Higher REVISION WORKBOOK - Pearson · PDF fileHigher REVISION WORKBOOK Series ... in combination with Edexcel’s main GCSE Mathematics 2010 series ... GCSE_0154_PRE.indd 2 24/5/11

1

Edexcel GCSEMathematics A Linear

HigherREVISION WORKBOOKSeries Director: Keith PledgerSeries Editor: Graham Cumming

Authors: Julie Bolter, Gwenllian Burns, Jean Linsky

The Edexcel Revision SeriesThese revision books work in combination with Edexcel’s main GCSE Mathematics 2010 series. The Revision Guides are designed for independent or classroom study. The Revision Workbooks use a write-in format to provide realistic exam practice.

Higher

Foundation

Specification A Linear Specification B Modular

A01_EMHL_WBK_GCSE_0154_PRE.indd 1 24/5/11 12:01:18

NUMBER1 Factors and primes2 Indices 13 Fractions4 Decimals5 Recurring decimals6 Rounding and estimation7 Upper and lower bounds8 Fractions and percentages9 Percentage change10 Reverse percentages and compound interest11 Ratio12 Proportion13 Indices 214 Standard form15 Calculator skills16 Surds17 Problem-solving practice: Number 18 Problem-solving practice: Number

ALGEBRA19 Algebraic expressions20 Arithmetic sequences21 Expanding brackets22 Factorising23 Linear equations 124 Linear equations 225 Straight-line graphs26 Parallel and perpendicular27 3-D coordinates28 Real-life graphs29 Formulae30 Rearranging formulae31 Inequalities32 Inequalities on graphs33 Quadratic and cubic graphs34 Graphs of k _ x and ax

35 Trial and improvement36 Simultaneous equations 137 Quadratic equations38 Completing the square39 The quadratic formula40 Quadratics and fractions41 Equation of a circle42 Simultaneous equations 243 Direct proportion44 Proportionality formulae45 Transformations 146 Transformations 247 Algebraic fractions48 Proof49 Problem-solving practice: Algebra50 Problem-solving practice: Algebra

GEOMETRY AND MEASURES51 Angle properties52 Solving angle problems53 Angles in polygons54 Plan and elevation55 Perimeter and area56 Prisms57 Circles and cylinders58 Sectors of circles

Contents59 Volumes of 3-D shapes60 Pythagoras’ theorem61 Surface area62 Converting units63 Units of area and volume64 Speed65 Density66 Congruent triangles67 Similar shapes 168 Similar shapes 269 Bearings70 Scale drawings and maps71 Constructions72 Loci73 Translations, re�ections and rotations74 Enlargements75 Combining transformations76 Line segments77 Trigonometry 178 Trigonometry 279 Pythagoras in 3-D80 Trigonometry in 3-D81 Triangles and segments82 The sine rule83 The cosine rule84 Circle facts85 Circle theorems86 Vectors87 Solving vector problems88 Problem-solving practice: Geometry89 Problem-solving practice: Geometry

STATISTICS AND PROBABILITY90 Collecting data91 Two-way tables92 Strati�ed sampling93 Mean, median and mode94 Frequency table averages95 Interquartile range96 Frequency polygons97 Histograms98 Cumulative frequency99 Box plots100 Scatter graphs101 Probability102 Tree diagrams103 Problem-solving practice: Statistics104 Problem-solving practice: Statistics

105 Formulae page106 Paper 1 Practice exam paper113 Paper 2 Practice exam paper119 Answers

A small bit of small printA grade allocated to a question represents the highest grade covered by that question. Sub-parts of the question may cover lower grade material.The grade range of a topic represents the usual grade range that the topic is assessed at. The topic may form part of a higher grade question if tested within the context of another topic.Questions in this book are targeted at the grades indicated.

A03A02

A03A02

A03A02

A03A02

A01_EMHL_WBK_GCSE_0154_PRE.indd 2 24/5/11 12:01:18

NUMBER

1

Factors and primes1 (a) Express the following numbers as products of their prime factors.

(i) 60 (ii) 150

32 …………

60

106

……2 …………

150

1510

60 5 2 3 …… 3 …… 3 …… 150 5 2 3 …… 3 …… 3 …… (2 marks) (2 marks)

(b) Find the highest common factor (HCF) of 60 and 150

60 5 2 3 3 3 …… 3 ……

150 5 2 3 …… 3 …… 3 ……

HCF 5 2 3 …… 3 ……

5 ……… (1 mark)

(c) Find the lowest common multiple (LCM) of 60 and 150

LCM 5 ……… 3 …… 3 ……

5 ……… (1 mark)

2 (a) Express 72 as a product of its prime factors.

………………… (2 marks)

(b) Find the highest common factor (HCF) of 72 and 120

HCF 5 ………………… (1 mark)

(c) Find the lowest common multiple (LCM) of 72 and 120

LCM 5 ………………… (1 mark)

C

Guided

Remember to circle the prime factors as you go along.

Guided Circle all the prime numbers which are common to both products of prime factors. Multiply the circled numbers together to find the HCF.

Guided To find the LCM, multiply the HCF by the numbers in both products that were not circled in part (b).

C

M01_EMHL_WBK_GCSE_0154_U01.indd 1 18/8/11 13:32:13

NUMBER

2

Indices 11 Write as a power of 7

(a) 73 3 710

73 3 710 5 73 1 10 5 ………… (1 mark)

(b) 715 4 7 9

715 4 79 5 715 2 9 5 ………… (1 mark)

(c) 712 ______

7437

712 _______ 74 3 7 5 712

_______ 74 3 71 5 712 ___ 7......

5 ………… (2 marks)

(d) (75)4

(75)4 5 75 3 4 5 ………… (1 mark)

2 Write as a power of 5

(a) 58 3 54 (b) 512 3 5 _______

54 3 53 (c) (52)3

……………… (1 mark) ……………… (2 marks) ……………… (1 mark)

3 68 3 63 5 65 3 6x

Find the value of x.

x 5 ………………… (2 marks)

4 Simplify 40

………………… (1 mark)

5 Write 93 3 272 as a single power of 3

93 3 272 5 (3……)3 3 (3……)2

5 3…… 3 3……

5 ………. (2 marks)

6 Write 86 4 43 3 25 as a single power of 2

………………… (2 marks)

C

Guided

Guided

Guided

Guided

C

C Use the index laws to simplify each side of the equation.

B

AGuided

A


NUMBER

3

Fractions1 Work out 3 2 _ 3 1 1 4 _ 5

Give your answer as a mixed number in its simplest form.

3 2 __ 3 11 4 __ 5

5 …… 1 … ___ 3 1 … ___ 5

5 …… 1 … ___ 15 1 … ___ 15

5 …… 1 … ___ 15

5 …… 1 1 … ___ 15

5 …… … ___ 15 (3 marks)

2 Work out (a) 7 1 _ 7 2 2 2 _ 3 (b) 8 9 __ 10 1 2 3 _ 5

Give each answer as a mixed number in its simplest form.

(a) …………………… (3 marks) (b) …………………… (3 marks)

3 Work out 2 1 _ 3 3 1 3 _ 5

2 1 __ 3 3 1 3 __ 5

5 … ___ 3 3 … ___ 5

5 … ___ …

5 …… … ___ …

(3 marks)

4 Work out (a) 2 1 _ 4 3 3 1 _ 3 (b) 5 1 _ 3 4 1 2 _ 9


(a) …………………… (3 marks) (b) …………………… (3 marks)

5 Work out (a) 8 5 _ 6 2 3 2 _ 5 (b) 4 1 _ 5 4 9 __ 10


(a) …………………… (3 marks) (b) …………………… (3 marks)

C

Guided

Add the whole numbers.

Write as equivalent fractions with the same denominator.

Write your final answer as a mixed number in its simplest form.

C

C Exam questions similar to this have proved especially tricky – be prepared!Guided

Write both mixed numbers as improper fractions.

Multiply numerators and multiply denominators.

EXAMALERT

Write your final answer as a mixed number in its simplest form.

C

C


NUMBER

4

Decimals1 Using the information that 67 3 29 5 1943

write down the value of

(a) 6.7 3 2.9

6.7 3 2.9 5 1943 4 …………

5 …………

(1 mark)

(b) 670 3 0.0029

670 3 0.0029 5 1943 4 …………

5 …………

(1 mark)

(c) 19 430 4 67

19 430 4 67 5 29 3 …………

5 …………

(1 mark)

2 Use the information that 127 3 84 5 10 668to �nd the value of

(a) 1270 3 84 (b) 0.127 3 8.4 (c) 10 668 4 1.27

………………… (1 mark) ………………… (1 mark) ………………… (1 mark)

3 Given that 63 3 48 5 3024write down the value of

(a) 6300 3 4.8 (b) 0.063 3 4.8 (c) 30 240 4 6.3

………………… (1 mark) ………………… (1 mark) ………………… (1 mark)

C

Guided 67 has been divided by 10 and 29 has been divided by 10. So the answer needs to be divided by 100.

Guided 67 has been multiplied by 10 and 29 has been divided by 10 000. So the answer needs to be divided by 1000.

Guided 1943 has been multiplied by 10 and 67 is unchanged. So multiply 29 by 10.

C

C


NUMBER

5

Recurring decimals1 Express 0. 1

. 5 . as a fraction in its simplest form. You must use algebra.

Let x 5 0. 1 . 5 .

100x 5 15.151 515…2 x 5 0.151 515 …

99x 5 ………

x 5 ……… _______ 99

x 5 ……… _______ ………

(3 marks)

2 Change the recurring decimal 0. 8 . to a fraction. You must use algebra.

………………… (2 marks)

3 Convert the recurring decimal 2. 4 . 1 7

. to a fraction. You must use algebra.

………………… (3 marks)

4 Convert the recurring decimal 0.4 7 . to a fraction. You must use algebra.

Let x 5 0.4 7 .

10x 5 4.777 7777…2 x 5 0.477 7777…

9x 5 …………

x 5 ……… _______ 9

x 5 ……… _______ ………

(3 marks)

5 Prove that 0.8 2 . 7 . can be written as the fraction 91

___ 110

(3 marks)

AGuided

A

A

AGuided

Multiply the top and bottom of the fraction by 10.

A


NUMBER

6

Rounding and estimation1 Work out estimates for each of the following.

(a) 145 3 78

100 3 ………… 5 ………………… (1 mark)

(b) 19.1 4 1.51

………… 4 2 5 ………………… (1 mark)

(c) 48.9 3 2.78 3 11.9

………… 3 ………… 3 10 5 ………………… (1 mark)

2 Work out an estimate for the value of 3981 _________ 2.3 3 18.7

………………… (2 marks)

3 Work out an estimate for the value of 612 3 39 ________ 0.53

………………… (2 marks)

4 Work out an estimate for the value of 40.7 3 1.6 _________ 0.053

40 3 ……… ____________ 0.05 5 ……… _______ ………

5 ………………… (2 marks)

5 Work out an estimate for the value of 9.73 3 4.12 __________ 0.0214

………………… (2 marks)

6 Work out estimates for the following calculations. State whether your answer is an underestimate or an overestimate.

(a) 995.3 _________ 5.3 3 11.3

………………… (2 marks)

(b) 101.7 _________ 3.7 3 4.72

………………… (2 marks)

7 Work out an estimate for the value of 2.52 3 11.72

………………… (2 marks)

D

Guided

Guided

Guided

D

C

C Exam questions similar to this have proved especially tricky – be prepared!

Guided First round each number to 1 significant figure.

EXAMALERT

C

C

C


NUMBER

7

Upper and lower bounds1 The length of a rectangle is 9.7 cm correct to 2 signi�cant �gures.

The width of the rectangle is 6.5 cm correct to 2 signi�cant �gures.Work out the upper bound for the area of the rectangle.

Upper bound of length 5 9.75

Upper bound of width 5 ………

Upper bound of area 5 9.75 3 …………………

5 …………………

5 ………………… cm2 (3 marks)

2 The length of a rectangle is 24 cm correct to 2 signi�cant �gures.The width of the rectangle is 9.6 cm correct to 2 signi�cant �gures.Work out the lower bound for the perimeter of the rectangle.

………………… cm (3 marks)

3 A ball is dropped from a window.The time that it takes to reach the ground is given by the formula t 5 √

___

2s __ a

where a m/s2 is the acceleration due to gravity and s m is the height of the window.s 5 117 m correct to 3 signi�cant �guresa 5 9.8 m/s2 correct to 2 signi�cant �gures

(a) Calculate the lower bound and the upper bound for the value of t.Give your answers correct to 4 decimal places.

………………… (4 marks)

(b) Use your answers to part (a) to write down the value of t to a suitable degree of accuracy.You must explain your answer.

t 5 ………………… because the upper bound and the lower bound both agree to 2 significant figures (1 mark)

A

Guided

A

A*

Guided


NUMBER

8

Fractions and percentages1 Uzma invests £4000 in a bank account for 1 year.

Interest is paid at a rate of 2.5% per annum.How much interest will Uzma get at the end of 1 year?

……… _______ 100 3 £4000 5 £………………… (2 marks)

2 A farmer has 48 llamas.30 of the llamas are female.(a) Work out 30 out of 48 as a percentage.

30 _______ ………

3 100 5 ………………… (2 marks)

60% of the female llamas are pregnant.(b) Write the number of pregnant female llamas as a fraction of the 48 llamas.

Give your answer in its simplest form.

………………… (2 marks)

3 Meera works in an electrical shop.Each week she gets paid £160 plus 15% of the value of the goods she sells.One week Meera sold £3200 of goods.Work out the total amount she was paid this week.

£………………… (3 marks)

4 Liam’s annual income is £16 000

He pays 1 _ 5 of the £16 000 in rent.

He spends 15% of the £16 000 on food.Work out how much of the £16 000 Liam has left.

£………………… (4 marks)

5 At an outdoor centre, 140 students each choose one activity.

1 _ 7 of the students choose rock climbing.

3 _ 7 of the students choose rafting.

All the rest of these students choose abseiling.How many students choose abseiling?

………………… (3 marks)

D

Guided

D

Guided

D

D

C


NUMBER

9

Percentage change1 A washing machine costs £420 plus 20% VAT.

Calculate the total cost of the washing machine.

VAT 5 20 ____ 100 3 ………

5 …………………

Total cost 5 420 1 ………

5 £………………… (3 marks)

2 Helen buys a jacket in a sale.The normal price is £84The normal price of the jacket is reduced by 35%.Work out the sale price of the jacket.

£………………… (3 marks)

3 Eliza went to New York.She changed pounds (£) into American dollars ($).The exchange rate was £1 5 $1.60The value of the pound has decreased from $1.60 to $1.56Calculate the percentage decrease in the value of the pound.

Percentage decrease 5 decrease ____________ original value 3 100

5 ……… _______ ………

3 100

5 …………………% (3 marks)

4 Ali buys 120 cans of drink for a total of £30He wants to make a pro�t of 40%.Work out the price for which he should sell each can of drink.

………………… (4 marks)

5 Jean books a holiday.The total cost of the holiday is £1430She pays a deposit of 35% of the total cost.She pays the rest in 10 monthly instalments.Work out how much she pays each month.

£………………… (4 marks)

D

Guided

D

C

Guided

C

C


NUMBER

10

Reverse percentages and compound interest

1 Linda bought a new car for £18 000Each year, the car depreciated in value by 15%.Work out the value of the car after 4 years.

Multiplier 5 1 2 15 ____ 100 5 ………

Value after 4 years 5 18 000 3 (………)4

5 …………………

5 £………………… (3 marks)

2 Jalin invested £3200 in a savings account for 3 years.He was paid compound interest at a rate of 3.5% per annum.Work out how much was in the account after 3 years.

£………………… (3 marks)

3 In a sale, normal prices are reduced by 35%.The sale price of a DVD player is £403Work out the normal price of the DVD player.

Multiplier 5 1 2 35 ____ 100 5 ………

Normal price 5 403 4 ………

5 £………………… (3 marks)

4 Jill’s weekly pay this year is £460This is 15% more than her weekly pay last year.Dave says, ‘This means Jill’s weekly pay last year was £391.’Dave is wrong. Explain why.

(2 marks)

5 Pete invested £5100 for n years in a savings account.He was paid 4.5% per annum compound interest.At the end of the n years he had £6641.53 in the savings account.Work out the value of n.

n 5 ………………… (2 marks)

B

Guided Work out the multiplier as a decimal.

When working with money, answers must be given to 2 decimal places.

B

BEXAMALERT

Exam questions similar to this have proved especially tricky – be prepared!

Guided

B

A

Choose some values for n and work out the amount in the savings account after n years.


NUMBER

11

Ratio1 There are 60 toy cars in a box.

18 of the toy cars are blue.The rest of the toy cars are red.Write down the ratio of the number of red toy cars to the number of blue toy cars.Give your ratio in its simplest form.

Number of red cars 5 60 2 ………

5 ………

Ratio of red cars to blue cars 5 ……… : ………

5 ……… : ……… (2 marks)

2 There are 32 students in a class.20 of the students are girls.Rosie says, ‘The ratio of the number of girls to the number of boys in this class is 3 : 5.’Is Rosie right?You must give a reason for your answer.

………………… (2 marks)

3 Ahmed and James share £120 in the ratio 1 : 3How much does James get?

Number of shares 5 1 1 3

5 ………

One share is worth £120 4 ……… 5 £…………………

James gets ………3 ……… 5 £…………………(2 marks)

4 Annie and Jamil share £160 in the ratio 3 : 5How much more money than Annie does Jamil get?

£………………… (3 marks)

5 Linda, Mel and Tomos share the driving on a journey in the ratio 2 : 3 : 4Mel drove a distance of 240 km.Work out the length of the journey.

………………… km (2 marks)

D

Guided Make sure you put the numbers in the ratio in the correct order.

D

D

Guided

C

C


NUMBER

12

Proportion1 Mike buys 6 pencils for a total cost of £5.34

Work out the cost of 11 of these pencils.

Cost of 1 pencil 5 5.34 4 ………

5 £…………………

Cost of 11 pencils 5 11 3 ………

5 £………………… (2 marks)

2 Punita buys 3 identical notebooks for a total cost of £10.44Work out the cost of 5 of these notebooks.

£………………… (2 marks)

3 The total cost of 4 kg of apples is £4.20The total cost of 3 kg of apples and 2 kg of bananas is £5.05Work out the cost of 1 kg of bananas.

………………… (3 marks)

4 A builder lays 180 bricks in 1 hour.He always works at the same speed.How long will it take the builder to lay 585 bricks?

………………… (2 marks)

5 4 workers can lay a stretch of road in 9 days. How long would it take 6 workers to lay the same stretch of road?

1 worker would take 4 3 ……… 5 ……… days to lay the stretch of road.

So 6 workers would take ……… 46 5 ……… days to lay the stretch of road. (2 marks)

6 It takes one machine at a factory 24 hours to pack 12 000 boxes of cakes.The owner of the factory buys two more machines.All the machines work at the same rate.How long would it take the 3 machines to pack a total of 30 000 boxes of cakes?

………………… (3 marks)

D

Guided

D

DFirst work out the cost of 1 kg of apples.

CRemember to include units with your answer.

C

Guided

CWork out the number of boxes that 1 machine can pack in 1 hour.


NUMBER

13

Indices 21 Work out the value of (a) 422 (b) 49

1 _ 2

(a) 422 5 1 ___ 42

5 …… _____ ……

(1 mark)

(b) 49 1

__ 2 5 √___

49

5 ………… (1 mark)

2 Work out the value of

(a) 27 1 _ 3 (b) 921 (c) 423 (d) 80

………………… ………………… ………………… ………………… (1 mark) (1 mark) (1 mark) (1 mark)

3 Work out the value of (a) 8 2 _ 3 (b) (� 9 __ 16 )

23 _ 2

(a) 8 2

__ 3 5 (� 8 1

__ 3 ) 2

5 (……)2

5 ……… (1 mark)

(b) (� 9 ___ 16 ) 2 3 __ 2 5 (� (� 16 __ 9 ) 1 __ 2 ) 3

5 (� …… _____ ……

) 3

5 …… _____ ……

(2 marks)

4 Work out the value of

(a) 4 9 2 1 _ 2 (b) 64 2 _ 3 (c) (� 81 ___

16 ) 2 3 _ 4

………………… (1 mark) ………………… (1 mark) ………………… (2 marks)

5 Work out the value of √

__ 3 ___

9 3 √

___ 27

………………… (2 marks)

BGuided

B

A*

Guided

A*

A* Write each number as a power of 3 and then use the index laws.


NUMBER

14

Standard form1 (a) Write 67 000 in standard form.

67 000 5 ………… 3 10…… (1 mark)

(b) Write 2 3 1025 as an ordinary number.

2 3 1025 5 ………………… (1 mark)

(c) Write 760 3 104 in standard form.

760 3 104 5 …………………

5 ………… 3 10…… (1 mark)

2 (a) Write 0.54 in standard form. ………………… (1 mark)

(b) Write 7 3 106 as an ordinary number. ………………… (1 mark)

3 Write these numbers in order of size.Start with the smallest number.3 3 108 32 3 106 0.031 3 1010 3400 3 105

………………… ………………… ………………… ………………… (2 marks)

4 Work out the value of 5 3 107 3 9 3 103

Give your answer in standard form.

5 3 107 3 9 3 103 5 (5 3 ………) 3 (107 3 10……)

5 ……… 3 10……

5 ……… 3 10…… (2 marks)

5 Work out the value of 1.04 3 103 4 2 3 1025

Give your answer in standard form.

………………… (2 marks)

6 Work out the value of 7 3 105 3 3000Give your answer in standard form.

………………… (2 marks)

7 The number of atoms in one kilogram of helium is 1.51 3 1026

Calculate the number of atoms in 30 kilograms of helium.Give your answer in standard form.

………………… (2 marks)

B

EXAMALERT

Exam questions similar to this have proved especially tricky – be prepared!Guided

Guided

Guided First write the number as an ordinary number.

B

B Write all the numbers in standard form first.

A

Guided

A

A

A


NUMBER

15

Calculator skills1 Use your calculator to work out the value of 23.5 3 9.4 _________

14.6 2 5.9

Write down all the �gures on your calculator display.Give your answer as a decimal.

23.5 3 9.4 ___________ 14.6 2 5.9 5 ……… _______ ………

5 ………………… (2 marks)

2 Use your calculator to work out the value of √

__________

13.5 1 3.42 ___________ 2.3 3 1.5

Write down all the �gures on your calculator display.

………………… (3 marks)

3 Use your calculator to work out the value of 45.8 3 sin 34° _____________ √

__________

8.72 1 5.22

Write down all the �gures on your calculator display.

………………… (3 marks)

4 Work out (8.2 3 1024) 4 (3.1 3 1027)Give your answer in standard form correct to 3 signi�cant �gures.

………………… (2 marks)

5 y2 5 a 1 b _____ ab

a 5 5 3 106 b 5 4 3 103

Find y.

Give your answer in standard form correct to 2 signi�cant �gures.

y2 5 ……… 1 ……… __________________ 5 3 106 3 4 3 103

y2 5 ………………… _______________ …………………

y 5 √________________

…………………l y 5 …………………

y 5 ………… 3 10…… (3 marks)

D

Guided Make sure that you give your answer as a decimal. If necessary, use the S D button.

C

B

B

A

Guided


NUMBER

16

Surds1 Simplify (a) √

___ 48 (b) √

____ 300

(a) √___

48 5 √___

16 3 √________

………l 5 …… √

________

………l (1 mark)

(b) √_____

300 5 √________

………l 3 √________

………l 5 …… √

________

………l (1 mark)

2 Rationalise the denominator of 10 ___ √

__ 2

10 ___ √

__ 2 5 10 ___

√__

2 3

√__

2 ___ √

__ 2

5 …… √__

2 _______ ……

5 …… √__

2 (2 marks)

3 Expand and simplify (2 2 √__

3 )(5 1 √__

3 )

(2 2 √__

3 )(5 1 √__

3 ) 5 10 1 2 √__

3 2 ……… √__

3 2 ………

5 ……… 2 ……… √__

3 (2 marks)


5 )(2 1 √__

5 )

………………… (2 marks)


2 )2

………………… (2 marks)

6 Rationalise the denominator of 12 2 5 √__

3 _________ √

__ 3

Give your answer in the form a 1 b √__

3 where a and b are integers.

………………… (3 marks)

AGuided

AGuided

A*

Guided

Use FOIL (First terms, Outer terms, Inner terms, Last terms) to expand the brackets.

A*

A*

A*


NUMBER

17

Problem-solving practice*1 Tickets R-US and Cheap Tickets both advertise tickets for the same concert.

Helen wants to pay the least money possible for a ticket.Which shop should she buy her ticket from, Tickets R-US or Cheap Tickets?

Work out the price plus the booking fee for each ticket.

(4 marks)

2 Last year, Kevin spent 1 _ 8 of his salary on entertainment 2 _ 5 of his salary on rent15% of his salary on living expenses.

He saved the rest of his salary.Last year Kevin’s salary was £32 000How much money did Kevin save?

Amount spent on entertainment = 32 000 4 …………

5 £………… You should show all your working.

Amount spent on rent = 32 000 4 ………… 3 …………

5 £…………

10% of 32 000 5 …………

5% of 32 000 5 …………

15% of 32 000 5 …………

Amount spent on living expenses 5 £…………

Total amount spent 5 ………… 1 ………… 1 …………

5 £…………

Amount of money saved 5 32 000 2 …………..

5 £………… (4 marks)

D

The question has a * next to it, so make sure that you show all your working and write your answer clearly in a sentence.

D

Guided

Tickets R-US

£36 plus 5% booking fee

Cheap Tickets£35 plus 7.5% booking fee

Tickets R-US

£36 plus 5% booking fee

Cheap Tickets£35 plus 7.5% booking fee


NUMBER

18

Problem-solving practice*3 Mr Li’s garden is in the shape of a rectangle.

8 m

15 m

Veg.Plot

Grass

5 m

Part of the garden is a vegetable plot in the shape of a triangle.The rest of the garden is grass.Mr Li wants to spread fertiliser all over the grass.One box of fertiliser is enough for 30 m2 of grass.How many boxes of fertiliser will he need?

(4 marks)

*4 Kevin invests £6000 for 3 years at 4.5% simple interest in Simple Bank. The interest is paid, by cheque, at the end of each year.Kevin also invests £6000 for 3 years at 4.2% compound interest in Compound Bank.Which bank pays Kevin the greater amount of total interest, Simple Bank or Compound Bank?

(4 marks)

5 Josip drove for 314 miles, correct to the nearest mile.He used 34.6 litres of petrol, to the nearest tenth of a litre.

Petrol consumption 5 Number of miles travelled ____________________________ Number of litres of petrol used

Work out the upper bound for the petrol consumption for Josip’s journey.Give your answer correct to 2 decimal places.

Use the upper bound for the number of miles travelled and the lower bound for the number of litres of petrol used.

………………… (3 marks)

C

First work out the area of the grass. Divide the area by 30 to find the number of boxes – remember that Mr Li can only buy a whole number of boxes.

B

Simple interest means that the interest is the same each year. Work out the interest for one year then multiply this amount by 3.

For compound interest, the interest will change each year. Work out the interest for one year, add this on to the amount in the account and then work out the interest for the next year, and so on.

AA*


ALGEBRA

19

Algebraic expressions1 Simplify

(a) m3 3 m9 (b) p10 4 p2 (c) (t4)5

(a) m3 3 m9 5 m3 1 9 (b) p10 4 p2 5 p 10 2 2 (c) (t 4)5 5 t 4 3 5

5 m ……… 5 p ……… 5 t ………

(1 mark) (1 mark) (1 mark)

2 Simplify

(a) g 3 g6 (b) k9 4 k3 3 k2 (c) ( y3)7

………………… (1 mark) ………………… (1 mark) ………………… (1 mark)

3 Simplify

(a) x5 3 x4

_______ x6

(b) y12

______ y3 3 y

(c) (� z6 __

z3 ) 2

……………… (2 marks) ……………… (2 marks) ………………… (2 marks)

4 Simplify

(a) 5e7f 2 3 3e4f 5 (b) 28x6y5

______ 7xy3

(c) (2m5p)4

(a) 5e7f 2 3 3e4f 5 5 5 3 3 3 e7 1 4 3 f 2 1 5

5 ………e ……… f……… (2 marks)

(b) 28x6y5

_______ 7xy3 5 28 4 7 3 x 6 2 1 3 y 5 2 3

5 ………x ……… y ……… (2 marks)

(c) (2m5p)4 5 24m5 3 4 p 1 3 4

5 ………m ……… p ……… (2 marks)

5 Simplify

(a) 6cd8 3 4c5d2 (b) 40a9c2 ______

8a3c (c) (5b3d2)3

……………… (2 marks) ……………… (2 marks) ………………… (2 marks)

6 Simplify

(a) (� 1 ___ 2x3

) 22 (b) (� 25 ______

64b2c8 ) 2 1 _ 2

………………… (2 marks) ………………… (2 marks)

C

Guided

C

C

B

Guided

B

A Use the index law a2n 5 1 __ an


ALGEBRA

20

Arithmetic sequences1 Here are the �rst �ve terms of an arithmetic sequence.

1 5 9 13 17

Find an expression, in terms of n, for the nth term of the sequence.

zero term 1 … 1 … 1 … 1 …

1

�…

…

zero term

nth term � ……n � ……

5 9 13 17

nth term 5 ………n 1 ……… 5 ……………… (2 marks)

2 Here are the �rst �ve terms of an arithmetic sequence.

17 12 7 2 23


………………… (2 marks)

3 (a) Here are the �rst �ve terms of an arithmetic sequence.

3 7 11 15 19


………………… (2 marks)

(b) Paul says that 72 is a term in this sequence.Paul is wrong. Explain why.

………………………………………………………………………………………………………(1 mark)

4 (a) The nth term of a sequence is 8n 1 3Write down the �rst three terms of this sequence.

1st term n 5 1 8 3 1 1 3 5 ………

2nd term n 5 ……… 8 3 ……… 1 3 5 ………

3rd term n 5 ……… 8 3 ……… 1 3 5 ……… (2 marks)

(b) Jenny says that 45 is a term in this sequence.Jenny is wrong. Explain why.

……………………………………………………………………………………… (1 mark)

5 The nth term of a sequence is 3n 2 1Work out the 50th term of this sequence.

…………………………………………………………………………………………… (1 mark)

C

GuidedWork out the difference between each term. Then work out the zero term.

C

C

Look at the type of numbers in the sequence.

C

Guided

Try and find a value for n that gives a result of 45.

C


Documents

Higher REVISION WORKBOOK - Pearson · PDF fileHigher REVISION WORKBOOK Series ... in combination with Edexcel’s main GCSE Mathematics 2010 series ... GCSE_0154_PRE.indd 2 24/5/11