free e-book 'worksheets' vol. #1 'number' from gcse maths tutor

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Contents

LCM & HCF I 3,4

number operators I 5,6

index notation I 7,8

growth & decay I 9,10

rationalising surds I 11,12

rationalising surds II 13,14

rationalising surds III 15,16

expanding surd expressions IV 17,18

surds +-/x V 19,20

sequences I 21,22

addition & subtraction I 23,24

vulgar fractions plus harder addition & subtraction 25,26

decimal multiplication I 27,28

standard form I 29,30

decimals to %'s I 31,32

%'s to decimals II 33,34

% of a number III 35,36

fractions to %'s IV 37,38

ratio & proportion I 39,40

significant figures I 41,42

upper & lower bounds I 43,44

decimal places I 45,46

©2009 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com

Number – LCM, HCF L.C.M. and H.C.F. question sheet N-LCM-HCF-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

GCSE Maths Tutor www.gcsemathstutor.com [email protected]

L.C.M – lowest common multiple H.C.F. – highest common factor 1. write down the L.C.M of the following pairs of numbers (a) 6 : 9 (b) 24 : 32 (c) 12 : 18 (d) 21 : 70 (e) 38 : 380 (f) 39 : 260 (g) 128 : 48 (h) 54 :78 (i) 28 : 140 2. write down the L.C.M of each group of numbers (a) 6 : 4 : 12 (b) 8 : 32 : 24 (c) 9 : 15 : 21 (d) 20 : 16 : 60 (e) 21 : 36 : 108 (f) 22 : 110 : 14 3. write down the H.C.F. of the following pairs of numbers (a) 18 : 12 (b) 14 : 70 (c) 108 : 78 (d) 256 : 96 (e) 42 : 140 (f) 390 : 26 (g) 380 : 38 (h) 18 : 8 (i) 210 : 100 4. write down the H.C.F. of each group of numbers (a) 20 : 60 : 108 (b) 42 : 54 : 72 (c) 260 : 39 : 78 (d) 78 : 48 : 18 (e) 98 : 28 : 56 (f) 51 : 510 : 170

Number – LCM, HCF L.C.M. and H.C.F. answer sheet N-LCM-HCF-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 18 (b) 96 (c) 36 (d) 210 (e) 380 (f) 780 (g) 384 (h) 702 (i) 140 2. (a) 12 (b) 96 (c) 315 (d) 240 (e) 756 (f) 770 3. (a) 6 (b) 14 (c) 6 (d) 32 (e) 14 (f) 26 (g) 38 (h) 2 (i) 10 4. (a) 4 (b) 6 (c) 13 (d) 6 (e) 14 (f) 17

Number - operators number operators (+ - x +) question sheet N-NO-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


+

1. evaluate: (a) 3 (b) 7 – 2 9 8+ × 8 3 3 7 – 2+ × + (c) 7 4 4 9 – 6+ × + (d ) 1 + (e) 5 – 8 13 + 4× 7 10 11 – 6× + (f) 2 3 19 – 5× + (g) 1 + 5 (h) – 8 + 9 12× 2 + 6 – 7 + 8 11× (i) 13 – 27 + 8 15× 2. evaluate: (a) 6 + 8 (b) 12 + 9 3× ÷ 4 6 7 12 2+ × + ÷ (c) 7 3 9 16 4+ × + ÷ (d) 15 (e) 3 3 10 17÷ + × + 27 9 11 9 1÷ + × + (f) 18 6 13 2 9÷ + × + (g) (h) 2 × 11 + 10 ÷ 2 – 3 2 12 14 7 – 1× + ÷ (i) 9 9 9 9 – 9× + ÷ 3. evaluate: (a) ( )3 6 8 10 2 1+ + ÷ + (b) ( )5 9 – 7 12 3 9+ ÷ + (c) ( )3 12 – 25 –1 2 3 8÷ + (d) ( )20 10 11 – 5 15 5÷ + + (e) ( )30 5 13 –3 11 2÷ + + (f) 39 13 3 – 5(2 – 3)÷ + (g) ( )11 – 2 12 – 5 10 5+ ÷ (h) ( )21 – 3 15 – 8 20 4+ ÷ (i) ( )7 – 4 5 –11 18 3+ ÷ 4. evaluate: (a) 3 (b) 6(5 8) 12 6 – 3× + ÷ (7 9) 9 3 – 5× + ÷ (c) 9(2 4) 8 4 – 6× + ÷ (d) 6( (e) 2(18 3) – 4 3 2÷ × + 15 5) – 2 2 9÷ × + (f) 9( 25 5) –1 2 3 1÷ × + (g) 7 (h) 2(8 4) – 9(2 2)+ ÷ × 5(15 5) – 2(16 2) 9÷ × + (i) 3(6 3) – 7 2(4 2)÷ + ×

Number - operators number operators (+ - x +) answer sheet N-NO-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 0 (b) 22 (c) 26 (d) -94 (e) 75 (f) 20 (g) 106 (h) 89 (i) 106 2. (a) 105 (b) 52 (c) 38 (d) 52 (e) 103 (f) 38 (g) 24 (h) 25 (i) 73 3. (a) 48 (b) 23 (c) -35 (d) -87 (e) -20 (f) 11 (g) -1 (h) 5 (i) 37 4. (a) 119 (b) 376 (c) 68 (d) 26 (e) 11 (f) 10 (g) -25 (h) –40 (i) 15

Number – powers & roots index notation question sheet N-PR-I-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

2 3 3 5 5 3 7

8 7 4 3 5 47 5

7 x 3 3 5 7 99 9

1. simplify: (a) 3 x 3 x 3 (b) 5 x 5 x 5 x 5 (c) 7 x 7 x 7 x 7 x 7 (d) 5 x 6 x 6 x 5 (e) 3 x 5 x 3 x 5 (f) 7 x 5 x 7 x 5 x 7 x 5 (g) 11 x 9 x 9 x 11 x 9 (h) 6 x 12 x 3 x 6 x 3 x 6 x 6 x 12 x 3 (i) 8 x 5 x 8 x 5 x 8 x 5 x 8 x 5 x 8 x 5 x 8 x 5 2. find the value of (a) 11 (b) 3 (c) 4 (d) 2 (e) 3 (f) 9 (g) 10 (h) 1 (i) 2 (j) 5 (l) 6 (m) 4 (n) (o) 9 3. simplify, leaving answer in index notation (a) (b) (c) 9 92 33 x 3 2 3 4 55 x 5 x 5 x 5 × × ×

7 94 4× 36 6 6 7 7

(d) (e) 3 53 3× × 1 2 3 5× × × × 2 3 6 2 40 5 5 7 7 (f) 1 × × × ×

34 2 4 3× × × × × 2 8 3 6 9 3 7 53 ×4 ×2 ×3 ×2 ×3 ×4

(g) 2 3 (h) 2 × 2 7 2 4 2

4. express each number as a power of a number (a) 512 (b) 128 (c) 343 (d) 625 (e) 243 (f) 169 (g) 10,000 (h) 256 (i) 1331 (j) 64 (k) 216 (l) 2048 (m) 81 (n) 121


Number – powers & roots index notation answer sheet N-PR-I-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) (b) (c) 33 45 57 (d) (e) (f) 2 25 6 2 23 5 3 37 5 (g) (h) (i) 3 29 11 3 4 23 6 12 6 65 8 2. (a) 121 (b) 27 (c) 64 (d) 32 (e) 243 (f) 729 (g)10,000,000 (h) 1 (i) 128 (j) 625 (l) 216 (m) 1024 (n) 2401 (o) 59049 3. (a) (b) (c) (d) (e) (f) 123 145 249 8 163 4 6 86 7 9 6 25 7 10 (g) (h) 6 9 52 3 4 11 24 82 3 4 4. (a) (b) (c) (d) (e) (f) (g) 38 72 37 45 53 213 410 (h) (i) (j) (k) (l) (m) (n) 82 311 62 36 112 43 211

Number – growth decay growth & decay question sheet N-GD-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. £10 000 is invested in a savings bond. How much money will the bond be worth at the % rate per annum given and term indicated?

(a) 3% , 4 years (b) 5% , 9 years (c) 7% , 15 years

(d) 4.75% , 19 months (e) 5.25% , 26 months (f) 6.25% , 37 months

2. A country of 21 million people increases its population by 3% every year. What will the population be after the following time has elapsed. Neglect any decimals in the answer.

(a) 5 years (b) 7 years 7 months (c) 1000 days

3. The level of activity of a radioactive source decreases by 3% per hour. For each initial level of activity given, what will the activity be after the time indicated? Answer to the nearest whole number.

(a) 2000 counts/sec. 5 hours (b) 10 000 counts/sec. 13 hours (c) 9600 counts/sec. 6.5 hours (d) 1700 counts/sec. 45 minutes (e) 850 counts/sec. 1 week (f) 3000 counts/sec. 17 minutes 4. A nurse wants to have savings of £5000 in two years to buy her first car. She finds an account that pays 5% interest compounded yearly. How much should she put into her account to have the £5000 at the end of two years? (answer to decimal places)

Number – growth decay growth & decay answer sheet N-GD-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) £11255.09 (b) £15513.28 (c) £27590.32

(d) £10762.27 (e) £11172.63 (f) £12055.14

2. (a) 24,344,755 (b) 26,276,285 (c) 22,771,586

3. (a) 1717 counts/sec. (b) 6730 counts/sec. (c) 7876 counts/sec. (d) 1662 counts/sec. (e) 5 counts/sec. (f) 2974 counts/sec. 4. £4319.19

Number - surds rationalising surds question sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] rationalise:

1. (a) 55

(b) 33

(c) 77

(d) 22

(e) 66

(f) 88

2. (a) 53

(b) 85

(c) 72

(d) 35

(e) 93

(f) 82

3. (a) 153

(b) 126

(c) 105

(d) 147

(e) 162

(f) 183

4. (a) 12 2

(b) 13 3

(c) 15 5

(d) 16 12

(e) 13 7

(f) 15 10


ref. alg/surds/01/2008

Number- surds rationalising surds answer sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 5 (b) 3 (c) 7 (d) 2 (e) 6 (f) 8

2. (a) 5 33

(b) 8 55

(c) 7 22

(d) 3 55

(e) 3 3 (f) 4 2

3. (a) 5 3 (b) 2 6 (c) 2 5 (d) 2 7 (e) 8 2 (f) 6 3

4. (a) 24

(b) 39

(c) 525

(d) 1272

(e) 721

(f) 1050



Number- surds rationalising surds question sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected] rationalise:

1. (a) 17 8+

(b) 111 2+

(c) 111 10+

(d) 19 8+

(e) 17 6+

(f) 16 5+

2. (a) 19 5−

(b) 17 3−

(c) 1

5 2−

(d) 14 3−

(e) 110 5−

(f) 111 7−

3. (a) 3

2 3+ (b) 5

7 2+ (c)

712 3+

(d) 98 5+

(e) 85 3+

(f) 211 6+

4. (a) 7

7 2− (b) 3

4 3− (c)

58 6−

(d) 211 7−

(e) 99 3−

(f) 64 2−



Number- surds rationalising surds answer sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

1. (a) 741− 8 (b) 11 2

119− (c) 11 10

111−

(d) 973− 8 (e) 7 6

43− (f) 6 5

31−

2. (a) 9 5

76+

(b) 7 346+

(c) 5 2

23+

(d) 413+ 3 (e) 10 5

95+ (f) 11 7

114+

3. (a) 6 3 3− (b) 35 5 247−

(c) 84 7 3

141−

(d) 72 9 559− (e) 20 4 3

11− (f) 22 2 6

115−

4. (a) 49 7 2

47+

(b) 12 3 313+

(c) 40 5 6

58+

(d) 11 757+ (e) 81 9 3

78+ (f) 12 3 2

7+



Number- surds rationalising surds question sheet 03 GCSE Maths Tutor www.gcsemathstutor.com [email protected] rationalise:

1. (a) 22 5+−

5 (b) 3 23 2+−

(c) 7 57 5+−

(d) 55 3+−

3 (e) 9 29 2+−

(f) 8 28 2+−

2. (a) 5 35 3−+

(b) 6 26 2−+

(c) 7 57 5−+

(d) 44 2−+

2 (e) 99 3−+

3 (f) 11 811 8

−+



Number- surds rationalising surds answer sheet 03 GCSE Maths Tutor www.gcsemathstutor.com [email protected] rationalise:

1. (a) 9 4 5− − (b) 11 6 27+ (c) 27 7 5

22+

(d) 14 5 311+ (e) 83 18 2

79+ (f) 33 8 2

31+

2. (a) 14 5 3

11−

(b) 19 6 217−

(c) 27 7 5

22−

(d) 9 4 27

− (e) 42 9 339− (f) 129 22 8

113−



Number- surds surds - expanding brackets question sheet 04 GCSE Maths Tutor www.gcsemathstutor.com [email protected] expand and evaluate: 1. (a) (1 3)(2 3)− + (b) (1 5)(1 5)+ − (c) (1 2)(3 2)+ + (d) (2 6)(5 6)− + (e) (4 7)(4 7)− + (f) (3 3)(2 3)+ + 2. (a) ( 2 3)( 2 3)+ − (b) ( 5 7)( 5 7)+ + (c) ( 3 7)( 3 7)− + (d) ( 7 3)( 7 3)+ + (e) ( 2 11)( 11 2)+ + (f) ( 6 3)( 3 6)+ − 3. (a) (1 2 3)(1 2 3)+ + (b) (1 3 5)(1 3 5)− + (c) (1 5 7)(1 5 7)+ − (d) (1 7 2)(1 7 2)+ + (e) (1 9 5)(1 9 5)− + (f) (1 7 7)(1 7 7)+ + 4. (a) (2 3 2)(1 2 2)− + (b) (5 2 2)(3 3 2)− + (c) (3 5 3)(2 3 3)+ + (d) (6 2 5)(4 3 5)+ + (e) (2 3 6)(5 2 6)− + (f) (9 2 7)(3 4 7)+ −



Number- surds surds - expanding brackets answer sheet 04 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 1− − 3 (b) 4− (c) 5 4 2+ (d) 4 3 6− (e) 9 (f) 9 5 3+ 2. (a) (b) 1− 12 2 35+ (c) 4− (d) 10 2 21+ (e) 13 2 22+ (f) 3− 3. (a) 13 4 3+ (b) 44− (c) 174− (d) 99 14 2+ (e) 404− (f) 344 14 7+ 4. (a) 10 2− + (b) 3 9 2+ (c) 51 19 3+ (d) 54 26 5+ (e) 26 19 6− − (f) 29 30 7− −



Number - surds surds + - / x question sheet 05 GCSE Maths Tutor www.gcsemathstutor.com [email protected] simplify: 1. (a) 12 27+ (b) 45 20+ (c) 63 28+ (d) 45 147+ (e) 44 99+ (f) 13 52+ 2. (a) 98 50− (b) 75 12− (c) 147 75− (d) 99 44− (e) 27 12− (f) 52 13−

3. (a) 4518

(b) 9850

(c) 14798

(d) 9927

(e) 17563

(f) 10812

4. (a) 2 × 3 (b) 5 × 7 (c) 2 2 3 3× (d) 5 3 7 5× (e) 6 5 11 7× (f) 9 3 2 17×


ref. num/surds/05/2008

Number - surds surds + - / x answer sheet 05 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 5 3 (b) 5 5 (c) 5 7 (d) 12 3 (e) 5 11 (f) 3 13 2. (a) 2 2 (b) 3 3 (c) 2 3 (d) 11 (e) 3 (f) 13

3. (a) 52

(b) 75

(c) 32

(d) 113

(e) 59

(f) 3

4. (a) 6 (b) 35 (c) 6 6 (d) 35 15 (e) 66 35 (f) 18 51


ref. num/surds/05/2008

Number - sequences Sequences question sheet N-SEQ-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. Write down the 6th and 8th terms in each case. (a) 2, 4, 6, 8 … (b) 3, 6, 9, 12 … (c) 4, 8, 12, 16 … (d) 5, 7, 9, 11 … (e) 4, 7, 10, 13 … (f) 7, 12, 17, 22 … (g) 2, 4, 8, 14 … (h) 3, 5, 9, 15 … (i) 4, 7, 13, 22 … (j) 8, 11, 17, 26 … (k) 5, 10, 20, 35 … (l) 6, 10, 18, 30 … (m) 13, 14, 16, 19 … (n) 13, 20, 34, 55 … (o) 11, 20, 38, 65 … 2. If n =1 is the first term, find the formula for the n th term in each case. (a) 5, 10, 15, 20 … (b) 4, 7, 10, 13 … (c) 2, 7, 12, 17 … (d) 1, 9, 17, 25 … (e) 6, 11, 16, 21 … (f) 5, 17, 29, 41 … (g) 9, 12, 15, 18 … (h) 21, 25, 31, 36 … (i) 10, 17, 24, 31 … (j) 19, 25, 31, 37 … (k) 13, 20, 27, 34 … (l) 29, 36, 43, 50 … (m) 11, 15, 19, 23 … (n) 9, 22, 35, 48 … (o) 3, 30, 57, 84 … 3. If n =1 is the first term, the n th term can be witten as a + b(n - 1) where a and b are constants. Find a and b (a) 2, 4, 6, 8 … (b) 4, 8, 12, 16 … (c) 5, 7, 9, 11 (d) 6, 19, 32, 45 … (e) 17, 22, 27, 32 … (f) 11, 15, 19, 23 … (g) 19, 25, 31, 37 … (h) 57, 64, 71, 78 … (i) 101, 103, 105, 107 … (j) 2, 58, 114, 170 … (k) 29, 42, 55, 68 … (l) 4, 31, 58, 85 … (m) 11, 22, 33, 44 … (n) 100, 200, 300, 400 (o) 17, 40, 63, 86 …

Number - sequences Sequences answer sheet N-SEQ-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 12, 16 (b) 18, 24 (c) 24, 32 (d) 15, 19 (e) 19, 25 (f) 32, 42 (g) 32, 58 (h) 33, 59 (i) 49, 88 (j) 53, 92 (k) 80, 145 (l) 66, 118 (m) 28, 41 (n) 118, 208 (o) 146, 279 2. (a) 5n (b) 4 + 3(n-1) (c) 2 + 5(n-1) (d) 1 + 8(n-1) (e) 6 + 5(n-1) (f) 5 + 12(n-1) (g) 3 + 7(n-1) (h) 1 + 6(n-1) (i) 1 + 11(n-1) (j) 19 + 6(n-1) (k) 13 + 7(n-1) (l) 29 + 7(n-1) (m) 11 + 4(n-1) (n) 9 + 13(n-1) (o) 3 + 27(n-1) 3. (a) 2, 2 (b) 4, 4 (c) 5, 2 (d) 6, 13 (e) 17, 5 (f) 11, 4 (g) 19, 6 (h) 57, 7 (i) 101, 2 (j) 2, 56 (k) 29, 13 (l) 4, 27 (m) 11, 11 (n) 100, 100 (o) 17, 23

Number - fractions fraction addition & subtraction question sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1.

(a) 1 12 3+ (b) 1 1

4 5+ (c)

1 13 7+

(d) 1 18 9+ (e)

1 110 5

+ (f) 1 16 3+

2.

(a) 2 43 5+ (b)

3 24 7+ (c)

5 28 3+

(d) 6 27 9+ (e)

3 210 7

+ (f) 4 29 3+

3.

(a) 5 17 4− (b)

3 14 3− (c)

2 15 11−

(d) 9 3

10 13− (e)

8 29 3− (f)

12 213 11

−

4. (a) 1

41 2+ 15 (b) 3 1

73 2 8− (c) 912 16 2 0+

(d) 32

32 1− 4 (e) 7 184 2 9+ (f) 91

12 115 1+


Ref. Num/fract/01/2009

Number - fractions fraction addition & subtraction answer sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1.

(a) 56

(b) 920

(c) 1021

(d) 1772

(e) 3

10 (f)

12

2. (a) 7

151 (b) 1281 (c) 7

241

(d) 5631 (e)

4170

(f) 191

3.

(a) 1328

(b) 5

12 (c)

1755

(d) 87

130 (e)

29

(f) 106143

4. (a) 9

203 (b) 17561 (c) 2

59

(d) 1112

(e) 71726 (f) 119

1326



Number - fractions vulgar & harder (+ -) of fractions question sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. convert the vulgar fraction to a number and a fraction

(a) 4410

(b) 329

(c) 1713

(d) 235

(e) 194

(f) 276

2. convert the number and fraction to a vulgar fraction (a) 2

31 (b) 343 (c) 9

105 (d) 3

134 (e) 7172 (f) 22

236 3. solve

(a) 1 1 12 3 4+ + (b)

1 1 15 10 2+ + (c)

1 1 112 3 4

+ +

(d) 1 16 12 3+ +

1 (e)

1 1 111 2 7

+ + (f) 1 1 120 5 10

+ +

4. solve

(a) 3 1 14 2 5+ − (b)

9 1 110 3 4

− − (c) 2 1 33 2 8+ −

(d) 8 39 10 5− +

1 (e)

3 3 55 4 8+ − (f)

7 1 28 3 5+ +



Number - fractions vulgar & harder (+ -) of fractions answer sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 2

54 (b) 593 (c) 2

35 (d) 3

54 (e) 344 (f) 1

24 2.

(a) 53

(b) 154

(c) 5910

(d) 5513

(e) 4117

(f) 16023

3.

(a) 1121 (b)

45

(c) 23

(d) 7

12 (e)

113154

(f) 720

4.

(a) 1201 (b)

1960

(c) 1924

(d) 7190

(e) 2940

(f) 731201



Number - decimals decimal multiplication question sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. without calculator (a) 0.5 x 6 (b) 0.1 x 16 (c) 0.2 x 25 (d) 0.75 x 24 (e) 0.6 x 30 (f) 0.05 x 40 2. without calculator (a) 0.5 x 1.5 (b) 0.1 x 25 (c) 0.25 x 16.4 (d) 0.75 x 2 (e) 0.2 x 15 (f) 0.05 x 10 3. without calculator – long multiplication – show working (a) 1.2 x 2.9 (b) 3.5 x 2.2 (c) 9.8 x 3.1 (d) 5.7 x 2.3 (e) 4.6 x 1.8 (f) 8.5 x 7.7 4. calculator allowed – answers to 3 d.p. (a) 2.57 x 3.62 (b) 12.01 x 5.97 (c) 23.63 x 13.81 (d) 56.2 x 1.951 (e) 122.08 x 7.002 (f) 443.1 x 0.0003


Ref. Num/dec/01/2009

Number - decimals decimal multiplication answer sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 3 (b) 1.6 (c) 5 (d) 18 (e) 18 (f) 2 2. (a) 0.75 (b) 2.5 (c) 4.1 (d) 1.5 (e) 3 (f) 0.5 3. (a) 3.48 (b) 7.7 (c) 30.38 (d) 13.11 (e) 8.28 (f) 65.45 4. (a) 9.303 (b) 71.700 (c) 326.330 (d) 109.646 (e) 854.804 (f) 0.133


Ref. Num/dec/01/2009

Number – powers & roots standard form question sheet N-PR-SF01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. write the following numbers in standard form (a) 2000 (b) 460 (c) 500000 (d) 40 (e) 3245 (f) 3100 (g) 324 (h) 1980 (i) 0.15 (j) 0.006 (k) 0.1092 (l) 0.00017 (m) 3 thousand (n) 0.5 hundred thousand (o) 0.011009 (p) 33.001 (q) 784.4 (r) 678002 2. correct the following and re-write in standard form (a) (b) 323 10× 424.5 10× (c) 274.5 10−× (d) (e) 30.79 10−× 20.8 10−× (f) 50.954 10−× (g) (h) 20.069 10−× 30.007 10−× (i) 30.091 10× (j) (k) 30.13 10× 40.053 10× (l) 60.09345 10× 3. express the following as ordinary numbers (a) (b) 39.345 10× 12.451 10−× (c) 56.51 10× (d) (e) 43.5 10−× 28.157 10−× (f) 31.1215 10× (g) (h) 22.98 10−× 29.198 10× (i) 67.8 10−× (j) (k) 33.1185 10× 48.854299 10× (l) 58.91 10−×


Number – powers & roots standard form answer sheet N-PR-SF01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) (b) 32 10× 24.6 10× (c) 55 10× (d) (e) 14 10× 33.245 10× (f) 33.1 10× (g) (h) 23.24 10× 31.98 10× (i) 11.5 10−× (j) (k) 36 10−× 11.092 10−× (l) 41.7 10−× (m) (n) 33 10× 52.5 10× (o) 21.1009 10−× (p) (q) 13.3001 10× 27.844 10× (r) 56.78002 10× 2. (a) (b) 42.3 10× 52.45 10× (c) 17.45 10−× (d) (e) 47.9 10−× 38 10−× (f) 69.54 10−× (g) (h) 46.9 10−× 67 10−× (i) 19.1 10× (j) (k) 21.3 10× 25.3 10× (l) 49.345 10× 3. (a) 9345 (b) 0.2451 (c) 651000 (d) 0.00035 (e) 0.08157 (f) 1121.5 (g) 0.0298 (h) 919.8 (i) 0.0000078 (j) 3118.5 (k) 88542.99 (l) 0.0000891


Number - percentages decimals to percentages question sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 0.5 (b) 0.75 (c) 0.33 (d) 0.1 (e) 0.97 (f) 0.25 2. (a) 1.1 (b) 2.6 (c) 4.05 (d) 3.95 (e) 10.01 (f) 15.75 3. (a) 0.025 (b) 0.037 (c) 0.0051 (d) 0.0064 (e) 0.0115 (f) 0.0794 4. (a) 1.001 (b) 1.096 (c) 2.113 (d) 3.0012 (e) 2.011 (f) 1.852


Ref. Num/percent/01/2009

Number - percentages decimals to percentages answer sheet 01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 50 % (b) 75 % (c) 33.3% (d) 10 % (e) 97 % (f) 25 % 2. (a) 110 % (b) 260 % (c) 405 % (d) 395 % (e) 1001 % (f) 1575% 3. (a) 2.5 % (b) 3.7 % (c) 0.51 % (d) 0.64 % (e) 1.15 % (f) 7.94 % 4. (a) 100.1 % (b) 109.6 % (c) 211.3 % (d) 300.12 % (e) 201.1 % (f) 185.2%



Number - percentages percentages to decimals question sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 51 % (b) 72 % (c) 39% (d) 15 % (e) 89 % (f) 27 % 2. (a) 150 % (b) 270 % (c) 358 % (d) 416 % (e) 1250 % (f) 1195% 3. (a) 1.5 % (b) 3.2 % (c) 0.67 % (d) 0.63 % (e) 1.94 % (f) 6.22 % 4. (a) 117.2 % (b) 102.9 % (c) 291.1 % (d) 298.18 % (e) 357.1 % (f) 102.9 %



Number - percentages percentages to decimals answer sheet 02 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 0.51 (b) 0.72 (c) 0.39 (d) 0.15 (e) 0.89 (f) 0.27 2. (a) 1.5 (b) 2.7 (c) 3.58 (d) 4.16 (e) 12.50 (f) 11.95 3. (a) 0.015 (b) 0.032 (c) 0.0067 (d) 0.0063 (e) 0.0194 (f) 0.0622 4. (a) 1.172 (b) 1.029 (c) 2.911 (d) 2.9818 (e) 3.571 (f) 1.029



Number - percentages percentage of a number question sheet 03 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

1. calculator not permitted (a) 50 % of 3 (b) 25 % of 8 (c) 150% of 12 (d) 10 % of 90 (e) 12.5 % of 16 (f) 33.3… % of 48 2. calculator not permitted (a) 75 % of 144 (b) 37.5 % of 48 (c) 30 % of 150 (d) 5 % of 240 (e) 85 % of 80 (f) 87.5 % of 64 3. calculator not permitted (a) 10 % of 5.18 (b) 20 % of 8.5 (c) 50 % of 4.6 (d) 75 % of 204.4 (e) 200 % of 97.8 (f) 125 % of 64.4 4. calculator permitted – answer to 3 d.p. (a) 13 % of 3.79 (b) 92 % of 5.12 (c) 36 % of 12.04 (d) 72 % of 3.8 (e) 12 % of 1.2 (f) 19 % of 2.85



Number - percentages percentage of a number answer sheet 03 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

1. (a) 1.5 (b) 2 (c) 18 (d) 9 (e) 2 (f) 16 2. (a) 108 (b) 18 (c) 45 (d) 12 (e) 68 (f) 56 3. (a) 0.518 (b) 1.7 (c) 2.3 (d) 153.3 (e) 195.6 (f) 80.5 4. (a) 0.493 (b) 4.710 (c) 4.334 (d) 2.736 (e) 0.144 (f) 0.542



Number - percentages fractions to percentages question sheet 04 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

1. without calculator

(a) 12

(b) 14

(c) 1

10

(d) 13

(e) 18

(f) 120

2. without calculator

(a) 38

(b) 6

10 (c)

78

(d) 720

(e) 25

(f) 23

3. without calculator (a) 1

21 (b) 342 (c) 1

101 (d) 2

33 (e) 582 (f) 9

201 4. calculator allowed(but not essential) – to one d.p.

(a) 19

(b) 27

(c) 56

(d) 2

113 (e) 162 (f) 2

131



Number - percentages fractions to percentages answer sheet 04 GCSE Maths Tutor www.gcsemathstutor.com [email protected]

1. (a) 50 % (b) 25 % (c) 10 % (d) 33.3… % (e) 12.5 % (f) 5 % 2. (a) 37.5 % (b) 60 % (c) 87.5 % (d) 35 % (e) 40 % (f) 66.6… % 3. (a) 150 % (b) 275 % (c) 110 % (d) 366.6… % (e) 262.5 % (f) 145 % 4. (a) 11.1… % (b) 28.6 % (c) 83.3 % (d) 318.2 % (e) 216.7 % (f) 115.4 %



Number – ratio & propn. ratio & proportion question sheet N-RP-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. simplify the following ratios: (a) 12 : 6 (b) 15 : 25 (c) 21 : 28 (d) 24 : 96 (e) 35 : 105 (f) 17: 68 (g) 27 : 9 : 54 (h) 18 : 72 : 144 (i) 38 : 76 : 19 2. divide 96 in the following ratios: (a) 1 : 2 (b) 2 : 6 (c) 11 : 5 (d) 7 : 5 3. divide 54 in the following ratios: (a) 13 : 5 (b) 7 : 11 (c) 1 : 17 (d) 8 : 10 4. divide 144 in the following ratios: (a) 3 : 1 (b) 1 : 5 (c) 7 : 2 (d) 11 : 13 5. divide 512 in the following ratios: (a) 13 : 3 (b) 3 : 1 (c) 7 : 1 (d) 1 : 63 6. divide 1000 in the following ratios: (a) 1 : 2 : 7 (b) 6 : 12 : 2 (c) 13 : 26 : 11 (d) 21 : 1 : 3


Number – ratio & propn. ratio & proportion answer sheet N-RP-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected] 1. (a) 2 : 1 (b) 3 : 5 (c) 3 : 4 (d) 1 : 4 (e) 1 : 3 (f) 1 : 4 (g) 3 ; 1 : 6 (h) 1 : 4 : 8 (i) 2 : 4 : 1 2. (a) 32, 64 (b) 24, 72 (c) 66, 30 (d) 56, 40 3. (a) 39, 15 (b) 21, 33 (c) 3, 51 (d) 24, 30 4. (a) 108, 36 (b) 24, 120 (c) 112, 32 (d) 66, 78 5. (a) 416, 96 (b) 384, 128 (c) 448, 64 (d) 8, 504 6. (a) 100, 200, 700 (b) 300, 600, 100 (c) 260, 520, 220 (d) 840, 40, 120


Number – approximation significant figures question sheet N-A-SF-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. express each number to 2 significant figures: (a) 45.9 (b) 0.256 (c) 0.001892 (d) 2.016 (e) 571.9 (f) 21.09 (g) 89.06 (h) 2.099 (i) 345.7 2. express each number to 3 significant figures: (a) 95.53 (b) 417.6 (c) 2.859 (d) 0.003912 (e) 49.83 (f) 0.0007919 (g) 0.039128 (h) 5.876 (i) 34.87 3. express each number to 4 significant figures: (a) 87.491 (b) 526.79 (c) 2.7482 (d) 0.0048219 (e) 58.949 (f) 0.00081128 (g) 0.041936 (h) 4.9897 (i) 49.219 4. express each number to 5 significant figures: (a)202.569 (b) 1592.56 (c) 2567.91 (d) 529211.6 (e) 679229.2 (f) 0.0192654 (g) 0.00911987 (h) 955.216 (i) 59.01256

Number – approximation significant figures answer sheet N-A-SF-01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 46 (b) 0.26 (c) 0.0019 (d) 2.0 (e) 570 (f) 21 (g) 89 (h) 2.1 (i) 350 2. (a) 95.5 (b) 418 (c) 2.86 (d) 0.00391 (e) 49.8 (f) 0.000792 (g) 0.0391 (h) 5.88 (i) 34.9 3. (a) 87.49 (b) 526.8 (c) 2.748 (d) 0.004822 (e) 58.95 (f) 0.0008113 (g) 0.04194 (h) 4.990 (i) 49.22 4. (a) 202.57 (b) 1592.6 (c) 2567.9 (d) 529210 (e) 679230 (f) 0.019265 (g) 0.0091199 (h) 955.22 (i) 59.013

Number - approximation upper & lower bounds question sheet N-A-ULB01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. write down the upper and lower bounds of the following measurements: (a) 121 mm correct to the nearest mm

(b) 345.2 mm correct to the nearest 0.1 mm

(c) 987 cm correct to the nearest cm

(d) 54 km correct to the nearest km

(e) 1023.4 kg correct to the nearest 0.1 kg 2. What is the smallest and largest area of a rectangle with the measurements below, given that the accuracy is to the nearest cm (answer to 2 decimal places). (a) 2 x 8 (b) 4 x 1 (c) 3 x 6 (d) 11 x 12 (e) 15 x 9 (f) 22 x 13 3. Circles are inscribed to an accuracy of 0.1 cm What are the smallest and largest areas for circles with the following radii? All measurements are in cm (answer to 2 decimal places) (a) 1.1 (b) 5.6 (c) 9.2 (d) 10.3 (e) 3.2 (f) 7.7 4. The base and height of triangles are measured to within 0.1 mm What are the smallest & largest areas of triangles with the heights and bases given. All measurements are in mm (answer to 2 decimal places) (a) 11.2 , 1.3 (b) 4.1 , 1.2 (c) 1.7 , 3.2 (d) 5.1 , 6.9 (e) 8.7 , 9.1 (f) 11.9 , 23.3

Number - approximation upper & lower bounds answer sheet N-A-ULB01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 121.5 , 120.5 2m.m. 2m.m.

(b) 345.25 , 345.15 2m.m. 2m.m.

(c) 987.5c.m. , 986.5c.m.

(d) 54.5k.m. , 53.5k.m.

(e) 1023.45k.g. , 1023.35k.g. 2. (a) 11.25 , 21.25 (b) 1.75 , 6.75 (c) 13.75 , 22.75 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. (d) 120.75 , 143.75 (e) 123.25 , 147.25 (f) 268.75 , 303.75 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. 3. (a) 3.46 , 4.15 (b) 96.77 , 100.29 (c) 263.02 , 268.80 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. (d) 330.06 , 336.54 (e) 31.17 , 33.18 (f)183.85 , 188.69 2c.m 2c.m. 2c.m. 2c.m. 2c.m. 2c.m. 4. (a) 6.97 , 7.59 (b) 2.33 , 2.59 (c) 2.60 , 2.84 2m.m. 2m.m. 2m.m. 2m.m. 2m.m. 2m.m. (d) 17.30 , 17.90 (e) 39.14 , 40.03 (f) 137.76 , 139.52 2m.m. 2m.m. 2m.m. 2m.m. 2m.m. 2m.m.

Number - approximation decimal places question sheet N-A-DP01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. Write the decimal 23.81254098 to the following number of decimal places: (a) 5 (b 3 (c) 2

(d) 1 (e) 7 (f) 4 2. Use your calculator to multiply out the pairs of numbers. In each case give your answer to three places of decimals. (a) 1.29×9.87 (b) 3.71×2.23 (c) 6.43×1.18 (d) 4.41×2.97 (e) 5.52×9.86 (f) 2.42×9.26 (g) 7.43×4.98 (h) 5.99×11.01 (i) 1.32 5.12 × 3. Use your calculator to divide the first number by the second. In each case give your answer to two places of decimals. (a) 23.14 2.11 (b) 12.97÷ ÷3.87 (c) 81.22 23.92 ÷ (d) 7.95 1.78 (e) 34.51÷ ÷29.22 (f) 67.21 3.45 ÷ (g) 21.08 4.92 (h) 88.17÷ ÷43.99 (i) 18.51 6.69 ÷ 4. Use your calculator to add the two numbers together. In each case give your answer to one place of decimals. (a) 1.23489 + 0.00912 (b) 3.22 + 2.91 (c) 7.89 + 33.003 (d) 89.0134 + 23.0018 (e) 77.091 + 21.099 (f) 45.67 + 67.911 (g) 0.093 + 0.0867 (h) 45.901 + 44.892 (i) 90.24 + 89.81

Number - approximation decimal places answer sheet N-A-DP01 GCSE Maths Tutor www.gcsemathstutor.com [email protected]


1. (a) 23.81254 (b 23.813 (c) 23.81

(d) 23.8 (e) 23.8125410 (f) 23.8125 2. (a) 12.732 (b) 8.273 (c) 7.587 (d) 13.098 (e) 54.427 (f) 22.409 (g) 37.001 (h) 65.950 (i) 6.758 3. (a) 10.97 (b) 3.35 (c) 3.40 (d) 4.47 (e) 1.18 (f) 19.48 (g) 4.28 (h) 2.00 (i) 2.77 4. (a) 1.2 (b) 6.1 (c) 40.9 (d) 112.0 (e) 98.2 (f) 113.6 (g) 0.2 (h) 90.8 (i) 180.1

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