THE ANSWER BOOK. Foundation Worksheets

Transcription

1 THE ANSWER BOOK Foundation Worksheets Grades to Grade Grade Grade Grade Grade Instructions for use Clicking on something like this Grade will take you to the Grade clip numbers and titles. Clicking on something like this Compound Units will take you to Worksheet. Clicking on something like this MathsWatch Clip Grade questions will take you back to the contents page.

2 Take me to... Grade Grade Grade Grade Grade 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 Grade 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 Grade 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 Grade 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 Grade 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 Grade 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 Grade Grade 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 Grade Grade 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 MathsWatch Clip Grade answers Place Value ) a) Write the number forty five thousand, two hundred and seventy three in figures. 7 b) Write the number five thousand, one hundred and three in figures. 0 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) 0 b) 0 c) One thousand, two hundred and fifty Three thousand, five hundred and two Seventy two thousand and sixty seven d) 9 00 One hundred and ninety two thousand and forty e) Thirty million ) a) Write down the value of the 7 in the number 7. b) Write down the value of the 6 in the number 6 0. c) Write down the value of the in the number d) Write down the value of the in the number or seven hundred or six thousand 0 or twenty or fifty thousand e) Write down the value of the in the number or two hundred thousand ) What is the value of the digit 7 in 8.7? Choose, and circle, the correct answer from the following: Page

11 MathsWatch Clip Grade answers Ordering Integers Put these numbers in order, starting with the smallest: ) 7, 7, 8, 8, 6 8, 8, 7, 6, 7 ) 9, 8,, 8,,, 9, 8, 8 ) 76, 0,, 0, 7, 7, 76, 0, 0 ),, 7, 0, 7,,,, 0 ),,,, 7,,,, 7 6), 6, 0, 6, 6,,, 0, 6 7) 0, 00, 0,, 00, 0, 0, 00, 00 8) 8, 6,, 6, 6,,, 6, 8 Page

12 MathsWatch Clip Grade answers Ordering Decimals ) Put these amounts of money in order, starting with the smallest: a).0,.8,.0,.99,. b).,.,.,.0,.99.,.8,.99,.0,.0.,.,.99,.0,. c).8,.8,.99, 6.0, ,.8,.8, 6.0, 6.0 ) Circle the smallest number: 0., 0.09, 0.99, 0., 0. ) Put these numbers in order, starting with the smallest:.0,.,.,.006,.0.006,.0,.,.0,. ) Put these numbers in order, starting with the smallest: 0.76, 0.668, 0.608, 0.099, , 0.608, 0.668, 0.76, ) Put these numbers in order, starting with the smallest:.00,.889,.099,.00,.09.09,.099,.889,.00,.00 Page

13 MathsWatch Clip Grade answers Reading Scales ) Estimate the reading on each of these scales: a). kg b). kg c).9 kg kg kg kg d) 6 kg 0 e) 00 f) kg 0 kg kg kg kg ) This scale shows degrees Centigrade. C a) What temperature is the arrow pointing to?. C b) Draw an arrow which points to -7 C. ) This is a diagram for converting between gallons and litres. Gallons Litres 0 0 Use the diagram to convert a) gallons to litres. b). gallons to litres..7 litres 0. litres c) 6 litres to gallons.. gallons Page

14 MathsWatch Clip Grade answers 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) more than or equal to c) > more than d) less than or equal to e) = not equal to ) Insert one of the two symbols < or > to make the following statements true: a) 8... > b) -... > -6 c) <.8 d) > + 7 e)? 7... <? 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

15 MathsWatch Clip 6 Grade answers Interpreting Real-Life Tables ) Calculate the difference in hours and minutes between 9.0 am and. pm. hours minutes ) Calculate the difference in hours and minutes between and. hour 0 minutes ) 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. 990 km One of the cities in the table is km from Los Angeles. b) Write down the name of this city. New York c) Write down the name of the city which is furthest from Chicago. San Francisco ) 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? 08 6 b) Jenny arrives at the Stockport train station at (i) How long should she expect to wait for a train to Stoke? minutes (ii) How long should her train journey take? 9 minutes 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

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

17 MathsWatch Clip 8 Grade answers y Coordinates ) Write down the coordinates of the points A to H. A (8, 8) B (, 9) C (, 6) D (0, ) E (6, ) F (, ) G (, 0) H (0, ) D C B F E A 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(, 0), C(, ) and D(, ). b) Join the points in order, to form a shape and name the shape. Parallelogram M is the midpoint of the line segment AC. c) Find the coordinates of M. (., ) ) Using the same pair of axes, a) Plot the points R(-, -), S(, ) and T(-, ). U x O T x y O A B - x S x D x M x x x x C x b) Join R to S and S to T. RSTU is a kite. c) Write the coordinates of point U. (-, ) x R Page 8

18 MathsWatch Clip 9 Grade answers 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 Has one angle of 90 c) A scalene triangle All the sides are different lengths. All the angles are different sizes. d) An isosceles triangle Two sides are the same length. Two angles are the same size. ) Next to each of the quadrilaterals, write down its special name. a) b) Parallelogram Rhombus c) d) Trapezium Kite Page 9

19 MathsWatch Clip 0 Grade answers Polygons ) Next to each of the shapes, write down its name. a) b) (Irregular) pentagon (Irregular) heptagon or septagon ) a) What is the name given to a 0-sided shape? Decagon b) What is the name given to an 8-sided shape? Octagon ) To be a regular polygon the shape must have equal sides and equal. angles Fill in the blanks. ) What are the names of these regular polygons? a) b) Pentagon Hexagon Page 0

20 MathsWatch Clip Grade answers 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 about point P. Complete the shape. ) On each of the shapes below, draw one plane of symmetry. Other answers are possible Other answers are possible Page

21 MathsWatch Clip Grade answers 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? b and d a) b) c) d) e) Page

22 MathsWatch Clip Grade answers Names of Angles ) Write the name of each angle, below. a) Obtuse angle b) Acute angle c) Right angle d) Reflex angle ) Draw a triangle which contains: a) Three acute angles. b) One obtuse angle and two acute angles. Other triangles are possible c) A right angle. Page

23 MathsWatch Clip Grade answers 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 when you roll an ordinary dice. 0 ) 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. 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 0 Page

24 MathsWatch Clip Grade answers Tally Charts and Bar Charts ) Here is a list of coins in Yvonne's purse. p 0p p 0p 0p p 0p p p p p p p p p p Complete the table for this information. Coin Tally Frequency p p p 0p 0p 0p 7 ) Tim made a note of how many minutes he spent on the internet over the period of a week. His results are as follows: 60 Monday Tuesday 0 mins 0 mins Wednesday 60 mins Thursday Friday Saturday Sunday 0 mins 0 mins 0 mins 0 mins Draw a bar chart to show this information. Time spent on internet 0 0 Number of minutes Mon Tue Wed Thu Fri Sat Sun Day Page

25 MathsWatch Clip 6 Grade answers Pictograms ) The pictogram shows the number of watches sold by a shop in January, February and March. January February March April May Key represents watches. a) How many watches were sold in January? 6 b) How many more watches were sold in March than in February? 9 watches were sold in April. 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? 0 (ii) Tuesday? On Wednesday, 0 DVDs were borrowed. On Thursday, DVDs were borrowed. b) Show this information in the pictogram. Page 6

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

27 MathsWatch Clip 8 Grade answers Subtracting Integers and Decimals ) a) 7 8 b) 7 c) ) a) 8 b) 7 7 c) ) a) 6 8 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 6 people. The film in the smaller room was watched by 67 people. How many more people saw the film in the larger room? 89 ) a) b) Page 8

28 MathsWatch Clip 9 Grade answers Multiplying Integers ) Work out a) 8 b) 7 c) 6 d) 6 e) 6 f) 8 9 g) 86 8 h) 8 i) ) MathsWatch Travel has 6 coaches. Each of these coaches can carry passengers. How many passengers in total can all the coaches carry? 908 ) MathsWatch Tours has a plane that will carry 7 passengers. To fly from Manchester to Lyon, each passenger pays 6 Work out the total amount that the passengers pay. 0 ) A Science textbook costs. Mr Jones buys a class set of books. How much do they cost him? ) A graphical calculator costs 8. How much would calculators cost? 77 Page 9

29 MathsWatch Clip 0 Grade answers Dividing Integers ) Work out a) 6 d) 77 9 g) 7 b) e) 7 6. h) 0 c) 7 f) 8. i) ) A box can hold 9 books. Work out how many boxes will be needed to hold 66 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. 0 km/h ) Pencils cost p each. Mr Smith spends on pencils. Work out the number of pencils he gets. 60 ) Yesterday, Gino was paid 9.6 for delivering pizzas. He is paid p for each pizza he delivers. Work out how many pizzas Gino delivered yesterday. 7 6) Emma sold 8 teddy bears for a total of She sold each teddy bear for the same price. Work out the price at which Emma sold each teddy bear..0 7) Canal boat for hire 8.00 for days Work out the cost per day of hiring the canal boat..0 8) A teacher has 9 to spend on books. Each book costs 6 How many books can the teacher buy? 0 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

30 MathsWatch Clip Grade answers Inverse Operations ) a) Which operation is the inverse of add? Subtract b) Which operation is the inverse of divide? Multiply ) Use inverse operations to complete the second equation each time. a) + 6 = 8 8 6? = b) 8? = + = 8 ) Use inverse operations to complete the second equation each time. a) = 8 = 8 b) 60 = = 60 ) Use inverse operations to complete the second equation each time. a) 9 + = = 9 b) 6? = + = 6 ) Use inverse operations to complete the second equation each time. a) 8 7 = 7 = 8 b) 6 = = Page

31 MathsWatch Clip Grade answers Money Questions ) Tony buys 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? 0 ) Bags of sweets.0 per bag Buy, get free How many bags of sweets can you buy for 9? 8 ) Cinema Prices Adult Child Family ticket ( adults and children a) adult and 7 children went to the cinema. How much did they pay altogether? 9.09 b) adults and children went to the cinema and bought a family ticket. How much did they save altogether?.8 Page

32 MathsWatch Clip Grade answers 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. - C At midday, the temperature was C. b) Work out the difference between the temperature at midday and the temperature at midnight. 0 C c) Work out the temperature which is halfway between -7 C and C. - C ) The table below gives the temperature recorded on th December in 7 cities across the world. City Edinburgh London New York Moscow Paris Rome Cairo Temperature -6 C 0 C - C - C C C 8 C a) Which city recorded the lowest temperature? Moscow b) What is the difference in temperature between New York and Paris? 8 C c) What is the difference in temperature between Cairo and Edinburgh? C d) The temperature in Madrid was 9 C lower than in Rome. What was the temperature in Madrid? - C e) The temperature in Mexico City was 6 C higher than in New York. What was the temperature in Mexico City? -9 C ) The table shows the temperature on the surface of each of five planets. Planet Temperature Venus 0 C Jupiter -0 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. 80 C 90 C c) Which planet has a temperature 0 C lower than Saturn? Neptune The temperature on Mars is 90 C higher than the temperature on Jupiter. d) Work out the temperature on Mars. -60 C Page

33 MathsWatch Clip Grade answers Introduction to Fractions ) What fraction of each of the following shapes is shaded? a) b) c) d) e) f) 8 ) Shade the given fraction in the following grids. 6 ) Which of these fractions is the smallest? 6 7 or (use the grids to help) 9 Page

34 MathsWatch Clip Grade answers Equivalent Fractions ) Each of the grids below has a fraction written at the side of it. a) Shade the grids to show these fractions. 8 6 b) What do you notice about how many little squares are shaded in each grid? It is always the same - 8 squares. ) 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? It is always the same - 8 squares. ) Find the missing values in these equivalent fractions. = = = 6 8 ) Find the missing values in these equivalent fractions. 6 = = = 0 ) How do you know that is not equivalent to? 7 6 You have to multiply 7 by 8 to get 6, but when you mulitply by 8 you get, not. Page

35 MathsWatch Clip 6 Grade answers 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

36 MathsWatch Clip 7 Grade answers Half-Way Values ) Write down the number which is in the middle of: a) and 9 6 b) and 8 0 c) and 6. d) 7 and. e) 7 and f) and g) 6 and ) Write down the number which is in the middle of: a). and b).9 and. 9. c) - 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). is in the middle of. and which other number?.7 Page 7

37 MathsWatch Clip 8 Grade answers Factors, Multiples and Primes ) Write the factors of a) 6 b) 6 c) 8 d) 0,,, 6,,, 8, 6,,, 6, 9, 8,,,, 6, 0,, 0 ) In a pupil s book the factors of are listed as 6 The above list contains a mistake. Cross it out from the list and replace it with the correct number. ) The factors of 0 and 0 are listed 0:,,,, 6, 0,, 0 0:,,,, 8, 0, 0, 0 Write the common factors of 0 and 0 (the numbers that are factors of 0 and 0).,,, 0 ) Write the first four multiples of a) b) c) 0 d), 6, 9,, 0,, 0 0, 0, 0, 0, 0,, 60 ) 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 and 0 are listed :, 8,, 6, 0 0: 0, 0, 0, 0, 0 From the two lists above, write the common multiple of and ) List the first five prime numbers,,, 7, 8) Using just this list of numbers: find the following: a) The prime numbers b) The factors of 8 c) The multiples of,,, 9 8,, 9,, 8,,, 9,, Page 8

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

39 MathsWatch Clip 0 Grade answers 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 = 6 0 = 7 0 = 9 0 = =. 000 = 00 = 8 00 = =.6 00 = = = 9 60 Page 0

40 MathsWatch Clip Grade answers Rounding to the Nearest 0, 00, etc ) Round these numbers to the nearest 0: a) 6 0 b) 6 60 c) 7 80 d) 0 e) f) 8 80 g) h) ) Round these numbers to the nearest 00: a) b) 00 c) 9 00 d) 0 00 e) 8 00 f) 7 00 g) h) ) Round these numbers to the nearest 000: a) b) 000 c) d) e) f) g) h) Page

41 MathsWatch Clip Grade answers Rounding to Decimal Places ) Round the following numbers to decimal place a).68 b).7 c) ) Round the following numbers to decimal places a) 8.86 b).7 c) ) Round the following numbers to decimal place a) 8.97 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 ) Work out the answer to 6..7 and give your answer correct to decimal place.. 7) Work out the answer to.7 giving your answer correct to decimal places..7 8) Find the answer to 7. giving your answer correct to decimal place.. Page

42 MathsWatch Clip Grade answers Simplifying - Addition and Subtraction ) Simplify the following a) x + x x b) x + x c) t t d) 7y 6y x t y e) x + x + x f) g g + 6g g) x 7x + 8x 6x 8g x h) y y y + 6y y ) Simplify the following a) xy + xy xy b) xy xy c) x y + x y d) xy xy xy x y xy e) x y + x y x y f) 6a bc + a bc a bc x y 9a bc ) Simplify the following a) x + y + x + y b) x + y + x + y c) a + b a + b d) x + y x y e) 6x y + x + y f) x y x y g) t + u + t 7u x + y x + 7y a + 6b x + y 8x + y x 8y t u h) xy + t xy t xy t Page

43 MathsWatch Clip Grade answers Simplifying - Multiplication ) Simplify the following a) x x x b) x x x x x x c) y y y y ) Simplify the following a) x x b) x x c) y y x 6 x 8 y x 7 d) x x x e) y y y y 9 ) Simplify the following a) x x x b) x x x c) t t d) y y 6t y 6x 6 e) x x x ) Simplify the following a) x y xy b) x y 6xy c) r s t d) 6x y z 0rst xyz ) Simplify the following a) x y xy b) x y x 8x y c) xy xy 6x y x y d) 6xy x y y e) x y x y f) tu t u tu 0x 6 y t u Page

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

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

46 MathsWatch Clip 6 Grade answers Function Machines ) Complete the table for the function machine. + In 7 9 Out ) Complete the table for the function machine. 7 In - 6 x Out x 7 ) Complete the table for the function machine. + 6 In x Out (x + ) Page 6

47 MathsWatch Clip 7 Grade answers Generating a Sequence - Term to Term ) Write the first terms of each of these sequences. a) Start at and add 6., 8,, 0, 6 b) Start at and subtract.,, 8,, c) Start at and subtract 7., -, -0, -7, - d) Start at and multiply by., 6, 8,,6 e) Start at 6 and divide by. 6,, 6, 8, f) Start at 600 and divide by , 60, 6, 0.6, 0.06 ) Find the term to term rule for each of these sequences. a), 7, 0,, 6 Add b),,, 9, 7 Subtract c), -, -8, -, -8 Subtract d) 7,, 8, 6, Multiply by e) 00, 0,, 0., 0.0 Divide by 0 Page 7

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

49 MathsWatch Clip 9 Grade answers Using Ratio for Recipe Questions ) Here are the ingredients needed to make 8 pancakes. James makes pancakes. Pancakes Ingredients to make 8 pancakes 0 ml milk egg 0 g flour g butter a) Work out how much milk he needs. 70 ml Kate makes pancakes. b) Work out how much flour she needs. 0 g ) Here are the ingredients for making fish pie for 6 people. Fish pie for 6 people 80 g flour 0 g fish 80 g butter eggs 80 ml milk Jill makes a fish pie for people. a) Work out how much flour she needs. 90 g Tim makes a fish pie for people. b) Work out how much milk he needs. 0 ml ) Here are the ingredients for making pineapple sorbet for 6 people. Pineapple sorbet for 6 people 800 g of pineapple egg whites ½ lemon 00 g caster sugar Trevor makes pineapple sorbet for 8 people. a) Work out how much caster sugar he uses. 00 g Sid makes a pineapple sorbet. He uses lemons. b) Work out how many people he makes pineapple sorbet for. people Page 9

50 MathsWatch Clip 0 Grade answers Introduction to Percentages ) What percentage of this grid is shaded? 7% ) 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? ) What percentage of this grid is shaded? % Page 0

51 MathsWatch Clip Grade answers Value for Money ) Which of the following offer better value for money? Working must be shown a) 00ml of toothpaste for 0p or 00ml of toothpaste for 90p 0 00 = = 0. b) 600g of bananas for 70p or 00g of bananas for p = = 0. c) litres of paint for.60 or litres of paint for.0.60 = = 0.7 d) 60 teabags for.6 or 0 teabags for = = 0.09 ) Which of these is the best buy? 0 exercise books for.00 exercise books for = 0 0p per book ) Hamza needs to buy litres of paint. At the shop he gets two choices: 00ml for. or litre for = = a) Work out which of these would be the best buy for Hamza. litre of paint for.79 b) How much does he save if he buys the best buy rather than the worst buy? 0.6 or 6p You must show all your working.. = = = 9.8 ) Honey pots are sold in two sizes. A small pot costs p and weighs 0g. A large pot costs 80p and weighs 80g. 780 =. p per book 0 = 0.p per g = 0.09p per g Which pot of honey is better value for money? You must show all your working. Large pot at 80p for 80g Page

52 MathsWatch Clip Grade answers Introduction to Proportion ) 8 bananas cost Work out the cost of bananas..0 ) Emily bought identical pairs of socks for.60 Work out the cost of 9 pairs of these socks. 8.0 ) The price of 6 chocolates is 7.0 Work out the cost of 8 chocolates..60 ) Theresa bought theatre tickets for 60 Work out the cost of 9 theatre tickets. 08 ) Jenny buys folders. The total cost of these folders is 6.0 Work out the total cost of 7 of these folders..0 6) The cost of litres of petrol is Work out the cost of 0 litres of petrol. 6 7) maths books cost 7.7 Work out the cost of of these.. 8) person can cut a large area of grass in hours. How long would it take people to cut the grass?. hours 9) people take hours to build a wall. How long would it take people to build the wall? 0 hours 0) 9 people can paint a bridge in hours. How long would it take people to paint the bridge?. hours Page

53 MathsWatch Clip Grade answers Properties of Solids ) Draw a sketch of each of the following solids: Cube a) A cube. b) A cylinder. ) Write down the mathematical name of each of these -D shapes. Cylinder a) b) c) Cuboid Sphere Cone ) Look at this solid. a) What is its name? Triangular prism b) How many vertices does it have? 6 c) How many edges are there? 9 d) How many faces does it have? ) 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? 7 0 Page

54 MathsWatch Clip Grade answers Nets ) Sketch nets of these solids. a) b) ) Cube Cuboid Right-angled triangular prism Triangular prism ) 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 at the dot B. Mark it with B. a) A b) A A B B Page

55 MathsWatch Clip Grade answers Angles on a Line and at a Point ) Work out the values of the unknown angles. a 6 6 b 8 80 c 0 60 d ) Work out the values of the unknown angles. 0 x 00 y Page

56 MathsWatch Clip 6 Grade answers Measuring and Drawing Angles ) Measure the following angles: a b d 7 c e f R ) Draw the following angles: a) Angle ABC = 60 b) Angle PQR = 7 c) Angle XYZ = 7 X C 7 Q B 60 A P Z Y 7 Page 6

57 MathsWatch Clip 7 Grade answers Drawing a Triangle Using a Protractor ) The diagram shows a sketch of triangle ABC. C 7. cm A 8. cm 8 B BC = 7. cm AC = 8. cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on your diagram. Angle A = 9 ) The diagram shows a sketch of triangle PQR. Q 7. cm P Make an accurate drawing of triangle PQR. 9 cm 7 R Page 7

58 MathsWatch Clip 8 Grade answers Reflections y = -x y ) 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. T O - x V V U U - y ) a) Describe fully the single transformation which maps triangle T to triangle U. T Reflection in the x axis. b) Describe fully the single transformation which maps triangle T to triangle V. Reflection in the line y = x O - x - U - V - - Page 8

59 MathsWatch Clip 9 Grade answers 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. U y T O - x V - y ) Describe fully the single transformation which maps triangle T to triangle U. Rotation 90 clockwise about the point (-, -) T U O - x Page 9

60 MathsWatch Clip 0 Grade answers Translations ) - a) Translate triangle T by vector and label it U. b) Translate triangle T by vector - and label it V. y 6 U T V O 6 V - x - - ) a) Describe fully the single transformation which maps triangle A to triangle B. -6 Translate triangle A by vector - b) Describe fully the single transformation which maps triangle A to triangle C. y Translate triangle A by vector -7 6 A B O 6 - x - - C Page 0

61 MathsWatch Clip Grade answers 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 A

62 MathsWatch Clip Grade answers 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. OR seen from the right seen from the left Page B

63 MathsWatch Clip Grade answers 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 C

64 MathsWatch Clip Grade answers Plans and Elevations ) The diagram shows a solid prism. cm cm cm 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 D

65 MathsWatch Clip Grade answers Perimeters ) Find the perimeters of the following two shapes. a) b) cm 9 cm 6 cm cm cm cm 8 cm ) The length of a rectangle is 9 cm. The total perimeter is 0 cm. Calculate the length of the width of the rectangle. 6 cm ) Work out the perimeter of this L shape. 68 cm cm 9 cm ) 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. 6 cm Page

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

67 MathsWatch Clip Grade answers Area of a Triangle ) Find the areas of the following two triangles. a) b) cm 6 cm 8 cm 0 cm 9 cm 7 cm ) Find the missing lengths. a) b) cm? Area = cm Area = 8 cm cm 6 cm? 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. 8 cm Page

68 MathsWatch Clip Grade answers Area of a Parallelogram ) Find the area of each of these parallelograms. a) b) 7 cm cm 70 cm 0 cm 6. cm 78 cm ) Find the missing lengths in these two parallelograms. a) b)? 9 cm Area = 6 cm cm Area = 9 cm cm? cm Page

69 MathsWatch Clip 6 Grade answers Area of a Trapezium ) Find the area of this trapezium. 6 cm cm 6 cm 8 cm ) The diagram shows a field. 70 m 86 m 88 m Work out the area of the field. 969 m ) In the trapezium, a = 6.6 cm, b = 8. cm and h =.6 cm. a h b Work out the area of the trapezium. 7 cm ) In the trapezium below, the area is cm. a = cm and b = 0 cm. Calculate the height, h, of the trapezium. a 6 cm h b Page 6

70 MathsWatch Clip 7 Grade answers 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 8 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 79 Full recovery 8 Not a full recovery 6 00 Not a full recovery Full recovery 8 Not a full recovery 7 Page 7

71 MathsWatch Clip 8 Grade answers Listing Outcomes ) List all the outcomes if two coins are flipped. H H, H T, T H, T T ) a) How many possible outcomes are there if three coins are flipped? 8 b) List them all - the first one has been done for you: H H H H H T, H T H, T H H, T T H, T H T, H T T, T T T ) a) How many possible outcomes are there if two six-sided dice are rolled? 6 b) List them all.,,,,, 6,,,,, 6,,,,, 6,,,,, 6,,,,, 6 6, 6, 6, 6, 6, 6 6 ) a) How many possible outcomes are there if a coin is flipped and a dice is rolled? b) List them all. H, H, H, H, H, H 6 T, T, T, T, T, T 6 ) a) How many possible outcomes are there if two coins are flipped and a dice is rolled? b) List them all. H H, H H, H H, H H, H H, H H 6 H T, H T, H T, H T, H T, H T 6 T H, T H, T H, T H, T H, T H 6 T T, T T, T T, T T, T T, T T 6 6) How many possible outcomes are there if 6 coins are flipped? 6 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? 909 Page 8

72 MathsWatch Clip 9 Grade answers 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, 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? 7 8 ) In a class there are 0 boys and girls. A teacher chooses a student at random from the class. Eric says that the probability a boy will be chosen is 0. 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. Jenny is correct because there are more girls than boys, so the probability of choosing a girl will be greater than that of choosing a boy. ) Spinner A has numbers to 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? Page 9

73 MathsWatch Clip 60 Grade answers Mutually Exclusive Events ) If the probability of passing a driving test is 0., what is the probability of failing it? 0.6 ) The probability that a football team will win their next game is. The probability they will lose is. 6 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. 0. b) Which option is most likely? Sausages 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 ) 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. 0. Page 60

74 MathsWatch Clip 6 Grade answers 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 6 Female 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? 7 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 Total of the 90 students are male. 9 of the 0 male students study Spanish. a) Complete the two-way table. b) How many females study French? c) How many people study Spanish? 6 ) 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 students who like plain chocolates best are girls. Work out the number of students who like milk chocolates the best. Page 6

75 MathsWatch Clip 6 Grade answers 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? minutes late. minutes late ) 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%, 8%, 9%, 6%, 8%, 77%, 6%, 7% Set B had these scores: 8%, 6%, 8%, 6%, 9% 8%, 90%, 8%, 7%, 8% How much bigger was Set B s mean average score than Set A s mean average score? Give your answer correct to decimal place. 0.% ) A rugby team played six games. The mean score for the six games is 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

76 MathsWatch Clip 6 Grade answers Data - Discrete and Continuous ) Out of the following types of data, decide which is continuous and which is discrete: The lengths of some roads. Continuous The number of cats eyes on a one mile stretch of road. Discrete The time it takes twenty students to complete an English essay. Continuous The number of pages in twenty students English essays. Discrete The weights of sacks of potatoes. Continuous The number of potatoes in some sacks of potatoes. Discrete 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. Continuous Discrete Continuous ) Write a short statement which explains what continuous data is. Continuous data is data that is measured using a continuous scale. ) Write a short statement which explains what discrete data is. Discrete data is data that is counted. Page 6

77 MathsWatch Clip 6 Grade answers 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? 8 c) What was the median test score? 7 ) The line chart shows the number of goals scored by a football team in their last 6 games. Frequency 0 0 Number of goals scored a) How many goals did they score altogether? 0 b) What was the median number of goals scored? Page 6

78 MathsWatch Clip 6 Grade answers 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 < t 0 0 < t < t < t Draw a frequency diagram to show this information. Time taken to solve a puzzle Frequency Time (mins) Page 6

79 MathsWatch Clip 66 Grade answers Multiplying Decimals ) Work out a) b) c) d) e) f) ) A box contains 7 books, each weighing. kg. Work out the total weight of the box. 7. kg ) Jim takes boxes out of his van. The weight of each box is. kg. Work out the total weight of the boxes.. kg ) Tim has a job which pays 6.8 per hour. If he works for hours, one week, how much does he earn?.90 ) Sue has a part-time job and the hourly pay is 7.0 per hour. How much does she earn if she works for 8. hours, one week? 6.7 6) Fencing costs. per metre. How much does. m cost? 6.6 Page 66

80 MathsWatch Clip 67 Grade answers Dividing Decimals ) Work out a) b) c) 0. 0 d) 0. 0 e) f) 0. 7 ) Work out a) b) c) d) e). 0.0 f) ) John takes boxes out of his van. The total weight of the boxes is.9 kg The weight of each box is 0.7 kg Work out the number of boxes in John s van. 7 ) 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. 0 Page 67

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

82 MathsWatch Clip 69 Grade answers 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. Soup, Chicken, Ice Cream Soup, Chicken, Trifle Melon, Chicken, Ice Cream Melon, Chicken, Trifle Soup, Steak, Ice Cream Soup, Steak, Trifle Melon, Steak, Ice Cream Melon, Steak, Trifle Soup, Vegetarian, Ice Cream Soup, Vegetarian, Trifle Melon, Vegetarian, Ice Cream Melon, Vegetarian, Trifle Starter Soup Melon Main Course Chicken Steak Vegetarian Dessert Ice Cream Trifle ) 7 a) Make a list of all the two-digit numbers that can be made with these three cards. 7,, 7, 7,, 7 b) Make a list of all the three-digit numbers that can be made with these three cards. 7, 7, 7, 7, 7, 7 ) Phil has three different coins. He has: a coin a coin a 0p coin a) If he chooses exactly two coins, what amounts of money can he make? or.0 or.0 b) If he chooses one or two coins, what amounts of money can he make? or or 0p or or.0 or.0 c) If he chooses one, two or three coins, what amounts of money can he make? or or 0p or or.0 or.0 or.0 Page 69

83 MathsWatch Clip 70 Grade answers Comparing Fractions ) Put these fractions in order of size, smallest to largest. Show your working for each question. a) 6 b) c) ) Put these fractions in order of size, smallest to largest. Show your working for each question. a) 8 8 b) c) 6 6 ) 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. Chocolates, magazines, games Page 70

84 MathsWatch Clip 7 Grade answers 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: ) 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. He spent of his pocket money on magazines. 0 What fraction of his pocket money did he have left? 0 a) b) c) d) ) Maisie buys a bag of flour. She uses to bake a cake and to make a loaf. a) What fraction of the bag of flour was used? b) What fraction of the bag of flour is left? ) Work out the total length of this shape. Give your answer as a mixed number. inches inches Page 7

85 MathsWatch Clip 7 Grade answers Finding a Fraction of an Amount ) Work out these amounts. a) of 0 b) of 60 kg 0 kg c) 8 9 d) 0 00 e) 9 of 80 cm 0 cm f) g) 60 h) 8 of 8 0 i) ) There are 600 apples on a tree and there are maggots in of them. How many apples have maggots in them? 60 apples ) Liz and Lee are travelling in a car from Glasgow to Poole (770 km). At midday they had already travelled 7 of the total distance. What distance, in km, had they travelled by midday? 0 km ) A digital camera that cost 9 was sold on ebay for 7 of the original price. What was the selling price? ) Yesterday Thomas travelled a total of 7 miles. He travelled of this distance in the morning. How many miles did he travel during the rest of the day? 0 miles 6) Debra received her pocket money on Saturday. She spent of her pocket money on magazines. She spent of her pocket money on a necklace. How much of the did she have left? Page 7

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

87 MathsWatch Clip 7 Grade answers Dividing Fractions In all the questions on this page, please give your answers in their simplest form. ) Work out the following: a) 8 b) c) d) ) Work out the following: a) b) c) d) 0 ) Work out the following: a) b) c) d) Page 7

88 MathsWatch Clip 7 Grade answers BODMAS/BIDMAS ) 6 + ) + 6 ) ) 8 ( ) ) 7 ( + 6) 6) ) (9 + ) + 8) ( + ) 6 7 9) 6 9 0) 9+ + ) ) 7 ) + 7 ) 6 ) 8 + 6) 7 7) 0 0 ( + ) 8) Page 7

89 MathsWatch Clip 76 Grade answers Reciprocals ) Write down the reciprocal of a) 8 8 b) c) d) ) Write down the reciprocal of a) b) c) d) 8 8 ) Write down the reciprocal of a) 0. 0 b) 0. c) 0. ) Why can t we have a reciprocal of 0? Because division by 0 does not exist. Page 76

90 MathsWatch Clip 77 Grade answers 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. ) Use your calculator to work out the value of Write down all the digits from your calculator. Give your answer as a decimal. ) 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

91 MathsWatch Clip 78 Grade answers Product of Primes ) List the first seven prime numbers.,,, 7,,, 7 ) Express the following numbers as the product of their prime factors: a) b) 0 c) 0 d) ) Express the following numbers as the product of their prime factors: a) 6 b) 00 c) 0 ) Express the following numbers as the product of their prime factors: a) 7 b) 9 c) 7 7 ) 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. m = and n = 6) The number 7 can be written as x y, where x and y are prime numbers. Find the value of x and the value of y. x = and y = Page 78

92 MathsWatch Clip 79 Grade answers Highest Common Factor (HCF) ) Find the Highest Common Factor of 6 and. 8 ) Find the Highest Common Factor of and 8. 7 ) Find the Highest Common Factor of 60 and 0. 0 ) Find the Highest Common Factor of 96 and 08. ) (i) Write and 6 as products of their prime factors. = 7 6 = 7 (ii) Work out the Highest Common Factor of and 6. Page 79

93 MathsWatch Clip 80 Grade answers Lowest Common Multiple (LCM) ) Find the Lowest Common Multiple of 0 and ) Find the Lowest Common Multiple of 8 and 7. 0 ) Find the Lowest Common Multiple of 70 and ) Find the Lowest Common Multiple of and. 8 ) (i) Write and 6 as products of their prime factors. = 7 6 = 7 (ii) Work out the Lowest Common Multiple of and 6. 6 Page 80 A

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

95 MathsWatch Clip 8 Grade answers Squares, Cubes and Roots ) What is the value of? ) What is the value of 8? 6 ) These are the first five square numbers:,, 9, 6, a) What is the sixth square number? b) What is the 0th square number? 6 00 ) Which square number lies between 60 and 70? 8 = 6 ) What is the value of? 8 6) What is the value of? 6 7) Work out ) Work out 9) Work out 9 7 0) Work out the value of ) Match together cards with the same answer Page 8

96 MathsWatch Clip 8 Grade answers Working with Indices ) Evaluate the following: a) b) 8 9 c) ) Evaluate the following: a) 8 b) 6 c) ) Find the value of a) + b) 7 c) + + ) Find the value of a) + 6 b) c) ) Find the value of Page 8

97 MathsWatch Clip 8 Grade answers Standard Form ) Change the following to normal (or ordinary) numbers. a). 0 c) e) b) d) 9. 0 f) ) Change the following to normal (or ordinary) numbers. a). 0 - c) e) b) d) f) ) Change the following to standard form. a) 60 c) e) 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) 0 g) b) e) h) c) f) i) Page 8

98 MathsWatch Clip 8 Grade answers Decimals and Fractions Write the following fractions as decimals ) 0 0. ) ) ) 0. ) 0.7 6) 0. 7) ) 0. 9) ) Page 8

99 MathsWatch Clip 8 Grade answers Fractions, Percentages, Decimals ) Write the following fractions as decimals and percentages: eg % a) = 0. = 0% 0 b) = c) = d) = e) = f) = g) = 0. = 0% 0. = 0% 0. = % 0.7 = 7% 0. = 0% 0. =.% ) Fill in the blanks in the table below: Fraction Decimal Percentage % 0% 90% 0% % 80% %.% 70% Page 8

100 MathsWatch Clip 86 Grade answers Percentage of an Amount with a Calculator ) Work out: a) % of 0 b) 6% of 080 c) 6% of d) 98% of.7 ) Work out: a) 7.% of 8 b) 0% of c) 6.7% of 000 d) 7.% of ) A computer costs 06 plus VAT at 0%. Work out the total cost of the computer ) A car is usually priced at 9800 but now has a discount of 8%. What is the new price of the car? 906 ) 900 people attend a festival and % of them are children. How many children are at the festival? 090 6) 6% 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 kg 7) Tony earns 7800 per year and receives a.8% pay rise. How much does he now earn? Page 86

101 MathsWatch Clip 87 Grade answers Percentage of an Amount without a Calculator ) Work out: a) 0% of 70 b) 0% of 6800 c) 0% of 9 d) 0% of ) Work out: a) 0% of 60 b) 0% of 90 c) % of 800 d) % of ) Work out: a) % of 80 b) 90% of 60 8 c) 7.% of 600 d) 7.% of ) Work out: a) % of.60 b) 0% of.80 c) 7.% of.0 d) 97.% of ) The normal price of a jacket is. In a sale, the price is reduced by 0% What is the sale price? ) A football costs plus 0% VAT. How much is the football? 6.80 Page 87

102 MathsWatch Clip 88 Grade answers Change to a Percentage with a Calculator ) Write the following as percentages, giving all your answers to decimal place. a) out of b) 6 out of 8 c) out of.% 7.9% 7.9% d) 0 out of 6.% ) Sarah sat a Science test and got a score of 6 marks out of possible marks. What was her mark as a percentage? Give your answer to decimal place. 7.% ) In a class of students, 8 of them are boys. What percentage of the class are boys? Give your answer to decimal place. 6.% ) In a French class there are girls and 6 boys. What percentage of the class are girls? Give your answer to decimal place. 68.% ) A new car usually costs 800. Henry gets a discount of 000. What is the discount as a percentage of the usual cost? Give your answer to decimal place..8% 6) Write out 8 as a percentage of 600. Give your answer to decimal place..7% 7) In a wood there are 00 oak trees, 60 silver birch trees and 00 wild cherry trees. What percentage of the trees are oak trees? 6% 8) In England in 00 there were 6880 deaths caused by cancer. Of these deaths, 700 were caused by smoking. What percentage of deaths due to cancer were caused by smoking? Give your answer to decimal place..% Page 88

103 MathsWatch Clip 89 Grade answers Change to a Percentage without a Calculator ) Write the following as percentages. a) out of 0 b) out of c) 8 out of 0 d) out of 0 e) out of f) out of 0 % 60% 80% % 80% 80% g) out of 80 % h) 60 out of % i) 6 out of 60 60% ) Tim got 7 out of 0 in a French test. Write 7 out of 0 as a percentage. 8% ) Write 9 as a percentage of 76% ) Work out as a percentage of 0 % ) A baker burnt loaves out of the 00 loaves he baked. What percentage of the 00 loaves did he burn? 6% 6) What is 80 as a percentage of 00? 9% 7) What is as a percentage of 0? % 8) If there are 9 girls and boys in a class, what percentage of the class are girls? % Page 89 A

104 MathsWatch Clip 86/87/88/89 Grade answers Percentages ) Find the following to the nearest penny: a) % of b) % of c) 8% of d) % of e) 87% of 8.8 f).7% of g).8% of 980. h) % of 6..6 i) 8.6% of j) 78.% of k).% of l) 0.7% of ) Change the following to percentages, giving all answers to decimal place: a) 6 out of 8.% b) 8 out of 7 8.6% c) out of 8 0.6% d) out of 96 % e) 7 out of 0 8.% f) out of 69.% g) 87 out of % h).7 out of 0.% i) 6.9 out of % j).8 out of.6 6.7% k) 6.8 out of 0.7.% ) A shop gives a discount of 0% on a magazine that usually sells for.80. Work out the discount in pence. 6p 6) A television costs 96 plus VAT at 7.%. Work out the cost of the television including VAT ) 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 00 c) 0% of 0 d) 0% of 0 e) 0% of 68 f) 0% of g) 0% of h) 0% of.0. i) 0% of j) 0% of k) 60% of l) 0% of 60 0 m) 0% of 0 8 n) % of 00 o) % of 60 p) 6% of q) % of r) 8% of s) 7.% of t) 7.% of 0 7 u) 7.% of ) Change the following to percentages: a) 6 out of 00 6% b) 8 out of 0 6% c) 7 out of 8% d) out of 9% e) 9 out of 0 % f) 6 out of 0 80% g) 7 out of 0 70% h) 9. out of 0 9% i) 0 out of 0 % j) 6 out of 0 0% k) 0 out of 0 7% l) out of 0 0% m) 8 out of 80 % n) out of 80 0% o) 60 out of 80 7% p) out of 60% q) out of 80% r) out of 7 0% s) out of 7 % t) 0 out of 7 0% 8) Jane scored 7 out of in a Maths test and 9 out of 6 in a Science test. What were her percentages in both subjects to decimal place? Maths: 6.% Science: 6.9% 9) 0) ) In class 9A there are 7 girls and 8 boys. What percentage of the class are girls? 8% A shop decides to reduce all the prices by %. The original price of a pair of trainers was 70. How much are they after the reduction? 9.0 VAT at 7.% is added to the price of a car. Before the VAT is added it cost How much does it cost with the VAT? 0 Page 89 B

105 MathsWatch Clip 90 Grade answers Rounding to Significant Figures ) Round the following numbers to significant figure: a) 8 b) 78 c) 608 d) e) 999 f) 79 0 ) Round the following numbers to significant figures: a) 86 b) 67 c) d) 6 87 e) 89 7 f) 9 08 ) Round the following numbers to significant figures: a) 9 9 b) 6 8 c) 08 d) e) 7 76 f) ) Round the following numbers to significant figure: a) b) c) d) ) Round the following numbers to significant figures: a) 0.08 b) c) d) ) Round the following numbers to significant figures: a) b) c) d) ) Round the following numbers to significant figures: a) 7.8 b) c) ) Work out the following and give your answer to significant figures: a) 6 8 b) c) ) Work out the following and give your answer to significant figures: a) 0.8 b) c) Page 90

106 MathsWatch Clip 9 Grade answers 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

107 MathsWatch Clip 9 Grade answers Using Place Value ) Using the information that write down the value of a) 7 98 b) c) = 9.8 ) Using the information that write down the value of a)..8. b) c) = ) Using the information that write down the value of a) b) = 708 ) Using the information that write down the value of a) 7 6 b) c) =. ) Using the information that write down the value of a) b) c) = 6 Page 9

108 MathsWatch Clip 9 Grade answers Expanding Brackets ) Expand these brackets a) (x + ) b) (x + ) c) (p q) d) (x + y ) e) 6(r r ) x + 6 6x + p 0q x + 8y 6r 6r ) Expand these brackets a) x(x ) b) x(x + ) c) p(p 7q) d) y(y + 6y ) e) x(r + r ) x x x + x p 7pq y + 6y xr + xr ) Expand these brackets a) x(x ) b) x(x + ) c) p(p q) d) y(y + x ) e) x(x + r ) x 0x 8x + x 0p 0pq 6y + 8x y x + r x ) Expand these brackets a) x(x ) b) x(x + ) c) p (p ) d) y (y + y) e) xy(x + y ) x x 6x + x 0p 0p 6y + 8y x y + xy Page 9

109 MathsWatch Clip 9 Grade answers Simple Factorisation ) Factorise a) x + b) y + 0 c) x + d) x 6 e) x (x + ) (y + ) (x + ) (x ) (x ) ) Factorise a) p + 7p b) x + x c) y y d) p p e) x + x p(p + 7) x(x + ) y(y ) p(p ) x(x + ) ) Factorise a) x + 6x b) y 8y c) p + 0p d) 7c c e) 6x + 9x x(x + ) y(y ) p(p + ) 7c(c ) x(x + ) ) Factorise a) x xy b) t + 0tu c) 6x 8xy d) x y + 9xy x(x y) t(t + u) x(x y) xy(xy + ) Page 9

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

111 MathsWatch Clip 96 Grade answers Straight Line Graphs ) a) Complete the table of values for y = x x y y b) On the grid, draw the graph of y = x, for values of x from - to. c) Use the graph to find the value of y when x =. y = 8 d) Use the graph to find the value of x when y = -8 x = O - - x ) a) Complete the table of values for y = x + x y b) On the grid, draw the graph of y = x +. y O x Page 96 A

112 MathsWatch Clip 96 Grade answers ) On the grid, draw the graph of y = x 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 - - c) Find the gradient of the graph of x + y = 6. Gradient is -. x Page 96 B

113 MathsWatch Clip 96 Grade answers Straight Line Graphs ) a) Complete the table of values for y = x y y = x x - 0 y y = x 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 =. y = d) Use your graph to work out the value of x when y =. ) a) Complete the table of values for y = x x - 0 y x =.7 - O x b) Using the axes on the right, again, draw the graph of y = x - - ) a) Complete the table of values for y = ½x x - 0 b) Draw the graph of y = ½x y -½ - -½ 0 ½ y y = ½x - O x - - c) Use your graph to find the value of y when x =. x = 0.7 Page 96 C

114 MathsWatch Clip 97 Grade answers ) Find the gradient of lines A, B, C and D. A: B: The Gradient of a Line 6 y A B C: - C 6 y D: -0 D O - x O - x ) The graph shows how Meg cycles at a constant speed for 60 minutes. Distance (km) 0 0 O Time (minutes) a) Find the gradient of the line. 0. b) What does the gradient show? Meg is cycling at 0. km per minute. Page 97

115 MathsWatch Clip 98 Grade answers Drawing Quadratic Graphs ) Complete the table of values for y = x x + x - 0 y On the grid, draw the graph of y = x x + 9 y x x x x x - O - x x x - - Page 98 A

116 MathsWatch Clip 98 Grade answers 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 9 x 8 x 7 6 x - - O - x - x x x x c) Use your graph to estimate the values of x when y = - x = -0. and x =. Page 98 B

117 MathsWatch Clip 98 Grade answers 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 x x x x O - x x - - x x - x - -6 Page 98 C

118 MathsWatch Clip 98 Grade answers Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y 0-9 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 = -. d) Use the graph to find the values of x when y = - y = 9 x = -0.8 and x =. ) 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 0 y =. - - O x c) (i) On the same axes draw the straight line y =. (ii) Write down the values of x for which x x =. - x = or x =.9 Page 98 D

119 MathsWatch Clip 98 Grade answers Drawing Quadratic Graphs ) The diagram shows the graph of y = x x y O x a) Use the graph to find estimates for the solutions of (i) x x = 0 x = -0. and. (ii) x x = 6 x = -. and 6. b) Use the graph to find estimates for the solutions of the simultaneous equations y = x x y = x x = 0. y = -.8 x =.8 y =.8 Page 98 E

120 MathsWatch Clip 99 Grade answers Sketching Functions ) 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 y = x O x - y = -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 y = x + O - x y = -x Page 99

121 MathsWatch Clip 00 Grade answers Solving Equations Using Flowcharts ) Solve the following equations. a) x 7 = x = 9 b) x + = x = 8 ) Solve the following equations. a) x + = 7 x = 0 b) x 6 =. x =7 ) Solve the following equations. a) (x ) = 6 x = 6 b) 6(x + 7) = 8 x = 0. ) Solve the following equations. a) x ( 7 + ) = 6 b) x = 0 x ( ) = 8 x = Page 00

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

123 MathsWatch Clip 0 Grade answers Generate a Sequence from the nth Term ) The nth term of a number sequence is n + Write down the first three terms of the sequence. 7, 9, ) The nth term of a number sequence is n Write down the first four terms of the sequence.,, 8, ) The nth term of a number sequence is n + Write down the first four terms of the sequence., 8,, ) The nth term of a number sequence is n 7 Write down the first four terms of the sequence. -,, 8, ) The nth term of a number sequence is n Write down the first three terms of the sequence.,, 9 6) The nth term of a number sequence is n + Write down the first three terms of the sequence., 7, 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. 0 Page 0

124 MathsWatch Clip 0 Grade answers Finding the nth Term ) Here are the first five terms of an arithmetic sequence. 7 9 Find, in terms of n, an expression for the nth term of this sequence. n ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. n + ) Here are the first five terms of an arithmetic sequence. 7 0 Find, in terms of n, an expression for the nth term of this sequence. n ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. n + ) Here are the first five terms of an arithmetic sequence Find, in terms of n, an expression for the nth term of this sequence. -n + 0 Page 0 A

125 MathsWatch Clip 0/0 Grade answers The nth Term ) Here are the first four terms of an arithmetic sequence. 7 0 Find an expression, in terms of n, for the nth term of the sequence. n + ) The nth term of a number sequence is n + Write down the first three terms of the sequence., 7, ) 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. n 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. - ) The nth term of a sequence is n (i) Find the th term of the sequence. (ii) Is the number 00 a term of the sequence? Give reasons for your answer. No, 00 = 00, but 00 is not a square number. Page 0 B

126 MathsWatch Clip 0/0 Grade answers The nth Term ) The nth term of a number sequence is given by n + a) Work out the first two terms of the number sequence., 9 Here are the first four terms of another number sequence. 7 0 b) Find, in terms of n, an expression for the nth term of this number sequence. n ) Here is a number pattern. Line Number a) Complete Line Number of the pattern. b) Complete Line Number 0 of the pattern. c) Use the number pattern to find the answer to Page 0 C

127 MathsWatch Clip 0 Grade answers Special Sequences ) What is the term to term rule for each sequence, below? a),, 6, 6, 6 b) 6,,, 8, 96 c) 80, 0, 0, 0, Multiply by Multiply by Divide by d) 8,,, 0.7, 0.87 Divide by ) a) What is the special name for this sequence?,, 9, 6, Square numbers b) What would be the 0th term of the sequence? 00 c) What is the nth term of the sequence? n ) By comparing the following sequences with the sequence of square numbers, find the nth term for each one. a), 7,, 9, 8 b) -,, 7,, c),, 7, 8, 7 n + n n ) a) What is the special name for this sequence?,, 6, 0, Triangular numbers b) What would be the 8th term of the sequence? 6 n(n + ) c) What is the nth term of the sequence? d) Use the nth term to work out the st term of the sequence. Page 0

128 MathsWatch Clip 0 Grade answers Exchanging Money ) Lance goes on holiday to France. The exchange rate is =. Euros. He changes 0 into Euros. a) How many Euros should he get? 0.0 In France, Lance buys a digital camera for Euros. b) Work out the cost of the camera in pounds. 00 ) 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 =.0 Euros. In which country were the glasses the cheapest, and by how much? Show all your working. Spain, by = =.99 ) Luke buys a pair of trainers in Switzerland. He can pay either 86 Swiss Francs or 6 Euros. The exchange rates are: =.0 Swiss Francs =.0 Euros Which currency should he choose to get the best price, and how much would he save? Give your answer in pounds ( ). Euros, saving 0.9 ) The exchange rate in London is =. 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. Paris eg Suppose Tony changes 00. In London he would get 00. = In Paris he would get = 6.8 Page 0

129 MathsWatch Clip 06 Grade answers Sharing Using Ratio ) Tom and Julie share 8 in the ratio : 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. Ben gets and Sue gets 6 ) 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 milk chocolates. Work out the total number of chocolates. 6 chocolates altogether ) Andy, Ben and Claire share Ben gets three times as much money as Andy. Claire gets twice as much money as Ben. How much money does Claire get?.0 ) 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. The ratio of the number of apples to the number of pears is : b) Work out the number of pears in the box. pears 6) A piece of string is 80 cm long. Jim cuts it into three pieces in the ratio : : Work out the length of the longest piece. 80 cm 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? 6.0 Page 06

130 MathsWatch Clip 07 Grade answers Ratios, Fractions and Graphs ) In a box of chocolates, the ratio of plain chocolates to milk chocolates is :. a) What fraction of the chocolates are plain ones? b) What fraction of the chocolates are milk ones? 7 7 ) If the ratio of x : y is : 7, which of the following statements are correct? b and d 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 :. a) Use the squares, below, to draw a conversion graph to illustrate this. b) Convert pounds to kilograms. c) Convert kilograms to pounds. kg 0.8 lb 0 kg 0 0 Pounds Page 07

131 MathsWatch Clip 08 Grade answers Increase/Decrease by a Percentage ) Increase: a) 00 by 0% c) 80 by % 0 9 b) 0 by 0% d) 7 by 0% 90 ) Decrease: a) 00 by 0% c) 0 by % 60 9 b) 80 by 0% d) by 0% 8 ) The price of a laptop is increased by %. The old price of the laptop was 00. Work out the new price. ) The price of a 6800 car is reduced by 0%. What is the new price? 60 ) Increase: a) 6 by % 7.8 c) 600 by 7.% b) 0 by % 7.6 d) 70 by 7.% ) Decrease: a) by %.7 c) by 8.% b) 79 by % 69. d) 8900 by 8% ) The price of a mobile phone is 78.0 plus VAT. VAT is charged at a rate of 7.%. What is the total price of the mobile phone? 9. 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 ) 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 0) A month ago, John weighed 97. kg. He now weighs.% more. Work out how much John now weighs. Give your answer to decimal place. 0.9 kg Page 08

132 MathsWatch Clip 09 Grade answers Percentage Change ) A car dealer is comparing his sales over the past two years. In 006, he sold 7 cars. In 007, he sold 96 cars. Work out the percentage increase in the number of cars sold. % ) In September 00, the number of pupils attending MathsWatch College was. In September 006, the number of pupils attending MathsWatch College was 0. Work out the percentage decrease in the number of pupils attending MathsWatch College. % ) The usual price of a shirt is.0 In a sale, the shirt is reduced to 9. What is the percentage reduction? 0% ) Olivia opened an account with 70 at the MathsWatch Bank. After one year, the bank paid her interest. She then had 79 in her account. Work out, as a percentage, MathsWatch Bank s interest rate. 6% ) 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, sold for 0 b) DVD recorder bought for, sold for c) Gold necklace bought for 90, sold for 78.0.% profit d) A DVD collection bought for 0, sold for 8.60 % profit % loss % loss Page 09

133 MathsWatch Clip 0 Grade answers 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..0 ) A car dealer offers a discount of % off the normal price of a car for cash. Emma pays 60 cash for a car. Calculate the normal price of the car. 700 ) In a sale, normal prices are reduced by %. The sale price of a DVD recorder is 08.7 Calculate the normal price of the DVD recorder. ) 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 60 Work out the value of the sales he made that week. 600 ) Jason opened an account at MathsWatch Bank. MathsWatch Bank s interest rate was %. 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 ) 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 Tess has calculated 0% of 960, and subtracted it. b) Work out Jonathan s weekly pay last year ) The price of all rail season tickets to London increased by %. a) The price of a rail season ticket from Oxford to London increased by.0 Work out the price before this increase. 060 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. 80 Page 0

134 MathsWatch Clip Grade answers Simple Interest ) Meg has 00 in her savings account. The account pays % simple interest per year. How much interest will she earn in years? 0 ) Dan has 000 in his savings account. This account pays % interest per year. How much interest will he earn in 6 years? 80 ) Chris borrows 6000 at a simple interest rate of 0% per year. He pays the money back after years. How much does he pay back in total? 800 ) Lisa borrows 000 at a simple interest rate of.% per year. She pays the money back after years. How much does she pay back in total? ) 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? 080 6) Neil invested 8000 in a savings account for years. He earned 60 simple interest over the two years. What was the interest rate? % Page

135 MathsWatch Clip Grade answers Metric Conversions ) Change 9 m into cm cm ) How many square metres are there in square kilometres? m ) Change cm into mm ) Convert 6. m into mm ) Change m into cm 00 mm mm cm 6) How many cubic millimetres are there in cubic centimetres? 000 mm 7) Change 7 m into mm mm 8) A tiler wants to tile a rectangular wall which measures m by. m. Each tile measures 6 cm by 0 cm. How many tiles will he need for the wall? 6 Tile 0 cm. m 6 cm m 9) A carpet-fitter is laying carpet tiles on a rectangular floor which measures 7. m by. m. Each carpet tile measures 0 cm by 0 cm. How many carpet tiles will he need for the floor? Carpet tile. m 0 cm 0 cm 7. m Page

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

137 MathsWatch Clip Grade answers Surface Area of a Prism - Cuboids ) A cube has sides of length cm. Find the total surface area of the cube. 0 cm cm cm cm ) A cuboid has sides of length 0 cm, 6cm and 7 cm. Find the total surface area of the cuboid. cm 6 cm 7 cm 0 cm ) A cuboid has sides of length cm,.cm and 6 cm. Find the total surface area of the cuboid. 06 cm. cm cm 6 cm Page A

138 MathsWatch Clip Grade answers Surface Area of a Prism - Triangular Prisms ) Find the surface area of this triangular prism. 8 cm cm cm cm 6 cm ) Find the surface area of this triangular prism. 660 cm cm cm cm 0 cm cm ) With the aid of Pythagoras Theorem, find the surface area of this triangular prism. Give your answer correct to significant figures. 0 cm 9. cm.6 cm. cm Page B

139 MathsWatch Clip Grade answers Volume of a Cuboid ) Find the volume of this cuboid. 00 cm cm 0 cm 6 cm ) Find the volume of this cuboid..8 m 0.8 m.7 m. m ) The volume of this cuboid is 80 cm. Find the length of the side marked x. 0 cm 6 cm x 8 cm ) Boxes A and B are both cuboids. How many of box B could be packed into box A? 80 0 cm 60 cm A 0 cm cm B 0 cm 80 cm Page

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

141 MathsWatch Clip 7 Grade answers Area of a Circle ) Find the areas of the following shapes. a) b) c) cm 7m 8cm 8.78 cm.98 m 0.7 cm ) Work out the areas of the following shapes. a) mm b) 0cm 78. cm 6.6 mm ) 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.. cm b) Work out the area of the base of the table cm ) 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. 87 cm cm 7 cm Page 7

142 MathsWatch Clip 8 Grade answers Circumference of a Circle ) Find the circumference of the following shapes. a) b) c) cm m 8 cm 8.8 cm. m.6 cm ) Work out the perimeter of the following shapes. a) mm b) 0 cm 0.8 mm.7 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 cm b) Work out the circumference of the base of the table. Let be. 9. cm ) 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 cm. Calculate the perimeter of the shape. Give your answer correct to significant figures cm cm cm Page 8 A

143 MathsWatch Clip 7/8 Grade answers Area and Circumference of a Circle ) A circle has a radius of cm. A square has sides of length cm. cm cm cm Work out the difference between the area of the circle and the area of the square if you take to be. 69 cm ) 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.. cm ) 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. cm ) A circle has a diameter of cm. cm Work out the circumference of the circle. Give your answer correct to three significant figures..0 cm Page 8 B

144 MathsWatch Clip 7/8 Grade answers Area and Circumference of a Circle ) The radius of a circle is 0 cm. 0 cm Work out the area of this circle.. cm ) 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. 0.8 m ) 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. 7.7 cm CDs of this size are cut from rectangular sheets of plastic. Each sheet is metre long and 0 cm wide. b) Work out the greatest number of CDs which can be cut from one rectangular sheet. 6 cm Page 8 C

145 MathsWatch Clip 9 Grade answers Volume of a Prism ) The diagram shows a cuboid. Work out the volume of the cuboid. 00 cm cm 0 cm 0 cm ) Calculate the volume of this triangular prism. cm cm 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. cm.. cm Work out the volume of the puck. Give your answer correct to significant figures..8 cm cm ) A cuboid has: a volume of 80cm a length of cm a width of cm Work out the height of the cuboid. 0 cm ) Work out the maximum number of boxes which can fit in the carton cm Carton 0 cm 80 cm Box 0 cm 0 cm 00 cm Page 9 A

146 MathsWatch Clip 9 Grade answers Volume of a Prism ) Work out the volume of the prism. 80 cm cm cm cm 0 cm ) A solid cylinder has a radius of cm and a height of 0 cm. 0 cm Work out the volume of the cylinder. Give your answer correct to significant figures. 786 cm 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. 00 cm Page 9 B

147 MathsWatch Clip 0 Grade answers 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. 6 Alternate angles 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 6 D E 6 F C B G H Page 0 A

148 MathsWatch Clip 0 Grade answers Angles and Parallel Lines ) A 67 9 B C y D AB is parallel to CD. (i) Write down the value of y. 9 (ii) Give a reason for your answer. Alternate angles ) 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. 0 (ii) Give a reason for your answer. Corresponding angles b) Work out the value of y. 0 Page 0 B

149 MathsWatch Clip 0 Grade answers Angles and Parallel Lines ) a (i) Write down the size of the angle marked a. (ii) Give a reason for your answer. Corresponding angles 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. Angle LNB = 67 C (corresponding angles) y = (angles on straight line add up to 80 ) M 67 D ) D C A B 6 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

150 MathsWatch Clip Grade answers Angles in a Triangle ) Work out the size of angle a. 6 7 a ) Work out the size of angle b b ) Work out the size of angle c. 8 7 c ) Work out the size of angle d. 8 d 0 Page

151 MathsWatch Clip Grade answers Properties of Special Triangles ) ABC is a triangle. a) Find the size of angle A. 60 C 60 Diagram NOT accurately drawn b) Triangle ABC is equilateral. Explain why. All of the angles are equal. A 60 B ) BCD is a triangle. ABC is a straight line. Angle CBD = 70. BD = CD. D y Diagram NOT accurately drawn a) (i) Work out the value of x. 0 x 70 (ii) Give a reason for your answer. A B C Angles on a straight line add up to 80. b) (i) Work out the value of y. 0 (ii) Give reasons for your answer. Base angles of an isosceles triangle are equal. Angles in a traingle add up to 80. ) The diagram shows a -sided shape. All the sides of the shape are equal in length. a) (i) Find the value of x. 60 (ii) Give a reason for your answer. Equilateral triangle y x b) (i) Work out the value of y. 0 (ii) Explain your answer. Angle in square + angle in equilateral triangle = = 0 Page

152 MathsWatch Clip Grade answers 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. Decagon b) Work out the size of an exterior angle and of an interior angle for this polygon. Exterior angle = 6 Interior angle = ) The size of each exterior angle of a regular polygon is 0. Work out the number of sides of the regular polygon. 9 ) The size of each interior angle of a regular polygon is 0. Work out the number of sides of the regular polygon. 6 Page A

153 MathsWatch Clip Grade answers Angle Sum of Polygons ) The diagram shows a regular hexagon and a square. Calculate the size of the angle a. 0 a ) x The diagram shows a regular octagon and a regular hexagon. Work out the size of angle x. 0 ) ABCDE and PQRSE are regular pentagons. AES is an equilateral triangle. Work out the size of angle DEP. 8 D P C Q E B R A S Page B

154 MathsWatch Clip Grade answers 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. 09 N B Another mast C is on a bearing of 60 from B. On the map, C is cm from B. b) Mark the position of C with a cross and label it C. A xc ) The diagram shows the positions of two boats, P and Q. N R N Q P The bearing of a boat R from boat P is 00 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 A

155 MathsWatch Clip Grade answers Bearings ) School B is due east of school A. C is another school. The bearing of C from A is 06. The bearing of C from B is. Complete the scale drawing below. Mark with a cross the position of C. N C 6 7 A ) 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 cm from A B B N 0 ) Work out the bearing of a) B from P b) P from A N A 0 A Diagram NOT P8 accurately drawn B Page B

156 MathsWatch Clip Grade answers 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 Two possible answers: No, you would expect to score about 00 times. Yes, although you would expect about 00 times, you could still get it 00 times. ) 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 0 times. Work out an estimate for the number of times the coin will land on a tail. times ) 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. 00 times ) On a biased dice, the probability of getting a three is 0. The dice is rolled 0 times. Work out an estimate for the number of times the dice will land on a three. 7 times ) 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. or b) If the dice is rolled 0 times, how many times would you expect to get a five? times Page

157 MathsWatch Clip 6 Grade answers Possibility Spaces ) Two dice are rolled and their scores are multiplied together. a) Complete the possibility space to show all the possible results. First dice 6 6 Second dice b) What is the probability of getting a result that is an even number? 7 6 ) 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

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

159 MathsWatch Clip 8 Grade answers 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 St Lucia Biarritz 9 Angle Draw a pie chart to illustrate the information. St Lucia Biarritz Ibiza Alicante Paris ) 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 Angle Draw a pie chart to illustrate the information Northern England Southern England Midlands London ) 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? people b) How many people spend minutes or more eating their breakfast? 0 people c) Find the median time that it took to eat breakfast. 8 minutes Page 8

160 MathsWatch Clip 9 Grade answers Scatter Diagrams ) The scatter graph shows some information about the marks of six students. It shows each student s marks in Maths and Science. 0 The table below shows the marks for four more students. Maths Science 0 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. There is a positive correlation 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. Science My answer is. Yours will depend on your line of best fit 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. A negative correlation d) Use your scatter graph to estimate the number of hours sleep for a year old child. My answers is.6 Yours will depend on your line of best fit. Number of hours sleep Age (years) Page 9 A

161 MathsWatch Clip 9 Grade answers 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) Time (Minutes) 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. Negative correlation c) Find an estimate for the time it takes a cm ice cube to melt when the temperature is C. 9 minutes (your answer will depend on your line of best fit) 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. Line of best fit would give a negative time or You cannot draw and use a line of best fit which goes beyond the values. Page 9 B

162 MathsWatch Clip 9 Grade answers 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. Positive correlation Henry reads another book. The book has 0 pages. b) Estimate the time it takes Henry to read it. 7 hours (your answer will depend on your line of best fit) Page 9 C

163 MathsWatch Clip 9 Grade answers 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? Positive correlation In February of this year, Mr Jones sold 0 umbrellas. c) Estimate the rainfall for February. 6.7 cm (your answer will depend on your line of best fit) Page 9 D

164 MathsWatch Clip 0 Grade answers 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 Number of pupils 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. 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. Thomas gave the highest a) Explain why. frequency instead of giving the number of 'goals scored' associated with it. b) Calculate the mean number of goals scored..9 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 < Frequency 8 9 Midpoint MP Frequency < t < Calculate an estimate for the mean time that her train was late. Give your answer to decimal place..8 minutes Page 0

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

166 MathsWatch Clip Grade answers Index Notation ) a) Simplify d d d d b) Simplify t t c) Simplify m m t m d ) a) Simplify (x ) 8x 6 x 7 y b) Simplify x x y ) a) Simplify t t t 9 b) Simplify x 8 x x c) Simplify (c ) c ) a) Simplify x 6 x b) Simplify x 8 x c) Simplify (t) x 8t x 8 d) Simplify x y x y x 7 y ) a) Simplify x x x 7 b) Simplify t 7 t t c) Simplify x y xy x y 6 6) a) Simplify x x x x b) Simplify x y 6xy x Page B

167 MathsWatch Clip Grade answers 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.. g b) Write down the greatest possible mass of the necklace.. g ) Each of these measurements was made correct to one decimal place. Write the maximum and minimum possible measurement in each case. a).6 cm b) 0.8 kg c). litres d).0 km/h max:.6 cm max: 0.8 kg max:. l max:.0 km/h min:. cm min: 0.7 kg min:. l min:.9 km/h e) 0. s f) 6. m g) 6.7 m/s h) 0. g max: 0. s max: 6. m max: 6.7 m/s max: 0. g min: 0. s min: 6.0 m min: 6.6 m/s min: 0.0 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. 0. cm b) Write down the greatest possible length of each side. 0.6 cm c) Write down the greatest possible perimeter of the octagon. 6. cm ) A girl has a pen that is of length cm, measured to the nearest centimetre. Her pencil case has a diagonal of length. cm, measured to the nearest millimetre. Explain why it might not be possible for her to fit the pen in the pencil case. cm to the nearest cm has a maximum possible length of. cm.. cm to the nearest mm has a minimum possible length of. cm. A. cm pencil won t fit into a pencil case with a diagonal length of. cm. ) A square has sides of length 7 cm, correct to the nearest centimetre. a) Calculate the lower bound for the perimeter of the square. 6 cm b) Calculate the upper bound for the area of the square. 6. cm Page

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

169 MathsWatch Clip Grade answers Expanding and Simplifying Brackets ) Expand these brackets ) Expand and simplify a) (x + ) x + 6 a) (x + y) + (x + y) x + y b) (x + ) 6x + b) (x + y) + (x + y) 6x + 9y c) (p q) p 0q c) (x + y) + (x + y) x + 8y d) (x + y ) x + 8y d) (c + d) + (c + d) 8c + d e) 6(r r ) 6r 6r e) (p + q) + (p + q) p + 7q ) Expand these brackets a) x(x ) x x 6) Expand and simplify a) (x + y) + (x y) x y b) x(x + ) x + x b) (x + y) + (x y) 6x + y c) p(p 7q) p 7pq c) (x y) + (x + y) 0x y d) y(y + 6y ) y + 6y d) 6(c d) + (c d) c 8d e) x(r + r ) xr + xr e) (p q) + (p q) p 8q ) Expand these brackets a) x(x ) x 0x 7) Expand and simplify a) (x + y) (x y) 9y b) x(x + ) 8x + x b) (x y) (x y) x y c) p(p q) 0p 0pq c) 7(x y) (x + y) x 7y d) y(y + x ) 6y + 8x y d) 6(x y) (x + y) 0x 0y e) x(x + r ) x + r x e) (p q) (p q) 9p + q ) Expand these brackets a) x(x ) b) x(x + ) c) p (p ) x x 6x + x 0p 0p d) y (y + y) e) xy(x + y ) 6y + 8y x y + xy Page A

170 MathsWatch Clip Grade answers Expanding and Simplifying Brackets ) Expand and simplify ) Expand and simplify a) (x + )(x + ) x + x + 6 a) (x 7)(x + ) x 6x 7 b) (x + )(x + ) x + 8x + b) (p 6)(p + ) p p c) (x + )(x + ) x + x + c) (e )(e 7) e 0e + d) (x + 6)(x + ) x + 0x + d) (x + 8)(x + ) x + 9x + 8 e) (x + )(x + 7) x + x + e) (x )(x ) x 0x + ) Expand and simplify ) Expand and simplify a) (x + )(x ) x + x 0 a) (x + )(x + ) x + 8x + b) (x 7)(x + ) x x b) (p )(p + ) 6p + 7p 0 c) (x )(x + ) x + x c) (e )(e ) e e + d) (x + )(x ) x + x d) (x 6)(x + ) 8x 8x 6 e) (x )(x + ) x e) (x )(x + ) x 9 ) Expand and simplify 6) Expand and simplify a) (x )(x ) x 7x + a) (x + y)(x + y) 6x + 7xy + y b) (x )(x 6) x 8x + b) (p q)(p + q) p + 7pq 0q c) (x )(x ) x x + c) (e f )(e f ) 8e ef + 6f d) (x 7)(x ) x 9x + d) (6x y)(6x + y) 6x y e) (x )(x ) x 9x + 0 e) (x y)(x y) x 7xy + 0y Page B

171 MathsWatch Clip Grade answers Solving Equations ) Solve x = 7 x = 0 ) Solve x + = x = ) Solve x 7 = x = 8 ) Solve x + 7 = 9 x = ) Solve x + x + x + x = 0 x = 7) Solve (x + ) = x + 9 x = 8) Solve x 7 = (x ) x = 9) Solve (x + ) = (x + 6) x = - 0) Solve (y + ) = ( y) y = ) Solve 7 x = (x + ) x = 6) Solve x + x = x = 6 ) Solve x = 0 x = 7) Solve (x + ) = 8 x = 8) Solve (x ) = x = 9) Solve (t ) = 0 t = 0) Solve (x + ) = 6 x =. ) Solve x + 7 = x + x = ) Solve y = y + 0 y = 6 ) Solve x + = x 0 x = 7 ) Solve p = p p = ) Solve d + = 0 d d = 6) Solve e = e 8 e = ) Solve x = 0 ) Solve x = 6 ) Solve x = 6 6) Solve x = 7) Solve x = 9 x = 6 x = x = x x + = = 7 8) Solve x + = x =. 9) Solve x = 0) Solve x = - x x + ) Solve x x =. ) Solve x + x =. = = x + = x = x Page

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

173 MathsWatch Clip 7 Grade answers Forming Formulae and Equations ) The width of a rectangle is x centimetres. The length of the rectangle is (x + ) centimetres. x + x a) Find an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form. x + 0 The perimeter of the rectangle is 8 centimetres. b) Work out the length of the rectangle. cm ) 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. x +0 = 60 b) Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral. 8 ) 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. x + 8 b) If the total cost of 6 cups and 6 mugs is 8, write an equation in terms of x. x + 8 = 8 c) Solve your equation to find the cost of a cup and the cost of a mug. Cup:.0, Mug:.0 Page 7A

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

175 MathsWatch Clip 7 Grade answers 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 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. T = 8x + y ) Batteries are sold in packets and boxes. Each packet contains 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. N = p + 0b ) Compasses cost c pence each. Rulers cost r pence each. Write down an expression for the total cost, in pence, of compasses and rulers. c + r ) P x + 0 ABC is a straight line. Angle APB = x + 0 Angle PAB = x 0 Angle PBC = y x 0 A B C a) Show that y = x + 0 Give reasons for each stage of your working. b) Given that y equals degrees (i) Work out the value of x. (ii) Work out the size of the largest angle in triangle APB. y Angle PAB + Angle APB = x + 0 Angle PBA = 80 (x + 0) = 0 x Angle y = 80 angle PBA = 80 (0 x) = 0 + x = x Page 7 C

176 MathsWatch Clip 8 Grade answers 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 - < x ) Write down the inequality shown - x ) If y is an integer, write down all the possible values of - < y < -, 0,,,,, 6) If x is an integer, write down all the possible values of -9 < x < - -8, -7, -6 Page 8

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

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

179 MathsWatch Clip 0 Grade answers 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 y y = x + 8 x = y = 7 6 y = 6 x 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 x = and y = 8 y = x + 7 y = 7 x 6 O x Page 0

180 MathsWatch Clip Grade answers Fibonacci Sequences ) Write down the next two terms of the Fibonacci sequence that begins,,,,, 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+ 9 ) 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+ 7 ) If the first three Fibonacci numbers are x =, x =, x =, what is the value of n for which x + x =? 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? 8 Page

181 MathsWatch Clip Grade answers Compound Units ) Jane runs 00 metres in. seconds. Work out Jane s average speed in metres per second. Give your answer correct to decimal place. S = 9. m/s ) 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. S = 6 mph ) A plane flies 0 miles at a speed of 0 mph. How long does it take? T = 6 hours ) A marathon runner runs at 7.6 mph for three and a half hours. How many miles has he run? D = 6.6 miles ) A car takes minutes to travel miles. Find its speed in mph. S = 96 mph 6) A cyclist takes 0 minutes to travel. miles. Calculate the average speed in mph. S =. mph 7) An ice hockey puck has a volume of cm. It is made out of rubber with a density of. grams per cm. Work out the mass of the ice hockey puck. M = 69. g 8) An apple has a mass of 60 g and a volume of 00 cm. Find its density in g/cm. D =.6 g/cm 9) A steel ball has a volume of 00 cm. The density of the ball is 9 g/cm. Find the mass of the ball in kg. M =. 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? V = 00 cm Page A

182 MathsWatch Clip Grade answers 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. 890 km/h ) A solid cylinder has a radius of cm and a height of 0 cm. 0 cm cm a) Work out the volume of the cylinder. Give your answer correct to significant figures. 0 cm 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. g ) 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 g/cm. Calculate the mass of the prism. Give your answer in kilograms..8 kg Page B

183 MathsWatch Clip Grade answers Distance-Time Graphs ) 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? 0 0 b) How far was Sarah from home at 0 0?. km 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. 0 minutes Sarah returned home at a steady speed. She arrived home at 0 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. 0 km/h f) Work out Sarah s average speed on her journey home from her friend s house. Give your answer in kilometres per hour. 0 km/h Page

184 MathsWatch Clip Grade answers Similar Shapes ) B 0 6 cm 8 A 0 cm D. C P Q 0 8 cm cm S R ABCD and PQRS are mathematically similar. a) Find the length of PQ. cm b) Find the length of AD..8 cm. Q ) B cm 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 = cm. PR = 9 cm. PQ = cm a) Work out the length of QR. b) Work out the length of AB. cm 0 cm Page A

185 MathsWatch Clip Grade answers Similar Shapes ) A cm B. cm C Triangle ABC is similar to triangle ADE. AC = cm. CE = 6 cm. BC =. cm. 6 cm Work out the length of DE. 7. cm D E ) ABC and AED are straight lines. EB is parallel to DC. Angle ACD = 90 A AB = 0 cm BC = cm EB = 6 cm 0 cm a) Work out the length of DC. 9 cm b) Work out the area of the trapezium EBCD. 7. cm E 6 cm B cm D C Page B

186 MathsWatch Clip Grade answers Similar Shapes ) The diagram shows two quadrilaterals that are mathematically similar. B P 8 cm Q A cm S cm R D cm C a) Calculate the length of AB 8 cm b) Calculate the length of PS 6 cm ) 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. cm R 9 cm 6 cm cm S V T 7cm U ) BE is parallel to CD. ABC and AED are straight lines. AB = cm, BC = 6 cm, BE = cm, AE =. cm a) Calculate the length of CD.. cm A b) Calculate the length of ED. 6.6 cm cm. cm B E 6 cm cm C D Page C

187 MathsWatch Clip Grade answers 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

188 MathsWatch Clip 6 Grade answers 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 6

189 MathsWatch Clip 7 Grade answers Drawing a Triangle Using Compasses ) The diagram shows a sketch of triangle ABC. B 7. cm A 8. cm 8 C BC = 7. cm AC = 8. cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on your diagram. Angle A = 9 ) 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 0. cm 7. cm P 9 cm a) Use ruler and compasses to make an accurate drawing of triangle PQR. R b) Measure angle P. Angle P = Page 7

190 MathsWatch Clip 8 Grade answers ) a) Enlarge triangle T by scale factor using point (-, ) 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. Enlargements y U T O - x W V ) Describe fully the single transformation which maps triangle S to triangle T. Enlargement, scale factor, centre of enlargement (0, ). y S T O x Page 8

191 MathsWatch Clip 9 Grade answers 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. Circumference Minor segment Radius Chord Minor sector Arc Diameter Tangent Page 9

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

193 MathsWatch Clip 0 Grade answers Pythagoras Theorem ) Find the length of side AC. Give your answer to decimal place. A.9 cm ) Below is a picture of a doorway. Find the size of the diagonal of the doorway. Give your answer to decimal place.. m cm.m 0.8m B 7cm ) Find the length of side QR.9 cm Give your answer to decimal place. Q.8cm P C ) In the sketch of the rectangular field, below, James wants to walk from B to D. A B 60m R 7.6cm D 0m 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. B to D is shorter, by m Give your answer to the nearest metre. C ) Find the length of side SU Give your answer to decimal place. T cm U cm 8. 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. Longest side 7 = 89 8 = 6 = cm No. The diagonal is only 8.8cm. 7cm Page 0 B

194 MathsWatch Clip 0 Grade answers Pythagoras Theorem ) Points P and Q have coordinates (, ) and (, ). Calculate the shortest distance between P and Q. Give your answer correct to decimal place.. y 6 P Q O 6 x ) Points A and B have coordinates (-, ) and (, -). Calculate the shortest distance between A and B. Give your answer correct to decimal place. 8.6 y A O - x 7 - B Page 0 C

195 MathsWatch Clip Grade answers 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 0. Fail Pass Fail 0. 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 = 0.6 ) Terri has 7 pens in a box. of the pens are blue. 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 Blue Red..... Red = b) Work out the probability that Terri takes exactly one pen of each colour from the box. Page A

196 MathsWatch Clip Grade answers Simple Tree Diagrams ) Tim puts red counters and 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 nd counter 7 Red 7 Red 7 Blue 7 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 0. Draw Win Draw Lose Lose Win Draw b) Work out the probability that Jane will win both games Lose Page B

197 MathsWatch Clip Grade answers 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. 6 st Throw Six nd Throw 6 six 6 not six.. 6 Not Six 6 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 7 nd Ball 0 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. 00 d) Work out the probability that Nathan will take two balls of the same colour Page C

198 MathsWatch Clip Grade answers 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? It is quicker. b) The Headteacher asked 00 KS students whether they liked the dinners and 0 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? KS students are as likely to like school dinners as d) What could be done to make your estimate more accurate? KS students. Include KS students in the sample, as well as KS students. 0 ) 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 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. 00 b) In finding your estimate, what assumption have you made? All of the fish are attracted to the specific bait that he is using. Page

199 MathsWatch Clip Grade answers Time Series The table on the right shows the sales figures for a manufacturing company over the course of years. a) Complete the time series graph to show this information. b) What is the range of the sales figures? 7.M c) Comment on the trend over the course of years. The sales are increasing. Year Sales ( M) Sales in M Year Page

200 MathsWatch Clip Grade answers Negative Indices ) Find the value of: - a) - b) - c) - d) ) Find the value of: - - a) - - b) 0 - c) - d) ) Write these numbers in order of size. Start with the smallest , -, 0., -, 0, 6 x ) If =, find the value of x. x = -6 Page

201 MathsWatch Clip Grade answers Error Intervals ) A number, x, rounded to decimal place is.7 Write down the error interval for x..6 x <.7 ) A number, y, rounded to decimal places is.6 Write down the error interval for y.. y <.6 ) A number, x, rounded to significant figure is 00. Write down the error interval for x. 0 x < 0 ) A number, y, rounded to significant figures is Write down the error interval for y y < 6700 ` ) A number, x, rounded to significant figures is 00. Write down the error interval for x. 00 x < 0 Page

202 MathsWatch Clip 6 Grade answers Mathematical Reasoning ) Meg says, The sum of three prime numbers is always odd. Write an example to show that Meg is incorrect. + + = 0 Other examples are possible, but one of the chosen prime numbers should be. ) Mike says. If you cube a prime number, the result will always be odd. Give an example to show that Mike is wrong. = 8 ) Explain why an odd number plus another odd number plus an even number is always even. odd + odd = even even + even = even ) P is an odd number. Q is an even number. Explain why P + Q is always odd. P = even Q = even ) 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. P + Q = even P + Q = odd P + Q will be odd, but not all odd numbers are prime numbers. For example, if P = and Q =, then P + Q = 9, but 9 is not a prime number as it is divisible by. Page 6

203 MathsWatch Clip 7 Grade answers Factorising and Solving Quadratics ) Factorise and solve the following equations: a) x + x + 6 = 0 b) x + 9x + 0 = 0 c) x + x 6 = 0 d) x + x = 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 x + 6 = 0 (x + )(x + ) = 0 x = - or - (x + )(x + ) = 0 x = - or - (x + )(x ) = 0 x = - or (x + 8)(x ) = 0 x = -8 or (x )(x ) = 0 x = or (x 7)(x + ) = 0 x = 7 or - (x + )(x + ) = 0 x = - or - (x + )(x + ) = 0 x = - or - (x + )(x ) = 0 x = - or 7 (x 7)(x 9) = 0 x = or 9 ) Lucy said that - is the only solution of x that satisfies the equation x + x + = 0 Was Lucy correct? Yes Show working to justify your answer x + x + = 0 (x + )(x + ) = 0 so x = - ) Ben said that - is the only solution of x that satisfies the equation x + 0x + = 0 Was Ben correct? Yes Show working to justify your answer x + 0x + = 0 (x + )(x + ) = 0 so x = - Page 7

204 MathsWatch Clip 8 Grade answers The Difference of Two Squares ) Factorise a) x 6 c) y 9 e) x (x )(x + ) (y )(y + ) (x )(x + ) b) a b d) x f) x 9 (a b)(a + b) (x )(x + ) (x )(x + ) ) Factorise a) x y c) 9x 6y e) x y (x y)(x + y) (x y)(x + y) (x y)(x + y) b) 9a b d) x y f) x 9 y (a b)(a + b) ( x y)( x + y) (x y)(x + y) ) Simplify a) y y+ y + (y ) y + b) x x + x (x ) x c) x + 8x 9x x x d) a 6b 0ab 8b a + b b ) Solve a) x 6 = 0 c) 9x = x =, x = - x = 7, x = - 7 b) x = d) 9x 9 = 7 x =, x = - x =, x = - Page 8

205 MathsWatch Clip 9 Grade answers Finding the Equation of a Straight Line ) Find the equations of lines A, B and C on the axes below y A 8 C 7 B A: y = x + B: y = 0.x + C: y = -x O x ) Find the equations of lines A, B and C on the axes below y C B 6 A A: y = x B: y = -0.x + C: y = -x O 6 x Page 9A

206 MathsWatch Clip 9 Grade answers Finding the Equation of a Straight Line ) Find the equation of line A on the grid below. y y = x A O 0.. x - - ) A straight line passes through points (0, ) and (, ). What is its equation? y = x + ) A straight line passes through points (0, 7) and (, -). What is its equation? y = -x + 7 ) A straight line is parallel to y = x and goes through (, 8). What is its equation? y = x + ) A straight line is parallel to y = x + and goes through (, 6). What is its equation? y = x 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. y = x A (-, ) C (0, -) B (, 6) Page 9B

207 MathsWatch Clip 60 Grade answers 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 (-, 0), (, 0) c) The intersection of the curve with the y-axis. 6 y (0, -) O - x Page 60

208 MathsWatch Clip 6 Grade answers ) a) Complete this table of values for y = x + x x y b) On the grid, draw the graph of y = x + x Cubic and Reciprocal Graphs y O - - x x x x c) Use the graph to find the value of x when y = x =.7 x ) a) Complete this table of values for y = x + x x - y x x 0 8 y - 0 x b) On the grid, draw the graph of y = x + x c) Use the graph to find the value of x when y = -6 x = x O - x x ) Sketch the graph of y = + x -8 x - Page 6

209 MathsWatch Clip 6 Grade answers Simultaneous Equations Algebraically ) Solve x + y = 6 x y = x = and y = - ) Solve x + y = 9 x y = 7 x = and y = ) Solve x + y = x + y = 8 x = and y = ) Solve x + y = x y = x = and y = 0. ) Solve a + b = a b = 0 a =. and b = - 6) Solve x + y = x + y = 9 x = - and y = 7) Solve 6x y = x + y = - x =. and y = - 8) Solve a b = a + b = a = and b = - 9) Solve x + y = x + 7y = 9 x = - and y = 0) Solve 6x y = 9 x + y = 6 x =. and y = - Page 6

210 MathsWatch Clip 6 Grade answers Geometric Progressions ) The st term of a geometric progression is and the common ratio is. a) Write down the first four terms of the progression., 0, 0, 0 b) What is the 0th term of the progression? 60 ) The st term of a geometric progression is and the common ratio is. a) Write down the first four terms of the progression., 8,, 8 b) What is the 7th term of the progression? 89 ) 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. 7,, 6, 89 c) Work out the th term of the progression ) The th term of a geometric progression is 66. The 6th term of the progression is What is the st term of the progression? 9 ) The first four terms of a geometric progression are 87, 7, 7,,... a) What is the common ratio of the progression? 0. b) Work out the 8th term of the progression ) The third term of a geometric progression is 9. The th term of the progression is 8. What is the st term of the progression? 07 Page 6

211 MathsWatch Clip 6 Grade answers Compound Interest and Depreciation ) Henry places 6000 in an account which pays.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 years ) Mary deposits 0000 in an account which pays.6% compound interest per year. How much will Mary have in her account after years?.66 ) Susan places 7900 in an account which pays.% compound interest per year. How much interest does she earn in years? 8.6 ) Harry puts money into an account which pays 6% compound interest per year. If he puts 000 in the account for years how much interest will he earn altogether? ) Laura buys a new car for 600. The annual rate of depreciation is %. How much is the car worth after years? ) The rate of depreciation of a particular brand of computer is 6% per year. If the cost of the computer when new is 60 how much is it worth after years? ) Sharon pays 00 for a secondhand car. The annual rate of depreciation of the car is % How much will it be worth four years after she has bought it? ) Dave places 7000 in an account which pays % compound interest per year. How many years will it take before he has 9.69 in the bank? years 0) A new motorbike costs The annual rate of depreciation is 8% per year. After how many years will it be worth 70.66? 6 years Page 6

212 MathsWatch Clip 6 Grade answers Loci ) A B D C ABCD is a rectangle. Shade the set of points inside the rectangle which are both more than 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 6A

213 MathsWatch Clip 6 Grade answers 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 6 B

214 MathsWatch Clip 6 Grade answers 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 cm from the rectangle ABCD A B D C Page 6 C

215 MathsWatch Clip 66 Grade answers 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. AB = CD (opp. sides of parallelogram are equal) AD = CB (opp. sides of parallelogram are equal) DB is a shared side. Therefore ABD is congruent to CDB (SSS) ) P Q T S R X PQRS is a square. PTS and SUR are equilateral triangles. a) Prove that triangle USP is congruent to triangle TSR. U US = TS SP = SR Angle USP = 60º + 90º = 0º Angle TSR = 60º + 90º = 0º USP is congruent to TSR (SAS) X is the point such that RUXT is a parallelogram. b) Prove that UP = UX UP = RT (corresponding sides of congruent triangles) RT = UX (opp. sides of parallelogram are equal) Therefore UP = UX Page 66 A

216 MathsWatch Clip 66 Grade answers Congruent Triangles ) B P A Q R C 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. Prove that triangle APQ and triangle QRC are congruent. You must give reasons for each stage of your proof. AQ = QC (Q is midpoint of AC) Angle AQP = angle QCR (corresponding angles) PQ = BR (opposite sides of parallelogram) BR = RC (R is midpoint of BC) PQ = RC APQ is congruent to QRC (SAS) ) A B D ABC is an equilateral triangle. D lies on BC. AD is perpendicular to BC. C Angle ADB = angle ADC = 90 (AD is perp. to BC) AB = AC (equilateral triangle) AD is a side in triangles ADC and ADB Triangle ADC is congruent to triangle ADB (RHS) a) Prove that triangle ADC is congruent to triangle ADB. b) Hence, prove that BD = AB ADC is congruent to ADB BD = DC BD = BC BC = AB (equilateral triangles) BD = AB Page 66 B

217 MathsWatch Clip 67 Grade answers Sectors of a Circle ) This sector of a circle has radius 6 cm. 6 cm a) Find the area of the sector cm b) Find the perimeter of the sector cm ) A quadrant of a circle is shown. 0 cm 0 cm Work out the area of the shaded section. 8. cm ) The diagram shows a sector of a circle. 0 The arc length is 7.6 cm. Work out the radius. cm Page 67

218 MathsWatch Clip 68 Grade answers Trigonometry A ) ABC is a right-angled triangle. AB = 0 cm. Angle ABC = 0 cm Work out the length of BC. Give your answer correct to decimal place. B C.7 cm 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 67. cm 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. cm A ) 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..8 B C A ) 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..9 B C Page 68A

219 MathsWatch Clip 68 Grade answers Trigonometry ) PQR is a right-angled triangle. PR = cm. QR =. cm Angle PRQ = 90 Q. cm Work out the value of x. Give your answer correct to decimal place.. P x cm R ) AC = cm. Angle ABC = 90 Angle ACB = A cm Calculate the length of BC. Give your answer correct to significant figures..6 cm B C ) PQR is a right-angled triangle. PQ = 8 cm. QR = 8. cm Angle PRQ = 90 8 cm Q 8. cm Work out the value of x. Give your answer correct to decimal place. 7.8 P x R ) AB = cm. Angle ABC = 90 Angle ACB = A Calculate the length of AC. Give your answer correct to significant figures. 6. cm cm B C ) A lighthouse, L, is. 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 km N L. km x Page 68 B

220 MathsWatch Clip 68 Grade answers Trigonometry D ) DEF is a right-angled triangle. DE = mm mm FE = mm F y mm E Calculate the size of angle y. Give your answer correct to one decimal place..6 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. 6.7 ) a) 9 cm Calculate the size of the angle marked x. Give your answer correct to one decimal place. 6.6 x cm b) y cm Calculate the value of y. Give your answer correct to one decimal place. y = cm Page 68 C

221 MathsWatch Clip 68 Grade answers 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 ) 7 ABC is a right-angled triangle. AC = m m Angle CAB = 7 C B Calculate the length of AB. Give your answer correct to three significant figures. 8.7 cm 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. 7.8 cm Page 68D

222 MathsWatch Clip 68 Grade answers 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 0 D. cm ) P cm Q 8 cm S 6 R PQRS is a trapezium. PQ is parallel to SR. Angle PSR = 90 Angle PRS = 6 PQ = cm. PS = 8 cm. Work out the length of PR. Give your answer correct to significant figures cm Page 68 E

223 MathsWatch Clip 69 Grade answers Spheres Volume of a sphere = r Surface area of a sphere = r ) a) Work out the volume of the sphere cm b) Work out the surface area of the sphere cm 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. 000 π cm 00π cm 0 cm ) a) Work out the volume of the solid hemisphere. 8.0 cm b) Work out the surface area of the solid hemisphere. 8. cm. cm Page 69

224 MathsWatch Clip 70 Grade answers 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. 80 cm ) Find the volume of this pyramid. 9. cm 8 cm cm 7 cm ) Find the volume of this pyramid. 8.6 cm 0 cm 6 cm 8 cm Page 70

225 MathsWatch Clip 7 Grade answers Cones Volume of a cone = r h Curved surface area = rl ) a) Work out the volume of the cone.. cm b) Work out the curved surface area of the cone. 0. cm c) The total surface area of the cone cm cm cm cm ) Work out the volume of the cone, leaving your answer in terms of. 8π cm 9 cm cm Page 7A

226 MathsWatch Clip 69/7 Grade answers Spheres and Cones ) A cone has a base radius of cm and a vertical height of 8 cm. a) Calculate the volume of the cone. Take to be.. Give your answer correct to significant figures. cm b) Use Pythagoras Theorem to find the slant height of the cone. Give your answer correct to decimal place. 8.9 cm c) Find the curved surface area of the cone. Take to be.. Give your answer correct to significant figures. cm 8 cm cm ) A sphere has a radius of cm. a) Calculate the volume of the sphere. Take to be.. Give your answer correct to significant figures. 70 cm b) Find the curved surface area of the sphere. Take to be.. Give your answer correct to significant figures. 80 cm cm ) 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. 8π cm 0 cm 8 cm Page 7B

227 MathsWatch Clip 69/7 Grade answers 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 or h = 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. h = 6x Page 7C

228 MathsWatch Clip 7 Grade answers Frustums ) A frustum is made by removing a small cone from a similar larger cone. Work out the volume of the frustum..9 cm cm 0 cm 9 cm cm ) The diagram shows a cone of height 0 cm and base radius 0 cm. A smaller cone of height 8 cm is removed to form a frustum. 8 cm 0 cm r r 0 cm 0 cm a) Work out the radius r of the base of the smaller cone. cm Calculate, to the nearest cm b) The volume of the larger cone. 89 cm c) The volume of the smaller cone. cm d) The volume of the frustum. 6 cm Page 7

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