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"'•,: &· Greg Byrd, Lynn Byrd and Chris Pearce Cambridge Checkpoint Mathematics Practice book ·1 Contents Adding and subtracting algebraic fracti ons 46 Introduction 5 9.6 1 Integers, powers and roots 7 9. 7 Expanding the product of two 47 1.1 Directed numbers 7 linear expressions 1.2 Square roots and cube roots 8 10 Processing and presenting data 48 1.3 Indices 9 48 IO.I Calculating statistics 1.4 Working with indices 10 50 10.2 Using statistics 2 Sequences and functions 11 11 Percentages 52 2.1 Generating sequences 11 Using mental methods 52 11.1 2.2 Finding the nth term 12 Comparing different quantit ies 53 11.2 2.3 Finding the inverse of a function 13 Percentage changes 54 11.3 11.4 Practical examples 55 3 Place value, ordering and rounding 14 3.1 Multiplying and dividing decimals mentally 14 12 Tessellations, transformations and loci 56 3.2 Multiplying and dividing by powers of IO 15 12.1 Tessellating shapes 56 3.3 Rounding 16 12.2 Solving transformation problems 57 3.4 Order of operations 17 12.3 Transforming shapes 59 18 12.4 Enlarging shapes 60 4 Length, mass, capacity and time 61 18 12.5 Drawing a locus 4.1 Solving problems involving measurements 4.2 Solving problems involving average speed 19 13 Equations and inequalities 62 Using compound measures 20 13.1 Solving linear equations 62 4.3 21 13.2 Solving problems 63 5 Shapes Simultaneous equations 1 64 21 13.3 5. 1 Regular polygons Simultaneous equations 2 65 22 13.4 5.2 More polygons Trial and improvement 66 23 13.5 5.3 Solving angle problems Inequalities 67 25 13.6 5.4 Isometric drawings 26 14 Ratio and proportion 68 5.5 Plans and elevations 27 14.1 Comparing and using ratios 68 5.6 Sym metry in three-dimensional shapes 28 14.2 Solving problems 70 6 Planning and collecting data 28 15 Area, perimeter and volume 72 6. 1 Identifying data 29 15.1 Converting units of area and volu me 72 6.2 Types of data 30 15.2 Using hectares 73 6.3 Des igning data-collection sheets 31 15.3 Solving circle problems 74 6.4 Collecti ng data 32 15.4 Calculating with prisms and cylinders 75 7 Fractions 32 7. 1 Writing a fraction in its si mplest fo rm 16 Probability 76 33 16. 1 Calculating probabilities 76 7.2 Adding and subtracting fractions 34 16.2 Sample space diagrams 77 7.3 Multiplying fractions 35 16.3 Using relative frequency 78 7.4 Dividi ng fractions 36 7.5 Working with fractions mentally 17 Bearings and scale drawings So 8 Constructions and Pythagoras' th eorem 37 17. 1 Using bearings 80 37 17.2 Making scale drawings 82 8.1 Constructing perpenclicular li nes 38 8.2 Inscribing shapes in circles 39 18 Graphs 83 8.3 Usi ng Pythagoras' theorem 18.1 Gradient of a graph 83 40 18.2 The graph of y = mx + c 85 9 Expressions and formulae . 40 9.1 Simplif},ing algebraic expresswns 18.3 Drawing graphs 86 41 18.4 Simultaneous equations 9.2 Co nstructing algebraic exp ressions 87 43 18.5 Direct proportion 9.3 Substituting into expressions 89 44 18.6 Prac tical graphs 9.4 Derivin g and using formulae 45 90 9.5 Factorising . 19 Interpreting and discussing results 91 19.1 Interpreting and drawing frequency diagrams 91 19.2 Interpreting and drawing line graphs 92 19.3 Interpreting and drawing scatter graphs 93 19.4 Interpreting and drawing stem-and- leaf diagrams 94 19.5 Comparing distributions and drawing conclusions 95 Introduction Welcome to Cambridge Checkpoint Mathematics Practice Book 9 The Cambridge Checkpoint Mathematics course covers the Cambridge Secondary 1 Mathematics framework. The course is divided into three stages: 7, 8 and 9. This Practice Book can be used with Coursebook 9. It is intended to give you extra practice in all the topics covered in the Coursebook. Like the Coursebook, the Practice Book is divided into 19 units. In each unit you will find an exercise for every topic. These exercises contain similar questions to the corresponding exercises in the Coursebook. This Practice Book gives you a chance to try further questions on your own. This will improve your understanding of the subject. It will also help you to feel confident about working on your own when there is no teacher available to help you. There are no explanations or worked examples in this book. If you are not sure what to do, or need to remind yourself about something, look at the explanations and worked examples in the Coursebook. - 1 Integers, powers and roots C Exercise 1.1 Directed numbers 1 Work these out. a -6 + 2.7 b - 6 + -2.7 C 16 + -2.7 d 2.7 + -16 2 Work these out. a 7--5 b 7.1 - -5.2 C -7.1- -5.2 d -5.2 - -7.1 3 Work these out. a -8.4 + 12.1 b -8.4 - 12.1 C 8.4--12.1 d -12.1 - -8.4 4 These are five temperatures, in degrees Celsius (°C). 1.5 -3.5 -7 -10 -3 Find the mean temperature. 5 Solve these equations. a N + 2.3 = -4.7 b 2N + 6.8 = -10.2 C N+4=-2.7 6 Work these out. a -2 X 3.4 b -4.8 + -4 C -3X9.2 d 14 + -4 fl) 7 Copy and complete this multiplication table. I -~-• 1-•-· 1-~, I Use the information in the box to work out the value of each expression. ~ 8 a r+s+t b (r-s)-t c (s- r)xt d t+(r-s) r=B-4 s = 6.4 t=-7.4 e (r+s) +t ~ 9 A + B = 0 and AB = - 36. What is the value of A - B? 1 Integers, powers and roots - - C Exercise 1.2 Square roots and cube roots 1 Estimate each root, to the nearest whole number. Do not use a calculator in th·1 a b except for questions s and _ s exercis e, 9 c~ d~ 2 Explain why: a ./95 must be between 9 and 10. b ¼s must be between 4 and 5. 3 3 < Ji.o:s < 4 Write a similar statement for each of these roots. a b °½oo c ../69i, d ½s.s 4 a 144 < N < 225 What can you say about b 100 < M < 400 What can you say about C o < R < 125 What can you say about ifii ? ~ 5 25.5' = 650.25 26.5' = 702.25 a Estimate ./6ii to the nearest whole number. b Estimate Ji,so to one decimal place. c Estimate to one decimal place. 6 Show that ½oo is less than half .Ji.oo. 7 a Show that is more than 80. b Show that {/7500 is less than 20. 8 Use a calculator to find the following square roots. a 30.25 b c d e 9 Use a calculator to find the following square roots. Ro und yo ur answers to two decimal places. a b c d e JiAj 1 Integers. powers and roo ts Exercise 1.3 Indices 1 Write each number as an integer or a fraction. a 54 b 35 C 6- 2 d 2- 3 e 4° 2 Write each number as a decimal. a s-1 b 2- 2 C 4- 1 d 3- 1 e 10- 3 3 Write these numbers in order of size, smallest first. 1 12 2 6 34 43 62 12 1 4 Write these numbers in order of size, smallest first. S Write each number as a power of 4. a 16 b 256 C 1 d ¼ 1 e 64 6 Write each of the numbers in question 5 as a power of 2. 7 3N= 9-2 Work out the value of N. 8 Write each expression as a single number. a 3- 1 + 6- 1 b 42 + 41 + 40 + 4-1 + 4-2 1 Integers, powers and roots • 11111 C 1 Simplify each expression. Write the answers in index form. a 83 X 8 2 b 7 x 73 2 2 C 22 X 2 X 2 d r2 X r4 e s3 xs7-xs 2 Simplify each expression. a 42 X 4 1 b 6 X 6° 2 C C: X C d l X 25 2 e ex e0 3 Simplify each expression in the box. One is different from the other four. Which one? a4 x a2 as x a a6 x d' cf x as a3 x a3 Give a reason for your answer. @ 4 This table shows powers of 9. 96 92 93 94 9s 91 6561 59 049 531441 9 81 729 Use the table to find the value of each expression. a .j531441 b ~531441 5 Simplify each expression, writing it as a single power. a a5 ..,.. a3 b 6 ..,.. 63 C 82 ..,.. 8 d d 2 + d2 e e + e2 6 Write each of these as a fraction. a 32 --;- 34 b k 2 + k3 C 10- X 10 X 10 4 d 4 2 + 25 <fl) 7 Simplify each expression. 2 a a xa 3 3 b 5 x5 3 a 5 fx f l 3 4 C d 10 2x 10 f l0 x 10 Cf?) 8 Find the value of n in each equation. a S" x 53 =625 b 10"--,- 10=0.l c n° x 112 x n = 64 - I 1 Intege rs, powers and roots
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