Exercises in GCSE Mathematics Intermediate level. Robert Joinson. Sumbooks

Transcription

1 Eercises in GCSE Mathematics Robert Joinson Sumbooks

2 Sumbooks Chester CH 8BB Eercises in GCSE Mathematics- First Published 997 Reprinted 998 Updated 00 Copyright R Joinson and Sumbooks This package of worksheets is sold subject to the condition that it is photocopied for educational purposes only on the premises of the purchaser ISBN 0 980

3 Preface This book covers the GCSE syllabi to be eamined for the first time in 00. It was written with year pupils in mind but can be used in year 0 for those pupils intending to do the higher papers at the end of year. Some areas have more questions than are needed for some pupils. Eercises on pages,,,,,, 6, 7, 8 and 0 contain lots of questions and are aimed at pupils requiring a great deal of practice. However the questions are graded and it might only be necessary for some students to do the first column and then each row when they begin to have problems. In general questions in the same row tend to be of the same difficulty, whereas the difficulty increases down the page. All graphs can be accommodated on A size graph paper used in 'portrait' mode. The answers to the questions on reflections, rotations, translations and enlargements can be drawn within the size of graph paper indicated in the question. I would like to thank my wife Jenny and my daughters Abigail and Hannah for all the help and encouragement they have given me in writing this. R Joinson August 00 Chester

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5 Contents Multiplication and Division Negative Numbers Use of the Calculator Estimation Fractions, Decimals and Percentages 6 Fractions, Decimals and Percentages 7 Interest 8 Scale Drawings and Ratio 9 Standard Form 0 Prime Factors Number Patterns and Sequences Number Patterns and Sequences Distance Time Diagrams Distance Time Diagrams Conversion Graphs 6 Conversion Graphs 7 Sketching and Recognising Graphs 8 Sketching and Recognising Graphs 9 Plotting Graphs 0 Plotting Graphs Substitution Simplifying Epressions Indices Multiplying Brackets Factorising 6 Equations 7 More Equations 8 Straight Line Graphs and Simultaneous Equations 9 Trial and Improvement 0 Inequalities Inequalities - Graphs Rearranging Formulae Bearings Parallel Lines Nets and Isometric Drawing 6 Triangles 7 Regular Polygons 8 Irregular Polygons 9 Pythagoras' Theorem 0 Trigonometry Trigonometry Trigonometry Trigonometry Reflections, Rotations and Translations Reflections, Rotations and Translations 6 Reflections, Rotations and Translations 7 Reflections, Rotations and Translations

6 8 Enlargements 9 Enlargements 0 Similar Shapes Locus Problems Locus Problems Degree of Accuracy Circumference of a Circle. Area and Perimeter 6 Volume 7 Compound Measure - Speed and Density 8 Compound Measure - Best Buy and a Mied Eercise 9 Formulae for Area, Volume and Perimeter 60 Formulae for Area, Volume and Perimeter 6 Questionnaires 6 Pie Charts 6 Frequency Polygons 6 Frequency Polygons 6 Mean, Median, Mode and Range 66 Mean 67 Mean 68 Mean - diagrams 69 Mean - Frequency distributions with class intervals 70 Mean - Histograms 7 Cumulative Frequency 7 Cumulative Frequency 7 Scatter Diagrams 7 Scatter Diagrams 7 Probability 76 Probability 77 Probability 78 Tree diagrams 79 Relative Frequency 80 Relative Frequency 8 Constructions 8 Simultaneous Equations 8 Using Simple Equations 8 Using Quadratic Equation 8 Surds 86 Recognising Graphs 87 Plans and Elevations () 88 Plans and Elevations () 89 Moving Averages 90 Recurring Decimals

7 Sumbooks 00 Eercise Short division with or without remainders Multiplication and Division Do not use a calculator ) 7 7 ) 8 6 ) 9 8 ) 06 ) 8 9 6) 0 6 7) 7 8) ) 97 0) 6 8 ) 9 ) 76 6 Eercise Long division with or without remainders ) 87 7 ) 96 ) 8 ) ) ) 67 7) 8) 8 9) ) 8 ) 6 ) 8 7 ) 8 ) 97 ) 67 6) 67 7) 8 8) 6 7 9) 8 0) 96 Eercise Division without remainders (answer in decimal form) ).0 ).0 ) 8 8 ) ) 0 6) 9 6 7) ) ) 8 0) 7 6 ) 7.6 ) 0 8 ) ) 8 8 ) 6) 6 8 7).7 8) 0. 9) ) 8 Eercise Long multiplication ) 7 ) 8 9 ) 6 7 ) ) 86 6) 7 7) 6 7 8) 9) 6 7 0) ) 7 6 ) 7 ) 86 ) 8 6 ) 7 7 6) ) 9 9 8) 76 9) ) 9 7

8 Sumbooks 00 Negative Numbers Do not use a calculator Eercise Calculate the final temperature. ) ºC increases by 9ºC ) ºC falls by ºC ) ºC falls by ºC ) ºC increases by ºC ) ºC falls by 8ºC 6) 9ºC ºC 7) 8ºC ºC 8) ºC + ºC 9) 8ºC ºC 0) 6ºC ºC ) 7ºC + ºC ) ºC + ºC ) 0ºC 6ºC ) ºC ºC ) 6ºC + 6ºC 6) 7ºC 6ºC 7) ºC + 6ºC 8) 7ºC + 6ºC 9) 7ºC 9ºC 0) ºC + 7ºC Eercise What is the change in temperature between each of the following? ) ºC and 7ºC ) 7ºC and ºC ) ºC and ºC ) 7ºC and ºC ) 6ºC and ºC 6) 7ºC and 0ºC 7) ºC and ºC 8) 7ºC and ºC 9) ºC and ºC 0) ºC and 7ºC ) 8ºC and ºC ) 0ºC and ºC ) 7ºC and ºC ) 8ºC and 6ºC ) 9ºC and ºC 6) ºC and ºC 7) ºC and ºC 8) 6ºC and 8ºC 9) 6ºC and 0ºC 0) ºC and 0ºC Eercise In each of the following, write down the number represented by the? )? = )? = )? = ) 7? = 9 ) +? = 6) +? = 7)? = 7 8) +? = 9)? + = 0)? = )? = )? = )? + = 7 ) +? = 9 )? = 6) 7 +? = 0 7) 8 +? = 8) 0? = 6 9) +? = 6 0)? = Eercise ) Two numbers are multiplied together to make 0. One of the numbers is 6. What is the other? ) Two numbers are multiplied together to make 8. One of the numbers is 6. What is the other? ) Two numbers are multiplied together to make 60. The sum of the two numbers is. What are they? ) Two numbers are multiplied together to make. The sum of the numbers is 0. What are the numbers?

9 Sumbooks 00 Use of the Calculator Eercise Calculate each of the following pairs of problems. Predict the answers before you do them. ) + 8 and ( + 8) ) + and ( + ) ) 8 and (8 ) ) 0 6 and (0 6) ) 6 + and 6 ( + ) 6) and 0 (8 + ) 7) 6 + and 6 ( + ) Eercise ( give your answer correct to significant figures wherever necessary ) ) ).8.6. ) ) ) 6) ). (.6.) 8) (. +.6) (.7.6) 9) ).. ( ) ) ) 7.8 (. 6.) 8 ) ) ) ) 7) 8. (.8 +.6) 6. ( ) 8) 9) (6..6).6 0) ( ) ) 6cos0 )..cos0 ) ( 6 + tan) ) 6 + sin0 ) tan + sin 6) (. + tan0 ) + (.6).6 +. sin 7) ) tan

10 Sumbooks 00 Estimation Do not use a calculator In each of the following questions a) write down a calculation that could be done mentally to check the answer to each of the following and b) write down your answer Eercise ) 7 6 ) 67 ) 8 ) 78 6 ) 8 6) 6 7) ) 0 9) ) 87 6 ) ) 0 7 ) 87 ) 6 8 ) 6 6) 8 7) ) 77 9) ) 6 Eercise ) ).9. ) ) )..00 6) ) ) )..98 0) ) ) ) ) ) ) ) ) ) ) ) 7. (.) ( 6.8) ) ).(.8 +.9) (.78) ) ) If v = estimate the value of v. 6) If c = estimate c ) t = estimate the value of t. 9.8.( ) 8) D = estimate the value of D ) Estimate the value of

11 Sumbooks 00 Fractions, Decimals and Percentages Eercise Change into decimals (correct to decimal places where necessary) 7 ) -- ) -- ) -- ) -- ) ) ) ) ) ) ) ) ) ) -- ) -- 6) ) ) Eercise Change these decimals into percentages ) 0.6 ) 0. ) 0.7 ) 0.87 ) 0.6 6) 0. 7) 0. 8) ) 0. 0) 0.6 ) 0.8 ) 0.86 ) 0.9 ) 0. ) 0.6 6).9 7).8 8) 6. Eercise Change into percentages correct to significant figures ) -- ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) Eercise Compare each of the following sets of numbers by first changing them into percentages and then writing them down in order of size, smallest to largest. ) % ) % 7 ) % ) % 7 ) % 6) % 8 9 7) % 8) % 6 8 9) % 0) % Eercise Calculate 7 ) -- of 0 ) -- of 0 ) -- of 90 ) -- of ) -- of 0 metres 6) -- of -- metres 7) of 7 8) of 8 metres ) of 66 0) of. metres ) -- of ) of 7.7 metres

12 Sumbooks 00 6 Fractions, Decimals and Percentages Eercise ) 7% of 600 ) % of 0 ) 6% of 90 ) % of00 ) % of 6 6) 0% of.0 7) 60% of 9 8) 7% of 8 metres 9) % of 9 0) 7% of.0 ) % of 6.0 ) 9% of 00 Eercise Change these marks into percentages. (Give your answer correct to the nearest whole number) ) out of 0 ) 8 out of 60 ) 7 out of 0 ) 7 out of 80 ) 6 out of 90 6) 97 out of 0 7) out of 00 8) 6 out of 70 9) 8 out of 0 0) 6 out of 0 ) 7 out of 0 ) 76 out of 0 ) out of 76 ) 8 out of 9 ) 6 out of 68 6) 7 out of Eercise Find the percentage profit on each of the following, correct to the nearest whole number. ) ) ) ) ) 6) 7) 8) 9) 0) Buying Price Selling Price ,00,700,000 7, Eercise Find the selling price for each of these. ) ) ) ) ) 6) 7) 8) 9) 0) Buying Price Profit 00 7% 00 % 0 0% 000 % 00 % 00 7.% 70 % 9,000 % 80 7% 0 %

13 Sumbooks 00 7 Interest Eercise Find the simple and compound interest (without using the compound interest formula) on each of the following. Wherever necessary give your answer correct to the nearest penny. ) 00 invested for years at % interest per annum. ) 0 invested for years at % interest per annum. ) 00 invested for years at 9% interest per annum. ) 000 invested for years at 0% interest per annum. ) 00 invested for years at 7% interest per annum. 6) 000 invested for years at % interest per annum. 7) 00 invested for years at % interest per annum. 8) 0 invested for years at 7% interest per annum. 9) 0 invested for years at 8% interest per annum. 0) 00 invested for years at 6% interest per annum. Eercise The Compound Interest Formula is R = P n 00 Where represents the amount in the bank after n years with a rate of R% on a principle of P. ) Use the compound interest formula to calculate the amount of money in a bank account when a) 00 Euros is invested for years at a rate of.% b) 00 Euros is invested for 7 years at a rate of.7% c),00 Euros is invested for years at a rate of.6% ) 6,000 Euros is invested in an account that pays interest at a compound rate of.7% R a) Calculate the value of = b) By using the key on your calculator, make a list of the amounts of money in the y account at the end of each of the 0 years the money is left in the account. ) Calculate the interest gained when 0,000 Euros is invested for years in a bond which pays an interest of.7% per annum. ) What is the difference between the simple and compound interest earned on an investment of,000 Euros over a period of years at a rate of.86%?

14 Sumbooks 00 8 Scale Drawings and Ratio Do not use a calculator Eercise Fill in the missing values for each of the following Scale Dimensions on Drawing Actual Dimensions : : 0cm :0 6.cm 0cm :0 0cm :0 0cm :8.8cm 0cm 6 metres cm metres :0. metres :00.cm.cm metres 7cm 7.cm :00 7.m :7 6cm cm.m : 8cm :0.6cm.cm.cm :7 600cm :0.6cm Eercise Divide each of the following into the ratios given. ) 900 into the ratio : ) 000 into the ratio :7 ) 00 into the ratio : ) 600 into the ratio 7:8 ) 800 into the ratio : 6) 700 into the ratio :9 7) 60 into the ratio 7: 8) 6 into the ratio 9: 9) 0 into the ratio 8: 0) 00 into the ratio :: ) 0 into the ratio :6:7 ) into the ratio :: ) 008 into the ratio 7:8:9 ) into the ratio 7:9: ) 0 into the ratio :8:9 6) 78.0 into the ratio ::7 7) 0 into the ratio 6:8: 8).86 into the ratio :7: 9) 86 into the ratio :7: 0) into the ratio ::7 Eercise Three people, A, B and C, share an amount of money in the ratios shown below. In each case calculate the total amount of money shared out and the amount C gets. ) Ratio ::. A gets 8 ) Ratio ::. B gets ) Ratio :8:0. B gets ) Ratio ::7. A gets ) Ratio 7::. B gets 99 6) Ratio ::. A gets.6 7) Ratio ::8. B gets. 8) Ratio :6:. B gets 6.7 9) Ratio :7:9. A gets. 0) Ratio ::. B gets 6.0

15 Sumbooks 00 9 Standard Form Eercise Write down these numbers in standard form ) 6 ) 6 ) 800 ) ) ) 0. 7) 0.0 8) ) ) ) 0.00 ) 7. Change these numbers from standard form. ). 0 ). 0 ).8 0 6) ). 0 8) ) ) ). 0 ).97 0 ) ).8 0 Eercise Calculate each of the following, leaving your answer in standard form. Round off to significant figures where necessary. ) (. 0 ) (.0 0 ) ) (. 0 ). 0 ) (.6 0 ) (. 0 ) 7) (. 0 0 ) (.7 0 ) 9) ( ).6 0 ( ) ( ) ( ) ) (.6 0 ).8 0 ) ( 6. 0 ) ( ) 6) (.8 0 ) ( ) 8) ( ) (. 0 ) 0) (. 0 ).6 0 ( ) ) 7 ),000,000 ( ) (. 0 ) ( ) (.6 0 ) ) ) Eercise ) If = 0 and y = 0 write down the value of a) y and b) + y leaving your answer in standard form. ) If = 0 and y = 0 write down the value of a) y and b) + y leaving your answer in standard form. ) If = 0 and y = 7 0 write down the value of y leaving your answer in standard form. ) The mass of the earth is kilograms and the mass of the moon is 7. 0 kilograms. Write down the ratio of the mass of the moon to that of the earth in the form : n. ) The distance of the moon from the earth is 8 00 kilometres. The speed of light is approimately.0 0 kilometres per second. How long does it take light to travel from the moon to the earth? 6) A neutron has a mass of kilograms and an electron kilograms. Calculate the ratio of the mass of a neutron to the mass of an electron in the form : n. 7) Light travels at a speed of approimately.0 0 kilometres per second. a) How far will it travel in year (6 days)? b) If the distance from the earth to a star is kilometres, how long will its light take to reach earth?

16 Sumbooks 00 0 Prime Factors Do not use a calculator Eercise The prime factors of a number can be found by using a tree diagram. The eample below shows how to find the prime factors of 6. In the same way find the prime factors of the other numbers Eercise Write down all the factors of the following numbers. ) ) 0 ) ) 0 ) 6) 0 7) 8) 60 9) 7 0) 8 ) 90 ) 00 ) 0 ) 0 ) 0 Eercise Epress the following numbers as products of their prime factors. ) 0 ) 60 ) 00 ) 0 ) 60 6) 67 7) 9 8) 7 9) 0)0 ) 680 ) 0 ) 60 ) 76 ) 0 Eercise Epress the following numbers as products of their prime factors. In each case state the smallest whole number it has to be multiplied by to produce a perfect square. ) ) 8 ) 80 ) 80 ) 6 6) 7) 8) 68 9) 608 0) 980 ) 600 ) 60 ) 00 ) 9 ) 80 Eercise Calculate the largest odd number that is a factor of each of the following. ) 08 ) 80 ) 00 ) 7 ) 9 6) 0 7) 88 8) 70 9) 780 0) 68 ) 8 ) 00 ) 60 ) 0 ) 90

17 Sumbooks 00 Number Patterns and Sequences Eercise In each of the following patterns write down the net two numbers ),, 6, 8, 0... ), 7, 9,,... ) 7, 0,, 6, 9... ), 9,, 7,... ), 8,, 8,... 6),,, 0, ),, 6, 9,... 8),, 6, 8,... 9), 7,, 7,... 0),,, 8,... ) 0,,, 6, 0... ),, 8,, 7... ),,, 9, 7... ) 0, 0, 9, 7,... ), 9, 6,, ),, 0, 6,... 7) 7,,,,... 8) 8, 8, 7,,... 9),,, 7,... 0),,, 7,... ),,, 7, 0... ),, 7,,... ),,, 8, 6... ),, 7,,... Eercise In each of the following patterns (a) write down the net two numbers, (b) write down in words the rule for finding the net number and (c) write down the rule for finding the nth number in the pattern in terms of n. ),,, 7, 9... ),, 8,,... ), 9,, 7,... ) 6,, 8,, 0... ) 7,, 9,,... 6), 7,, 7,... 7) 0, 8, 6,,... 8) 7,,, 8,... 9), 6, 0,, ) 7,,,,... ), 0,, 0,... ), 8,,, 0... ),,,,... ), 9, 6,, 0... ),,, 7, 9... Eercise ) The diagrams below show square 'holes' surrounded by centimetre squares. Length of side Number of squares 8 6 Find the number of squares needed for holes of side a) cm b) cm c) n cm d) Calculate the number of squares needed for a hole of side 0cm. ) A child places blocks on a floor making the pattern shown below. The first row contains block, the second blocks, the third and so on. Row st nd rd th How many blocks will be in a) row b) row 6 c) row n d) Calculate how many will be in row 0.

18 Sumbooks 00 Number Patterns and Sequences ) The diagram shows a number of rectangles where the length is unit longer than the width. Rectangle number Find the areas of a) Rectangle b) Rectangle c) rectangle n d) Calculate also the area of rectangle 0 ) A library shelving system is made from uprights and shelves as shown below. upright uprights uprights no shelves shelves 0 shelves How many shelves can be made from a) uprights b) uprights c) n uprights. d) How many shelves are needed for 0 uprights. ) Shapes are made from matchsticks as shown below. layer layers layers 7 matches matches 7 matches Write down the number of matches needed for shapes with a) layers b) layers c) n layers Calculate how many matches are needed for a shape having layers. ) Pens, in which animals are kept are made from posts and cross bars. One pen requires posts and 8 cross bars, bars along each side. pen 8 cross bars posts pens cross bars 6 posts pens 0 cross bars 8 posts If more pens are made in this way, write down the number of posts and cross bars needed for a) pens b) pens c) n pens. Calculate the number of posts needed if there are cross bars.

19 Sumbooks 00 Distance Time Diagrams ) D 00 Distance (miles) ) Distance (miles) 0 H 0 G 0 00 F 8.00 ) Town B Distance from town A H 0 Town A.00 Time taken (hours) Time (Hrs and mins) Time The diagram shows the journey of a lorry from home H to destination D. a) What is the distance between H and D? b) For how long did the driver stop? c) What was his average speed when travelling slowest? d) What was the average speed for the whole journey? The diagram shows a distance time graph for two buses A and B, travelling between towns F, G and H. Bus A travels from F to H and bus B from H to F. Find a) the average speed of bus A between F and G in miles per hour. b) the length of time bus A stops at G c) the time at which bus B leaves H d) the average speed of bus B in m.p.h e) the approimate time at which the buses pass each other f) the approimate distance from G at which the buses pass g) the time at which bus B arrives at F. Two towns are 0 miles apart. The graph shows the journeys of two trains. The first goes from A to B. The second goes from B to A. From the graph find a) the speed of the first train over the first part of its journey. b) the time at which the first train stopped and for how long. c) the speed of the first train during the second part of its journey. d) the average speed of the second train. e) the time and distance from town A of the two trains when they passed each other.

20 Sumbooks 00 ) 0 Distance Time Diagrams B Distance travelled from home (km) 0 0 A 0:00 :00 :00 :00 :00 :00 6:00 7:00 8:00 Time The diagram shows a distance-time graph for two journeys. One journey is by bicycle, the other is jogging. a) Which journey do you think is by bicycle and why, A or B? b) What is the average speed of the cyclist on her outward journey? c) Who travelled furthest? d) What is the average speed of the jogger on his homeward journey? e) For how long did the jogger stop? f) If both journeys were made along the same road, at what approimate times did they meet? g) At what time did the cyclist arrive home? ) Two cars, A and B travel between two towns X and Y Y. The distance time graph shows the distance from town X. 0 Dist. (miles) 80 Half the journey is along a motorway and half is not. a) How far apart are the two towns? b) Calculate the speeds of car A over the two sections. c) Calculate the speeds of car B over the two sections. 0 X 0:00 Car B Car A 0:00 0:00 0:00 06:00 07:00 08:00 Time d) For how long did car B stop? e) At what time, and how far from town X, are the two cars when they pass each other? f) Approimately how far apart are the two cars at 06:00? g) At what times will the cars be 0 miles apart?

21 Sumbooks 00 Conversion Graphs ) The graph can be used to convert pounds ( ) into Euros. Use it to convert; a).0 into Euros b).00 Euros into pounds and pence. 6 Pounds ( ) Euros ) The graph can be used to convert pounds ( ) into US dollars ($). Use it to convert; a) 70 into dollars b) $60 into pounds. 0 Dollars ($) Pounds ( )

22 Sumbooks 00 6 Conversion Graphs ) kg is approimately.lbs. Calculate what 0 kg is in pounds. From this information draw a conversion graph to convert kg into pounds. Use a horizontal scale of cm to 0kg and a vertical scale of cm to 0lbs. From your graph convert; a) kg into pounds b) 7 pounds into kg. ) It is known that gallon is approimately equal to. litres. Use this information to change 0 gallons into litres. Plot a graph to convert gallons into litres using a scale of cm to represent gallons on the horizontal ais and cm to represent litres on the vertical ais. From your graph; a) convert gallons into litres b) convert litres into gallons In each case give your answer correct to decimal place. ) The table below shows the cost of gas. There is a fied charge of Cost Units Used 0,000,000 0,000 Use this information to plot a conversion graph with a scale of cm to represent 000 units on the horizontal ais and cm to represent 0 on the vertical ais. From your graph find; a) the cost of,00 units b) the number of units that can be bought for.00. ) Water is run from a tap into a container which has a large base and narrower neck. The height of the water in the container is measured every 0 seconds. The following table gives the results; Height of water (cm) Time (secs) Using a vertical scale of cm to represent 0cm for the height of the water and a horizontal scale of cm to represent 0 secs for the time, plot the above information to produce a conversion chart. From your graph find; a) the time it takes to reach a height of cm b) the height of water after the tap has been running for -- minutes. ) David has to make pastry but his scales measure in ounces and the recipe uses grammes. He has a tin of beans which say on the label that -- ounces is equivalent to 0 grammes. Using a scale of cm to represent oz on the horizontal ais and cm to represent 0 grammes on the vertical ais, draw a line to show the relationship between ounces and grammes. From the graph convert the following to the nearest half ounce, so that David can use his scales; a) 8g of butter b) 00 g of flour When he has mied all the ingredients together he weighs out -- ounces of pastry. c) What is this weight in grammes?

23 Sumbooks 00 7 Sketching and Recognising Graphs ) Sammi walks to school, keeping at the same speed all the way. Which of these graphs represents her journey. a) b) c) Distance travelled Distance travelled Distance travelled Time taken Time taken Time taken ) The Swimming Pool Corporation makes round swimming pools. The table below shows their prices. Diameter 8 metres 0 metres metres metres 6 metres Cost 90,000,0,880 7,680 Which of these graphs represents the prices of the pools. a) b) c) Price Price Price Diameter Diameter Diameter ) A train travels from Dorcaster to Newchester. Its speed increases from 0 to 60mph. It then travels at a constant 60mph and finally it slows down from 60mph to 0mph. Which of these diagrams shows that journey. a) b) c) d) Speed Speed Speed Speed Time Time Time Time ) A shop sells stamps which cost p each. In order to help calculate their cost, the assistant uses the following list of prices to help him. Number of stamps Cost p..0.0 Sketch the graph which represents their price plotted against the number sold.

24 Sumbooks 00 8 Sketching and Recognising Graphs ) A water tank with straight sides is full. A tap at the bottom is turned on and the water drained out at a constant rate. Which of these diagrams shows this. a) b) c) d) Height Height Height Height of water of water of water of water Time Time Time Time ) A car is bought for 000. During each year it loses 0% of its value at the beginning of that year. (compound depreciation). Which of these diagrams represents its value? a) b) c) d) Value Value Value Value Time Time Time Time ) Niki travels to her gran's house. The first part of her journey she travels by bike, the second part she walks, and the last part she goes by bus. Which of these diagrams represents her journey? a) b) c) Distance Distance Distance Time Time Time ) The table below shows the volume of some cubes. Sketch a graph of the length of their side against their volume. Length of side (cm) 0 0 Volume of cube (cm ) ,000

25 Sumbooks 00 9 Plotting Graphs ) a) Complete the table below which gives the values of y = + for values of ranging from to +. y b) On graph paper, draw the graph of y = +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) From your graph determine, correct to decimal place, the values of when y=6 d) Draw the line y =7 on the same graph and write down the co-ordinates of the points where they cross. ) a) Complete the table below which gives the values of y = + for values of ranging from to +. y b) On graph paper, draw the graph of y = +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) Draw the line y =+ on the same graph and write down the co-ordinates of the points where they cross. d) Show that the solution to the equation + = 0 can be found at these points. Write down the solution to this equation ) a) Complete the table below which gives the values of y = +6 for values of ranging from. to +.. y b) On graph paper, draw the graph of y = +6. Use the scale of cm to unit on the ais and cm to unit on the y ais. c) Draw the line y = + 6 on the same graph and write down the co-ordinates of the points where they cross. d) Show that the solution to the equation = 0 can be found at these points. Write down the solution to this equation ) a) Complete the table below which gives the values of y = 6 for values of ranging from to +. y 0 6 b) On graph paper, draw the graph of y = 6. Use the scale of cm to unit on the ais and cm to units on the y ais. c) Draw the line y =0 on the same graph and write down the co-ordinates of the points where they cross, correct to decimal place. d) Show that the solution to the equation 6= 0 can be found at these points. Write down the solution to this equation

26 Sumbooks 00 0 Plotting Graphs ) a) Complete the table below which gives the values of y = + -- for values of ranging from 0. to 8. y b) On graph paper, draw the graph of y = Use the scale of cm to unit on the ais and cm to unit on the y ais. c) From your graph determine, correct to decimal place, the value of when y=6.. d) Draw the line y = 8 -- on the same graph and write down the co-ordinates of the points where they cross, correct to decimal place. e) Show that the solution to the equation = 0 can be found at these points. Write down the solution to this equation. ) a) Complete the table below which gives the values of y = ++ for values of ranging from to +. y 0 8 b) On graph paper draw the graph of y = + +. Use the scale of cm to unit on the ais and cm to units on the y ais. c) By drawing a suitable straight line on the grid, solve the equation ++= 7 ) a) Complete the table below which gives the values of y = for values of ranging from. to +. y b) On graph paper, draw the graph of y =. Use the scale of cm to unit on the ais and cm to units on the y ais. c) By drawing a suitable straight line on the grid, solve the equation = 0 ) a) Complete the table below which gives the values of y = -- for values of ranging from 0. to y b) On graph paper, draw the graph of y = --. Use the scale of cm to unit on the ais and cm to unit on the y ais. c) By drawing a suitable straight line on the grid, solve the equation = 0

27 Sumbooks 00 Substitution Calculate the following values given that a =, b = and c = ) a + b ) a b ) a b c ) a + b c ) c 7a 6) a b + 6 Calculate the values of the epressions in questions 7 to given that a =, b = and c = 7) a + b c 8) a + b c 9) 6a 7b 0) a + b c ) a b c ) a b c ) If v = u + at, find v when u =, a = 0. and t = 6 ) Find the area of a circle of radius.cm if A = πr and π =. ) Find the circumference of a circle of diameter 6.cm if C = πd 6) If y = m + c find the value of y when m = 6, = and c = 7) The volume of a cone is given by V = -- πr h. Find its volume when π =., r = cm, and h =.cm. 8) The temperature F ( o Fahrenheit) is connected to the temperature C ( o Celsius) by the formula C = -- (F ). Find, to the nearest degree, the value of C when F = 8 o 9 9) Find the simple interest paid if the principal (P) is 0, the time (T) is years and the rate PTR of interest (R) is 9.% using the formula I = ) If v = u + as find v when u = 7., a =. and s = 0. ) If v = gh find v when g = 9.8 and h =. ) If S = -- (u + v)t find S when u = 0, v = 7. and t =.. + y ) If A = find A when = 6 and y = 9 R ) If P = find P when (a) R = 6, = 7 and y =, (b) R =, =, and y = y bc ) If = find when b = and c = 9. b c 6) If y = + find y when is (a) (b) 7) If y = + find y when is (a) (b) 8) If y = ( + )( ) find y when is (a) (b) 9) If y = ( )( + ) find y when is (a) 7 (b) 0) If y = + -- find y when = ) If v = u + at, calculate v when u = 0, a = 9.8 and t = 6. ) If v = u + as, calculate the value of v when u = 0, a = 9.8 and s = 0

28 Sumbooks 00 Simplifying Epressions Eercise Simplify ) 7 + ) ) 6 9 7) + 8 9) + 0 ) 7 ) + ) 9 + 7) + 6 9) 8 + ) ) ) ) ) Eercise Simplify ) y + 8y ) 9y 6y ) 6y 8y 7) y + y 9) 6a 7a ) b + b + a + a ) b + a + b + a ) 6a a + b + b 7) a + b a b 9) 6 + 8y 0 9y ) 6 + y 8 6y ) y + y 6y ) 7ab + 6b ab b ab 7) ab + bc ab + bc 6ab bc 9) 9y + y + y ) + ) + y + + y ) y + + y 7) 6 y + y + y + y 9) + ) 0 ) 8 9 6) 7 0 8) ) ) 9 6 ) ) 6 0 8) ) + 9 ) ) ) ) ) ) y + y ) 6) 7 9 8) + 7 0) w w ) 9 + 7y + + 6y ) + 6y + y + 6) p p + q + 7q 8) + 7y y 0) a + b 7a b ) a + 9b 6a b ) y + y + y 6) y + 7 y y 8) 7y + 9yz y yz + 7y yz 0) ab a ab + a + 9ab ) 7y + 6y ) 7 + y y 6) 9 + 8) 7 y y y + y 0) y y

29 Sumbooks 00 Indices Eercise Write down the values of the following. ) ) ) ) ) 0 6) 0 7) 0 8) 0 Eercise Use a calculator to write down the values of the following. ) 6 ) 6 ) 7 ) 7 6 ) 9 6) 7) 6 8) 7 9 Eercise Write down the answers to these both in inde form and, where necessary, numerical form. ) ) ) ) 0 0 ) 7 7 6) ) 8) a a 0 9) b b b 0) y 0 y Eercise Write down the answers to each of the following in inde form. ) 8 ) 9 ) ) ) 7 0 6) 0 7) 9 7 8) 6 9) 8 0 0) 0 7 ) a a ) y y ) Eercise Write down the answers to each of the following in inde form. ) ) ) ) ) 6) ( ) ( ) ( 7 ) ( ) ( ) ( ) ( ) 8 ( 7 ) ( ) ( ) ( ) ( y ) 7) 8) 9) 0) ) ) Eercise 6 Calculate the answers to each of these in numerical form. ) ( ) ) ( ) ) ( 7 ) ) ) 6) ( ) 7) ( ) 8) ( 7 ) 9) 0) ( ) ( ) ( ) ( ) Eercise 7 Simplify each of the following ) a) b) 6 c) a a 8 d) y y ) a) a a b) a a c) d) 0 ) a) ( a 6 ) b) ( ) 6 c) ( y ) d) ( b ) 6 ) a) ( y) b) ( ab) a c) ( y) y d) ( ab) b ) a) ( ) b) ( ) c) ( ) d) ( a) 0b ) a) a a b) 7 c) d) 0b 0 7) a) b) 9a a c) 6y y 8) a) b) c) 8

30 Sumbooks 00 Eercise Calculate ) 8 ) 6 ( ) ( ) 7) 0) 6 Multiplying Brackets ) 7 ) 8) 6 ( ) ) ( ) ) ( 6) 6) 8 9) 7 ( ) ( ) ) 8 7 Eercise Epand and simplify ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )+ 6 ( 7y) ( ) ( y) ( ) ( + ) ( ) ( + ) ( ) ( ) ) + y ) ) + 7) 9) ) y + y ) 7 y + y ) y + y 7) + y 9) 7 y ) ) 6 + ) + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )+ ( + y) ( ) ( + y) ( ) ( ) ( )+ ( ) ( ) ( ) ( ) ( + ) ) 6 + ) + 6) 7 8) + 0) 7 + 8y + + y ) + 8y 66 y ) + y y 6) + y 8) y 0) + ) + ) 6) 6 Eercise Epand and simplify ( )( + ) ( )( + ) ( )( ) ( )( 6) ( )( + ) ( )( + ) ( )( 7 ) ( )( 9 ) ) + ) + ) + 7) 6 + 9) ) 6 ) 6 ) 8 6 7) ( + ) 9) ( ) ( )( + ) ( )( 6 + 7) ( )( ) ( )( ) ( )( + ) ( )( 8) ( )( ) ( )( ) ) + ) + 6) + 8) + 0) ) 7 ) 6 6) + 7 8) ( 6 ) 0) ( 9)

31 Sumbooks 00 Factorising Eercise Factorise ) + 6 ) z + 7) 6 0 0) + 6y ) 8 8z 6) a + 9) 6a b + 8c ) ) 8y + 0 8) 6 ) + 6y ) 8y + 7z 7) ) a + 0b c ) 6 6) 8y 6 9) a 6 ) a + b ) p 0q 8) ) 9a + b Eercise Factorise ) a a ) 7) y + y 0) 6 9 ) 0a a ) 6y y ) a + 6a 8) 0 ) 6y + 0y ) 8 ) 9 6) b b 9) z z ) z 6z ) 7a 8a Eercise Factorise ) ab + a ) a + 6a 7) ab a + a 0) 0y + y ) 6p q pq ) y ) 9 6 8) 7a ab ) 6y 8yz ) 9ab a b ) 6a ab 6) y + 6 9) πr 6πrh ) 8pq p q ) 6 y y Eercise (mied) Factorise ) a + b ) y + y 7) y 0) 6a + 0 ) 8a + 6a ab ) ah a ) abc bc 8) 7 y + ) 9ab 7b ) 8 + y 6z ) a + b + 0c 6) 6y y 9) πd 7πd ) 6a + 8a ) + + y

32 Sumbooks 00 6 Equations Find the value of the letter in each of the following equations Eercise ) + = 6 ) = 7) 6 y = 0) a = 6 ) 7b = 6) a + = 0 9) 7 = 8 ) y + = ) + 7 = 7 ) y 7 = 8) = ) 6 = ) y = 7) 9a + 6 = 0) 7 = 7 ) b + = ) 7 + y = 9 6) a 9 = 8 9) 9 = ) 8y = 6 ) b = 0 8) + 6 = 0 ) 6 7 = ) 6y = Eercise ) + = ) + = 7) = 0) + 6 = ) + = 6) + 7 = 9) + 9 = + ) 6 = ) + = 8) 6 = ) 8 + = 0 ) + = 7) 6 = + 0) + 7 = ) 7 6 = 6 6) + = 9) 7 = ) = 9 ) = + 6 8) = + ) + = Eercise ) ( + ) = 8 ) ( + ) = 6 7) ( ) = 7 0) ( + ) = ) ( + ) = 0 6) ( + ) = 8 9) ( + ) = ( ) ) ( + ) + = ) ( ) = 9 ) 7( ) = 8) ( + ) = 8 ) ( ) = ) ( ) = 7) 6( 6) = + 0) ( + ) = ( 9) ) ( ) + = 9 ) ( + ) = 6) ( + ) = 6 9) ( 7) = ) ( + 6) = ) 6( + 7) = 8) ( + ) = + 8 ) ( ) = ( ) ) ( + ) = 87

33 Sumbooks 00 7 More Equations Find the value of the letter in each of the following Eercise ) = 6 ) = 6 7) 7 9 = 0) + = ) + = 6) = + 9) = ) + = 6 ) 8) + = + + = ) = ) 7 0 = 8) 7 = ) + 7 = ) = 6 7) 6 + = 7 0) + = 7 + ) = 7 6) + = 9) + = ) -- ( + ) + -- ( ) = ) ) -- ( + ) + -- ( + ) = 7 ) ) -- ( ) + -- ( ) = 6) ) 6 = 8 6) = 9) = 9 ) 6 = ) + = 9 8) = ) = ) 7 = 6 7) 0) 7 = ( + ) = 6 -- ( 0 ) + -- ( + 7) = -- ( 8 + ) -- ( ) = 8 -- ( + ) -- ( 7 ) = Eercise ) ( )( ) = 0 ) ( + )( ) = 0 7) = 0 0) + = 0 ) = 0 6) 0 = 0 9) + = 0 ) = 0 ) ( + )( ) = 0 ) ( + 6)( ) = 0 8) + 6 = 0 ) = 0 ) = 0 7) + 6 = 0 0) 8 0 = 0 ) 0 + = 0 ) ( + )( + ) = 0 6) ( + 0)( + ) = 0 9) + + = 0 ) + 8 = 0 ) = 0 8) 9 0 = 0 ) = 0 ) = 0

34 Sumbooks 00 8 Straight Line Graphs and Simultaneous Equations Eercise Draw the graph of each of the following equations ) y = + ) y = 7) y = + 0) y = + ) y = + 6) y = + 9) y = ) y = + ) y = + ) y = 6 8) y = + ) y = ) y = 7) y = + 0) y = + ) y = ) y = + 6) y = 9) y = ) y = 6 ) y = 7 8) y = ) y = + 7 ) y = + ) y = 8) + y = 6 ) y = 0 ) + y = 0 7) + y = 0 6) y = + 9) + y = 0 ) 6 y = 0 ) y = 0 8) y + + = 0 7) y = 7 0) 6 + y = ) y = 0 6) + y = 0 9) + y = 0 Eercise Solve each of the following pairs of simultaneous equations by drawing them. All diagrams can be drawn on aes where lies between and 6, and y lies between and 6. ) y = and + y = 9 ) + y = and y = + ) y = and y = 7) y = and y = + 9) y = + and + y = ) + y + = 0 and y = ) y = and y = + ) y = and + y = 6 ) y = + and + y = 6 6) y = + and + y = 8) + y = and y = + 0) y = 0 and y = 0 ) y = + and + y = 6 ) y = + and + y =

35 Sumbooks 00 9 Trial and Improvement Eercise Calculate the value of, correct to decimal place for each of the following, using a trial and improvement method. Show all your attempts. ) = ) = 7 ) = 86 ) = 97 ) = 6) = 77 7) = 60 8) = 7 9) = Eercise By using a suitable trial and improvement method find the value of, correct to one decimal place, which satisfies each of the following equations. Show all your attempts. ) + = ) + = 7 ) = ) = 9 ) + = 6) + = 7) = 8) = 7 9) + = 67 0) + = ) = 67 ) = 00 ) If = 0, find the value of correct to decimal place. ) If + = 7, what is the value of correct to decimal place? ) Calculate the value of in the equation + = 6, correct to one decimal place. 6) Solve the equation = 0, correct to decimal place. 7) A square has an area of cm. Use a trial and improvement method to calculate the length of one side. 8) The longer side of a rectangle is cm greater than the shorter side. If its area is cm use a trial and improvement method to calculate the size of the shorter side? 9) The perpendicular height of a right angled triangle is cm more than its base. If its area is 9cm, what is the length of its base. 0) A cuboid has a height and length which are each 6cm greater than its width. If its volume is 600cm, calculate its width correct to one decimal place.

36 Sumbooks 00 0 Inequalities Solve these inequalities in the form a number, a number, > a number or < a number. ) + > ) + < ) 7 < + ) + < 8 ) > 7 6) > 7 7) 8) 9) 0) + 7 ) 6 < 6 ) < ) ) + 0 ) + 7 < 0 6) 6 > 7) < + 0 8) > + 7 9) + 8 0) 8 + < 60 ) + ) + > 8 ) > + ) 7 < ) + 7 6) ) ) 7 < 9) > + 0) + < + ) -- 7 ) -- ) ) -- + > ) -- 6> 0 6) > 0 6 7) ) 9 -- > ) -- 8 > ) ( + ) > ) ( + 8) > ) ( + 7) > 0 ) ( + ) 6 ) ( + ) 6 ) ( + ) 6) > ( + ) 7) + > ( + ) 8) 9 > ( + ) 9) ( + ) + 0 0) ( 7) + ) 6( 7) + 8

37 Sumbooks 00 Inequalities - Graphs ) 6 The diagram shows the graphs of y = --, y = and =. From the diagram write down the co-ordinates of a point (,y) which satisfies the inequalities y > --, y < and >. ) The diagram shows the graphs of y = +, 7y + = and =. From the diagram write down a point (,y) which satisfies the inequalities y +, 7y + > and ) Using a scale of 0 to 8 on the ais and 0 to 0 on the y ais, plot the following graphs; y =, y = 7 and y =. Shade in the region which satisfies all the inequalities y<, < 7 and y >. ) Using a scale of 0 to 9 on the ais and 0 to 9 on the y ais, plot the following graphs; y =, y = 6 and 8 + 8y = 6. Shade in the region which satisfies all the inequalities y>, y < 6 and 8 + 8y > 6. ) Using a scale of 0 to 8 on the ais and 0 to 0 on the y ais, plot the following graphs; y = --, = and 8 + y = 0. Shade in the region which satisfies all the inequalities y > --, and 8 + y < 0. 6) Using a scale of 0 to 8 on the ais and 6 to 6 on the y ais, plot the following graphs; y =, = 6 and y =. Shade in the region which satisfies all the inequalities y<, < 6 and y>. Which of the following points lie within this region? (,), (, ), (,), (,) 7) Using a scale of 0 to 8 on the ais and 0 to 8 on the y ais, plot the following graphs; y = -- +, = and 7 + 6y =. Shade in the region which satisfies all the inequalities y -- +, > and 7 + 6y <. Which of the following points lie within this region? (,), (,), (,), (,).

38 Sumbooks 00 Rearranging Formulae Rearrange each of the following formulae to make its subject the letter indicated in the brackets. ) C = πd (D) ) C = πr (r) ) F = ma (m) ) V = lbh (h) ) A = --bh (h) 6) = --πr h (h) 7) y = m + c (c) 8) y = m + c (m) 9) v = πr h (h) 0) v = πr h (r) ) C = -- ( F ) (F) ) y = -- ( a+ b) (b) 9 ) = gh (h) ) v = u + as (s) v ) ut + --at = (a) 6) s = -- ( u+ v)t (v) 7) N = π l (l) 8) X = lr (r) 9) A = + y ( y) () 0) p = () ) p = R D () ) C = y zy (y) ) I = PTR -- w (w) ) I = y 00 (R) ) C = d + t () 6) A = π( R r ) (R) 7) A = π( R r ) (r) 8) = a+ b (b) C( c) a 9) a = (b) 0) = (b) b a+ b

39 Sumbooks 00 Bearings Eercise Draw diagrams to show the following bearings. ) A is 00 from B ) C is from D ) G is from H ) J is from K ) L is 7 from M 6) P is 08 from Q 7) R is 098 from T 8) U is 076 from V Eercise By measuring these angles, write down the bearing of point P from point A in each case. ) P A ) P N N ) P A ) A ) N S A P P S A Eercise ) If the bearing of A from B is what is the bearing of B from A? ) If the bearing of C from D is what is the bearing of D from C? ) A ship sails from port P on a bearing of 0 for 6km until it reaches point X. It then changes course onto a bearing of for a distance of 8km until it reaches point Y. Draw the ship s path accurately using a scale of cm to km. What is the bearing and distance of point Y from the port P? ) An aeroplane flies from airport A on a bearing of 0 for 7km until it reaches point B. It then changes course onto a bearing of for a distance of 80km until it reaches point C. Draw the aircraft s path accurately using a scale of cm to 0km. What is the bearing and distance of point C from the airport A?

40 Sumbooks 00 Parallel Lines In each of the following diagrams find the sizes of the marked angles. ) ) 6 7 a b c ) ) d e g f ) 6) h 87 i j 7 80 l k n m 7) 8) p 8 q u v 8 t 68 r w s 9) 0) y z β α δ

41 Sumbooks 00 Nets and Isometric Drawing ) Draw the net of a cube whose sides are cm. ) Draw the net of this cuboid. Also draw, on triangular dotty paper or isometric paper, a cuboid whose volume is the same as this one. cm 6cm cm ) This diagram shows part of the net of a triangular prism. Copy and complete the diagram. On triangular dotty paper or isometric paper, draw a diagram of the shape. 6cm cm cm ) Draw the net of this triangular prism cm cm 6cm ) The diagram on the right shows part of the net of a square based pyramid. Copy and complete the diagram. On triangular dotty or isometric paper, sketch a diagram of the shape. cm cm 6) The diagram shows a square based pyramid. Its base edges measure cm and its sloping edges are 6cm. Draw the net of its shape. 7) The diagram shows part of the net of a rectangular based pyramid. Copy and complete the diagram. On triangular dotty or isometric paper, sketch a diagram of the shape. cm cm cm cm 8) The diagram shows a rectangular based pyramid. Its base edges measure.cm and cm and its sloping edges are each cm. Draw the net of the shape.

42 Sumbooks 00 6 Triangles Calculate the sizes of each of the marked angles. ) º 0º ) 0º 0º y ) y 0º ) 0º ) y y 0º 0º 6) y º z 7º º z y 7) y z 8) 9) y º 6º z 0) ) º 7º º z y y z ) y 0º ) A BC=AC º B 70º y C

43 Sumbooks 00 7 Regular Polygons Calculate the interior and eterior angles in each of the regular shapes in questions to. ) A Heagon ) A Nonagon (9 sides) ) A sided figure ) A 0 sided figure ) 6) A E A B z F B y D C ABCDE is a regular pentagon. Line BF is a line of symmetry. a) What is the size of angle? b) Calculate the sizes of angles y and z. H G r s q C D ABCDEFGH is a regular octagon. CG is a line of symmetry. Calculate the sizes of angles p, q, r, s and t. F p t E 7) A G w B F y E z D v C ABCDEFG is a regular heptagon. Three lines of symmetry are shown. What are the sizes of angles v, w,, y and z? 8) What is the order of rotational symmetry of a regular octagon? 9) Eplain why a regular pentagon will not tessellate and a regular heagon will. 0) How many lines of symmetry has a regular nonagon? ) ABCDEFGHIJ is a regular 0 sided polygon (decagon) with centre O (where the lines of symmetry cross). Calculate the sizes of the angles ABC and AOC.

44 Sumbooks 00 8 Irregular Polygons ) A quadrilateral has internal angles of 90º, 00º and 0º. What is the size of the fourth angle? ) A heagon has angles of 00º, 0º, º, 0º and 0º. What is the size of the sith angle? ) An octagon has si angles of º. If the remaining two angles are equal, what is the size of them? ) A heptagon has si angles each of 0º. What is the size of the other angle? ) A decagon has two angles of the same size and a further eight angles of twice the size. What are the sizes of the angles? 6) What is the size of the angle? 60º 7) This heagon is symmetrical about the line AD. The angles at A and B are 0º and 0º. If the side BC is parallel to FE and the angle at C is twice the angle at D, what are the sizes of the other angles? A B F C E D A 8) The pentagon ABCDE has three angles of 90º. If the other two angles are equal, what are their size? E B D C 9) In the diagram, the octagon has two lines of symmetry. There are two different sizes of angle in the shape. If one of them is 0º, what is the other? A 0) The diagram shows the cross section of a steel bar. It is symmetrical about the line AB. If it has si interior angles of 90º and another of 60º, what are the sizes of the other interior angles? B

45 Sumbooks 00 9 Pythagoras' Theorem ) Calculate the length of the hypotenuse in each of the following triangles a) b) c) 6cm cm 8cm cm 9cm 6cm ) Calculate the length of the side marked in each of the following right angled triangles. a) 7cm b) cm.cm c) cm 6cm 6cm ) ) A 6 cm 6 cm cm Calculate the height of this isosceles triangle O cm B cm Find the distance of point T from the centre of the circle T ) Calculate the base radius R of this cone 6) 0cm cm 7cm of height cm and slant height of 7 cm 0cm R A kite has sides measuring 0cm and 0cm with the small diagonal measuring 8cm. Find the length of the longer diagonal 7) Calculate the length of the diagonal of a rectangle measuring 9cm by cm. 8) A rhombus has diagonals of 7cm and cm. Find the length of its sides. 9) A square has a side of 7cm. Find the length of its diagonals. 0) How far from the centre of a circle of radius 7cm is a chord of length 7cm ) A ladder rests against a wall. The ladder is metres long. The base of the ladder is m from the foot of the wall. How far up the wall will the ladder rest? ) A ladder, 6 metres long, rests against the side of a house. The ladder reaches metres up the side of the house. How far, to the nearest centimetre, is the bottom of the ladder from the base of the house? ) Calculate the length of the side of a square whose diagonal is cm.

46 Sumbooks 00 0 Trigonometry Use the sine ratio ) Calculate the length of the unknown side () in each of the following triangles. a) 8.cm 7 o b) 6 o cm c) 7 o.7cm d) 7 o 9.7cm e) cm 79 o ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) 8.cm c) 7.cm cm 7cm cm cm d) cm 9cm e) 8.cm cm ) Calculate the length of the unknown side () in each of the following triangles a).cm b) 8.cm 80 o c) 7 o 67 o.6cm d).cm o e) o 7.cm

47 Sumbooks 00 Trigonometry Use the cosine ratio ) Calculate the length of the unknown side () in each of the following triangles. a) cm b) c) 70 o 6 o o 7.cm.6cm d) e) o cm 6 o 6.cm ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) 7cm c) cm.6cm 0cm 7.cm 6.cm d) 8.6cm e) 9.7cm cm 7.cm ) Calculate the length of the unknown side () in each of the following triangles a) o cm b) 7cm 6 o c).6cm 7 o d) 6 o.cm e).cm 9 o

48 Sumbooks 00 Trigonometry Use the tangent ratio ) Calculate the length of the unknown side () in each of the following triangles. a) b) 9.cm 9 o 7 o 6.8cm c).cm 7 o d) e).cm 7 o 7cm 9 o ) Calculate the sizes of the unknown angles in each of the following triangles. a) b) c) cm 7cm cm cm 0cm d) cm 6cm e) cm.cm cm ) Calculate the length of the unknown side () in each of the following triangles. a) cm b) c) cm o d) 7 o 6cm cm 6 o e) 7 o 8 o 6.7cm

49 Sumbooks 00 Trigonometry Use the sine, cosine or tangent ratios. a) b).6cm Calculate the length of side 67 7cm Calculate the length of side c) d) e) f) g).6cm.6cm.cm Calculate the sizes of the two unknown angles 7.9cm Calculate the sizes of the two unknown angles.6cm 7.cm 6.cm Calculate the length of side Calculate the sizes of the two unknown angles A ladder rests against a wall. If the ladder is metres long and its base is. metres from the bottom of the wall, what angle does it make with the wall? h) m 6m A boat B is 6 metres from the bottom of a cliff of height metres. Calculate the angle of depression,, of the boat from the top B of the cliff. i) A ladder,. metres long, rests against a wall at an angle of to the wall. How far up the wall does the ladder reach and how far is its base from the wall? j) The angle between the diagonal and longest side of a rectangle is. If the longest side measures 6cm, what is the length of the shortest side? k) A swimming pool is metres long. If its depth varies from metre to. metres, at what angle to the horizontal is its base?

50 Sumbooks 00 Reflections, Rotations and Translations ) The diagram shows a triangle A,B,C. Copy this diagram and show the reflections; a) A',B',C' about the ais b) A'', B'', C'' about the y ais. y A B C ) The diagram shows a rectangle A,B,C,D. Copy this diagram and show the reflections; a) A',B',C',D' about the line = b) A'',B'',C'',D'' about the line y =. y A D B C ) The diagram shows a shape A,B,C,D,E. Copy this diagram and show; a) the reflection A,B,C,D,E about the line = b) the reflection y A,B,C,D,E about the line y = 0. c) The translation to A,B,C,D,E. 6 6 A E 0 B D C 6

51 Sumbooks 00 Reflections, Rotations and Translations y ) The diagram shows a square A, B, C, D. Copy this diagram and show the reflections A B a) A', B', C', D' about the line y = b) A'', B'', C'', D'' about 6 D 0 C 6 the line y = y ) The diagram shows a rectangle A, B, C, D. Copy this diagram and show the reflections A a) A', B', C', D' about D the ais b) A'', B'', C'', D'' about the y ais 6 0 B 6 C y ) The diagram shows a triangle A, B, C. Copy this diagram and show the reflections B a) A', B', C' about the line y = b) A'', B'', C'' about 6 A 0 6 the line y = C

52 Sumbooks 00 6 Reflections, Rotations and Translations ) The diagram below shows the triangle A, B, C. Copy this diagram and show the rotation a) to A, B, C of 90º clockwise about (0,0) b) to A, B, C of 90º anticlockwise about (0,0) Also show the translation 6 to A, B, C. 6 y B A C ) The diagram below shows the rectangle A, B, C, D. Copy this diagram and show the rotation a) to A', B', C', D' of 90º clockwise about (,) b) to A", B", C", D" of 80º about (,) y A B D C 6 0 6

53 Sumbooks 00 7 Reflections, Rotations and Translations ) The diagram below shows the heagon A, B, C, D, E, F. Copy this diagram and show: a) the rotation to A', B', C', D', E', F' of 90º clockwise about (0,0) b) the translation to A", B", C", D", E", F", y A B 6 F 0 C 6 E D ) The diagram below shows the parallelogram A, B, C, D. Copy this diagram and show a) the rotation to A', B', C', D' of 90º clockwise about (0,0) b) the translation to A", B", C", D". y A B D C