MathsWatch Worksheets FOUNDATION and HIGHER Questions

Transcription

1 MathsWatch Worksheets FOUNDATION and HIGHER Questions MathsWatch

2 MathsWatch Clip No Name of clip Tier Grades Pg No Place value F G to E Ordering Decimals F G to E Round to nearest 0, 00, etc F G to E 4 Reading scales F G to E 4 5 Multiply or divide by powers of 0 F G to E 5 6 Negatives in real life F G to E 6 7 Multiplication and division with negatives F G to E 7 8 Fraction of an amount F G to E 8 9 Square and Cube Numbers F G to E 9 0 Fractions, Decimals and Percentages F G to E 0 Money questions F G to E Shading fractions of rectangles F G to E Ordering Fractions, Decimals & Percentages F G to E 4 Estimating answers F G to E 4 5 Place value when multiplying F G to E 5 6 Addition and subtraction F G to E 6 7 Long multiplication F G to E 7 8 Long division F G to E 8 9 Multiplication & Division with Decimals F G to E 9 0 Decimal places and significant figures F G to E 0 Half way points F G to E Reciprocals F G to E Proportion F G to E 4 Distance tables F G to E 4 5 Timetables F G to E 5 6 Powers F G to E 6 7 Line Graphs F G to E 7 8 Coordinates F G to E 8 9 Number Sequences F G to E 9 0 Number Machines F G to E 0 Angles F G to E Congruent and Similar Shapes F G to E Area and Perimeter F G to E 4 Volume of cuboids F G to E 4 5 Converting Metric Measures F G to E 5 6 Triangles, Quadrilaterals & Other Polygons F G to E 6 7 Names of solids F G to E 7 8 Tessellations F G to E 8 9 Isometric drawing F G to E 9 40 The probability scale F G to E 40 4 The averages F G to E 4 4 Pictograms F G to E 4 4 Conversion graphs F G to E 4

3 MathsWatch Clip No Name of clip Tier Grades Pg No 44 Factors, Multiples and Primes F and H D Evaluate powers F and H D Understand squares, cubes, roots F and H D Equivalent fractions F and H D Simplification of fractions F and H D Put fractions in order F and H D Value for money F and H D 47 5 Percentage of an amount with a calculator F and H D 48 5 Percentage of an amount without a calculator F and H D 48 5 Change to a percentage with a calculator F and H D Change to a percentage without a calculator F and H D Find a fraction of an amount F and H D Addition and subtraction of fractions F and H D 5 57 Multiply and divide fractions F and H D 5 58 Change fractions to decimals F and H D 5 59 BODMAS F and H D Long Multiplication of Decimals F and H D 55 6 Ratio F and H D 56 6 Recipe type ratio questions F and H D 57 6 Hard calculator questions F and H D Real-life money questions F and H D Generate a sequence from the nth term F and H D Substitution F and H D 6 67 Parallel lines F and H D 6 68 Angle sum of a triangle F and H D Properties of special triangles F and H D Finding angles of regular polygons F and H D 65 7 Area of circle F and H D 66 7 Circumference of circle F and H D 67 7 Area of compound shapes F and H D Rotations F and H D Reflections F and H D Enlargements F and H D 7 77 Translations F and H D 7 78 Find the mid-point of a line F and H D 7 79 Measuring and drawing angles F and H D Drawing triangles F and H D 75 8 Plans and elevations F and H D 76 8 Nets F and H D 77 8 Symmetries F and H D Questionnaires and data collection F and H D Two-way tables F and H D Pie charts F and H D 8 87 Scatter graphs F and H D 8 88 Frequency diagrams F and H D 8 89 Stem and leaf diagrams F and H D List of outcomes F and H D 85 9 Mutually Exclusive Events F and H D 85

4 MathsWatch Clip No Name of clip Tier Grades Pg No 9 Overview of percentages F and H C 86 9 Increase/decrease by a percentage F and H C Ratio F and H C Products of prime factors F and H C LCM and HCF F and H C Standard form F and H C Recurring decimals into fractions F and H C 9 99 Four rules of negatives F and H C 9 00 Division by -digit decimals F and H C 9 0 Estimate answers F and H C 9 0 Algebraic simplification F and H C 94 0 Expanding & simplifying brackets F and H C Factorisation F and H C Solving equations F and H C Forming equations F and H C Changing the subject of a formula F and H C Inequalities F and H C Solving inequalities F and H C 0 0 Trial and improvement F and H C 0 Index Notation for Multiplication & Division F and H C 0 Find the Nth term F and H C 04 Drawing straight line graphs F and H C 05 4 Equation of a straight line F and H C 06 5 Simultaneous Equations Graphs F and H C 07 6 Drawing Quadratic Graphs F and H C 08 7 Real-life Graphs F and H C 09 8 Pythagoras' Theorem F and H C 0 9 Pythagoras - line on a graph F and H C 0 -D coordinates F and H C Surface area of cuboids F and H C Volume of a prism F and H C 4 Similar shapes F and H C 5 4 Dimensions F and H C 6 5 Bounds F and H C 7 6 Compound measures F and H C 8 7 Bisecting a line F and H C 9 8 Drawing a perpendicular to a line F and H C 0 9 Bisecting an angle F and H C 0 Loci F and H C - Bearings F and H C 4 Experimental probabilities F and H C 5 Averages from a table F and H C 6 4 Questionnaires F and H C 7

5 MathsWatch Clip No Name of clip Tier Grades Pg No 5 Standard form calculation H B 8 6 Percentage increase/decrease H B 9 7 Compound interest/depreciation H B 0 8 Reverse percentage H B 9 Four rules of fractions H B 40 Solving quadratics by factorising H B 4 Difference of two squares H B 4 4 Simultaneous linear equations H B 5 4 Understanding y = mx + c H B 6 44 Regions H B 7 45 Graphs of cubic and reciprocal functions H B 8 46 Recognise the shapes of functions H B 9 47 Trigonometry H B Bearings by Trigonometry H B 4 49 Similar shapes H B 4 50 Circle theorems H B 4 5 Cumulative frequency H B 44 5 Boxplots H B 45 5 Moving averages H B Tree diagrams H B Recurring decimals H A to A* Fractional and negative indices H A to A* Surds H A to A* Rationalising the denominator H A to A* Direct and inverse proportion H A to A* 5 60 Upper and lower bounds H A to A* 5 6 Solving quadratics using the formula H A to A* 5 6 Solving quadratics by completing the square H A to A* 54 6 Algebraic fractions H A to A* Rearranging difficult formulae H A to A* Sim. equations involving a quadratic H A to A* Gradients of parallel and perpendicular lines H A to A* Transformation of functions H A to A* Graphs of trigonometric functions H A to A* Transformation of trigonometric functions H A to A* 6 70 Graphs of exponential functions H A to A* 6 7 Enlargement by negative scale factor H A to A* 64 7 Equations of circles and Loci H A to A* 65 7 Sine and Cosine rules H A to A* Pythagoras in D H A to A* Trigonometry in D H A to A* Areas of triangles using ½ ab sin C H A to A* Cones and Spheres H A to A* Segments and Frustums H A to A* 7 79 Congruent triangles H A to A* 7 80 Vectors H A to A* Histograms H A to A* 75 8 Probability And and Or questions H A to A* 76 8 Stratified sampling H A to A* 77

6 Clip Place Value ) a) Write the number forty five thousand, two hundred and seventy three in figures. b) Write the number five thousand, one hundred and three in figures. c) Write the number three hundred thousand, seven hundred and ninety one in figures. d) Write the number two and a half million in figures. e) Write the number one and three quarter million in figures. ) Write the following numbers in words a) 50 b) 50 c) d) e) ) a) Write down the value of the 7 in the number 75. b) Write down the value of the 6 in the number c) Write down the value of the in the number d) Write down the value of the 5 in the number e) Write down the value of the in the number Page

7 Clip Ordering Numbers Put these numbers in order, starting with the smallest: ) 74, 57, 8, 8, 6 ) 9, 84,, 8, 4 ) 76, 0,, 40, 7 4).,,.,,.0 5) 0., 0.,.04,. 6) 0.4, 0.047, 0.4, 0.4, ) 0.79, 0.709, 0.97, ).7,.074,.07,.70 9) 0.875, 0.88, , 0.008, 0. 0),, 7, 0, ),,, 5, 7 ) 4, 6, 0, 6, Page

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

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

10 Clip 5 Multiply and Divide by Powers of 0 ) Multiply the following numbers by 0, 00 and 000: e.g ) Divide the following numbers by 0, 00 and 000: e.g ) Work out the following: 00 = 65 0 = 7 0 = 59 0 = =. 000 = 4 00 = = = = = = Page 5

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

12 Clip 7 Multiplication & Division with Negatives Work out the following: ) - 6 = ) 4 = ) 0 - = 4) -6 - = 5) -5-7 = 6) 7 - = 7) 4 = 8) -4 6 = 9) -8 = 0) -9 = ) 4 - = ) - -9 = ) = 4) -6 = 5) 4 - = 6) -5-4 = 7) = 8) = 9) = 0) = Page 7

13 Clip 8 Fraction of an Amount ) Work out the following: a) of 0 b) of 9 c) 5 of 5 d) of 4kg e) 4 of 6cm f) 6 of 4kg g) 8 of 48kg h) of 66 i) 9 of 90km j) 7 of 8 k) 5 of 5kg l) 6 of 40km ) Work out the following: a) 4 of 0 b) 4 of 0 c) of d) of e) 4 of 44 f) of 4 g) 5 of 5 h) 4 of 6 i) 7 9 of 8 j) 5 7 of 56 k) 0 of 50 l) 6 of m) 4 of 4 n) 4 of 4 o) 8 of 0 ) The highest possible mark for a Maths test was 64. Dora got 7 8 of the full marks. How many marks did she get? 4) At MathsWatch School there are 500 students. 7 of these students are male. 5 a) What fraction of students are female? b) How many are male? c) How many are female? Page 8

14 Clip 9 Square and Cube Numbers ) a) In the numbers, above, find six of the first seven square numbers. b) Which of the first seven square numbers is missing? ) Work out the following: a) 0 b) 9 c) 7 + d) 8 ) For each pair of numbers, below, there is just one square number that lies between them. In each case, write the square number: a) 7 5 b) 9 c) 7 96 d) ) Work out the following: a) 5 b) 8 c) ) The first cube number is = Write out the nd, rd, 4th and 0th cube numbers. 6) Work out the following: a) + b) ) Work out the following: a) + 6 b) ) Work out what should go in the boxes: a) = 6 b) = 8 Page 9

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

16 Clip Money Questions ) Bill buys melons at.09 each. a) How much does he spend? b) How much change does he get from 5? ) Jenny is taking her family to the cinema. Jenny pays for adult and children. a) How much does she spend? b) How much change does she get from 0? Cinema Adult: 6.50 Child: 4.00 ) Bob is paid 7 per hour. a) Last monday Bob worked for 8 hours Work out his pay for that day. b) Yesterday Bob was paid 4. Work out how many hours Bob worked. 4) Complete this bill. ½ kg of carrots at 40p per kg =... kg of potatoes at 5p per kg = boxes of tea bags at 90p each =.80 4 packs of yogurts at... each = 4.80 Total =... Page

17 Clip Shading Fractions ) What fraction of each of the following shapes is shaded? a) b) c) d) e) f) ) Shade the given fraction in the following grids ) Which of these fractions is the smallest? or (use the grids to help) 9 4) Which of these fractions is the largest? 7 or (you must show your working) Page

18 Clip Ordering Fractions, Percentages & Decimals. Change these fractions to decimals eg a) b) c) d) e) f) Change these percentages to decimals eg % 0. 5 a) 6% b) 8% c) 59% d) 8% e) 8.5% f) 6.5%. Write the following numbers in order of size (smallest to largest) a) % b) 8% c) 0. 85% d) 0. % 9. % 5 00 e) % Page

19 Clip 4 Estimation ) Work out an estimate eg = 4000 a) 04 c) 56 b) 8 7 d) 77 ) Work out an estimate eg = 50 a).8 5 c) b) d) 5.4 ) Work out an estimate eg = 4 a) 5 c) 4 8 b) 7 44 d) ) Work out an estimate eg = 40 a) 68.7 c) b) d) ) Work out an estimate eg = a) 45 4 c) 4 5. b) d) Page 4

20 Clip 5 Place Value When Multiplying ) Use the information that 68 = 564 work out the value of: a). 68 b). 6.8 c) d) e) 0 68 f) g) h) 564 i) 564. j) 5640 ) Using the information that 46 5 = 4560 work out the value of: a) b) c) d) e) f) g) h) i) j) ) If 78.5 =., what do you have to divide 78 by to get an answer of 0.? 4) If 8.9 = 54.8, what do you have to multiply 8. by to get an answer of 548? Page 5

21 Clip 6 Addition and Subtraction ) a) 4 b) 5 7 c) ) a) 6 7 b) 9 8 c) ) a) b) c) ) There were two exhibitions at the NEC one Sunday. 86 people went to one of the exhibitions and 47 people went to the other exhibition. How many people went to the NEC, in total, on the Sunday? 5) a).6 +. b) c) ) a) +.5 b) c) ) a) 7 8 b) 7 4 c) ) a) b) 7 7 c) ) a) b) 6 8 c) ) There were two films showing at a cinema one Saturday. One of the films was shown in a large room and the other was in a smaller room. The film in the larger room was watched by a total of 56 people. The film in the smaller room was watched by 67 people. How many more people saw the film in the larger room? ) a) b) Page 6

22 Clip 7 Long Multiplication ) Work out a) 8 d) 64 4 g) b) 5 7 e) 6 4 h) 48 4 c) 6 4 f) 8 59 i) ) MathsWatch Travel has 6 coaches. Each of these coaches can carry 5 passengers. How many passengers in total can all the coaches carry? ) MathsWatch Tours has a plane that will carry 47 passengers. To fly from Manchester to Lyon, each passengers pays 65 Work out the total amount that the passengers pay. 4) A litre of petrol costs 86p. Work out the cost of 5 litres of petrol. Give your answer in pounds ( ). 5) Last week, MathsWatch posted 49 parcels. Each parcel needed a 97p stamp. Work out the total cost of the stamps. Give your answer in pounds ( ). 6) A stationery supplier sells rulers for p each. MathsWatch college buys 455 of these rulers. Work out the total cost of these 455 rulers. Give your answer in pounds ( ). 7) A Maths book costs.99 Mr Smith buys a class set of 6 books. Work out the total cost of the 6 books. 8) The cost of a calculator is 7.9 Work out the cost of of these calculators. 9) Salvatore makes pizzas. He receives an order for 4 pizzas. Salvatore charges.55 for each pizza. Work out the total amount he would charge for 4 pizzas. 0) A ream of tracing paper costs. Work out the cost of 45 reams of tracing paper. Page 7

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

24 Clip 9 Multiplication and Division with Decimals ) Work out a) 6 0. d) b) e) c) f).5 0. ) A box contains 7 books, each weighing.5 kg. Work out the total weight of the box. ) John takes boxes out of his van. The weight of each box is 5.5 kg Work out the total weight of the boxes. 4) Work out a) 9 0. d) b) 6 0. e) 0. c) 0.4 f) ) Work out a) d) b) e) c) f) ) John takes boxes out of his van. The total weight of the boxes is 4.9 kg The weight of each box is 0.7 kg Work out the number of boxes in John s van. 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. Page 9

25 Clip 0 Decimal Places and Significant Figures ) Round the following numbers to decimal place a).68 b) c) 0.76 ) Round the following numbers to decimal places a) b) c) 46.6 ) Round the following numbers to significant figure a) 45 b) 6 c) ) Round the following numbers to significant figure a) 96 b) 956 c) 996 5) Round the following numbers to significant figure a) b) c) ) Round the following numbers to significant figures a) 7505 b) c) 964 7) Round the following numbers to significant figures a) b) c) ) Round the following numbers to significant figures a) 946 b) c) 996 9) Use a calculator to work out the following sums. Give all answers to significant figures. a) 6 49 b) c) d) e) f) Page 0

26 Clip Half-Way Values ) Which number is in the middle of a) and 9 b) and 8 c) and d) 7 and e) 7 and 08 f) and 00 g) 6 and h) 9 and i). and.8 j) 5.7 and 6. k) 58. and 7.5 ) a) 7 is in the middle of and which other number? b) 6 is in the middle of 9 and which other number? c).4 is in the middle of. and which other number? Page

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

28 Clip Proportion ) 8 bananas cost.60 Work out the cost of 5 bananas. Calculator Non-Calculator ) Emily bought 4 identical pairs of sock for.60 Work out the cost of 9 pairs of these socks. ) The price of a box of chocolates is 7.0 There are 6 chocolates in the box. Work out the cost of one chocolate. 4) Theresa bought 5 theatre tickets for 60 Work out the cost of 9 theatre tickets. 5) Jenny buys 4 folders. The total cost of these 4 folders is 6.40 Work out the total cost of 7 of these folders. 6) The cost of 5 litres of petrol is Work out the cost of 0 litres of petrol. 7) maths books cost 7.47 Work out the cost of 5 of these. 8) Five litre tins of paint cost a total of Work out the cost of seven of these litre tins of paint. 9) William earns 9.0 for hours of work. Work out how much he would earn for: a) 0 minutes b) 5 hours 0) It took hour for Emyr to lay 50 bricks. He always works at the same speed. How long will it take Emyr to lay 70 bricks? Give your answer in hours and minutes. Page

29 Clip 4 Distance Tables ) The table shows the distances in kilometres between some cities in the USA. San Francisco 487 New York 4990 Miami Los Angeles Chicago a) Write down the distance between San Francisco and Miami. One of the cities in the table is 454 km from Los Angeles. b) Write down the name of this city. c) Write down the name of the city which is furthest from Chicago. ) The table shows the distances in miles between four cities. London 55 Cardiff 45 York Edinburgh a) Write down the distance between London and York. b) Write down the distance between Edinburgh and Cardiff. c) Which two cities are the furthest apart? Tom travels from London to York. He then travels from York to Edinburgh. He finally travels back to London from Edinburgh. d) Work out the total distance travelled by Tom. Peter and Jessica both drive to York. Peter travels from London whilst Jessica travels from Cardiff. e) Who travels the furthest out of Peter and Jessica and by how much? Page 4

30 Clip 5 Timetables ) Change the following to the 4 hour clock a) 4.0 pm d) 7.5 pm b) 5 am e) Quarter past midnight c) 0.6 am f) Half past noon ) Change the following to the hour clock a) 06 5 d) 9 5 b) 4 0 e) c) 45 f) Half past midnight ) What is the difference in hours and minutes between the following a) 0.5 pm and.0 pm b) 4 0 and 7 0 c).50 pm and.0 am d) 45 and ) Here is part of a train timetable Manchester Stockport Macclesfield Stoke Stafford Euston a) Tim catches the train from Manchester. At what time should he expect to arrive at Euston? b) Jenny arrives at the Stockport train station at (i) How long should she expect to wait for a train to Stoke? (ii) How long should her train journey take? c) Sarah needs to travel to Euston from Macclesfield. She has to arrive at Euston before What is the departure time of the latest train she can catch to get there on time? Page 5

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

32 Clip 7 Line Graphs ) The graph shows the number of ice creams sold each day during one week. 00 Number of ice creams sold Sun Mon Tue Wed Thu Fri Sat Day a) How many more ice creams were sold on Sunday than on Friday? b) Explain what might have happened on Monday. c) On Saturday, 50 ice creams were sold. Update the graph with this information. d) About how many ice creams were sold on Wednesday? ) The average temperature, in degrees Centigrade, was recorded for each month. The results are as follows: January 5 C February C March 8 C April C May 5 C June C July 4 C August 9 C September 0 C October C November 8 C December 6 C Draw a line graph to show these results. 0 Temperature in C 0 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Page 7

33 Clip 8. Write down the coordinates of the points A to H. 0 Coordinates y 9 8 B A C E 4 D F H O G x. a) Write down the coordinates of: (i) A (ii) B b) Write down the coordinates of the midpoint of the line AB. y B A. Using the pair of axes, a) Plot the points A(, 0), B(4, 0), C(5, ) and D(, ). b) Join the points in order, to form a shape and name the shape. M is the midpoint of the line segment AC. c) Find the coordinates of M. O y 5 4 x 4. Using the same pair of axes, a) Plot the points R(-, -), S(, ) and T(-, ). b) Join R to S and S to T. RSTU is a kite. c) Write the coordinates of point U O x Page 8

34 Clip 9 Number Sequences ) Here are some patterns made from matchsticks Pattern Pattern Pattern a) Draw pattern 4. b) How many matchsticks are used in (i) Pattern 5 (ii) Pattern 0 c) Which pattern will have 46 matchsticks? ) A pattern is made of rectangles and circles Pattern Pattern Pattern a) Draw pattern 4. b) Complete the table below. Pattern number Number of rectangles Number of circles 4 Total rectangles + circles 6 c) Which pattern will have 64 circles? d) Which pattern will have a total (rectangles + circles) of 90? ) For each of the following sequences write down the next two terms. a) 5, 0, 5, 0... c) 7,, 9, 5... b) 9, 6,, 0... d), 7,,... 4) Look at this number sequence:4, 0, 6,... The 50 th term of the sequence is 98. a) Write down the 5 st term. b) Will 64 be a term in this sequence? Explain your answer. Page 9

35 Clip 0 Number Machines ) Here is a table for the rule then then Input Output Complete the table. ) Here is the table for the rule +5 then +5 then Input Output Complete the table. ) Here is a table for the rule 4 then then 4 then then Input Output Complete the table. Page 0

36 Clip Angles ) a) One of these angles is an acute angle. Which one? b) Write the names of the other three angles next to them. A B C D ) a) Sketch a triangle which has three internal (inside) acute angles. b) Sketch a right-angled triangle. c) Sketch a triangle with one internal obtuse angle. ) Debbie says she is going to draw a triangle with two internal obtuse angles. Harry says that this is impossible. Is Harry correct? Explain why. 4) Draw a quadrilateral with a) Two internal acute angles, one reflex angle and one obtuse angle. b) Three internal acute angles and one reflex angle. Page

37 Clip Congruent and Similar Shapes A B C D E F G H I J Congruent to Similar to Fill in the table on the left. You are allowed to use tracing paper to help get the correct answers. A B C D E F H G I J Page

38 Clip Perimeter and Areas ) Find the perimeter of the following rectangle and pentagon: 4 cm 4 cm 4 cm 6 cm 4.5 cm 4.5 cm ) A rectangle has a perimeter of 40 cm. The length of the longest side is cm. Sketch the rectangle, and find the length of the shorter side. cm ) Find the area of the following rectangles: 4 cm 8 cm. cm 6. cm 7 cm.5 cm 4) A rectangle has an area of 40cm and a length of 8 cm. Sketch the rectangle and find the width. 5) Why can t we find the area of this parallelogram? 5 cm 8 cm 6) What is the area of the parallelogram, below? 4 cm 9 cm 7) Find the area of the following triangles: 6 cm 8 cm 0 cm 0 cm 6.4 cm 4 cm 8) The area of a triangle is 60 cm The base of the triangle is cm long. Sketch a triangle with this area and base and work out the height of the triangle. Page

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

40 Clip 5 Converting Metric Measures ) Complete this table by writing down a sensible unit for each measurement. Four have been done for you. The distance between London and Manchester The length of a pen The weight of your Maths Teacher The amount of petrol in a car The length of an ant Metric cm Imperial miles pounds gallons ) Change the following measurements: a) 4 cm to mm d) 0 cm to mm g) km to m b) 7 m to cm e) 5 m to mm h) km to cm c) 5 m to mm f) 4 m to cm i) km to m ) Change the following measurements: a) 00 cm to m d) 6 cm to m g) 486 cm to m b) 4 mm to cm e) 4 cm to m h) 549 mm to cm c) 745 mm to m f) 500 m to km i) 0. km to m 4) Change the following measurements: a) 5 m to cm d) 8. m to cm g) 5. m to cm b) 8 cm to mm e) 70 mm to cm h) 5478 mm to cm c) 50 cm to m f) 8 m to cm i) 8000 cm to m Page 5

41 Clip 6 Triangles, Quadrilaterals, Polygons For each of the shapes A to N, below: a) Name the shape. b) Mark on the shape, or write in words, the features that make it special. eg) Shape A is a square because it has four equal sides and four right angles. A B C D E F G G H J K I M L N Page 6

42 Clip 7 Names of Solids ) Draw a sketch of each of the following solids: a) A cube. b) A cylinder. ) Write down the mathematical name of each of these -D shapes. a) b) c) ) Look at this solid. a) What is its name? b) How many vertices does it have? c) How many edges are there? d) How many faces does it have? 4) This is a picture of a pentagonal prism. a) How many faces does it have? b) How many edges does it have? c) How many vertices does it have? Page 7

43 Clip 8 Tessellations ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. ) On the grid below, show how the shaded shape will tessellate. You should draw at least six shapes. Page 8

44 Clip 9 Isometric Drawing ) Copy the shape below, onto the isometric grid. 4 cm cm 5 cm ) The shape below, is made out of cm by cm by cm cubes. Copy the shape onto the isometric grid. 4 cm 6 cm cm Page 9

45 Clip 40 The Probability Scale ) a) On the probability scale below, mark with a cross ( ) the probability that it will snow in Birmingham in July. 0 b) On the probability scale below, mark with a cross ( ) the probability that it will rain in Wales next year. 0 c) On the probability scale below, mark with a cross ( ) the probability that you will get a tail when you flip a fair coin. 0 d) On the probability scale below, mark with a cross ( ) the probability that you will get a number bigger than 4 when you roll an ordinary dice. 0 ) 4 jelly babies are in a bag. are red, is green and is black. Without looking in the bag, a jelly baby is taken out. a) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green. 0 b) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is green or black. 0 c) On the probability scale below, mark with a cross ( ) the probability that the jelly baby taken from the bag is red or black. 0 Page 40

46 Clip 4 The Averages ) 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. c) Work out the range of her scores. ) 0 students scored goals for the school football team. The table gives information about the number of goals they scored. Goals scored Number of students a) Write down the modal number of goals scored. b) Work out the range of the number of goals scored. c) Work out the mean number of goals scored. 4) Laura spun a 4-sided spinner 00 times. The sides of the spinner are labelled,, and 4. Her results are shown in the table. Score Frequency Work out the mean score. Page 4

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

48 Clip 4 Conversion Graphs ) Use the graph to convert: a) gallons to litres b) 40 litres to gallons c) 5 gallons to litres d) 5 litres to gallons Litres Gallons ) The conversion graph below converts between kilometres and miles. a) Bob travels 50 miles. What is this distance in kilometres? b) Terry travels 00 kilometres. What is this distance in miles? c) The distance between the surgery and the hospital is 5 kilometres. What is this distance in miles? d) Bill completes a 0 mile run. How far is this in kilometres? Distance in miles Distance in kilometres Page 4

49 Clip 44 Factors, Multiples and Primes ) Write the factors of a) 6 b) 6 c) 8 d) 0 ) In a pupil s book the factors of are listed as 4 5 The above list contains a mistake. Cross it out from the list and replace it with the correct number. ) The factors of 0 and 40 are listed 0:,,, 5, 6, 0, 5, 0 40:,, 4, 5, 8, 0, 0, 40 Write the common factors of 0 and 40 (the numbers that are factors of 0 and 40). 4) Write the first four multiples of a) b) 5 c) 0 d) 5 5) In a pupil s book the first 7 multiples of 8 are listed as The above list contains mistakes. Cross them out and replace them with the correct numbers. 6) The first five multiples of 4 and 0 are listed 4: 4, 8,, 6, 0 0: 0, 0, 0, 40, 50 From the two lists above, write the common multiple of 4 and 0. 7) List the first five prime numbers 8) Using just this list of numbers: find the following: a) The prime numbers b) The factors of 8 c) The multiples of Page 44

50 Clips 45, 46 Evaluate Powers, Squares, Cubes & Roots. Evaluate a) 7 b) 4 c) 5 d) e) 6. Work out the square of a) b) c) 4 d) 6 e). Work out a) b) 9 c) 0 d) e) Work out the cube of a) b) c) 5 d) 6 e) Work out a) b) 4 c) 0 6. Work out the square root of a) b) 9 c) 8 7. Work out a) 5 b) 49 c) 8. Work out the cube root of a) 7 b) c) 5 9. From the following numbers Find a) The square numbers b) The cube numbers c) The square root of 64 d) The cube root of 7 0. Match together cards with the same answer Page 45

51 Clips Equivalent Fractions, Simplifying and Ordering Fractions ) Write down three equivalent fractions for each of these a) b) c) ) Match together equivalent fractions ) Find the missing values in these equivalent fractions 4 a) = = = c) 4 0 = = = = b) = = = = d) = = = = ) Write these fractions in their simplest form a) 4 48 b) 8 0 c) 45 6 d) 9 45 e) ) Write these fractions in order of size (smallest first) a) c) b) d) ) Ben spent his pocket money this way: 7 on magazines; on chocolates; on games. 4 Order the items Ben bought by value (largest first). Show all working Page 46

52 Clip 50 Value for Money ) Which of the following offer better value for money? Working must be shown a) 00ml of toothpaste for 50p or 400ml of toothpaste for 90p Without a calculator, please, for question. b) 600g of bananas for 70p or 00g of bananas for p c) litres of paint for.60 or 5 litres of paint for.50 d) 60 teabags for.6 or 40 teabags for 0.96 ) Which of these is the best buy? Working must be shown 0 exercise books for exercise books for 7.80 ) Hamza needs to buy litres of paint. At the shop he gets two choices: 500ml for.55 or litre for Without a calculator, please, for question. a) Work out which of these would be the best buy for Hamza. b) How much does he save if he buys the best buy rather than the worst buy. You must show all your working. 4) Honey pots are sold in two sizes. A small pot costs 45p and weighs 450g. A large pot costs 80p and weighs 850g. Which pot of honey is better value for money? You must show all your working. Page 47

53 Clip 5 Find a Percentage with a Calculator ) Work out a) % of 40 d).5% of 78.6 b) 9% of 700 e) 80.5% of 00 c) 7.5% of 40 f) 7.5% of 5 ) Work out the total cost (including VAT) of the following items. Trainers plus 7.5% VAT Tennis racquet 8.99 plus 7.5% VAT Football boots 57 plus 7.5% VAT ) 850 people attended a festival. 6% of the people were children. Work out the number of children at the festival. Mathswatch Clip 5 Find a Percentage Without a Calculator ) Work out (i) 0% and (ii) 5% and (iii) 5% of: a) 00 b) 0 c) 450 d) 54 ) Work out a) 0% of 80 d) 7.5% of 00 b) 80% of 500 e) 55% of 700 c) 5% of 540 f) 7.5% of 80 ) Work out the total cost (including VAT) of the following items. Video recorder % VAT Tape player % VAT Laptop % VAT 4) There are 00 students at MathsWatch College. 45% of these students are boys. Work out the number of boys. Page 48

54 Clip 5 Change to a Percentage With a Calculator ) In a class of 7 pupils, are boys. a) What percentage of the class are boys? b) What percentage of the class are girls? ) Sarah sat a mock examination and gained the following marks: Subject English Maths Science Mark a) Write each of Sarah s marks as a percentage. b) Which is Sarah s best subject in terms of percentage score? ) A brand new car costs A discount of 7.50 is negotiated with the dealer. What is the percentage discount? MathsWatch Clip 54 Change to a Percentage Without a Calculator ) Write the following as percentages: a) out of 50 d) 4 out of 40 b) 6 out of 0 e) out of 80 c) 7 out of 5 f) 7 out of 60 ) In a football tournament, Team A won 6 of the 0 games they played, whilst team B won 9 of their 5 games. What percentage of their games did they each win? ) 60 participants were invited to a conference. 6 of the participants were females. a) Work out the percentage of female participants. b) What is the percentage of male participants? 4) A company has 800 employees. 440 of these 800 employees are males. 76 of these 800 employees are under 5 years old. a) What percentages of males are employed in this company? b) What percentage of employees are under 5? Page 49

55 Clip 55 Find a Fraction of an Amount. Work out these amounts. a) 4 of 0 b) of 60 kg c) 8 4 d) 50 e) 9 of 80 cm f) g) 60 4 h) 5 8 of 48 i) There are 600 apples on a tree and there are maggots in 5 of them. How many apples have maggots in them?. Liz and Lee are travelling in a car from Glasgow to Poole (770 km). At midday they had already travelled 5 7 of the total distance. What distance, in km, had they travelled by midday? 4. A digital camera that cost 49 was sold on ebay for 7 of the original price. What was the selling price? 5. Yesterday Thomas travelled a total of 75 miles. He travelled 5 of this distance in the morning. How many miles did he travel during the rest of the day? 6. Debra received her 5 pocket money on Saturday. She spent of her pocket money on magazines. She spent 5 of her pocket money on a necklace. How much of the 5 did she have left? Page 50

56 Clip 56 Addition and Subtraction of Fractions. Work out the following giving your answer as a fraction in its simplest form a) 5 + b) c) d) 7 8. Work out the following giving your answer as a fraction in its simplest form a) + b) + c) d) Change the following to mixed numbers a) 8 5 b) 4 c) 5 6 d) Change the following to top heavy (or improper) fractions a) 5 b) 4 c) 6 5 d) Work out the following giving your answer as a fraction in its simplest form a) + 6 b) + c) 4 d) 7 6. Work out the following giving your answer as a fraction in its simplest form a) b) 5 + c) 5 d) e) f) + g) h) Ted received his pocket money on Friday He spent 5 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? 8. Maisie buys a bag of flour. She uses 4 to bake a cake and 5 to make a loaf. a) What fraction of the bag of flour was used? b) What fraction of the bag of flour is left? 9. Work out the total length of this shape. Give your answer as a mixed number. Diagram NOT accurately drawn 4 inches inches Page 5

57 Clip 57 Multiplication and Division of Fractions Work out the following giving your answer as a fraction in its simplest form. ) 4 ) ) ) ) 4 ) ) 5 4) ) 6 5 5) ) 4 6) ) 7) 0 8) 8) 5 5 9) 4 9) ) 5 0) 9 Page 5

58 Clip 58 Change a Fraction to a Decimal Write the following fractions as decimals ) 0 ) 7 0 ) ) 5) 4 6) 5 7) 7 0 8) 9) 8 0) 5 8 Page 5

59 Clip 59 BODMAS Work out ) ) ) 5 4 4) 48 (4 ) 5) 7 ( + 6) 6) ) (9 + ) + 5 8) 4 ( + 4) 6 9) ) ) ) ) ) ) ) 4 7 7) 0 0 ( 5+ 4) 8) Page 54

60 Clip 60 Long Multiplication of Decimals. Work out a) 7 4. b) 5.6 c).. d) e) f) g) h) i) David buys 5 books for 8.75 each. How much does he pay?. A DVD costs.5. Work out the cost of 9 of these DVDs. 4. John takes 7 boxes out of his van. The weight of each box is 4.7 kg. Work out the total weight of the 7 boxes. 5. Nina bought 4 teddy bears at 9.5 each. Work out the total amount she paid. 6. Elliott goes shopping. He buys 0.5 kg of pears at 0.84 per kg..5 kg of grapes at.89 per kg. 6 kg of potatoes at 0.5 per kg. How much does he pay? 7. Brian hires a car for days. Tariffs are: for the first day and 7.50 for each extra day. How much does he pay? Page 55

61 Clips 6, 94 Ratio. Write the following ratios in their simplest form a) 6 : 9 b) 0 : 5 c) 7 : d) 4 : 4 e) : 40 f) 8 : 7 g) 4 : : 8 h) 8 : 6 : 9. Complete the missing value in these equivalent ratios a) : 5 = : b) 4 : 9 = : 7 c) : 7 = 6 : 4 d) : = :. Match together cards with equivalent ratios: : 4 0 : 5 50 : 00 : 5 : 5 : 0 5 : 6 : 4. The ratio of girls to boys in a class is 4 : 5. a) What fraction of the class are girls? b) What fraction of the class are boys? 5. A model of a plane is made using a scale of : 5. a) If the real length of the plane is 0m, what is the length of the model in metres? b) If the wings of the model are 00cm long, what is the real length of the wings in metres? 6. Share out 50 in the following ratios: a) : 4 b) : c) 7 : d) 9 : : 4 7. Share out 80 between Tom and Jerry in the ratio :. 8. A box of chocolates has milk chocolates for every white chocolates. There are 60 chocolates in the box. Work out how many white chocolates are in the box. 9. In a bracelet, the ratio of silver beads to gold beads is 5 :. The bracelet has 5 silver beads. How many gold beads are in the bracelet? 0. To make mortar you mix shovel of cement with 5 shovels of sand. How much sand do you need to make 0 shovels of mortar? Page 56

62 Clip 6 Recipe Type Ratio Questions ) Here are the ingredients for making a vegetable soup for 6 people: carrots onion 800ml stock 50g lentils 4g thyme Work out the amount of each ingredient for a) people b) 9 people c) 0 people. ) Here are the ingredients for making apple crumble for 4 people: 80g plain flour 60g ground almonds 90g sugar 60g butter 4 apples Work out the amount of each ingredient for a) people b) 6 people c) 8 people. ) Here are the ingredients for making 500 ml of parsnip soup: 450g parsnips 00g leeks 50g bramley apples onions pints of chicken stock Work out the amount of each ingredient for a) 500 ml of soup b) 000 ml of soup c) 500 ml of soup. Page 57

63 Clip 6 Hard Calculator Questions ) Find the value of the following: (write down all the figures on your calculator display) a) (0. +.8) b) c) d) 6 ( 7 4) ) Find the value of the following: (write your answers correct to decimal place) 4 a) b) ( 9 + ) c) 4. d) ) Work out a) Write down all the figures on your calculator display. b) Write your answer to part (a) correct to decimal place. 4) Work out ( ) 0. Write down all the figures on your calculator display. 5) Use your calculator to work out the value of a) Write down all the figures on your calculator display. b) Write your answer to part (a) to an appropriate degree of accuracy. Page 58

64 Clip 64 Real-Life Money Questions ) Lance goes on holiday to France. The exchange rate is =.40 Euros. He changes 50 into Euros. a) How many Euros should he get? In France, Lance buys a digital camera for 6 Euros. b) Work out the cost of the camera in pounds. ) Whilst on holiday in Spain, Gemma bought a pair of sunglasses for 77 Euros. In England, an identical pair of sunglasses costs The exchange rate is =.40 Euros. In which country were the glasses the cheapest, and by how much? Show all your working. ) Luke buys a pair of trainers in Switzerland. He can pay either 86 Swiss Francs or 56 Euros. The exchange rates are: =.0 Swiss Francs =.40 Euros Which currency should he choose to get the best price, and how much would he save? Give your answer in pounds ( ). 4) The total cost of 5 kg of potatoes and kg of carrots is kg of potatoes cost.98. Work out the cost of kg of carrots. 5) The cost of 4 kg of bananas is The total cost of kg of bananas and.5 kg of pears is 5.6. Work out the cost of kg of pears. Page 59

65 Clip 65, Nth Term. Write down the first 5 terms and the 0 th term of the following sequences: eg. n +, 5, 7, 9,... a) n + d) 7n b) n + e) n c) n + f) 7n. Find the n th term of the following sequences: a) 5, 0, 5, 0... d), 8, 4, 0... b) 5, 8,, 4... e),, 9, 5... c), 8, 5,... f) 4,, 6,.... Here are some patterns made from sticks. Pattern Pattern Pattern a) Draw pattern 4 in the space, below.. b) How many sticks are used in (i) pattern 0 (ii) pattern 0 (iii) pattern 50 c) Find an expression, in terms of n, for the number of sticks in pattern number n. d) Which pattern number can be made using 0 sticks? Page 60

66 Clip 66 Substitution ) Work out the value of 5x when a) x = b) x = 6 c) x = 0 ) Work out the value of x when a) x = b) x = 0 c) x = ) Work out the value of x when a) x = b) x = 4 c) x = 0 4) Work out the value of x when a) x = 5 b) x = 4 c) x = 0 5) Work out the value of x + 5 when a) x = b) x = 6 c) x = 6) Work out the value of 4 + x when a) x = 7 b) x = c) x = 7) Work out the value of x + y when a) x = and y = b) x = 4 and y = c) x = 5 and y = 4 8) Work out the value of 6x y when a) x = and y = b) x = and y = c) x = and y = 4 9) Work out the value of x + 4y when a) x = and y = 5 b) x = and y = c) x = and y = 0) Using the formula P = H R, where P is the total pay, H is the number of hours worked, and R is the hourly rate of pay. Work out the total pay (P) of the following people: a) Betty worked 0 hours at 7 per hour b) John worked 5 hours and is paid 9 per hour c) Mike worked for 90 minutes at 6 an hour. ) The equation of a straight line is given as y = x + a) Work out the value of y when (i) x = 0 (ii) x = (iii) x = b) What is the value of x when y = 7? Page 6

67 Clip 67 Parallel Lines ) Line PQ is parallel to line RS If angle PQR is equal to 6 a) What is the size of angle QRS? b) Give a reason for your answer. P 6 Q R S ) Line DCE is parallel to line AB a) Find the size of angle ABC b) Find the size of angle DCA c) Calculate the size of angle ACB D C E A 68 B ) a) Find the size of angle DBF b) Find the size of angle HGC D E C 6 54 F B G H Page 6

68 Clips 68, 69 Angle Sum of Triangles - of ) Work out the size of the angles marked with letters. 0 b 0 70 a c 0 d e f ) Work out the size of the angles marked with letters. a b c 55 d e f g 45 0 h i j j ) Work out the size of the angles marked with letters. 00 a b c 70 d f 50 e 70 g Page 6

69 Clips 68, 69 ) ABC is a triangle. a) Find the size of angle A. Angle Sum of Triangles - of C 60 Diagram NOT accurately drawn b) Triangle ABC is equilateral. Explain why. A 60 B ) BCD is a triangle. ABC is a straight line. Angle CBD = 70. BD = CD. a) (i) Work out the value of x. D y Diagram NOT accurately drawn (ii) Give a reason for your answer. x 70 A B C b) (i) Work out the value of y. (ii) Give reasons for your answer. ) The diagram shows a 5-sided shape. All the sides of the shape are equal in length. a) (i) Find the value of x. (ii) Give a reason for your answer. y x Diagram NOT accurately drawn b) (i) Work out the value of y. (ii) Explain your answer. Page 64

70 Clip 70 Angles of Regular Polygons ) a) Work out the size of an exterior angle of a regular hexagon. b) Work out the size of an interior angle of a regular hexagon. ) a) Name the regular polygon, above. b) Work out the size of an exterior angle and of an interior angle for this polygon. ) The size of each exterior angle of a regular polygon is 90. Work out the number of sides of the regular polygon. 4) The size of each exterior angle of a regular polygon is 40. Work out the number of sides of the regular polygon. 5) The size of each interior angle of a regular polygon is 0. Work out the number of sides of the regular polygon. 6) The size of each interior angle of a regular polygon is 50. Work out the number of sides of the regular polygon. Page 65

71 Clip 7 Area of Circles ) Find the areas of the following shapes. Take to be.4 Diagrams NOT accurately drawn a) b) c) cm 5m 8cm ) Work out the areas of the following shapes. a) mm b) 0cm ) The diagram shows a circular garden comprising a rectangular pond enclosed by grass. The circular garden has a diameter of 0 m. The rectangular pond measures 8 m by 6 m. Work out the area of the garden covered in grass. Take to be.4 and give your answer to the nearest m. 8 m 6 m 4) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the area of the top of the table. b) Work out the area of the base of the table. 5) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 7 cm. Calculate the area of the shape. Give your answer correct to significant figures. cm 7 cm Page 66

72 Clip 7 Circumference of Circles ) Find the circumference of the following shapes. Take to be.4. Diagrams NOT accurately drawn a) b) c) cm 5 m 8 cm ) Work out the perimeter of the following shapes, taking to be.4. a) mm b) 0 cm ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the circumference of the top of the table. Let be.4 b) Work out the circumference of the base of the table. Let be.4 4) The diameter of a wheel on Kyle s bicycle is 0.75 m. a) Calculate the circumference of the wheel. Give your answer correct to decimal places. Kyle cycles 000 metres. b) Using your answer in (a), calculate the number of complete turns the wheel makes. 5) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 5 cm. Calculate the perimeter of the shape. Give your answer correct to significant figures. cm 5 cm Page 67

73 Clip 7 Area of Compound Shapes ) Find the area of each shape. a) b) cm 0 cm 0 cm 4 cm cm 8 cm 8 cm 5 cm 5 cm c) d) 4 m 6 m 6 mm 9 m 5 mm 9 mm 6 mm mm ) Find the shaded area of each shape. a) b) cm cm cm 6 cm 7 cm 7 cm 4 cm 0 cm c) d) 6 mm mm mm mm 4 mm m 0 mm m Page 68

74 Clip 74 Rotations y ) 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 5 4 T O x y ) Describe fully the single transformation which maps triangle T to triangle U. 5 4 T U O x Page 69

75 Clip 75 Reflections y = -x 5 y ) a) Reflect triangle T in the x axis. Label your new triangle U. 4 T b) Reflect triangle T in the line with equation y = -x. Label your new triangle V. x O y ) a) Describe fully the single transformation which maps triangle T to triangle U. T 4 b) Describe fully the single transformation which maps triangle T to triangle V O 4 5 x - - U - V -4-5 Page 70

76 Clip 76 Enlargements 5 y ) a) Enlarge triangle T by scale factor using point (-5, ) as the centre of enlargement. Label your new triangle U. b) Enlarge triangle V by scale factor a half using the point (-, -) as the centre of enlargement. Label your new triangle W. 4 T O x - - V -4-5 ) Describe fully the single transformation which maps triangle S to triangle T y S O T x Page 7

77 Clip 77 Translations ) -4 a) Translate triangle T by vector and label it U b) Translate triangle T by vector - and label it V y T O x - - ) a) Describe fully the single transformation which maps triangle A to triangle B. b) Describe fully the single transformation which maps triangle A to triangle C. y A B O x - - C Page 7

78 Clip 78 Find the Mid-Point of a Line ) Find the midpoint of A and B where A has coordinates (-, 5) and B has coordinates (4, -). y O x - ) Find the midpoint of A and B where A has coordinates (, 0) and B has coordinates (8, 6). ) Find the midpoint of A and B where A has coordinates (-4, -) and B has coordinates (, 4). 4) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (7, 5). 5) Find the midpoint of A and B where A has coordinates (, -5) and B has coordinates (7, 4). 6) Find the midpoint of A and B where A has coordinates (-7, -4) and B has coordinates (-, -). 7) The midpoint of A and B is at (, ). The coordinates of A are (-, 4). Work out the coordinates of B. 8) The midpoint of A and B is at (.5,.5). The coordinates of A are (, 5). Work out the coordinates of B. Page 7

79 Clip 79 Measuring and Drawing Angles ) Measure the following angles: a b d c e f ) Draw the following angles: a) angle ABC = 60 b) angle PQR = 7 c) angle XYZ = 75 X Q B A P Y Page 74

80 Clip 80 Drawing Triangles ) The diagram shows the sketch of triangle ABC. B Diagram NOT accurately drawn 7.4 cm A 8.5 cm 8 C BC = 7.4 cm AC = 8.5 cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on your diagram. ) Use ruler and compasses to construct an equilateral triangle with sides of length 6 centimetres. You must show all construction lines. ) The diagram shows the sketch of triangle PQR. Q Diagram NOT accurately drawn 0.5 cm 7. cm P 9 cm R a) Use ruler and compasses to make an accurate drawing of triangle PQR. b) Measure angle P. Page 75

81 Clip 8 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 76

82 Clip 8 Nets ) Sketch nets of these solids. a) b) ) On squared paper draw accurate nets of these solids. a) Cube b) Cuboid 4 cm 5 cm 4 cm 4 cm 8 cm 6 cm c) Right-angled triangular prism d) Triangular prism 5 cm cm 5 cm 4 cm 8 cm 7 cm 7 cm cm ) The two nets, below, are folded to make cubes. Two other vertices will meet at the the dot, A. Mark them with As. One other vertex will meet the dot B. Mark it with B. a) A b) B Page 77

83 Clip 8 Symmetries ) Draw all the lines of symmetry on the triangle and the rectangle. ) What is the order of rotational symmetry of the two shapes below. S ) The diagram below, shows part of a shape. P The shape has rotational symmetry of order 4 about point P. Complete the shape. 4) On each of the shapes below, draw one plane of symmetry. Page 78

84 Clip 84 Questionnaires and Data Collection ) Claire wants to find how much time pupils spend on their homework. She hands out a questionnaire with the question How much time do you spend on your homework? A lot Not much a) Write down two things that are wrong with this question b) Design a suitable question she could use. You should include response boxes. ) Tony wants to know which type of programme pupils in his class like watching on TV. Design a suitable data collection sheet he could use to gather the information. ) Emma asked 0 people what was their favourite pet. Here are their answers. cat cat hamster cat mouse hamster cat dog dog dog snake hamster cat cat hamster dog cat hamster snake cat Design and complete a suitable data collection sheet that Emma could have used to collect and show this information. Page 79

85 Clip 85 Two-Way Tables. Billy has been carrying out a survey. He asked 00 people the type of water they like to drink (still, sparkling or both). Here are part of his results: Still Sparkling Both Total Male 6 5 Female 0 0 Total 6 00 a) Complete the two-way table. b) How many males were in the survey? c) How many females drink only still water? d) How many people drink only sparkling water?. 90 students each study one of three languages. The two-way table shows some information about these students. French German Spanish Total Female Male 7 Total of the 90 students are male. 9 of the 50 male students study Spanish. a) Complete the two-way table. b) How many females study French? c) How many people study Spanish? Page 80

86 Clip 86 Pie Charts ) Patrick asked some of his colleagues which was their favourite holiday destination. The table shows the results. City Frequency Alicante 8 Paris 7 Ibiza 5 St Lucia Biarritz 9 Draw a pie chart to illustrate the information. ) Brian asked 60 people which region their favourite rugby team came from. The table shows the results. Region Frequency Southern England 9 London Midlands 6 Northern England Total 60 Draw a pie chart to illustrate the information. Diagram accurately drawn ) Sophie represents her monthly expenses using a pie chart. Books Magazines Make up Clothes Eating out Numbers from her table have been rubbed out by mistake. Use the pie chart to complete the table. Angle Clothes 5 Eating out Make up 7 4 Magazines Books Total 80 Page 8

87 Clip 87 Scatter Graphs ) The scatter graph shows some information about the marks of six students. It shows each student s marks in Maths and Science. 40 The table below shows the marks for four more students. Maths Science a) On the scatter graph, plot the information from the table. b) Draw a line of best fit. c) Describe the correlation between the marks in Maths and the marks in Science. Science Another student has a mark of 8 in Science. d) Use the line of best fit to estimate the mark in Maths of this student Maths ) The table below shows the average daily number of hours sleep of 0 children. Age (years) Number of hours sleep The first five results have been plotted on the scatter diagram. 6 a) Plot the next five points. b) Draw a line of best fit. c) Decribe the relationship between the age of the children and their number of hours sleep per day. d) Use your scatter graph to estimate the number of hours sleep for a year old child. Number of hours sleep Age (years) Page 8

88 Clip 88 Frequency Diagrams A class of pupils is asked to solve a puzzle. The frequency table below shows the times taken by the pupils to solve the puzzle. Time (t ) in min Frequency 0 < t 5 5 < t < t < t < t 5 5 a) Draw a frequency diagram to show this information. b) Draw a frequency polygon to show this information. Page 8

89 Clip 89 Stem and Leaf Diagrams ) 6 students sat a Maths test. Here are their marks: Draw a stem and leaf diagram to show this information. ) Pat is carrying out a survey on how tall pupils in her class are. Here are their heights in cm: Draw a stem and leaf diagram to show this information. ) The stem and leaf diagram below, shows information about the times, in minutes, it takes a group of people to eat their breakfast Key: 0 represents 0 minutes. a) How many people are in the group? b) How many people spend 5 minutes or more eating their breakfast? c) Find the median time that it took to eat breakfast. Page 84

90 Clip 90 List of Outcomes ) Three coins are flipped. a) How many possible outcomes are there? b) List all the possible outcomes. ) Two coins are flipped and a dice is rolled. a) How many possible outcomes are there? b) List all the possible outcomes. Mathswatch Clip 9 Mutually Exclusive Events ) If the probability of passing a driving test is 0.54, what is the probability of failing it? ) The probability that a football team will win their next game is. The probability they will lose is. What is the probability the game will be a draw? ) On the school dinner menu there is only ever one of four options. Some of the options are more likely to be on the menu than others. The table shows the options available on any day, together with three of the probabilities. Food Curry Sausages Fish Casserole Probability a) Work out the probability of the dinner option being Fish. b) Which option is most likely? c) Work out the probability that it is a Curry or Sausages on any particular day. d) Work out the probability that it is not Casserole. 4) Julie buys a book every week. Her favourite types are Novel, Drama, Biography and Romance. The table shows the probability that Julie chooses a particular type of book. Type of book Novel Drama Biography Romance Probability x x a) Work out the probability that she will choose a Novel or a Drama. b) Work out the probability that she will choose a Biography or a Romance. The probability that she will choose a Biography is the same as the probability she will choose a Romance. c) Work out the probability that she will choose a Biography. Page 85

91 Clip 9 Overview of Percentages With a calculator ) Find the following to the nearest penny: a) % of 670 b) % of 580 c) 48% of 64 d) % of 7.50 e) 87% of 44 f) 5.7% of 7000 g).8% of 980 h) 4% of 6.4 i) 48.6% of 97.6 j) 78.4% of.8 k) 4.5% of l) 0.57% of Without a calculator ) Find the following: a) 0% of 700 b) 0% of 400 c) 0% of 50 d) 0% of 50 e) 0% of 68 f) 0% of 46 g) 0% of 6.50 h) 0% of.0 i) 0% of 600 j) 0% of 900 k) 60% of 800 l) 0% of 650 m) 40% of 0 n) 5% of 00 o) 5% of 60 p) 65% of 000 q) 45% of 64 r) 85% of 96 s) 7.5% of 800 t) 7.5% of 40 u) 7.5% of 8.80 With a calculator ) Change the following to percentages: a) 6 out of 8 b) 8 out of 7 c) 4 out of 8 d) 4 out of 96 e) 7 out of 40 f) 4 out of 659 g) 87 out of 90 h) 4.7 out of i) 6.9 out of 79 j) 4.8 out of.6 k) 65.8 out of 0.7 l) out of 4 Without a calculator 4) Change the following to percentages: a) 46 out of 00 b) 8 out of 50 c) 7 out of 5 d) out of 5 e) 9 out of 0 f) 6 out of 0 g) 7 out of 0 h) 9.5 out of 0 i) 0 out of 40 j) 6 out of 40 k) 0 out of 40 l) out of 40 m) 8 out of 80 n) out of 80 o) 60 out of 80 p) out of 5 q) 4 out of 5 r) 5 out of 75 s) 4 out of 75 t) 0 out of 75 No calculator 5) A shop gives a discount of 0% on a magazine that usually sells for.80. Work out the discount in pence. With a calculator 6) A television costs 595 plus VAT at 7.5%. Work out the cost of the television including VAT. With a calculator 7) Peter has 8 trees in his garden. 6 of the trees are pear trees. What percentage of the trees in his garden are pear trees? With a calculator 8) A battery operated car travels for 0m when it is first turned on. Each time it is turned on it travels 90% of the previous distance as the battery starts to run out. How many times does the car travel at least 8 metres? With a calculator 9) Jane scored 7 out of 4 in a Maths test and 9 out of 6 in a Science test. What were her percentages in both subjects to decimal place? 0) ) ) No calculator In class 7A there are 7 girls and 8 boys. What percentage of the class are girls? No calculator A shop decides to reduce all the prices by 5%. The original price of a pair of trainers was 70. How much are they after the reduction? No calculator VAT at 7.5% is added to the price of a car. Before the VAT is added it cost How much does it cost with the VAT? Page 86

92 Clip 9 Increase/Decrease by a Percentage ) Increase: a) 500 by 0% c) 80 by 5% b) 0 by 0% d) 75 by 0% Calculator Non-Calculator ) Decrease: a) 400 by 0% c) 40 by 5% b) 80 by 0% d) 5 by 0% ) The price of laptop is increased by 5%. The old price of the laptop was 00. Work out the new price. 4) The price of a 6800 car is reduced by 0%. What is the new price? 5) Increase: a) 65 by % c) 600 by 7.5% b) 0 by % d) 70 by 7.5% 6) Decrease: a) 4 by 5% c) 5 by 8.5% b) 79 by % d) 8900 by 8% 7) The price of a mobile phone is plus VAT. VAT is charged at a rate of 7.5%. What is the total price of the mobile phone? 8) In a sale, normal prices are reduced by 7%. The normal price of a camera is 89. Work out the sale price of the camera. 9) A car dealer offers a discount of 0% off the normal price of a car, for cash. Peter intends to buy a car which usually costs He intends to pay by cash. Work out how much he will pay. 0) A month ago, John weighed 97.5 kg. He now weighs 4.5% more. Work out how much John now weighs. Give your answer to decimal place. Page 87

93 Clips 6, 94 Ratio. Write the following ratios in their simplest form a) 6 : 9 b) 0 : 5 c) 7 : d) 4 : 4 e) : 40 f) 8 : 7 g) 4 : : 8 h) 8 : 6 : 9. Complete the missing value in these equivalent ratios a) : 5 = : b) 4 : 9 = : 7 c) : 7 = 6 : 4 d) : = :. Match together cards with equivalent ratios: : 4 0 : 5 50 : 00 : 5 : 5 : 0 5 : 6 : 4. The ratio of girls to boys in a class is 4 : 5. a) What fraction of the class are girls? b) What fraction of the class are boys? 5. A model of a plane is made using a scale of : 5. a) If the real length of the plane is 0m, what is the length of the model in metres? 4m b) If the wings of the model are 00cm long, what is the real length of the wings in metres? 5m 6. Share out 50 in the following ratios: a) : 4 b) : c) 7 : d) 9 : : 4 7. Share out 80 between Tom and Jerry in the ratio :. 8. A box of chocolates has milk chocolates for every white chocolates. There are 60 chocolates in the box. Work out how many white chocolates are in the box. 9. In a bracelet, the ratio of silver beads to gold beads is 5 :. The bracelet has 5 silver beads. How many gold beads are in the bracelet? 0. To make mortar you mix shovel of cement with 5 shovels of sand. How much sand do you need to make 0 shovels of mortar? Page 88

94 Clip 95 Product of Prime Factors ) List the first seven prime numbers. ) Express the following number as the product of their prime factors: a) 0 b) 60 c) 60 d) 0 ) Express the following number as the product of powers of their prime factors: a) 4 b) 64 c) 9 d) 75 4) 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. 5) The number 75 can be written as 5 x y, where x and y are prime numbers. Find the value of x and the value of y. Mathswatch Clip 96 HCF and LCM ) Find the Highest Common Factor (HCF) of each of these pairs of numbers. a) 6 and 4 b) and 8 c) 60 and 50 d) 96 and 08 ) Find the Least (or Lowest) Common Multiple (LCM) of each of these pairs of numbers. a) 6 and 4 b) and 8 c) 60 and 50 d) 96 and 08 ) a) Write 4 and 6 as products of their prime factors. b) Work out the HCF of 4 and 6. c) Work out the LCM of 4 and 6. 4) a) Write 40 and 500 as products of their prime factors. b) Work out the HCF of 40 and 500. c) Work out the LCM of 40 and 500. Page 89

95 Clip 97 Standard Form ) Change the following to normal (or ordinary) numbers. a) c) e) b) d) f) ) Change the following to normal (or ordinary) numbers. a) c) e) b) d) f) ) Change the following to standard form. a) 60 c) e) 00 b) d) 6 85 f) ) Change the following to standard form. a) 0.7 c) e) b) d) f) ) Work out the following, giving your answer in standard form. a) d) g) b) e) h) c) f) i) Page 90

96 Clip 98 Recurring Decimals into Fractions ) Write each recurring decimal as an exact fraction, in its lowest terms. a) 05. b) 07. c) 04. d) 04. e) 075. f) 08. g) h) 06. i) 074. j) 04. k) l) Page 9

97 Clip 99 Four Rules of Negatives Work out the following without a calculator a) 6 9 = l) = b) 4 - = m) = c) -0-5 = n) = d) -7-6 = o) = e) 5-5 = p) = f) = q) = g) 7 - = r) + - = h) 6-9 = s) 6-4 = i) = t) = j) -8 4 = u) = k) + - = v) = Mathswatch Clip 00 Division by Two-Digit Decimals ) Work out the following without a calculator a) e) b) 0.5 f) c) g) d) h) ) Sam is filling a jug that can hold.575 litres, using a small glass. The small glass holds 0.05 litres. How many of the small glasses will he need? Page 9

98 Clip 0 Estimating Answers. Work out an estimate for the value of a) b) c) d) a) Work out an estimate for b) Use your answer to part (a) to find an estimate for a) Work out an estimate for b) Use your answer to part (a) to find an estimate for Page 9

99 Clip 0 Algebraic Simplification ) Simplify a) x + x b) x x c) x + x d) x x e) x y + 4x y f) x y xy ) Simplify a) x + y + x + y b) x + y + x + 5y c) 6y + x y x 5) a) Simplify pq + pq b) Simplify 5x + y x 4y 6) a) Simplify 6a + 5b b + a b) Simplify x 4 + x 4 7) a) Simplify x + y + x + y + x b) Simplify t + t + t 8) a) Simplify a a b) Simplify x y 4xy d) 5p q + p + q 9) a) Simplify d + e d + 4e ) Expand and simplify a) (x + y) + (x + y) b) (x + y) + (5x + y) c) 5(x + y) + (x y) d) (c + d) (c + d) e) 4(p + q) (p q) f) (4x y) + (x + y) g) 6(x y) (x 5y) b) Simplify x x c) Simplify 5t + 8d t d d) Simplify 4t q 0) The table shows some expressions. (p + p) p p p + p + p p + p Two of the expressions always have the same value as 4p. Tick the boxes underneath the two expressions. 4) Expand and simplify a) 5(p + ) (4p ) b) 4(x + ) (x ) ) Expand and simplify (i) 4(x + 5) + (x 6) (ii) (x ) (x 4) (iii) 5(y + ) (y + ) Page 94

100 Clip 0 Expanding and Simplifying Brackets ) Expand these brackets a) (x + ) b) (x + 4) c) 5(p q) d) 4(x + y ) e) r(r r ) ) Expand and simplify a) (x + )(x + ) b) (x + )(x + 4) c) (x + )(x + ) ) Expand and simplify a) (x + )(x ) b) (x )(x + 4) c) (x )(x ) 4) Expand and simplify a) (p + )(p ) b) (t )(t + ) c) (x 5)(x ) 5) Expand and simplify a) (x + y)(x + 4y) b) (p + q)(p + q) 6) Expand and simplify a) (x + ) b) (x ) c) (p + q) Page 95

101 Clip 04 Factorisation ) Factorise a) x + 4 b) y + 0 c) x + d) x 6 e) 5x 5 ) Factorise a) p + 7p b) x + 4x c) y y d) p 5p e) x + x ) Factorise a) x + 6x b) y 8y c) 5p + 0p d) 7c c e) 6x + 9x 4) Factorise a) x 4xy b) t + 0tu c) 6x 8xy d) x y + 9xy Page 96

102 Clip 05 Solving Equations Solve the following equations ) p = 0) 4y + = y + 0 ) 4y + = ) x + 7 = 5x 4 ) 6x 7 = ) x + 7 = 6 4x 4) x + x + x + x = 0 ) 5(x + ) = (x + 6) 5) x + x = 40 4) 4(y + ) = ( y) 6) 5(t ) = 0 5) 7 x = (x + ) 7) 4(5y ) = 5 6) x = 5 8) 4(y + ) = 4 7) x + 4 = 7 9) 0x 5 = 8x 7 8) 40 x = 4 + x Page 97

103 Clip 06 Forming Equations ) The width of a rectangle is x centimetres. The length of the rectangle is (x + 5) centimetres. x + 5 x a) Find an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form. The perimeter of the rectangle is 8 centimetres. b) Work out the length of the rectangle. ) x + 80 x + 0 x + 0 Diagram NOT accurately drawn x The sizes of the angles, in degrees, of the quadrilateral are x + 0 x x + 80 x + 0 a) Use this information to write down an equation in terms of x. b) Use your answer to part (a) to work out the size of the smallest angle of the quadrilateral. ) Sarah buys 6 cups and 6 mugs A cup costs x A mug costs (x + ) a) Write down an expression, in terms of x, for the total cost, in pounds, of 6 cups and 6 mugs. b) If the total cost of 6 cups and 6 mugs is 48, write an equation in terms of x. c) Solve your equation to find the cost of a cup and the cost of a mug. Page 98

104 Clip 07 Changing the Subject of a Formula ) Make c the subject of the formula. a = b + cd ) Make t the subject of the formula. u = v + t ) Make n the subject of the formula. M = n +5 4) Make z the subject of the formula. x = y + z 5) r = 5s + t a) Make t the subject of the formula. b) Make s the subject of the formula. 6) Rearrange y = x + to make x the subject. 7) Rearrange y = x+ to make x the subject. 8) Rearrange y = x+ to make x the subject. Page 99

105 Clip 08 Inequalities ) Represent this inequality on the number line - < x < ) Represent this inequality on the number line - < x < ) Write down the inequality shown ) Write down the inequality shown ) If y is an integer, write down all the possible values of - < y < 5 6) If x is an integer, write down all the possible values of -9 < x < -5 Page 00

106 Clip 09 Solving Inequalities ) Solve a) x > 5 b) 7y + 0 c) x d) 5+ x > 7 e) 8< 5p f) y + 5 g) x 5 h) 6x 5> x + i) p 9< 6 p j) 5 y < y 0 ) a) Solve the inequality z + 7 b) Write down the smallest integer value of z which satisfies the inequality z + 7 ) 5x + y < 0 x and y are both integers. Write down two possible pairs of values that satisfy this inequality. x =..., y =... and x =..., y =... Page 0

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

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

109 Clip 65, Nth Term. Write down the first 5 terms and the 0 th term of the following sequences: eg. n +, 5, 7, 9,... a) n + d) 7n b) n + e) n c) n + f) 7n. Find the n th term of the following sequences: a) 5, 0, 5, 0... d), 8, 4, 0... b) 5, 8,, 4... e),, 9, 5... c), 8, 5,... f) 4,, 6,.... Here are some patterns made from sticks. Pattern Pattern Pattern a) Draw pattern 4 in the space, below.. b) How many sticks are used in (i) pattern 0 (ii) pattern 0 (iii) pattern 50 c) Find an expression, in terms of n, for the number of sticks in pattern number n. d) Which pattern number can be made using 0 sticks? Page 04

110 Clip ) a) Complete the table of values for y = x Drawing Straight Line Graphs 5 y x y b) Using the axes on the right draw the graph of y = x c) Use your graph to work out the value of y when x =.5 d) Use your graph to work out the value of x when y = 4.5 ) a) Complete the table of values for y = x x O x y - - b) Using the axes on the right, again, draw the graph of y = x -4-5 ) a) Complete the table of values for y = ½x b) Draw the graph of y = ½x x y 0 y - O 4 x - - c) Use your graph to find the value of y when x =.5 Page 05

111 Clip 4 Finding the Equation of a Straight Line ) Find the equations of lines A, B and C on the axes below 8 y C A B O x ) Find the equations of lines A, B and C on the axes below y C B 6 A O x Page 06

112 Clip 5 Solving Simultaneous Equations Graphically ) On the axes below, the graphs of y = x + and y = 6 x have been drawn. Use the graphs to solve the simultaneous equations y = x + and y = 6 x 8 7 y y = x + 6 y = 6 x 5 4 O x ) On the axes below draw the graphs of y = x + and y = 7 x Use your graphs to solve the simultaneous equations y = x + and y = 7 x y O x Page 07

113 Clip 6 Drawing Quadratic Graphs ) a) Complete the table of values for y = x x x y b) On the grid, draw the graph of y = x x for values of x from - to y O x c) Use the graph to find the value of y when x = -.5 d) Use the graph to find the values of x when y = 4-5 ) a) Complete the table of values for y = x x x y 8 0 b) On the grid, draw the graph of y = x x for values of x from - to y O x -5 c) (i) On the same axes draw the straight line y =.5 (ii) Write down the values of x for which x x =.5 Page 08

114 Clip 7 Real Life Graphs 5 ) Sarah travelled 0 km from home to her friend s house. She stayed at her friend s house for some time before returning home. Here is the travel graph for part of Sarah s journey. 0 Distance from home (km) Time of day a) At what time did Sarah leave home? b) How far was Sarah from home at 0 0? Sarah left her friend s house at 0 to return home. c) Work out the time in minutes Sarah spent at her friend s house. Sarah returned home at a steady speed. She arrived home at 50 d) Complete the travel graph. e) Work out Sarah s average speed on her journey from her home to her friend s house. Give your answer in kilometres per hour. f) Work out Sarah s average speed on her journey home from her friend s house. Give your answer in kilometres per hour. Page 09

115 Clip 8 Pythagoras Theorem ) Find the length of side AC. Give your answer to decimal place. A 4) Below is a picture of a doorway. Find the size of the diagonal of the doorway. Give your answer to decimal place. cm.m 0.8m B 7cm ) Find the length of side QR Give your answer to decimal place. Q 4.8cm P C 5) In the sketch of the rectangular field, below, James wants to walk from B to D. A B 60m R 7.6cm D 50m C Which of the following routes is shorter and by how much? From B to C to D or straight across the field from B to D. Give your answer to the nearest metre. ) Find the length of side SU Give your answer to decimal place. T 4cm cm S 6) Fiona keeps her pencils in a cylindrical beaker as shown below. The beaker has a diameter of 8cm and a height of 7cm. Will a pencil of length 9cm fit in the beaker without poking out of the top? All workings must be shown. U Page 0

116 Clip 9 Pythagoras - Line on a Graph ) Points P and Q have coordinates (, 4) and (5, ). Calculate the shortest distance between P and Q. Give your answer correct to decimal place. y P Q O x ) Points A and B have coordinates (-4, ) and (, -). Calculate the shortest distance between A and B. Give your answer correct to decimal place. y 5 4 A O 4 5 x - - B Page

117 Clip 0 Coordinates in Dimensions ) A cuboid lies on the coordinate axes. y U P Q O T x z R S The point Q has coordinates (5,, 4) a) Write down the coordinates of the point P b) Write down the coordinates of the point T c) Write down the coordinates of the point S d) Write down the coordinates of the point R e) Write down the coordinates of the point U ) A cuboid lies on the coordinate axes. y C A P B x z Point P lies half way between A and B and has coordinates (, 4, 5) a) Write down the coordinates of B. b) Write down the coordinates of C. Page

118 Clip Surface Area of Cuboids ) Find the surface area of this cube and cuboid. Cube 6 cm Cuboid 4 cm 4 cm 4 cm 5 cm 0 cm ) Find the surface area of this cuboid. 0.8 m.7 m. m ) A water tank measures m by m by 4 m. It has no top. The outside of the tank, including the base, has to be painted. Calculate the surface area which will be painted. m 4 m 4) A water tank measures m by 5 m by 6 m. It has no top. The outside of the tank, including the base, has to be painted. A litre of paint will cover an area of 4. m. Paint is sold in 5 litre tins and each tin costs.50. How much will it cost to paint the tank? You must show all your working. m m 6 m 5 m Page

119 Clip Volume of a Prism ) The diagram shows a cuboid. Work out the volume of the cuboid. 50 cm 5 cm 0 cm ) Calculate the volume of this triangular prism. 4 cm 5 cm cm 9 cm ) An ice hockey puck is in the shape of a cylinder with a radius of.8 cm and a thickness of.5 cm. Take to be.4.5 cm Work out the volume of the puck..8 cm 4) A cuboid has: a volume of 80cm a length of 5 cm a width of cm Work out the height of the cuboid. 5) Work out the maximum number of boxes which can fit in the carton. 50 cm Box 0 cm 00 cm Carton 80 cm 0 cm 00 cm Page 4

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

121 Clip 4 Dimensions ) The table shows some expressions. The letters a, b, c and d represent lengths. and are numbers that have no dimensions. Underneath each one write L if it is a length A if it is an area V if it is a volume N if it is none of the above. abc d a a a + b (a + b) (c + d ) ad ) The table shows some expressions. The letters a, b, c and d represent lengths. and are numbers that have no dimensions. Underneath each one write L if it is a length A if it is an area V if it is a volume N if it is none of the above. a ab bc ac + bd d(a + b) (c + d) d bc Page 6

122 Clip 5 Bounds. A silver necklace has a mass of grams, correct to the nearest gram. a) Write down the least possible mass of the necklace. b) Write down the greatest possible mass of the necklace.. Each of these measurements was made correct to one decimal place. Write the maximum and minimum possible measurement in each case. a) 4.6 cm b) 0.8 kg c).5 litres d) 5.0 km/h e) 0. s f) 6. m g) 6.7 m/s h) 0. g. Each side of a regular octagon has a length of 0.6 cm, correct to the nearest millimetre. a) Write down the least possible length of each side. b) Write down the greatest possible length of each side. c) Write down the greatest possible perimeter of the octagon. 4. A girl has a pencil 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. 5. A square has sides of length 7 cm, correct to the nearest centimetre. a) Calculate the lower bound for the perimeter of the square. b) Calculate the upper bound for the area of the square. Page 7

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

124 Clip 7 Bisecting a Line ) Using ruler and compasses, bisect line AB. B A ) Using ruler and compasses a) Bisect line AB b) Bisect line BC c) Bisect line AC d) Place your compass point where your three lines cross* Now open them out until your pencil is touching vertex A. Draw a circle using this radius. C B A * If your three lines don t cross at a point then you have a mistake somewhere or just haven t been accurate enough. Page 9

125 Clip 8 Drawing a Perpendicular to a Line ) Use ruler and compasses to construct the perpendicular to the line segment AB that passes through the point P. You must show all construction lines. B P 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 0

126 Clip 9 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 RSUV 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

127 Clip 0 Loci - page of ) A B D C ABCD is a rectangle. Shade the set of points inside the rectangle which are both more than 4 centimetres from the point D and more than centimetre from the line AB. ) Two radio transmitters, A and B, are situated as below. B A Transmitter A broadcasts signals which can be heard up to km from A. Transmitter B broadcasts signals which can be heard up to 6 km from B. Shade in the area in which radio signals can be heard from both transmitters. Use a scale of cm = km. Page

128 ) Clip 0 A Loci - page of B C Point C is equidistant from points A and B. Sarah rolls a ball from point C. At any point on its path the ball is the same distance from point A and point B. a) On the diagram above draw accurately the path that the ball will take. b) On the diagram shade the region that contains all the points that are no more than cm from point B. ) The map shows part of a lake. In a competition for radio-controlled ducks, participants have to steer their ducksso that: its path between AB and CD is a straight line this path is always the same distance from A as from B a) On the map, draw the path the ducks should take. Scale: cm represents 0 m B C E A There is a practice region for competitors. D This is the part of the lake which is less than 0 m from point E. b) Shade the practice region on the map. Page

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

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

131 Clip 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. a) Explain why. b) Calculate the mean number of goals scored. Goals scored Frequency ) Tina recorded how long, in minutes, she watched TV for each day during a month. a) Find the class interval in which the median lies. b) Work out an estimate for the mean amount of time Tina watched TV each day of this month. Give your answer to the nearest minute. Time (t in minutes) Frequency 0 < t < < t < < t < < t < < t < 90 Page 6

132 Clip 4 Questionnaires ) A survey into how people communicate with each other is carried out. A questionnaire is designed and two of the questions used are shown below. The questions are not suitable. For each question, write down a reason why. a) Do you prefer to communicate with your friend by phone (voice call) or by text message? Yes No Reason b) How many text messages do you send? 4 Reason ) A restaurant owner has made some changes. He wants to find out what customers think of these changes. He uses this question on a questionnaire. What do you think of the changes in the restaurant? Excellent Very good Good a) Write down what is wrong with this question. This is another question on the questionnaire. How often do you come to the restaurant? Very often Not often b) i) Write down one thing that is wrong with this question. ii) Design a better question to use. You should include some response boxes. Page 7

133 Clip 5 Standard Form Calculation ) Work out the following, giving your answer in standard form. a) (6 0 ) (8 0 4 ) c) b) ( 0 5 ) + ( 0 4 ) d) ( ) ( 0 ) ) A spaceship travelled for 5 0 hours at a speed of km/h. a) Work out the distance travelled by the spaceship. Give your answer in standard form. Another spaceship travelled a distance of 0 7 km, last month. This month it has travelled km. b) Work out the total distance travelled by the spaceship over these past two months. Give your answer as a normal (or ordinary) number. ) Work out the following, giving your answer in standard form, correct to significant figures a) c) b) ( ) ( ) d) ) Work out the following, giving your answer in standard form correct to significant figures. a) c) b) d) ) A microsecond is seconds. a) Write the number in standard form. A computer does a calculation in microseconds. b) How many of these calculations can the computer do in second? Give your answer in standard form, correct to significant figures. 6) tomato seeds weigh gram. Each tomato seed weighs the same. a) Write the number in standard form. b) Calculate the weight, in grams, of one tomato seed. Give your answer in standard form, correct to significant figures. Page 8

134 Clip 6 Percentage Increase and Decrease ) A car dealer is comparing his sales over the past two years. In 006, he sold 75 cars. In 007, he sold 96 cars. Work out the percentage increase in the number of cars sold. ) In September 005, the number of pupils attending MathsWatch College was 5. In September 006, the number of pupils attending MathsWatch College was 04. Work out the percentage decrease in the number of pupils attending MathsWatch College. ) The usual price of a shirt is.50 In a sale, the shirt is reduced to 9.5 What is the percentage reduction? 4) Olivia opened an account with 750 at the MathsWatch Bank. After one year, the bank paid her interest. She then had 795 in her account. Work out, as a percentage, MathsWatch Bank s interest rate. 5) Ken buys a house for and sells it two years later for What is his percentage profit? Give your answer to significant figures. 6) Shelley bought some items at a car boot sale and then sold them on ebay. Work out the percentage profit or loss she made on each of these items. a) Trainers bought for 5, sold for 0 b) DVD recorder bought for 4, sold for c) Gold necklace bought for 90, sold for 78.0 d) A DVD collection bought for 0, sold for 8.60 Page 9

135 Clip 7 Compound Interest/Depreciation ) Henry places 6000 in an account which pays 4.6% compound interest each year. Calculate the amount in his account after years. ) Sarah puts 8600 in a bank. The bank pays compound interest of.8% per year. Calculate the amount Sarah has in her account after 4 years. ) Mary deposits 0000 in an account which pays 5.6% compound interest per year. How much will Mary have in her account after 5 years? 4) Susan places 7900 in an account which pays.4% compound interest per year. How much interest does she earn in years? 5) Harry puts money into an account which pays 6% compound interest per year. If he puts 000 in the account for 5 years how much interest will he earn altogether? 6) Laura buys a new car for The annual rate of depreciation is %. How much is the car worth after years? 7) The rate of depreciation of a particular brand of computer is 65% per year. If the cost of the computer when new is 650 how much is it worth after years? 8) Sharon pays 500 for a secondhand car. The annual rate of depreciation of the car is 4% How much will it be worth four years after she has bought it? 9) Dave places 7000 in an account which pays 4% compound interest per year. How many years will it take before he has 9.68 in the bank? 0) A new motorbike costs The annual rate of depreciation is 8% per year. After how many years will it be worth ? Page 0

136 Clip 8 Reverse Percentages ) In a sale, normal prices are reduced by 0%. The sale price of a shirt is 6 Calculate the normal price of the shirt. ) A car dealer offers a discount of 5% off the normal price of a car for cash. Emma pays 60 cash for a car. Calculate the normal price of the car. ) In a sale, normal prices are reduced by %. The sale price of a DVD recorder is Calculate the normal price of the DVD recorder. 4) A salesman gets a basic wage of 60 per week plus a commision of 0% of the sales he makes that week. In one week his total wage was 640 Work out the value of the sales he made that week. 5) Jason opened an account at MathsWatch Bank. MathsWatch Bank s interest rate was 4%. After one year, the bank paid him interest. The total amount in his account was then 976 Work out the amount with which Jason opened his account 6) Jonathan s weekly pay this year is 960. This is 0% more than his weekly pay last year. Tess says This means Jonathan s weekly pay last year was 768. Tess is wrong. a) Explain why b) Work out Jonathan s weekly pay last year. 7) The price of all rail season tickets to London increased by 4%. a) The price of a rail season ticket from Oxford to London increased by.40 Work out the price before this increase. b) After the increase, the price of a rail season ticket from Newport to London was 9.80 Work out the price before this increase. Page

137 Clip 9 Four Rules of Fractions Work out ) + ) 5 ) ) + ) 5 ) ) 5 + ) 8 4 ) + 5 4) 4 + 4) 6 4 4) ) 5) + 5) ) 4 5 6) 9 ( + ) 6) ) 4 4 7) ( + ) 7) ( + ) ) 9 0 8) 7 8) ) 4 9) ) 5 0) ) ) ( + ) 5 Page

138 Clip 40 Solving Quadratic Equations by Factorising ) Factorise and solve the following equations: a) x + 5x + 6 = 0 b) x + 9x + 0 = 0 c) x + x 6 = 0 d) x + 5x 4 = 0 e) x 6x + 8 = 0 f) x x 8 = 0 g) x + 7x + = 0 h) 6x + x + = 0 i) x + x 0 = 0 j) x 4x + 6 = 0 ) Lucy said that - is the only solution of x that satisfies the equation x + x + = 0 Was Lucy correct? Show working to justify your answer ) Ben said that -5 is the only solution of x that satisfies the equation x + 0x + 5 = 0 Was Ben correct? Show working to justify your answer Page

139 Clip 4 Difference of Two Squares x y = (x y)(x + y) ) Factorise a) x 6 c) y 9 e) x 4 b) a b d) x f) x 9 ) Factorise a) x 4y c) 9x 6y e) 4x 5y b) 9a b d) 4 x y f) x 9 y ) Simplify a) y 4 5 y+ y + 5 b) 4x x + x c) x + 8x 9x 4 d) 5a 6b 0ab 8b 4) Solve a) 4x 6 = 0 c) 49x = b) 5x = d) 9x 9 = 7 Page 4

140 Clip 4 Simultaneous Linear Equations ) Solve 4x + y = 6 5x y = ) Solve 4x + y = 9 x 5y = 7 ) Solve x + 5y = x + y = 8 4) Solve x + 4y = 5 4x y = 5) Solve a + b = 4a 5b = 0 6) Solve 5x + y = 4 x + 4y = 9 7) Solve 6x y = x + y = - 8) Solve a b = 4 4a + b = 9) Solve 5x + 4y = 5 x + 7y = 9 0) Solve 6x 4y = 9 x + y = 6 Page 5

141 Clip 4 Understand y = mx + c gradient cuts the y-axis ) a) Find the equation of line A. b) Draw the line B, with equation y = x. c) Draw the line C, with equation y = x. y A O x - - ) A straight line passes through points (0, 4) and (, ). What is its equation? ) A straight line passes through points (0, 7) and (, -). What is its equation? 4) A straight line is parallel to y = x and goes through (, 8). What is its equation? 5) A straight line is parallel to y = x + 5 and goes through (5, 6). What is its equation? 6) A is the point (-, ). B is the point (, 6). C is the point (0, -). Find the equation of the line which passes through C and is parallel to AB. A (-, ) C (0, -) B (, 6) Page 6

142 Clip 44 Regions ) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities x > y > x x + y < 7 y O x ) On the grid below, draw straight lines and use shading to show the region R that satisfies the inequalities y > x + y < 5 x > y O x Page 7

143 Clip 45 ) a) Complete this table of values for y = x + x 4 x y 4 0 b) On the grid, draw the graph of y = x + x 4 Cubic and Reciprocal Functions O - -4 y x c) Use the graph to find the value of x when y = ) a) Complete this table of values for y = x + x x 0 8 y 0 4 b) On the grid, draw the graph of y = x + x c) Use the graph to find the value of x when y = O ) Sketch the graph of y = + in your book. x Page 8

144 Clip 46 Recognise the Shapes of Functions Match each of the functions below, with the correct sketch of its graph. y = x y = - x y = x y = x y = x + y = x y = 5x x y = -x Page 9

145 Clip 47 Trigonometry ) PQR is a right-angled triangle. PR = cm. QR = 4.5 cm Angle PRQ = 90 Q 4.5 cm Work out the value of x. Give your answer correct to decimal place. P x cm R ) AC = 4 cm. Angle ABC = 90 Angle ACB = 4 A 4 cm Calculate the length of BC. Give your answer correct to significant figures. B 4 C ) PQR is a right-angled triangle. PQ = 8 cm. QR = 8.4 cm Angle PRQ = 90 8 cm Q 8.4 cm Work out the value of x. Give your answer correct to decimal place. P x R 4) AB = cm. Angle ABC = 90 Angle ACB = Calculate the length of AC. Give your answer correct to significant figures. cm A B C 5) A lighthouse, L, is.4 km due West of a port, P. A ship, S, is.8 km due North of the lighthouse, L. Calculate the size of the angle marked x. Give your answer correct to significant figures. S N.8 km N L.4 km x P Page 40

146 Clip 48 Bearings by Trigonometry ) Crowdace N Diagram NOT accurately drawn. 7.6 km Appleby 9.8 km Brompton Appleby, Brompton and Crowdace are three towns. Appleby is 9.8 km due west of Brompton. Brompton is 7.6 km due south of Crowdace. a) Calculate the bearing of Crowdace from Appleby. Give your answer correct to decimal place. b) Calculate the bearing of Appleby from Crowdace. Give your answer correct to decimal place. ) Froncham Diagram NOT accurately drawn. N Denton. km Egleby Denton, Egleby and Froncham are three towns. Egleby is. km due East of Denton. Froncham is due north of Denton and on a bearing of 0 from Egleby. Calculate the distance between Froncham and Egleby. Give your answer correct to decimal place. Page 4

147 Clip 49 Similar Shapes ) BE is parallel to CD. AB = cm, BC = cm, CD = 7 cm, AE = 8 cm. A a) Calculate the length of ED. b) Calculate the length of BE. cm 8 cm cm B E Diagram NOT accurately drawn. C 7 cm D ) Diagram NOT accurately drawn. A B Two prisms, A and B, are mathematically similar. The volume of prism A is 6000 cm. The volume of prism B is 88 cm. The total surface area of prism B is cm. Calculate the total surface area of prism A. ) P and Q are two geometrically similar solid shapes. The total surface area of shape P is 540 cm. The total surface area of shape Q is 960 cm. The volume of shape P is 700 cm. Calculate the volume of shape Q. Page 4

148 Clip 50 ) In the diagram, A, B and C are points on the circumference of a circle, centre O. PA and PB are tangents to the circle. Angle ACB = 7. a) (i) Work out the size of angle AOB. (ii)give a reason for your answer. b) Work out the size of angle APB. Circle Theorems B O C 7 A Diagram NOT accurately drawn P ) P, Q, R and S are points on the circle. PQ is a diameter of the circle. Angle RPQ =. S b R a) (i) Work out the size of angle PQR. (ii) Give reasons for your answer. P a Q b) (i) Work out the size of angle PSR. (ii)give a reason for your answer. ) The diagram shows a circle, centre O. AC is a diameter. Angle BAC =. D is a point on AC such that angle BDA is a right angle. B Diagram NOT accurately drawn a) Work out the size of angle BCA. Give reasons for your answer. A O D C b) Calculate the size of angle DBC. c) Calculate the size of angle BOA. 4) A, B, C and D are four points on the circumference of a circle. ABE and DCE are straight lines. Angle BAC =. Angle EBC = 58. a) Find the size of angle ADC. A B 58 Diagram NOT accurately drawn b) Find the size of angle ADB. Angle CAD = 69. c) Is BD a diameter of the circle? You must explain your answer. D C E Page 4

149 Clip 5 Cumulative Frequency The heights of 80 plants were measured and can be seen i n the table, below. Height (cm) Frequency 0 < h < 0 0 < h < < h < < h < < h < < h < 60 a) Complete the cumulative frequency table for the plants. Height (cm) 0 < h < 0 0 < h < 0 0 < h < 0 0 < h < 40 0 < h < 50 Cumulative Frequency CF 80 0 < h < 60 b) Draw a cumulative frequency graph for your table c) Use your graph to find an estimate for (i) the median height of a plant. (ii) the interquartile range of the heights of the plants. 40 d) Use your graph to estimate how many plants had a height that was greater than 45cm Height (cm) Page 44

150 Clip 5 Box Plots ) The ages of 0 teachers are listed below.,, 4, 5, 7, 7, 8, 9, 9, 9, 4, 5, 4, 4, 44, 49, 55, 57, 58, 58 a) On the grid below, draw a boxplot to show the information about the teachers b) What is the interquartile range of the ages of the teachers? ) A warehouse has 60 employees working in it. The age of the youngest employee is 6 years. The age of the oldest employee is 55 years. The median age is 7 years. The lower quartile age is 9 years. The upper quartile age is 4 years. On the grid below, draw a boxplot to show information about the ages of the employees Page 45

151 Clip 5 Moving Averages ) The table shows the number of board games sold in a supermarket each month from January to June. Jan Feb Mar Apr May Jun Work out the -month moving averages for this information.,,, ) The table shows the number of computers sold in a shop in the first five months of 007. Jan Feb Mar Apr May June x a) Work out the first two -month moving averages for this information., b) Work out the first 4-month moving average for this information. The third 4-month moving average of the number of computers sold in 007 is 96. The number of computers sold in the shop in June was x. c) Work out the value of x. Page 46

152 Clip 54 Tree Diagrams ) Lucy throws a biased dice twice. Complete the probability tree diagram to show the outcomes. Label clearly the branches of the tree diagram. st Throw nd Throw 6 Six... Not Six ) A bag contains 0 coloured balls. 7 of the balls are blue and of the balls are green. Nathan is going to take a ball, replace it, and then take a second ball. a) Complete the tree diagram.... st Ball nd Ball... Blue Blue... Green... Green Blue Green b) Work out the probability that Nathan will take two blue balls. c) Work out the probability that Nathan will take one of each coloured balls. d) Work out the probability that Nathan will take two balls of the same colour. Page 47

153 Clip 55 Recurring Decimals ) a) Convert the recurring decimal 06. to a fraction in its simplest form. 8 b) Prove that the recurring decimal 07. = ) a) Change 4 9 to a decimal. 9 b) Prove that the recurring decimal 057. = ) a) Change to a decimal. 5 b) Prove that the recurring decimal 045. = 4) a) Change 6 to a decimal. 5 b) Prove that the recurring decimal 0. 5 = 7 5) a) Convert the recurring decimal 06. to a fraction in its simplest form. b) Prove that the recurring decimal 07. = 5 8 6) a) Convert the recurring decimal 5. to a fraction in its simplest form. b) Prove that the recurring decimal 06. = Page 48

154 Clip 56 Fractional and Negative Indices a x a y a x a y = a x+y = a x y (a x ) y = a xy a 0 = a -x = a y y = ( a x ) a = a x y ( a ) x x y x ) Simplify a) (p 5 ) 5 c) x 5 x e) (m -5 ) - b) k k d) (p ) - f) (xy ) ) Without using a calculator, find the exact value of the following. a) c) e) (8 5 ) b) d) f) ( ) ) Work out each of these, leaving your answers as exact fractions when needed. a) 4 0 e) 4 i) 49 m) 49 b) 7 0 f) 8 j) 5 n) 5 c) 5 0 g) 5 k) 7 o) 7 d) 9 0 h) 0 5 l) 6 p) 6 4) 5 5 can be written in the form 5 n. Find the value of n. 5) 8 = m Find the value of m. 6) Find the value of x when 5 = 5 x 7) Find the value of y when 8 = y 8) a = x, b = y a) Express in terms of a and b i) x + y ii) x iii) x + y ab = 6 and ab = 6 b) Find the value of x and the value of y. Page 49

155 Clips 57, 58 Surds 5 is not a surd because it is equal to exactly 5. is a surd because you can only ever approximate the answer. We don t like surds as denominators. When we rationalise the denominator it means that we transfer the surd expression to the numerator. ) Simplify the following: a) 7 7 b) c) 0 d) 4 e) 7 f) 00 g) 5 ) Simplify the following: a) 8 b) 8 c) 99 d) 45 0 e) 8 8 f) 8 75 ) Expand and simplify where possible: a) ( ) b) ( 6+ ) c) 7( + 7) d) ( 8) 4) Expand and simplify where possble: a) ( + )( ) b) ( + 5)( 5) c) ( + )( + 4) d) ( 5 )( 5+ ) e) ( + 7)( 7) f) ( 6 ) 5) Rationalise the denominator, simplifying where possible: a) b) c) d) e) f) g) ) 7 = n Find the value of n 7) Express 8 8 in the form m where m is an integer. 8) Rationalise the denominator of 9) Work out the following, giving your answer in its simplest form: a) b) c) d) e) f) 8 8 the form ( 5+ )( 5 ) ( 4 5)( 4+ 5) ( )( + ) 4 ( + ) ( 5+ ) giving the answer in 0 p ( 5 5)( + 5) 0 Page 50

156 Clip 59 Direct and Inverse Proportion ) x is directly proportional to y. When x =, then y =. a) Express x in terms of y. b) Find the value of x when y is equal to: (i) (ii) (iii) 0 ) a is inversely proportional to b. When a =, then b = 4. a) Find a formula for a in terms of b. b) Find the value of a when b is equal to: (i) (ii) 8 (iii) 0 c) Find the value of b when a is equal to: (i) 4 (ii) 4 (iii). ) The variables u and v are in inverse proportion to one another. When u =, then v = 8. Find the value of u when v =. 4) p is directly proportional to the square of q. p = 75 when q = 5 a) Express p in terms q. b) Work out the value of p when q = 7. c) Work out the positive value of q when p = 7. 5) y is directly proportional to x. When x =, then y = 6. a) Express y in terms of x. z is inversely proportional to x. When x = 4, z =. b) Show that z = c y n, where c and n are numbers and c > 0. You must find the values of c and n. Page 5

157 Clip 60 Upper and Lower Bounds ) A =. correct to decimal place B = 00 correct to significant figure C = 9 correct to the nearest integer a) Calculate the upper bound for A + B. b) Calculate the lower bound for B C. c) Calculate the least possible value of AC. d) Calculate the greatest possible value of A + B B + C ) An estimate of the acceleration due to gravity can be found using the formula: L g = T sinx Using T =. correct to decimal place L = 4.50 correct to decimal places x = 40 correct to the nearest integer a) Calculate the lower bound for the value of g. Give your answer correct to decimal places. b) Calculate the upper bound for the value of g. Give your answer correct to decimal places. ) The diagram shows a triangle ABC. C AB = 7mm correct to significant figures. BC = 80mm correct to significant figure. Diagram NOT accurately drawn A (a) Write the upper and lower bounds of both AB and BC. B AB upper =... BC upper =... AB lower =... BC lower =... (b) Calculate the upper bound for the area of the triangle ABC....mm Angle CAB = x (c) Calculate the lower bound for the value of tan x. Page 5

158 Clip 6 Solve Quadratics Using the Formula ax + bx + c = 0 x, = b± b 4 ac a ) Solve the equation x + 4x + = 0 Give your answers correct to decimal places. ) Solve the equation x + 8x + 6 = 0 Give your answers correct to significant figures. ) Solve the equation x x = 0 Give your answers correct to significant figures. 4) Solve the equation x 7x + = 0 Give your answers correct to significant figures. 5) Solve the equation x + 6x = 0 Give your answers correct to significant figures. 6) Solve the equation x x 0 = 0 Give your answers correct to significant figures. 7) Solve the equation x 4x 6.5 = 0 8) Solve the equation 7x 9x 06 = 0 Give your answers correct to significant figures. 9) x + 0x = 00 Find the positive value of x. Give your answer correct to significant figures. 0) (x + )(x ) = a) Show that x x 7 = 0 b) Solve the equation x x 7 = 0 Give your answers correct to significant figures. Page 5

159 Clip 6 Completing the Square ) Show that if y = x + 8x then y 9 for all values of x. ) Show that if y = x 0x + 0 then y 5 for all values of x. ) The expression x + 4x + 0 can be written in the form (x + p) + q for all values of x. Find the values of p and q. 4) Given that x 6x + 7 = (x p) + q for all values of x, find the value of p and the value of q. 5) For all values of x, x + 6x = (x + p) + q a) Find the values of p and q. b) Find the minimum value of x + 6x. 6) For all values of x, x 8x 5 = (x p) + q a) Find the value of p and the value of q. y b) On the axes, sketch the graph of y = x 8x 5. O x c) Find the coordinate of the minimum point on the graph of y = x 8x 5. 7) The expression 0x x can be written in the form p (x q) for all values of x. a) Find the values of p and q. b) The expression 0x x has a maximum value. (i) Find the maximum value of 0x x. (ii) State the value of x for which this maximum value occurs. Page 54

160 Clip 6 Algebraic Fractions ) Simplify fully a) 9x x c) 8 ab ab e) ab 4 ab 6ab b) 0 xy 5y d) 4 x + x 0x f) 5xy+ 5xy 0xy ) Simplify fully a) x x + x + 6x+ 5 c) x x x + x b) x 6 x + 8 x 8x d) x + 7 x + 0 x + 5x ) a) Factorise 4x x+ 9 b) Simplify 6x 7x 4x x+ 9 4) Write as single fractions in their simplest form a) x + x c) x+ x + 5 b) 5 x 4x d) 5 x+ x+ 5) a) Factorise x + 7x+ 6 b) Write as a single fraction in its simplest form 4x x + + x + 7x+ 6 6) Solve a) + = c) x x 6 x 5 + x = e) 7 x+ + x = x 4 b) x + x+ 6 = d) 7 4 x+ + x = f) x x + x+ = Page 55

161 Clip 64 Rearranging Difficult Fomulae ) Make c the subject of the formula. v = a + b + c ) Make t the subject of the formula. A = π t + 5t ) Make s the subject of the formula. R = s + π s + t l 4) k = m l a) Make l the subject of the formula. b) Make m the subject of the formula. 5) A k ( = x + 5) Make x the subject of the formula. 6) R = u+ v u+ v Make u the subject of the formula. 7) x+ y = 5 0+ y Make y the subject of the formula. 8) a = 5 4b Rearrange this formula to give a in terms of b. 9) S = πd h + d Rearrange this formula to make h the subject. Page 56

162 Clip 65 Simultaneous Equations With a Quadratic ) Solve these simultaneous equations. y = x y = x 6 ) Solve these simultaneous equations. y = x 4 y = x ) Solve these simultaneous equations. y = x x y = x + 4) Solve these simultaneous equations. y = x 5 x y = 5 5) Solve these simultaneous equations. x + y = 6 y + 6 = x 6) Sarah said that the line y = 7 cuts the curve x + y = 5 at two points. a) By eliminating y show that Sarah is not correct. b) By eliminating y, find the solutions to the simultaneous equations x + y = 5 y = x 9 Page 57

163 Clip 66 Gradients of Lines ) y Diagram NOT accurately drawn B (0, 7) A (0, ) 0 x A is the point (0, ) B is the point (0, 7) The equation of the straight line through A and B is y = x + a) Write down the equation of another straight line that is parallel to y = x + b) Write down the equation of another straight line that passes through the point (0, ). c) Find the equation of the line perpendicular to AB passing through B. ) A straight line has equation y = x 5 The point P lies on the straight line. The y coordinate of P is -6 a) Find the x coordinate of P. A straight line L is parallel to y = x 5 and passes through the point (, ). b) Find the equation of line L. c) Find the equation of the line that is perpendicular to line L and passes through point (, ). ) In the diagram A is the point (0, -) B is the point (-4, ) C is the point (0, ) B y C a) Find the equation of the line that passes through C and is parallel to AB. b) Find the equation of the line that passes through C and is perpendicular to AB O - - A x - Page 58

164 Clip 67 Transformations of Functions ) This is a sketch of the curve with equation y = f(x). It passes through the origin O. The only vertex of the curve is at A (, -) a) Write down the coordinates of the vertex of the curve with equation (i) y = f(x ) (ii) y = f(x) 5 (iii) y = f(x) (iv) y = f(x) y A (, -) x b) The curve y = x has been translated to give the curve y = f(x). Find f(x) in terms of x. ) The graph of y = f(x) is shown on the grids. a) On this grid, sketch the graph of y = f(x ) b) On this grid, sketch the graph of y = f(x) ) Sketch the graph of y = (x ) + State the coordinates of the vertex. 4) Sketch the graph of y = x + 4x State the coordinates of the vertex and the points at which the curve crosses the x - axis. Page 59

165 Clip 68 Graphs of Trigonometric Functions - of ) On the axes below below, draw a sketch-graph to show y = sin x y x Given that sin 0 = 0.5, write down the value of: (i) sin 50 (ii) sin 0 ) On the axes below, draw a sketch-graph to show y = cos x y x Given that cos 60 = 0.5, write down the value of: (i) cos 0 (ii) cos 40 Page 60

166 Clip 68 Graphs of Trigonometric Functions - of ) On the axes below, draw a sketch-graph to show y = tan x y x ) The diagram below shows the graph of y = cos ax + b, for values of x between 0 and 00. Work out the values of a and b. ) Here is the graph of the curve y = cos x for 0 < x < 60. y 4 a) Use the graph to solve cos x = 0.75 for 0 < x < 60 b) Use the graph to solve cos x = for < x < x Page 6

167 Clip 69 Transformation of Trig. Functions ) The diagram below shows the graph of y = sin x, for values of x between 0 and 60. y B A x The curve cuts the x axis at the point A. The graph has a maximum at the point B. a) (i) Write down the coordinates of A. (ii) Write down the coordinates of B. b) On the same diagram, sketch the graph of y = sin x + for values of x between 0 and 60. ) The diagram below shows the graph of y = cos ax + b, for values of x between 0 and 00. Work out the values of a and b. y x Page 6

168 Clip 70 Graphs of Exponential Functions ) y (4, 75) (, ) x The sketch-graph shows a curve with equation y = pq x. The curve passes through the points (, ) and (4, 75). Calculate the value of p and the value of q. ) The graph shows the number of bacteria living in a petri dish. The number N of bacteria at time t is given by the relation: N = a b t The curve passes through the point (0, 400). a) Use this information to show that a = 400. The curve also passes through (, 900). b) Use this information to find the value of b. Number of bacteria N t c) Work out the number of bacteria in the dish at time t =. Time (hours) Page 6