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Edexcel GCSE
Mathematics A Linear

Higher

REVISION
WORKBOOK
Series Director: Keith Pledger
Series Editor: Graham Cumming

Authors: Julie Bolter,
Gwenllian Burns, Jean Linsky

The Edexcel Revision Series
These revision books work in combination with Edexcel’s main GCSE Mathematics 2010 series
...
The Revision Workbooks
use a write-in format to provide realistic exam practice
...
indd 1

24/5/11 12:01:18

Contents
NUMBER
1
Factors and primes
2
Indices 1
3
Fractions
4
Decimals
5
Recurring decimals
6
Rounding and estimation
7
Upper and lower bounds
8
Fractions and percentages
9
Percentage change
10 Reverse percentages and compound interest
11 Ratio
12 Proportion
13 Indices 2
14 Standard form
15 Calculator skills
16 Surds
17 Problem-solving practice: Number A
02 A03
18 Problem-solving practice: Number
ALGEBRA
19 Algebraic expressions
20 Arithmetic sequences
21 Expanding brackets
22 Factorising
23 Linear equations 1
24 Linear equations 2
25 Straight-line graphs
26 Parallel and perpendicular
27 3-D coordinates
28 Real-life graphs
29 Formulae
30 Rearranging formulae
31 Inequalities
32 Inequalities on graphs
33 Quadratic and cubic graphs
k
34 Graphs of _ and ax
x
35 Trial and improvement
36 Simultaneous equations 1
37 Quadratic equations
38 Completing the square
39 The quadratic formula
40 Quadratics and fractions
41 Equation of a circle
42 Simultaneous equations 2
43 Direct proportion
44 Proportionality formulae
45 Transformations 1
46 Transformations 2
47 Algebraic fractions
48 Proof
49 Problem-solving practice: Algebra
50 Problem-solving practice: Algebra
GEOMETRY AND MEASURES
51 Angle properties
52 Solving angle problems
53 Angles in polygons
54 Plan and elevation
55 Perimeter and area
56 Prisms
57 Circles and cylinders
58 Sectors of circles

A01_EMHL_WBK_GCSE_0154_PRE
...
Sub-parts of the question may
cover lower grade material
...
The topic may form part
of a higher grade question if tested within the context of
another topic
...


24/5/11 12:01:18

NUMBER

Factors and primes
C

1

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


60 5 2 3 …… 3 …… 3 ……
(2 marks)

150 5 2 3 …… 3 …… 3 ……
(2 marks)

(b) Find the highest common factor (HCF) of 60 and 150
60 5 2 3 3 3 …… 3 ……

Guided

150 5 2 3 …… 3 …… 3 ……
HCF 5 2 3 …… 3 ……


5 ………

Circle all the prime numbers
which are common to both
products of prime factors
...


(1 mark)

(c) Find the lowest common multiple (LCM) of 60 and 150
LCM 5 ……… 3 …… 3 ……

Guided



C

2

5 ………

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


…………………

(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)
1

M01_EMHL_WBK_GCSE_0154_U01
...


712
_______

Guided

4

5 …………



(2 marks)

(d) (75)4
(75)4 5 75 3 4 5 …………

Guided

C

2

Write as a power of 5
512 3 5
(b) _______
54 3 53

(a) 58 3 54

………………

C

3

(1 mark)

(1 mark)

68 3 63 5 65 3 6x
Find the value of x
...


x 5 …………………

B

4

5

(1 mark)

Write 93 3 272 as a single power of 3
93 3 272 5 (3……)3 3 (3……)2

Guided



6

5 3…… 3 3……



A

(2 marks)

Simplify 40
…………………

A

(1 mark)

5 ………
...
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18/8/11 13:32:13

NUMBER

Fractions
C

1

2
4
Work out 3_ 1 1_
3
5

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


…
…
5 …… 1 ___ 1 ___
15
15

Write as equivalent fractions with the same denominator
...

1
2
(a) 7_ 2 2_
7
3

(3 marks)

9
3
(b) 8__ 1 2_
5
10

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


…
5 ……___
…
4

Write both mixed numbers as improper fractions
...


Work out

1
1
(a) 2_ 3 3_
3
4

(3 marks)

1
2
(b) 5_ 4 1_
3
9

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


(a) ……………………

(3 marks)

3
M01_EMHL_WBK_GCSE_0154_U01
...
7 3 2
...
7 3 2
...
So the answer needs to be divided by 100
...
0029
670 3 0
...
So the answer needs to be divided by 1000
...

So multiply 29 by 10
...
127 3 8
...
27

(1 mark)

…………………

(1 mark)

Given that 63 3 48 5 3024
write down the value of
(a) 6300 3 4
...
063 3 4
...
3

(1 mark)

…………………

(1 mark)

4
M01_EMHL_WBK_GCSE_0154_U01
...


Express 0
...
You must use algebra
...


Let x 5 0
...
151 515…
2 x 5 0
...


Change the recurring decimal 0
...
You must use algebra
...


Convert the recurring decimal 2
...
You must use algebra
...


Convert the recurring decimal 0
...
You must use algebra
...


Let x 5 0
...
777 7777…
2 x 5 0
...


(3 marks)


...
827 can be written as the fraction ___
110

(3 marks)
5
M01_EMHL_WBK_GCSE_0154_U01
...

(a) 145 3 78
100 3 ………… 5 …………………

Guided

(1 mark)

(b) 19
...
51
………… 4 2 5 …………………

Guided

(1 mark)

(c) 48
...
78 3 11
...
3 3 18
...
7 3 1
...
053


5

(2 marks)

612 3 39
Work out an estimate for the value of ________
0
...
05
………

Guided

(2 marks)

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

First round each number
to 1 significant figure
...
73 3 4
...
0214

…………………

C

6

(2 marks)

Work out estimates for the following calculations
...

995
...
3 3 11
...
7
(b) _________
3
...
72

…………………

(2 marks)

Work out an estimate for the value of 2
...
72

6
M01_EMHL_WBK_GCSE_0154_U01
...
7 cm correct to 2 significant figures
...
5 cm correct to 2 significant figures
...

Upper bound of length 5 9
...
75 3 …………………
5 ………………… cm2

(3 marks)

The length of a rectangle is 24 cm correct to 2 significant figures
...
6 cm correct to 2 significant figures
...


………………… cm

A*

3

(3 marks)

___
A ball is dropped from a window
...

s 5 117 m correct to 3 significant figures
a 5 9
...

Give your answers correct to 4 decimal places
...

You must explain your answer
...
indd 7

18/8/11 13:32:14

NUMBER

Fractions and percentages
D

1

………
_______

Guided

D

Uzma invests £4000 in a bank account for 1 year
...
5% per annum
...

30 of the llamas are female
...

30
_______

Guided

3 100 5 …………………

(2 marks)

………
60% of the female llamas are pregnant
...

Give your answer in its simplest form
...

Each week she gets paid £160 plus 15% of the value of the goods she sells
...

Work out the total amount she was paid this week
...

5

He spends 15% of the £16 000 on food
...


C

5

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

7

3
_ of the students choose rafting
...

How many students choose abseiling?

8
M01_EMHL_WBK_GCSE_0154_U01
...

Calculate the total cost of the washing machine
...

The normal price is £84
The normal price of the jacket is reduced by 35%
...


£…………………

C

3

Eliza went to New York
...

The exchange rate was £1 5 $1
...
60 to $1
...

decrease
Percentage decrease 5 ____________ 3 100
original value

Guided



4

………
5 _______ 3 100
………



C

(3 marks)

5 …………………%

(3 marks)

Ali buys 120 cans of drink for a total of £30
He wants to make a profit of 40%
...


…………………

£…………………

C

5

(4 marks)

(4 marks)

Jean books a holiday
...

She pays the rest in 10 monthly instalments
...


9
M01_EMHL_WBK_GCSE_0154_U01
...

Work out the value of the car after 4 years
...


Value after 4 years 5 18 000 3 (………)4



B

2

5 …………………
5 £…………………

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

He was paid compound interest at a rate of 3
...

Work out how much was in the account after 3 years
...

The sale price of a DVD player is £403
Work out the normal price of the DVD player
...

Dave says, ‘This means Jill’s weekly pay last year was £391
...
Explain why
...

He was paid 4
...

At the end of the n years he had £6641
...

Work out the value of n
...


n 5 …………………

(2 marks)

10
M01_EMHL_WBK_GCSE_0154_U01
...

18 of the toy cars are blue
...

Write down the ratio of the number of red toy cars to the number of blue toy cars
...

Number of red cars 5 60 2 ………

Guided



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

20 of the students are girls
...
’
Is Rosie right?
You must give a reason for your answer
...

Work out the length of the journey
...
indd 11

18/8/11 13:32:15

NUMBER

Proportion
D

1

Mike buys 6 pencils for a total cost of £5
...

Cost of 1 pencil 5 5
...
44
Work out the cost of 5 of these notebooks
...
20
The total cost of 3 kg of apples and 2 kg of bananas is £5
...


First work out the cost
of 1 kg of apples
...

He always works at the same speed
...

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
...


C

(3 marks)

Remember to include
units with your answer
...

The owner of the factory buys two more machines
...

of boxes that 1 machine
How long would it take the 3 machines to pack a total of
can pack in 1 hour
...
indd 12

18/8/11 13:32:15

NUMBER

Indices 2
B

1

Work out the value of

1
_

(a) 422

(b) 492

1
(a) 422 5 ___
42
……

5 _____
……

Guided

(1 mark)

___

__
1

(b) 492 5 √ 49

5 …………

B

2

(1 mark)

Work out the value of
1
_

(a) 273

3

(c) 423

…………………
(1 mark)

A*

(b) 921
…………………
(1 mark)

(d) 80

…………………
(1 mark)

2
_

Work out the value of

(a) 83

…………………
(1 mark)

3
_
(b) (__ )22
9
16

2
(a) 83 5 (83 )

__
2

Guided

__
1

5 (……)2
5 ………

( )

9
(b) ___
16

3
2 __
2

5

(1 mark)

16
((__ ) )3
9
__
1
2

(

……
5 _____
……
……
5 _____
……

A*

4

)

3

(2 marks)

Work out the value of

( )

3
2_
4

(a) 49

(b) 643

81
(c) ___
16

………………… (1 mark)

………………… (1 mark)

…………………

2
_

1
2_
2

A* 5

(2 marks)

__

___
√3
Work out the value of ___ 3 √27
9

Write each number as a power of 3 and then use the index laws
...
indd 13

18/8/11 13:32:15

NUMBER

Standard form
B

1

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

2 3 1025 5 …………………

Guided

(1 mark)

(c) Write 760 3 104 in standard form
...


5 ………… 3 10……

(1 mark)

B

3

(a) Write 0
...


…………………

(1 mark)

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

Start with the smallest number
...
031 3 1010
3 3 108

…………………

A

4

…………………

3400 3 105

…………………

…………………

(2 marks)

Work out the value of 5 3 107 3 9 3 103
Give your answer in standard form
...


5 ……… 3 10……

(2 marks)

Work out the value of 1
...


…………………

…………………

A

6

7

(2 marks)

…………………

A

(2 marks)

(2 marks)

Work out the value of 7 3 105 3 3000
Give your answer in standard form
...
51 3 1026
Calculate the number of atoms in 30 kilograms of helium
...


14
M01_EMHL_WBK_GCSE_0154_U01
...
5 3 9
...
6 2 5
...

Give your answer as a decimal
...
5 3 9
...
6 2 5
...
If necessary,
use the S D button
...
5 1 3
...
3 3 1
...


…………………

…………………

B

3

(3 marks)

(3 marks)

45
...
72 1 5
...


B

4

Work out (8
...
1 3 1027)
Give your answer in standard form correct to 3 significant figures
...

Give your answer in standard form correct to 2 significant figures
...
indd 15

18/8/11 13:32:16

NUMBER

Surds
A

1

___

Simplify

____

(a) √48

(b) √300

________

l

(a) √48 5 √ 16 3 √………
___

Guided

___

________



l

5 …… √………



________

l

(1 mark)
________

l

(b) √ 300 5 √ ……… 3 √ ………
_____

________



A

2

Guided

l

5 …… √………



(1 mark)

10
__
Rationalise the denominator of ___
√2
__
√2
10
10
___
__ 5 ___ 3 ___
__
__
√2
√2
√2
__

……√ 2
_______




A*

3

5

5 ……√ 2

……

__

__

__

Expand and simplify (2 2 √3 )(5 1 √ 3 )
__

__

__

__

(2 2 √ 3 )(5 1 √ 3 ) 5 10 1 2√3 2 ………√3 2 ………

Guided



A*

(2 marks)

4

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


…………………

(3 marks)

16
M01_EMHL_WBK_GCSE_0154_U01
...

The question has a * next
to it, so make sure that you
show all your working and
write your answer clearly
in a sentence
...
5% booking fee
£35 plus 7
...

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
...

He saved the rest of his salary
...


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 …………
...
indd 17

18/8/11 13:32:16

NUMBER

Problem-solving practice
C

*3 Mr Li’s garden is in the shape of a rectangle
...

The rest of the garden is grass
...

One box of fertiliser is enough for 30 m2 of grass
...

Plot

Grass

8m

5m
First work out the area of the grass
...


(4 marks)

B

*4 Kevin invests £6000 for 3 years at 4
...

The interest is paid, by cheque, at the end of each year
...
2% compound interest in Compound Bank
...

Work out the interest for one year then multiply this amount by 3
...
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
...

He used 34
...

Number of miles travelled
Petrol consumption 5 ____________________________
Number of litres of petrol used
Work out the upper bound for the petrol consumption for Josip’s journey
...

Use the upper bound for the number
of miles travelled and the lower bound
for the number of litres of petrol used
...
indd 18

18/8/11 13:32:16

ALGEBRA

Algebraic expressions
C

1

Simplify
(a) m3 3 m9

(c) (t4)5

(a) m3 3 m9 5 m3 1 9

Guided

(b) p10 4 p2
(b) p10 4 p2 5 p 10 2 2

(c) (t 4)5 5 t 4 3 5



C

2

5 m ………
(1 mark)



(1 mark)

………………
4

…………………

(1 mark)

( )

(2 marks)

Simplify

………………

z6
(c) __
z3

2

…………………

(2 marks)

28x6y5
(b) ______
7xy3

(2 marks)

(c) (2m5p)4

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

Guided



5 ………e ……… f ………



28x6y5
(b) _______
7xy3


5

5 24m5 3 4 p 1 3 4



5 ………m ……… p ………



5 28 4 7 3 x 6 2 1 3 y 5 2 3
(2 marks)

(2 marks)

Simplify
40a9c2
(b) ______
8a3c

(a) 6cd8 3 4c5d2

………………

6

(2 marks)

5 ………x ……… y ………

(c) (2m5p)4

A

…………………

(1 mark)

y12
(b) ______
y3 3 y

(a) 5e7f 2 3 3e4f 5

B

(c) ( y3)7

Simplify
x5 3 x4
(a) _______
x6

B

(1 mark)

(b) k9 4 k3 3 k2

…………………
3

5 t ………

Simplify
(a) g 3 g6

C

5 p ………
(1 mark)

Simplify

(2 marks)

………………

…………………

(2 marks)

(2 marks)

1
Use the index law a2n 5 __
an

( )

1
(a) ___
2x3

(c) (5b3d2)3

(

…………………

)

25
(b) ______
64b2c8

22

(2 marks)

1
2_

2

…………………

(2 marks)
19

M02_EMHL_WBK_GCSE_0154_U02
...

1

5

9

13

17

Find an expression, in terms of n, for the nth term of the sequence
...
Then
work out the zero term
...

17

12

7

2

23

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

3

7

11

15

19

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

Paul is wrong
...


(2 marks)

Look at the type of numbers in the 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 ………

Guided

8 3 ……… 1 3 5 ………

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


………………………………………………………………………………………

C

5

(2 marks)

(1 mark)

The nth term of a sequence is 3n 2 1
Work out the 50th term of this sequence
...
indd 20

18/8/11 13:35:11



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