm Calculate the length of BC. Give your answer correct to significant figures. B 4 C ) PQR is a right-angled triangle. PQ = 8 cm. QR = 8.4 cm Angle PRQ = 90 8 cm Q 8.4 cm Work out the value of x. Give your answer correct to decimal place. P x R 4) AB = cm. Angle ABC = 90 Angle ACB = Calculate the length of AC. Give your answer correct to significant figures. cm A B C 5) A lighthouse, L, is.4 km due West of a port, P. A ship, S, is.8 km due North of the lighthouse, L. N Calculate the size of the angle marked x. Give your answer correct to significant figures. S.8 km N L.4 km x Page 68 B

223 MathsWatch Clip 68 Grade 5 questions Trigonometry D ) DEF is a right-angled triangle. DE = mm mm FE = 45 mm F y 45 mm E Calculate the size of angle y. Give your answer correct to one decimal place. Q ) PQR is a right-angled triangle. QR = cm cm PR = 0 cm P 0 cm R Work out the size of angle RPQ. Give your answer correct to three significant figures. ) a) 9 cm Calculate the size of the angle marked x. Give your answer correct to one decimal place. x 4 cm b) y cm Calculate the value of y. Give your answer correct to one decimal place cm Page 68 C

224 MathsWatch Clip 68 Grade 5 questions Trigonometry ) A ABC is a right-angled triangle. AC = 9.7 cm 9.7 cm BC = 8. cm B 8. cm x C Calculate the size of the angle marked x. Give your answer correct to three significant figures. A ) 57 ABC is a right-angled triangle. AC = 5 m 5 m Angle CAB = 57 C B Calculate the length of AB. Give your answer correct to three significant figures. C ) ABC is a right-angled triangle. AC = 9 m 9 m Angle CAB = 6 A 6 B Calculate the length of AB. Give your answer correct to three significant figures. Page 68D

225 MathsWatch Clip 68 Grade 5 questions Trigonometry E ) AC = 9 cm AB = cm C DE = 0 cm Angle ABC = angle CBD = angle BDE = 90 9 cm 0 cm Calculate the length of CD. Give your answer to significant figures. A cm B 50 D ) P 4 cm Q 8 cm S 64 R PQRS is a trapezium. PQ is parallel to SR. Angle PSR = 90 Angle PRS = 64 PQ = 4 cm. PS = 8 cm. Work out the length of PR. Give your answer correct to significant figures. Page 68 E

226 MathsWatch Clip 69 Grade 5 questions Spheres Volume of a sphere = r Surface area of a sphere = 4 r ) a) Work out the volume of the sphere. b) Work out the surface area of the sphere. cm ) a) Work out the volume of the sphere, leaving your answer in terms of. b) Work out the surface area of the sphere, leaving your answer in terms of. 0 cm ) a) Work out the volume of the solid hemisphere. b) Work out the surface area of the solid hemisphere. 5.5 cm Page 69

227 MathsWatch Clip 70 Grade 5 questions Pyramids Volume of a pyramid = base area height ) The pyramid has a rectangular base and E is vertically above A. E 0 cm A D 9 cm B 6 cm C Find the volume of the pyramid. ) Find the volume of this pyramid. 8 cm 5 cm 7 cm ) Find the volume of this pyramid. 0 cm 6 cm 8 cm Page 70

228 MathsWatch Clip 7 Grade 5 questions Cones Volume of a cone = r h Curved surface area = rl ) a) Work out the volume of the cone. b) Work out the curved surface area of the cone. c) The total surface area of the cone. cm cm 5 cm ) Work out the volume of the cone, leaving your answer in terms of. 9 cm 4 cm Page 7A

229 MathsWatch Clip 69/7 Grade 5 questions Spheres and Cones ) A cone has a base radius of 4 cm and a vertical height of 8 cm. a) Calculate the volume of the cone. Take to be.4. Give your answer correct to significant figures. b) Use Pythagoras Theorem to find the slant height of the cone. Give your answer correct to decimal place. 8 cm c) Find the curved surface area of the cone. Take to be.4. Give your answer correct to significant figures. 4 cm ) A sphere has a radius of cm. a) Calculate the volume of the sphere. Take to be.4. Give your answer correct to significant figures. cm b) Find the curved surface area of the sphere. Take to be.4. Give your answer correct to significant figures. ) A cone has a base radius of 8 cm and a slant height of 0 cm. Calculate the volume of the cone. Leave your answer in terms of. 0 cm 8 cm Page 7B

230 MathsWatch Clip 69/7 Grade 5 questions Spheres and Cones ) h x x The diagram shows a solid cone and a solid hemisphere. The cone has a base of radius x cm and a height of h cm. The hemisphere has a base of radius x cm. The surface area of the cone is equal to the surface area of the hemisphere. Find an expression for h in terms of x. ) h x x x A cylinder has base radius x cm and height x cm. A cone has base radius x cm and height h cm. The volume of the cylinder and the volume of the cone are equal. Find h in terms of x. Give your answer in its simplest form. Page 7C

231 MathsWatch Clip 7 Grade 5 questions Frustums ) A frustum is made by removing a small cone from a similar larger cone. Work out the volume of the frustum. 5 cm 0 cm 9 cm cm ) The diagram shows a cone of height 40 cm and base radius 0 cm. A smaller cone of height 8 cm is removed to form a frustum. 8 cm 40 cm r r 0 cm 0 cm a) Work out the radius r of the base of the smaller cone. Calculate, to the nearest cm b) The volume of the larger cone. c) The volume of the smaller cone. d) The volume of the frustum. Page 7

232 MathsWatch Clip 7 Grade 5 questions Exact Trigonometric Values ) Write down the exact values of: a) sin 0 b) sin 0 c) sin 45 d) sin 60 e) sin 90 ) Write down the exact values of: a) cos 0 b) cos 0 c) cos 45 d) cos 60 e) cos 90 ) Write down the exact values of: a) tan 0 b) tan 0 c) tan 45 d) tan 60 Page 7

233 MathsWatch Clip 74 Grade 5 questions Introduction to Vectors ) The translation of triangle P to triangle Q is described by column vector v. Write down v. P Q ) Here are two column vectors: - f = g = 5 - Work out a) f b) -g c) f + g d) f g e) f + 4g f) g f Page 74

234 MathsWatch Clip 75 Grade 5 questions Harder Tree Diagrams ) There are 5 red pens, blue pens and green pens in a box. Jerry takes at random a pen from the box and gives the pen to his friend. Jerry then takes at random another pen from the box. Work out the probability that both pens are the same colour. ) There are red sweets, blue sweets and 4 green sweets in a bag. Jack takes a sweet at random. He eats the sweet. He then takes another sweet at random. Work out the probability that both sweets are the same colour. ) There are buttons in a bag. 9 buttons are white. 4 buttons are black. Carol takes a button at random from the bag, and keeps it. She now takes another button from the bag. Work out the probability that Carol takes a button of each colour. Page 75A

235 MathsWatch Clip 75 Grade 5 questions Harder Tree Diagrams ) A bag contains 7 green and yellow balls. A ball is taken from the bag at random and not replaced. Another ball is taken from the bag at random. a) Draw a tree diagram to show all the possibilities. b) What is the probability that both balls are different colours? ) A box contains 5 red counters and blue counters. A counter is taken from the box at random and not replaced. Another counter is taken at random. a) Draw a tree diagram to show all the possibilities. b) What is the probability of choosing at least one blue counter? c) What is the probability of choosing two counters of the same colour? d) What is the probability of choosing two counters of different colours? ) A box contains 4 red counters and blue counters. A counter is taken from the box at random and not replaced. A second counter is taken from the box at random and not replaced. A third counter is taken from the box. a) Draw a tree diagram to show all the possibilities. b) What is the probability that all three counters are the same colour? c) What is the probability that exactly two of the counters are red? Page 75B

236 MathsWatch Clip 75 Grade 5 questions Harder Tree Diagrams ) Sara has two boxes. There are 6 black and 4 white counters in box A. There are 7 black and white counters in box B. Sara takes at random a counter from box A and puts it in box B. She then takes at random a counter from box B and puts it in box A. a) Complete the probability tree diagram. From A to B From B to A Black Black White White Black White b) Find the probability that after Sara has put the counters from box B into box A there will still be 6 black counters and 4 white counters in box A. Page 75C

237 MathsWatch Clip 76 Grade 5 questions Stratified Sampling ) Ellen wants to do a survey with Years 9, 0 and at her school. The table shows the number of students in each of these year groups. Year Year 0 Year Ellen takes a sample of 50 students stratified by year group. Work out the number of students from Year 0 in the sample. ) The table shows information about the year groups of 000 students in a school. Year group Number in year Tony takes a sample of 50 of these students, stratified by year group. Calculate the number of Year 8 students he should have in his sample. ) The table shows information about Ben s collection of 65 coins. Country Number of coins France Spain Germany Italy Total Ben takes a sample of 50 coins stratified by country. Work out the number of coins from Italy in this sample. 4) Male Female Lower sixth Upper sixth The table gives information about the number of students in the two years of a sixth form. Amy wants to interview some of these students. She takes a random sample of 70 students stratified by year and by gender. Work out the number of students in the sample who are male and in the lower sixth. Page 76A

238 MathsWatch Clip 76 Grade 5 questions Stratified Sampling ) The table below shows the number of employees in each section of a company. Department Managerial Sales Technical Production Number of employees A survey on job satisfaction is to be carried out. a) Explain why a simple random sample of employees is unsuitable. b) A stratified random sample of 00 is used. Complete the table below to show how many employees from each department will be included. Department Managerial Sales Technical Production Number of employees in sample ) MathsWatch High-School has 798 pupils. The size of each year group is shown below. Year Group Boys Girls The headteacher wants to find out the opinions of the pupils on changing the timing of the school day. A stratified sample of 80 pupils is taken. a) Complete the table below to show the numbers of pupils to be sampled. Year Group Boys in Sample Girls in Sample The table below shows the number of pupils in the sample who answered YES to a change in the timing of the school day. Year Group Boys in Sample Girls in Sample who answered YES who answered YES b) Use the table to estimate the percentage of pupils in the school who would answer YES to the question. Page 76B

239 MathsWatch Clip 77 Grade 6 questions Recurring Decimals to Fractions Write each recurring decimal as an exact fraction, in its lowest terms. a) 05. b) 07. c) 04. d) 04. e) 075. f) 08. g) h) 06. i) 074. j) 04. k) l) Page 77

240 MathsWatch Clip 78 Grade 6 questions Product of Three Binomials ) Expand and simplify: a) x(x + )(x + ) b) x(x + 4)(x + 7) c) x(x + )(x + 9) ) Expand and simplify: a) x(x + 5)(x ) b) x(x 4)(x + ) c) x(x + 8)(x ) ) Expand and simplify: a) (x + )(x + 5)(x + ) b) (x )(x )(x ) c) (x )(x + 5)(x ) 4) Expand and simplify: a) (x 4)(x + 4)(x ) b) (x )(x )(x + ) c) (x + 6)(x + )(x 6) 5) Expand and simplify: a) (x )(x + )(x + ) b) (x + 5)(x )(x + ) c) (x )(x )(4x ) Page 78

241 MathsWatch Clip 79 Grade 6 questions Iteration - Trial and Improvement ) The equation x x = 9 has a solution between and 4 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. ) The equation x 4x = 5 has a solution between and 4 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. ) The equation x x = 68 has a solution between 4 and 5 Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. 4) The equation x + 4x = 0 has one solution which is a positive number. Use a trial and improvement method to find this solution. Give your answer correct to decimal place. You must show all your working. Page 79

242 MathsWatch Clip 80 Grade 6 questions Iterative Processes ) A sequence is defined by the term-to-term rule u n+ = u n un Given that u =, find u, u and u. 4 ) A sequence is defined by the term-to-term rule x x n n+ = + x n Given that x =, find x, x and x 4. ) x = 4 n+ x n x = 4 Use a starting value of x = to find a solution to n+ x n to decimal place. 4) x = + n+ x n Use a starting value of x = to find a solution to x = + n+ x n to decimal place. Page 80

243 MathsWatch Clip 8 Grade 6 questions Enlargement - Negative Scale Factor ) Enlarge triangle T by scale factor - using coordinates (, ) as the centre of enlargement. y T O x ) Describe fully the single transformation which maps triangle T to triangle U. y U O x T Page 8

244 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations ) O P y x a) Rotate triangle P 80 about the point (-, ). Label the new triangle A. b) Translate triangle P by the vector Label the new triangle B. ( ( 6 - ) ) y 5 y = x 4 c) Reflect triangle Q in the line y = x. Label the new triangle C. Q O 4 5 x Page 8A

245 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations ) 8 y x = 6 4 A O x Triangle A is reflected in the x-axis to give triangle B. Triangle B is reflected in the line x = to give triangle C. Describe fully the single transformation that takes triangle A to triangle C. ) 5 y A 4 a) Reflect shape A in the y-axis O b) Describe fully the single transformation which takes shape A to shape B. x - B Page 8 B

246 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations 8 y O x a) Rotate the shaded shape 90 clockwise about the point y 4 S T O b) Describe fully the single transformation that will map shape S onto shape T. x Page 8 C

247 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations ) a) On the grid, draw an enlargement, scale factor, of the shaded shape. 5 y A 4 B O x - b) Describe fully the single transformation that maps triangle A onto triangle B. Page 8D

248 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations T Triangle T has been drawn on a grid. a) On the grid, draw an enlargement of the triangle T with scale factor. 4 y U O 4 - x Triangle U has been drawn on a grid. b) On the grid, rotate triangle U 90 clockwise about the centre O. Page 8 E

249 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations ) 5 y 4 A O x B Describe fully the single transformation that maps triangle A onto triangle B. ) y 5 4 T O x Triangle T has been drawn on the grid. Rotate triangle T 80 about the point (, 0) Label the new triangle A. Page 8 F

250 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations ) 9 y T 4 S O x Describe fully the single transformation which maps shape S onto shape T. ) 7 y P O x - Q Triangle P and triangle Q are drawn on the grid. a) Describe fully the single transformation which maps triangle P onto triangle Q. b) Translate triangle P by the vector Label the new triangle R. ( ( - ) ) Page 8G

251 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations 5 y y = x 4 O 4 5 x a) Reflect the shaded shape in the line y = x. y O x b) On the grid, enlarge the shaded shape by a scale factor of, centre O. Page 8H

252 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations 6 5 y 4 A O x a) On the grid above, reflect shape A in the line x = - y 5 4 P Q O x - - b) Describe fully the single transformation that will map shape P onto shape Q. Page 8 I

253 MathsWatch Clip 8 Grade 6 questions Combinations of Transformations Q a) On the grid, enlarge the shape with scale factor, centre Q. y O 4 x - - b) Rotate the shape 90 clockwise, centre O. - Page 8 J

254 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) D A 55 o x y C B In the diagram, A, B, C, and D are points on the circumference of a circle, centre O. Angle BAD = 55. Angle BOD = x. Angle BCD = y. a) (i) Work out the value of x. (ii) Give a reason for your answer. b) (i) Work out the value of y. (ii) Give a reason for your answer. B ) O C A The diagram shows a circle centre O. A, B and C are points on the circumference. DCO is a straight line and DA is a tangent to the circle. Angle ADO = 4 a) Work out the size of angle AOD. b) (i) Work out the size of angle ABC. (ii) Give a reason for your answer. 4 D Page 8A

255 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) B C A O A, B and C are points on the circumference of a circle centre O. AC is a diameter of the circle. a) (i) Write down the size of angle ABC. (ii) Give a reason for your answer. E F O 0 D D, E and F are points on the circumference of a circle, centre O. Angle DOF = 0. b) (i) Work out the size of angle DEF. (ii) Give a reason for your answer. ) B, D and E are points on a circle centre O. ABC is a tangent to the circle. BE is a diameter of the circle. Angle DBE = 5. a) Find the size of angle ABD. Give a reason for your answer. A D E b) Find the size of angle DEB. Give a reason for your answer. B 5 C Page 8 B

256 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) In the diagram, A, B and C are points on the circumference of a circle, centre O. PA and PB are tangents to the circle. Angle ACB = 7. a) (i) Work out the size of angle AOB. C 7 O B Diagram NOT accurately drawn P (ii) Give a reason for your answer. b) Work out the size of angle APB. A ) P, Q, R and S are points on the circle. PQ is a diameter of the circle. Angle RPQ =. S b R Diagram NOT accurately drawn a) (i) Work out the size of angle PQR. (ii) Give reasons for your answer. P a Q b) (i) Work out the size of angle PSR. (ii) Give a reason for your answer. ) The diagram shows a circle, centre O. AC is a diameter. Angle BAC =. D is a point on AC such that angle BDA is a right angle. B Diagram NOT accurately drawn a) Work out the size of angle BCA. Give reasons for your answer. A O D C b) Calculate the size of angle DBC. c) Calculate the size of angle BOA. 4) A, B, C and D are four points on the circumference of a circle. ABE and DCE are straight lines. Angle BAC =. Angle EBC = 58. a) Find the size of angle ADC. A B 58 Diagram NOT accurately drawn b) Find the size of angle ADB. Angle CAD = 69. c) Is BD a diameter of the circle? You must explain your answer. D C E Page 8 C

257 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) a = ) b = ) c = a 46 O b O O c ) d = 5) e = f = 6) g = 9 e 85 f O O O g d 4 7) h = 8) i = 9) j = k = h k 6 O i O O j 0) l = m = ) n = p = q = m p q 00 O n O 8 l 0 Page 8D

258 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) a = b = ) c = d = ) e = f = b a 5 O O O d e c 0 f 4) g = h = 5) i = 6) j = g 85 0 O O O 88 h 00 i j 7) k = l = m = 8) n = p = q = 9) r = s = m 4 O l k O p 0 O n q 40 r 4 s 0) t = ) u = t u 0 O 5 O 48 Page 8 E

259 MathsWatch Clip 8 Grade 6 questions Circle Theorems ) a = ) b = c = ) d = e = b e 8 O O O a ) f = g = 5) h = i = 6) j = k = l = m = g 40 O O 50 O 78 h 65 m k l j 7) n = 8) p = q = 9) r = s = t = r 6 O O q O 40 s t n 0) u = v = w = p 76 8 v O u w Page 8 F

260 MathsWatch Clip 84 Grade 6 questions Proof of Circle Theorems ) Prove that the angle subtended at the centre of a circle is twice the angle at the circumference. ) Prove that angles in the same segment are equal. ) Prove that opposite angles of a cyclic quadrilateral add up to 80. Page 84

261 MathsWatch Clip 85 Grade 6 questions Probability Using Venn Diagrams ) In a class of 0 students, all of them have brothers or sisters or both. 9 have a brother. 6 have a sister. a) Complete the Venn diagram. Brothers Sisters b) Find the probability that a student in the class has a brother and a sister. c) If it is known that a student has a sister, what is the probability that they also have a brother? ) A cafeteria serves only main courses and desserts. Some people just have a main, some have just a dessert and some have both. One day, 65% of the customers had a main course and 90% had a dessert. a) Show this information on a Venn diagram. b) What is the probability that a customer had a main course and a dessert? c) If it is known that a customer had a dessert, what is the probability that they also had a main course? Page 85

262 MathsWatch Clip 86 Grade 6 questions Cumulative Frequency The heights of 80 plants were measured and can be seen i n the table, below. Height (h cm) Frequency 0 < h < 0 0 < h < < h < < h < < h < < h < 60 a) Complete the cumulative frequency table for the plants. Height (h cm) 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 40 0 < h < 50 Cumulative Frequency CF < h < 60 b) Draw a cumulative frequency graph for your table c) Use your graph to find an estimate for (i) the median height of a plant. (ii) the interquartile range of the heights of the plants. 40 d) Use your graph to estimate how many plants had a height that was greater than 45cm Height (h cm) Page 86A

263 MathsWatch Clip 86 Grade 6 questions Cumulative Frequency The table shows information about the amount spent by 00 customers in a supermarket. Amount spent ( n) 0 < n < 0 Frequency 7 a) Complete the cumulative frequency table for this information. 0 < n < 40 Amount spent ( n) Cumulative frequency 40 < n < < n < < n < < n < < n < < n < < n < 0 0 < n < 80 0 < n < 00 0 < n < 0 b) On the grid, draw a cumulative frequency graph for your table. 00 Cumulative frequency O Amount spent ( n) c) Use your graph to find an estimate for the median amount spent. d) Use your graph to find an estimate for the interquartile range of the amount of money spent. Page 86 B

264 MathsWatch Clip 86 Grade 6 questions Cumulative Frequency Fred did a survey about the amount of money spent by 0 men at Christmas. The cumulative frequency table gives some information about the amounts of money spent by the 0 men. a) On the grid, draw a cumulative frequency diagram. Amount ( A) spent 0 < A < 00 0 < A < 50 0 < A < 00 Cumulative frequency 6 4 Cumulative frequency < A < 50 0 < A < 00 0 < A < 50 0 < A < b) Use your cumulative frequency diagram to estimate the median. c) Use your cumulative frequency diagram to estimate the interquartile range of the amount of money spent. d) Use your cumulative frequency diagram to estimate the number of men who spent more than 0. O Amount spent ( ) Page 86 C

265 MathsWatch Clip 86 Grade 6 questions Cumulative Frequency The table gives some information about the delay, in minutes, of 80 trains. a) Complete the cumulative frequency table. Delay (n minutes) Frequency Delay (n minutes) Cumulative Frequency 0 < n < < n < 0 0 < n < < n < 0 0 < n < 40 0 < n < < n < < n < < n < < n < 60 b) On the grid below, draw a cumulative frequency graph for your table. Cumulative frequency O Delay (n minutes) c) Use your graph to find an estimate for (i) the median delay. (ii) the interquartile range of the delays. (iii) the number of trains delayed for more than 5 minutes. Page 86D

266 MathsWatch Clip 86 Grade 6 questions Cumulative Frequency There are 00 teachers at Sam s school. Sam found out the age of each teacher. The table gives information about her results. a) Complete the cumulative frequency table Age (A years) 0 < A < 0 Frequency 5 Age (A years) 0 < A < 0 Cumulative Frequency 5 0 < A < < A < < A < < A < < A < 40 0 < A < 50 0 < A < 60 0 < A < 70 b) On the grid, draw a cumulative frequency graph for your table Cumulative frequency O Age (A years) c) Use your graph to find an estimate for the median age. d) Use your graph to find an estimate for the number of these teachers who are older than 56 years old. Page 86 E

267 MathsWatch Clip 86 Grade 6 questions This table shows information about the time, m minutes, it takes to show each of 0 films. Time (m minutes) 70 < m < 80 Frequency Cumulative Frequency a) Write down the modal class interval. b) Complete this cumulative frequency table. Time (m minutes) 70 < m < 80 Cumulative frequency 80 < m < < m < < m < 0 0 < m < 0 0 < m < < m < < m < < m < 0 70 < m < 0 70 < m < 0 c) On the grid, draw a cumulative frequency graph for your cumulative frequency table Cumulative frequency d) Use your graph to find an estimate for the median. Time (m minutes) e) Use your graph to find an estimate for the interquartile range of times. f) Use your graph to find an estimate for the number of films which take longer than 5 minutes to show. Page 86 F

268 MathsWatch Clip 87 Grade 6 questions Boxplots ) The ages of 0 teachers are listed below.,, 4, 5, 7, 7, 8, 9, 9, 9, 4, 5, 4, 4, 44, 49, 55, 57, 58, 58 a) On the grid below, draw a box plot to show the information about the teachers b) What is the interquartile range of the ages of the teachers? ) A warehouse has 60 employees working in it. The age of the youngest employee is 6 years. The age of the oldest employee is 55 years. The median age is 7 years. The lower quartile age is 9 years. The upper quartile age is 4 years. On the grid below, draw a box plot to show information about the ages of the employees Page 87A

269 MathsWatch Clip 87 Grade 6 questions Boxplots Terry drew a line of length 60 cm. He asked some children to estimate the length of the line he had drawn. He recorded their estimates. The box plot gives some information about these estimates. Children s estimates Size of estimate in cm Adults estimates a) Write down the median of the children s estimates. b) Write down the interquartile range of the children s estimates. Terry then asked some adults to estimate the length of the line he had drawn. The table gives some information about the adults estimates. Length Lowest estimate Lower quartile Median Upper quartile Highest estimate 0 cm 45 cm 6 cm 75 cm 95 cm c) On the grid above, draw a box plot to show this information. d) Use the two box plots to compare the distribution of the children s estimates with the distribution of the adults estimates. Page 87B

270 MathsWatch Clip 87 Grade 6 questions Boxplots ) The box plot gives information about the distribution of the weights of bags on a plane Weights (kg) a) Claude says that the heaviest bag weighs 4 kg. He is wrong. Explain why. b) Write down the median weight. c) Work out the interquartile range of the weights. There are 40 bags on the plane. d) Work out the number of bags with a weight of 0 kg or less. ) The box plots show the distribution of marks in a Science and Maths test for a group of students. Science Maths Marks a) What is the highest mark in the Science test? b) Compare the distribution of the marks in the Science test and marks in the Maths test Page 87C

271 MathsWatch Clip 87 Grade 6 questions Boxplots ) The incomplete box plot and table show some information about some marks Marks Marks Lowest mark 4 Lower quartile Median Upper quartile Highest mark a) Use the information in the table to complete the box plot. b) Use the information in the box plot to complete the table. ) Kim measured the height, in cm, of each tomato plant in her greenhouse. She used the results to draw the box plot shown below Height (cm) a) Write down the median height. b) Work out the interquartile range. c) Explain why the interquartile range may be a better measure of spread than the range. Page 87D

272 MathsWatch Clip 88 Grade 7 questions Fractional Indices ) Simplify the following: a) y 4 y 5 b) x x 6 c) (p 4 ) 5 d) (x ) e) (x 4 ) f) (x ) 5 g) x 7 x h) t 5 t ) Work out the value of the following, leaving your answer in fraction form when necessary a) 5 0 b) 4 c) 5 d) 49 e) 8 f) g) 6 h) 7 i) 64 5 ) 5 5 can be written in the form 5 n. Calculate the value of n. 4) 8 can be written in the form n. Calculate the value of n. 5) a = x, b = y Express in terms of a and b (i) (ii) (iii) x + y x x + y Page 88

273 MathsWatch Clip 89 Grade 7 questions Recurring Decimals - Proof ) a) Convert the recurring decimal 06. to a fraction in its simplest form. 8 b) Prove that the recurring decimal 07. = ) a) Change 4 9 to a decimal. 9 b) Prove that the recurring decimal 057. = ) a) Change to a decimal. 5 b) Prove that the recurring decimal 045. = 4) a) Change 6 to a decimal. 5 b) Prove that the recurring decimal 0. 5 = 7 5) a) Convert the recurring decimal 06. to a fraction in its simplest form. b) Prove that the recurring decimal 07. = 5 8 6) a) Convert the recurring decimal 5. to a fraction in its simplest form. b) Prove that the recurring decimal 06. = Page 89

274 MathsWatch Clip 90 Grade 7 questions Rearranging Difficult Formulae ) Make c the subject of the formula. v = a + b + c ) Make t the subject of the formula. A = π t + 5t ) Make s the subject of the formula. R = s + π s + t l 4) k = m l a) Make l the subject of the formula. b) Make m the subject of the formula. 5) A k ( = x + 5) Make x the subject of the formula. 6) R = u+ v u+ v Make u the subject of the formula. 7) x+ y = 5 0+ y Make y the subject of the formula. 8) a = 5 4b Rearrange this formula to give a in terms of b. 9) S = πd h + d Rearrange this formula to make h the subject. Page 90

275 MathsWatch Clip 9 Grade 7 questions Solving Quadratics with the Formula ) Solve the equation x + 4x + = 0 Give your answers correct to decimal places. ) Solve the equation x + 8x + 6 = 0 Give your answers correct to significant figures. ) Solve the equation x x = 0 Give your answers correct to significant figures. 4) Solve the equation x 7x + = 0 Give your answers correct to significant figures. 5) Solve the equation x + 6x = 0 Give your answers correct to significant figures. 6) Solve the equation x x 0 = 0 Give your answers correct to significant figures. 7) Solve the equation x 4x 6.5 = 0 8) Solve the equation 7x 9x 06 = 0 Give your answers correct to significant figures. 9) x + 0x = 00 Find the positive value of x. Give your answer correct to significant figures. 0) (x + )(x ) = a) Show that x x 7 = 0 b) Solve the equation x x 7 = 0 Give your answers correct to significant figures. Page 9

276 MathsWatch Clip 9 Grade 7 questions Factorising Hard Quadratics ) Factorise the following: a) x + 7x + b) x + 5x c) 6x x + d) 8x + 0x + e) 6x 7x 0 f) 4x 4x 5 ) Solve the following: a) 5x + 9x = 0 b) 6x + 5x 6 = 0 c) x + 5x + 7 = 0 d) 8x 4x 5 = 0 e) 0x 4x 0 = 5 f) 4x 8x + = 7 Page 9

277 MathsWatch Clip 9 Grade 7 questions Algebraic Proof ) Show algebraically that the sum of two consecutive numbers is always odd. ) Show algebraically that the product of two even numbers is always a multiple of four. ) Show algebraically that the square of an odd number is always odd. 4) Prove, using algebra, that the difference between the squares of any two consecutive even numbers is always a multiple of four. 5) n is an integer. Prove that (n + )(n + ) + (n + )(n ) is not a multiple of. 6) Prove that (4n + ) (4n ) is a multiple of eight for all positive integer values of n. 7) Prove algebraically that the sum of the squares of any three consecutive even numbers is always a multiple of 4. Page 9

278 MathsWatch Clip 94 Grade 7 questions Exponential Functions ) y (4, 75) (, ) x The sketch-graph shows a curve with equation y = pq x. The curve passes through the points (, ) and (4, 75). Calculate the value of p and the value of q. ) The graph shows the number of bacteria living in a petri dish. The number N of bacteria at time t is given by the relation: N = a b t The curve passes through the point (0, 400). a) Use this information to show that a = 400. The curve also passes through (, 900). b) Use this information to find the value of b. Number of bacteria N t c) Work out the number of bacteria in the dish at time t =. Time (hours) Page 94