Two-Tier GCSE Mathematics Homework · 2015-04-15 · Two-Tier GCSE Maths Homework Pack 1:...

Two-Tier GCSE MathematicsHomework

Pack 1: Foundation Tier

Stafford BurndredConsultant editor: Duncan Smith

ISBN-10: 1 84070 641 4

ISBN-13: 978 184070 641 3

© Pearson Publishing 1997

Published by Pearson Publishing 1997

Revised 2006

A licence to copy the material in this pack is only granted to the purchaser strictly within their

school, college or organisation. The material must not be reproduced in any other form without

the express written permission of Pearson Publishing.

Pearson Publishing, Chesterton Mill, French’s Road, Cambridge CB4 3NP Tel 01223 350555 Fax 01223 356484

www.pearsonpublishing.co.uk

AB

CD

EFG

HIJ

KLM

NO

PQ

RS

TUV

WX

YZ

abcd

efgh

ijklm

nopq

rstu

vwxy

z-&

!?,'’

.()[]/

\*@

;:123

4567

890

St Bernadette Catholic Secondary School

Two-Tier GCSE Maths Homework Pack 1: Foundation Tier Name:.......................................................

Pearson Publishing Tel: 01223 350555 3

1 Place value

13

1 What is the next whole number after fifty thousand? Write your answer in figures. 1 ................................... ■■

2 What is the number before one thousand? Write your answer in figures. 2 ................................... ■■

3 Write seventeen thousand and thirty in figures. 3 ................................... ■■

4 Write six thousand and four in figures. 4 ................................... ■■

5 Write 23 001 in words. 5 ...................................

.....................................

..................................... ■■

6 Write 5030 in words. 6 ...................................

..................................... ■■

7 Here is a list of numbers:

989 1010 897 1009

a Which is the largest number? 7a ................................. ■■

b Which is the smallest number? b................................. ■■

c Write the numbers in ascending order. c .................................

...................................

...................................

................................... ■■

d Write the numbers in descending order. d.................................

...................................

...................................

................................... ■■

8 What is the value of the 4 in these numbers?

a 246 8a ................................. ■■

b 324 b................................. ■■

c 481 c ................................. ■■


What is the missing number in these sums?

1 7 x 6 = ■■ 1....................... ■■

2 ■■ x 8 = 56 2....................... ■■

3 6 x ■■ = 54 3....................... ■■

4 72 ÷ 8 = ■■ 4....................... ■■

5 ■■ ÷ 4 = 9 5....................... ■■

6 21 ÷ ■■ = 3 6....................... ■■

Work out the following:

7 4 x 100 7....................... ■■

8 10 x 16 8....................... ■■

9 73 x 1000 9....................... ■■

10 4000 ÷ 10 10..................... ■■

11 3600 ÷ 100 11..................... ■■

12 47 000 ÷ 1000 12..................... ■■

13 Mr Smith bought 100 pencils at 14p each. What was the total cost? 13..................... ■■

14 Mrs Green bought 10 trees for £70. What was the cost of each tree? 14..................... ■■



2 Multiplication facts

14

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 The picture shows the heights, in metres, of several objects.

Give the difference in height between the following:

a coastguard station and submarine 1a .................................. ■■

b submarine and treasure chest b .................................. ■■

c car and treasure chest c .................................. ■■

d coastguard station and treasure chest d.................................. ■■

e car and submarine e .................................. ■■

f coastguard station and car f................................... ■■

2 Place these numbers in order, smallest first:

a -5, 3, -7, 1, 6 2a .................................. ■■

b 4, -2, -6, -8, 3 b .................................. ■■

c 5, 0, -2, -6, 7 c .................................. ■■

3 Work out the answers to these questions:

a -3 – 5 3a .................................. ■■

b -4 + 6 b .................................. ■■

c 3 – 5 c .................................. ■■



3 Negative numbers – 1

12

250

200

150

100

50

0

-50

-100

-150

-200

Sea level

Coastguard station

Car

Treasure chest

Submarine


1 Place these numbers in order, smallest first:a -6, 4, -9, -2, 5 1a...................................... ■■b 0, -2, -7, 6, 1 b....................................... ■■c -2, -7, -5, 1, -3, 4 c ....................................... ■■d -2, -8, 1, 2, 0, -4 d....................................... ■■

2 Place these numbers in order, largest first:a -8, -7, 3, 0, -4, 1 2a...................................... ■■b -2, -5, 6, 0, -3, 2 b....................................... ■■c -4, -2, 2, 0, 6, -1 c ....................................... ■■d 8, 3, -5, -1, -3, 2 d....................................... ■■

3 Work out the answers to these questions without usinga calculator:a 6 – 10 3a...................................... ■■b -3 – 1 b....................................... ■■c -7 + 4 c ....................................... ■■d -2 + 8 d....................................... ■■

4 Work out the answers to these questions. You must usea calculator. Show the calculator keys:

a -8 – 7 ■■ ■■ ■■ ■■ ■■ ■■ ■■ 4a...................................... ■■

b -5 – -2 ■■ ■■ ■■ ■■ ■■ ■■ ■■ b....................................... ■■

c 6 – -4 ■■ ■■ ■■ ■■ ■■ ■■ ■■ c ....................................... ■■

d -7 + -3 ■■ ■■ ■■ ■■ ■■ ■■ ■■ d....................................... ■■

e -8 x -3 ■■ ■■ ■■ ■■ ■■ ■■ ■■ e....................................... ■■

f 6 x -4 ■■ ■■ ■■ ■■ ■■ ■■ ■■ f ....................................... ■■

g -7 x 3 ■■ ■■ ■■ ■■ ■■ ■■ ■■ g....................................... ■■

h -50/10 ■■ ■■ ■■ ■■ ■■ ■■ ■■ h....................................... ■■

i -30/-6 ■■ ■■ ■■ ■■ ■■ ■■ ■■ i........................................ ■■

j 8/-80 ■■ ■■ ■■ ■■ ■■ ■■ ■■ j ........................................ ■■

5 The temperature at 15.00 is 3°C. The temperature at18.00 is -7°C. By how much has the temperature fallen? 5........................................ ■■

6 The temperature at 03.00 is -12°C. The temperaturerises by 4°C. What is the new temperature? 6........................................ ■■



24

4 Negative numbers – 2


1 361 2 429 1....................... ■■

+ 127 + 178 2....................... ■■

3 572 4 680 3....................... ■■

– 135 – 197 4....................... ■■

5 37 6 68 5....................... ■■

x 8 x 4 6....................... ■■

7 72 ÷ 8 8 63 ÷ 9 7....................... ■■

8....................... ■■

9 John had 287 stamps. He bought 468 more. How many stamps did he have altogether? 9....................... ■■

10 A classroom had 36 chairs. They were placed in rows of 4. How many rows were there? 10..................... ■■

11 Sally had £128. She spent £86. How much did she have left? 11 £.................. ■■

12 There were 7 buses in a bus station. Each bus had 17 passengers. How many passengers were there? 12..................... ■■



5 Solving problems without a calculator

12

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


Write the following correct to the nearest whole number:

1 16.8 1 ................................. ■■

2 17.289 2 ................................. ■■

3 19.7 3 ................................. ■■

Write the following correct to the nearest ten:

4 3863 4 ................................. ■■

5 428 5 ................................. ■■

6 721.8 6 ................................. ■■

7 596 7 ................................. ■■

Write the following correct to the nearest hundred:

8 4218 8 ................................. ■■

9 353 9 ................................. ■■

10 472.83 10 ............................... ■■

11 3999 11 ............................... ■■

Estimate the total amount of money:

12 £38 + £27 + £76 + £31 12 £ ............................ ■■

13 £371 + £238 + £527 13 £ ............................ ■■

14 £6010 + £7613 + £4571 + £2106 14 £ ............................ ■■

15 £5995 + £7782 + £2534 + £3124 15 £ ............................ ■■



6 Calculation checks

15


1 60 x 200 1.................................... ■■

2 800 x 400 2.................................... ■■

3 6000 x 300 3.................................... ■■

4 70 x 30 4.................................... ■■

5 400 x 50 5.................................... ■■

6 80 000 ÷ 200 6.................................... ■■

7 600 ÷ 20 7.................................... ■■

8 7200 ÷ 80 8.................................... ■■

9 36 000 ÷ 90 9.................................... ■■

10 4500 ÷ 500 10.................................. ■■



7 Mental arithmetic shortcuts – 1

10

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 40 x 300 1....................... ■■

2 700 x 60 2....................... ■■

3 5000 x 30 3....................... ■■

4 700 x 800 4....................... ■■

5 6000 x 400 5....................... ■■

6 40 x 500 6....................... ■■

7 60 000 ÷ 200 7....................... ■■

8 420 ÷ 70 8....................... ■■

9 5600 ÷ 800 9....................... ■■

10 4800 ÷ 60 10..................... ■■

11 54 000 ÷ 900 11..................... ■■

12 72 000 ÷ 30 12..................... ■■




12

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

1 5.8 x 10 1 ......................... ■■

2 3.2 x 100 2 ......................... ■■

3 12.3 x 1000 3 ......................... ■■

4 62.8 ÷ 10 4 ......................... ■■

5 32.4 ÷ 1000 5 ......................... ■■

6 76.3 ÷ 100 6 ......................... ■■

7 57 x 100 7 ......................... ■■

8 0.62 x 10 8 ......................... ■■

9 38.1 ÷ 1000 9 ......................... ■■

10 0.37 ÷ 100 10 ....................... ■■

11 0.06 x 10 11 ....................... ■■

12 3.6 ÷ 100 12 ....................... ■■

13 4.2 x 100 13 ....................... ■■

14 0.7 ÷ 100 14 ....................... ■■

15 0.54 x 10 15 ....................... ■■

16 2.6 ÷ 1000 16 ....................... ■■





16

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 3.65 x 10 1....................... ■■

2 2.8 x 100 2....................... ■■

3 47.3 ÷ 10 3....................... ■■

4 5.82 ÷ 10 4....................... ■■

5 6.81 x 1000 5....................... ■■

6 0.37 x 100 6....................... ■■

7 0.21 ÷ 10 7....................... ■■

8 0.73 ÷ 1000 8....................... ■■

9 486.3 x 10 9....................... ■■

10 5.27 x 1000 10..................... ■■

11 3.8 ÷ 1000 11..................... ■■

12 4.7 ÷ 10 12..................... ■■

13 3.64 x 10 13..................... ■■

14 0.047 x 10 14..................... ■■

15 0.032 ÷ 10 15..................... ■■

16 0.06 ÷ 100 16..................... ■■

17 0.0204 x 1000 17..................... ■■

18 6.08 x 10 18..................... ■■

19 0.3 ÷ 100 19..................... ■■

20 0.3 x 100 20..................... ■■

21 7.3 ÷ 1000 21..................... ■■

22 7.3 x 1000 22..................... ■■

23 6.8 ÷ 100 23..................... ■■

24 0.68 x 10 24..................... ■■



24

10 Mental arithmetic shortcuts – 4C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

You must show all of your working.

1 3.8 + 0.7 + 4.6 1 ......................... ■■

2 3.7 + 1.26 + 0.1 2 ......................... ■■

3 8.52 – 4.67 3 ......................... ■■

4 3.6 – 2.93 4 ......................... ■■

5 4.72 x 0.03 5 ......................... ■■

6 15.2 x 0.4 6 ......................... ■■

7 3.72 ÷ 0.3 7 ......................... ■■

8 18.78 ÷ 0.02 8 ......................... ■■

9 John had £5. He spent £1.20. How much change did he receive? 9 £...................... ■■

10 Sara bought 4 packs of coffee at £1.36 each. What was the total cost? 10 £.................... ■■




11 Decimals – 1

10

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 5.6 + 0.04 + 10.7 1....................... ■■

2 4.3 + 28 + 0.06 + 0.82 2....................... ■■

3 8.73 – 2.36 3....................... ■■

4 5.8 – 1.93 4....................... ■■

5 5.32 x 0.06 5....................... ■■

6 18.3 x 0.7 6....................... ■■

7 2.52 ÷ 0.6 7....................... ■■

8 7.74 ÷ 0.04 8....................... ■■

9 A woman had a £10 note. She bought a loaf at £0.76 and a book at £3.95. 9 £.................... ■■How much change did she receive?

10 John bought six Christmas cards at £1.27 each. What was the total cost? 10 £.................. ■■




12 Decimals – 2

10

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 358

x 63

1....................... ■■

2 482

x 24

2....................... ■■

3 531 x 73

3....................... ■■

4 681 x 28

4....................... ■■

In each question, give the whole number answer and the remainder.

5 32 ) 7 8 3 5....................... ■■

6 17 ) 8 8 6 6....................... ■■

7 427 ÷ 13 7....................... ■■

8 638 ÷ 14 8....................... ■■




13 Long multiplication and division – 1

8

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


1 357 x 42 1....................... ■■

2 574 x 63 2....................... ■■

3 871 x 48 3....................... ■■

4 307 x 96 4....................... ■■

In each question, give the whole number answer and the remainder.

5 876 ÷ 27 5....................... ■■

6 937 ÷ 18 6....................... ■■

7 868 ÷ 16 7....................... ■■

8 4978 ÷ 23 8....................... ■■




14 Long multiplication and division – 2

8

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


Check the following sums. Show how you checked. If the answer is correct, write ‘correct’ in the answer column. If the answer is wrong, write the answer you get in the answer column.

1 372

+ 289

617 1 ......................... ■■

2 873

– 246

633 2 ......................... ■■

3 568

– 179

389 3 ......................... ■■

What are the missing numbers in these sums?

4 283

+ ...... 4 ......................... ■■

817

5 637

– ...... 5 ......................... ■■

209

6 Jayne bought 89 pens at 21p each. Estimate the total cost.

6 £..................... ■■

7 Estimate the cost of 387 packs of coffee at £2.11 each.

7 £..................... ■■

8 Estimate the cost of 62 calculators at £7.95 each.

8 £..................... ■■




15 Checking – 1

8

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =


Check the following sums. Show how you checked. If the answer is correct, write ‘correct’ in the answercolumn. If the answer is wrong, write the answer you get in the answer column.

1 478 1....................... ■■

+ 364

842

2 574 2....................... ■■

– 138

444

3 John bought 478 cans of Coke at 31p each. Estimate the total cost. 3 £.................... ■■

Fill in the missing rows of numbers.

4 617 4....................... ■■

– .......

429

5 378 5....................... ■■

+ ........

1052

6 ......... 6 ....................... ■■

– 489

134

7 Estimate the cost of 685 boxes of nails at £2.95 each. 7 £.................... ■■

8 Estimate the cost of 811 m2 of carpet at £6.95 per m2. 8 £.................... ■■




16 Checking – 2

8

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

Round the following numbers to one significant figure.

1 687 1....................... ■■

2 580 2....................... ■■

3 729 3....................... ■■

4 52.79 4....................... ■■

5 32.51 5....................... ■■

6 0.068 6....................... ■■

7 0.0308 7....................... ■■

8 0.998 8....................... ■■

Estimate the answers to these questions (show your working).

9 5879 x 31 9....................... ■■

10 731 x 0.088 10..................... ■■

11 0.0813 x 297 11..................... ■■

12 5.19 x 0.082 12..................... ■■

13 8128 ÷ 41 13..................... ■■

14 6081 ÷ 0.0214 14..................... ■■

15 4983 ÷ 0.0049 15..................... ■■

16 8.102 ÷ 0.391 16..................... ■■




17 Checking – 3

16

C = / x

7 8 9 +

4 5 6 -

1 2 3

.0 =

Give your answer correct to six significant figures where appropriate. Show your calculator keys for questions 1 and 5.

1 5.3 (7.8 + 2.93) 1....................... ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

2 7.42 (8.68 - 2.71) 2....................... ■■

3 (5.64 - 8.73) 5.46 3....................... ■■

4 (8.73 + 2.7 - 1.84) 3.27 4....................... ■■

5 6.384 x 2.97 5....................... ■■

4.729 - 3.68

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

6 78.734 - 12.69 6....................... ■■5.81 x 0.873

7 5.8 (3.67 - 8.91) 7....................... ■■(7.8 x 3.69) 4.72

8 782 x 386 8....................... ■■67 x 4.89

The make and type of my calculator is .................................................




18 Using a calculator: Brackets and memory

8

Use your calculator to find the answers. Show your calculator keys.Give your answer correct to six significant figures where appropriate.

1 3.72 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 1....................... ■■

2 4.25 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 2....................... ■■

3 √74 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 3....................... ■■

4 3√285 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 4....................... ■■

5 6√832 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 5....................... ■■

6 282/3 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 6....................... ■■

7 16-1/4 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 7....................... ■■

8 2-3 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 8....................... ■■

9 y = 4x3 + 3x2 - 2x + 1 9....................... ■■Calculate the value of y when x = 3.74. Use an efficient calculator method.

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

10 y = 7x3 – 4x2 + 3x – 2 10..................... ■■Calculate the value of y when x = -3.521. Use an efficient calculator method.

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■

The make and type of my calculator is .................................................




19 Using a calculator: Powers, roots, memory

10

Write the following as ordinary numbers.

1 6.3 x 104 1............................... ■■

2 4.2 x 103 2............................... ■■

3 3.72 x 10-2 3............................... ■■

4 2.63 x 10-4 4............................... ■■

5 5.1 x 106 5............................... ■■

6 4.3 x 102 6............................... ■■

7 2.8 x 10-1 7............................... ■■

8 7.1 x 10-5 8............................... ■■

Write the following numbers in standard form.

9 360 9............................... ■■

10 2400 10............................. ■■

11 482000 11............................. ■■

12 0.37 12............................. ■■

13 0.00682 13............................. ■■

14 0.072 14............................. ■■

15 38000 15............................. ■■

16 0.00035 16............................. ■■

Give the answers to the following: a in standard form (correct to three significant figures); b as an ordinarynumber (correct to six significant figures where appropriate). Show your calculator keys for question 17.

17 3.87 x 103 x 2.6 x 102 ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 17a........................... ■■

■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ ■■ 17b........................... ■■

18 5.71 x 106 + 8.34 x 105 18a........................... ■■18b........................... ■■

19 3.6 x 10-3 x 4.72 x 107 19a........................... ■■19b........................... ■■

20 4.2 x 104 x 3.6 x 105 20a........................... ■■2.8 x 102 + 3.42 x 103 20b........................... ■■

21 2.7 x 10-2 x 4.3 x 106 21a .......................... ■■1.8 x 10-1 x 3.6 x 104 21b .......................... ■■

22 (6.82 x 102)3 22a .......................... ■■22b .......................... ■■

The make and type of my calculator is ................................................




20 Standard form

28

1 a Shade 2/3 of this shape:

1a ■■

b What fraction is left unshaded? b..................... ■■

2 a Shade 3/5 of this shape:

2a ■■

b What fraction is left unshaded? b..................... ■■

3 John has 12 squares of chocolate. He eats 1/4.

a How many squares does he eat? 3a..................... ■■

b How many squares does he have left? b..................... ■■

4 a Shade 25% of this shape:

4a ■■

b What percentage is left unshaded? b..................... ■■

5 Shade 50% of this shape:

5 ■■




21 Fractions and percentages – 1

9

1 Find 3% of 24. 1....................... ■■

2 Find 24% of 32. 2....................... ■■

3 Increase 40 by 18%. 3....................... ■■

4 Increase 32 by 7%. 4....................... ■■

5 Decrease 69 by 5%. 5....................... ■■

6 Decrease 40 by 20%. 6....................... ■■

7 Find 4/5 of 16. 7....................... ■■

8 Find 2/7 of 28. 8....................... ■■

9 Increase 35 by 3/5. 9 ....................... ■■

10 Decrease 40 by 5/8. 10..................... ■■

11 A woman earns £25 000 pa. She receives a 5% increase each year.a How much does she receive after one year? 11a................... ■■

b How much does she receive after three years? b ................... ■■(Give your answer to the nearest pound.)

12 A washing machine costs £320 plus 17.5% VAT. What is the total cost? 12..................... ■■

13 A car was bought for £12 000. It depreciates by 15% each year. How much is it worth after:a one year? 13a................... ■■

b three years? b ................... ■■




22 Fractions and percentages – 2

17

For questions 1 and 2, show your working or the calculator keys you used.

1 23/5 x 12/3 1....................... ■■

2 51/2 + 22/3 2....................... ■■

3 42/3 – 11/6 3....................... ■■

4 63/5 ÷ 12/3 4....................... ■■

5 Find 2/3 of 63. 5....................... ■■

6 Find 3/8 of 27. 6....................... ■■

7 Find 3/5 of 714. 7....................... ■■

8 Write 81/99 as a fraction in its lowest terms. 8....................... ■■


10 Write 236/448 as a fraction in its lowest terms. 10..................... ■■

11 12 people out of 80 owned a computer. Write this as a fraction in its lowest terms. 11..................... ■■

12 A tennis club had 360 members. 160 were female.a What fraction of the members were female? Give your answer

in its lowest terms. 12a................... ■■b What fraction of the members were male? Give your answer in

its lowest terms. b ................... ■■

13 There were 480 people in a cinema. 1/4 were men, 2/5 were women, 1/8 were boys. The rest were girls.a How many men were in the cinema? 13a................... ■■

b How many women were in the cinema? b ................... ■■

c How many boys were in the cinema? c.................... ■■

d What fraction were girls? d ................... ■■




23 Fractions – 1

17

For questions 1 and 2, show your working or the calculator keys used.

1 34/5 x 21/3 1....................... ■■

2 53/4 + 35/6 2 ....................... ■■

3 31/2 ÷ 7/8 3....................... ■■

4 83/5 – 25/8 4....................... ■■

5 Find 2/3 of 12. 5....................... ■■

6 Find 3/5 of 72. 6....................... ■■

7 Find 3/8 of 50. 7....................... ■■

8 Find 7/8 of 19. 8....................... ■■



11 Write 64/136 as a fraction in its lowest terms 11..................... ■■


13 15 people out of 40 wore glasses. 13..................... ■■Write this as a fraction in its lowest terms.

14 A golf club had 480 members. 150 were female.a What fraction of the members were female? 14a................... ■■

Give the answer in its lowest terms.

b What fraction of the members were male? 14b................... ■■Give the answer in its lowest terms.

15 There were 360 people in a hall.2/5 were men, 1/6 were boys, 1/3 were women. The rest were girls.

a How many men were in the hall? 15a................... ■■

b How many women were in the hall? 15b................... ■■

c What fraction were girls? 15c ................... ■■




24 Fractions – 2

18

Convert the following percentages to decimals.

1 32% 1....................... ■■

2 24% 2....................... ■■

3 60% 3....................... ■■

4 5% 4....................... ■■

5 42.7% 5....................... ■■

6 3.84% 6....................... ■■

7 30.2% 7....................... ■■

8 0.7% 8....................... ■■

Convert the following decimals to percentages.

9 0.38 9....................... ■■

10 0.17 10..................... ■■

11 0.4 11..................... ■■

12 0.234 12..................... ■■

13 0.072 13..................... ■■

14 0.06 14..................... ■■

15 0.502 15..................... ■■

16 0.003 16..................... ■■




25 Changing between decimals and percentages – 1

16

Convert the following percentages to decimals.

1 28% 1....................... ■■

2 34% 2....................... ■■

3 20% 3....................... ■■

4 6% 4....................... ■■

5 32.8% 5....................... ■■

6 6.52% 6....................... ■■

7 20.6% 7....................... ■■

8 0.3% 8....................... ■■

Convert the following decimals to percentages.

9 0.52 9....................... ■■

10 0.78 10..................... ■■

11 0.6 11..................... ■■

12 0.632 12..................... ■■

13 0.084 13..................... ■■

14 0.07 14..................... ■■

15 0.308 15..................... ■■

16 0.002 16..................... ■■




26 Changing between decimals and percentages – 2

16

Convert the following percentages to fractions. Give the answer in its lowest terms.

1 6% 1....................... ■■

2 24% 2....................... ■■

3 75.4% 3....................... ■■

4 0.3% 4....................... ■■

Convert the following decimals to fractions. Give the answer in its lowest terms.

5 0.45 5....................... ■■

6 0.8 6....................... ■■

7 0.04 7....................... ■■

8 0.036 8....................... ■■

Convert the following fractions to decimals.

9 5/8 9....................... ■■

10 3/5 10..................... ■■

11 3/40 11..................... ■■

12 13/80 12..................... ■■

Convert the following fractions to percentages.

13 1/8 13..................... ■■

3/4014 14..................... ■■

2/515 15..................... ■■

16 37/80 16..................... ■■




27 Changing between decimals, percentages and fractions – 1

16

Convert the following percentages to fractions in their lowest terms.

1 4% 1....................... ■■

2 34% 2....................... ■■

3 25.5% 3....................... ■■

4 0.7% 4....................... ■■

Convert the following decimals to fractions in their lowest terms.

5 0.28 5....................... ■■

6 0.6 6....................... ■■

7 0.05 7....................... ■■

8 0.072 8....................... ■■

Convert the following fractions to decimals.

9 2/5 9....................... ■■

10 3/8 10..................... ■■

11 7/40 11..................... ■■

12 17/80 12..................... ■■

Convert the following fractions to percentages.

13 3/16 13..................... ■■

14 4/5 14..................... ■■

15 7/80 15..................... ■■

16 29/40 16..................... ■■




28 Changing between decimals, percentages and fractions – 2

16


Simplify these ratios.

1 25:40 1....................... ■■

2 36:48 2....................... ■■

3 50:60 3....................... ■■

4 320:240 4....................... ■■

5 Write 4:11 in the ratio 1:n. 5 ....................... ■■


7 Write 14:20 in the ratio n:1. 7 ....................... ■■


9 The scale of a map is 1:100 000.

a The distance between Ayton and Beton is 12 cm on the map. What is the actual distance? Give your answer in kilometres. 9a..................... ■■

b The distance between Beton and Cedon is 32 cm on the map. What is the actual distance? Give your answer in kilometres. b..................... ■■

c The distance between Cedon and Deton is 27 km. What is the distance on the map? Give your answer in centimetres. c ..................... ■■

d The distance between Deton and Exton is 41 km. What is the distance on the map? Give your answer in centimetres. d .................... ■■

10 This is a recipe for soup for four people:

800 ml water

12 g salt

40 g beef

2 tomatoes

How much of each ingredient should be used for six people? 10a Water ........................... ■■

b Salt................................ ■■

c Beef ............................... ■■

d Tomatoes ...................... ■■



29 Ratio – 1

16

Simplify these ratios.

1 20:30 1....................... ■■

2 64:72 2....................... ■■

3 55:35 3....................... ■■

4 800:450 4....................... ■■





9 The scale of a map is 1:1 000 000.

a The distance between Hayle and Langham is 14 cm on the map. What is the actual distance? 9a ................km ■■

b The distance between Langham and Melbury is 25 cm on the map. What is the actual distance? 9b ................km ■■

c The distance between Melbury and Whitchurch is 36 kilometres. What is the distance on the map? 9c.................cm ■■

d The distance between Whitchurch and Sarum is 820 kilometres. What is the distance on the map? 9d ................cm ■■

10 This is a recipe for vegetable soup for six people:900 ml water18 g salt3 carrots2 onions

How much of each ingredient should you use for 15 people? 10a Water ............... ■■b Salt.................... ■■c Carrots............... ■■d Onions............... ■■




30 Ratio – 2

16

1 The ratio of men to women on a train was 5:8. There were 200 men.

a How many women were on the train? 1a..................... ■■

b What was the total number of men and women on the train? b..................... ■■

2 A drink is made by mixing pineapple juice, orange juice and lime juice in the ratio 2:7:3. Sally makes 600 ml of the fruit drink.

a How much pineapple juice is used? 2a..................... ■■

b How much orange juice is used? b..................... ■■

c How much lime juice is used? c ..................... ■■

Karen has 600 ml of lime juice and an unlimited supply of pineapple juice and orange juice.

d What is the maximum amount of the drink Karen can make? d .................... ■■

e How much pineapple juice would she use? e..................... ■■

f How much orange juice would she use? f ..................... ■■

3 £8000 is left in a will to be shared between Alan, Ben and Carol in the ratio 5:7:4.

a How much does Alan receive? 3a..................... ■■

b How much does Ben receive? b..................... ■■

c How much does Carol receive? c ..................... ■■




31 Ratio – 3

11

1 The ratio of boys to girls on a school trip was 5:7. There were 56 girls.

a How many boys were on the school trip? 1a..................... ■■

b How many pupils were on the school trip? b...................... ■■

2 A fruit drink is made by mixing lemon juice, orange juice and lime juice in the ratio 5:2:3. James makes 400 ml of the fruit drink.

a How much lemon juice is used? 2a..................... ■■

b How much orange juice is used? b...................... ■■

c How much lime juice is used? c ...................... ■■

Kelly has 420 ml of lime juice and an unlimited supply of lemon juice and orange juice.

d What is the maximum amount of fruit drink Kelly can make? d...................... ■■

e How much lemon juice would she use? e ...................... ■■

f How much orange juice would she use? f....................... ■■

3 Andrea, Barbara and Carolyn share £4400 in the ratio 4:5:2.

a How much does Andrea receive? 3a..................... ■■

b How much does Barbara receive? b...................... ■■

c How much does Carolyn receive? c ...................... ■■




32 Ratio – 4

11

Show your working or your calculator keys.

1 Write 24 out of 120 as a percentage.

1....................... ■■2 Write 57 out of 190 as a percentage.

2....................... ■■3 Jayne had £400. She spent £68.

a What percentage did she spend?

3a..................... ■■b What percentage did she have left?

b..................... ■■4 Mr Brown earned £320 per week. Calculate his percentage increase

if he received a rise of:

a £6.40

4a..................... ■■b £24

b..................... ■■c £10.24

c ..................... ■■5 There were 300 people in a room. 45 wore glasses.

What percentage wore glasses?

5....................... ■■6 In a sale, a video recorder was reduced from £360 to £288.

Calculate the percentage reduction.

6....................... ■■




33 Percentages – 1

9

Show your working or your calculator keys.

1 Write 48 out of 160 as a percentage. 1....................... ■■

2 Write 68 out of 170 as a percentage. 2....................... ■■

3 John had £250. He spent £132.50.

a What percentage did he spend? 3a..................... ■■

b What percentage did he have left? b...................... ■■

4 A man earned £360 per week. Calculate his percentage increase if he receives a rise of:

a £18 4a..................... ■■

b £11.52 b...................... ■■

c £4.32 c ...................... ■■

5 There were 400 men on a train. 28 had beards. What percentage had beards? 5....................... ■■

6 The price of a coat was reduced from £40 to £26. Calculate the percentage reduction. 6....................... ■■




34 Percentages – 2

9

1 Find 20% of 84. 1....................... ■■

2 Find 32% of 24. 2....................... ■■

3 Find 5% of 17. 3....................... ■■

4 Increase 36 by 12%. 4....................... ■■

5 Increase 7 by 18%. 5....................... ■■

6 Decrease 38 by 16%. 6....................... ■■

7 Decrease 70 by 80%. 7....................... ■■

8 Mrs Randall earns £235 per week. She receives a 3% pay rise. Calculate:

a the pay rise 8a..................... ■■

b her new weekly wage b..................... ■■

9 In a sale, everything is reduced by 20%. A DVD player normally costs £240. Calculate the sale price. 9 ....................... ■■




35 Calculating percentage parts

10


a Write the next two numbers in each pattern.

b What is the name of the pattern?

1 1, 3, 6, 10, 15, 21 1a.................................................. ■■

b.................................................. ■■

2 1, 4, 9, 16, 25, 36 2a.................................................. ■■

b.................................................. ■■

3 1, 8, 27, 64, 125, 216 3a.................................................. ■■

b.................................................. ■■

4 1, 1, 2, 3, 5, 8, 13, 21 4a.................................................. ■■

b..................................................

5 Here is a list of numbers: ................................................... ■■

1, 3, 5, 6, 8, 25, 30, 64, 125

a Which numbers are prime? 5a.................................................. ■■

b Which numbers are multiples of 5? b.................................................. ■■

c Which numbers are factors of 6? c .................................................. ■■

d Which numbers are square numbers? d.................................................. ■■

e Which numbers are cube numbers? e.................................................. ■■


2, 3, 5, 8, 18, 27, 36, 49, 75, 729

a Which numbers are prime? 6a.................................................. ■■

b Which numbers are multiples of 4? b.................................................. ■■

c Which numbers are factors of 15? c .................................................. ■■

d Which numbers are square numbers? d.................................................. ■■

e Which numbers are cube numbers? e.................................................. ■■



36 Patterns you must recognise – 1

18


1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Find: a The next two numbers in the pattern. 1a................................................. ■■

b The name of the pattern. b ................................................... ■■

2 Here is a list of numbers: 1, 2, 3, 4, 7, 9, 11, 24, 64

a Which numbers are prime? 2a................................................ ■■

b Which numbers are factors of 12? b ............................................... ■■

c Which numbers are multiples of 3? c................................................ ■■

d Which numbers are square numbers? d ............................................... ■■

3 Here is a list of numbers: 1, 2, 4, 7, 25, 27, 28, 29, 343

a Which numbers are prime? 3a................................................ ■■

b Which numbers are factors of 14? b ............................................... ■■

c Which numbers are multiples of 7? c................................................ ■■

d Which numbers are square numbers? d ............................................... ■■




37 Patterns you must recognise – 2

10

1 Here is a pattern made out of matchsticks:

a Draw the next pattern. 1a........................... ■■

b What is the rule to find the nth term? (Give your answer using algebra.) b........................... ■■

c Use your rule to find the number of matchsticks in:i the 10th term ci ......................... ■■

ii the 54th term cii ........................ ■■

d Which term has 82 matchsticks? d........................... ■■

2 Here is a pattern: 7, 11, 15, 19.

a What is the next number in this pattern? 2a .......................... ■■

b What is the rule to find the nth term? (Give your answer using algebra.) b ........................... ■■

c Use your rule to find:i the 15th term ci .......................... ■■

ii the 28th term cii.......................... ■■

3 Here is a pattern: 2, 8, 14, 20.

a What is the next number in the pattern? 3a .......................... ■■

b What is the rule to find the nth term? (Give your answer using algebra.) b ........................... ■■

c Use your rule to find:i the 20th term ci .......................... ■■

ii the 54th term cii.......................... ■■




38 Number patterns: The nth term

13

1 Write 2646 as a product of primes. 1....................... ■■


3 Find:

a the HCF of 2646 and 2100. 3a..................... ■■

b the LCM of 2646 and 2100. b...................... ■■



6 Find:

a the HCF of 3675 and 882. 6a..................... ■■

b the LCM of 3675 and 882. b...................... ■■

7 What is the reciprocal of:

a 4? 7a..................... ■■

b 2/5? b...................... ■■

c -8? c ...................... ■■




39 Product of primes, highest common factor

11

This is an instruction:

Choose a number multiply by 4 take away 3

What is the result if you choose:

1 8 1....................... ■■

2 12 2....................... ■■

3 -5 3....................... ■■

What number was chosen if the result was:

4 65 4....................... ■■

5 17 5....................... ■■

6 -35 6....................... ■■

The cost of hiring a bus is calculated as follows:

Fixed daily rate + £2 per kilometre = total cost

7 Calculate the total cost if the fixed daily rate is £17 and the bus travels 120 kilometres. 7 ....................... ■■

8 Calculate the total cost if the fixed daily rate is £17 and the bus travels 52 kilometres. 8 ....................... ■■

9 Calculate the number of kilometres travelled if the total cost is £161 and the fixed daily rate is £17. 9....................... ■■




40 Using formulae

9

1 John is x cm tall. Andy is 4 cm taller. How tall is Andy? 1.......................... ■■

2 Sharon has y books. Andrea has 6 more than Sarah.

a How many books does Andrea have? 2a........................ ■■

b What is the total number of books? b........................ ■■

3 Amy has £x. Barry has twice as much money. Carolyn has £4 more than Barry.

a How much money does Barry have? 3a........................ ■■

b How much money does Carolyn have? b........................ ■■

c What is the total amount of money? c ........................ ■■

4 Julie buys 7 kg of potatoes at £x per kilogram.

a What is the total cost in £s? 4a........................ ■■

b What is the total cost in pence? b........................ ■■

5 Here is a room. A m

It is A m long, B m wide.

B ma What is the area? 5a ...................m2 ■■

b What is the perimeter? b.....................m ■■

c The room is H m high. What is the volume? c ...................m3 ■■

6 Pens cost x pence each.

a What is the cost of y pens? 6a......................p ■■

b How many pens can be bought with z pence? b........................ ■■




41 Writing in algebra – 1

13

1 John has £x, Louise has £3 more. How much does Louise have? 1....................... ■■

2 Michelle weighs k kilograms. Paula is 8 kilograms heavier.

a How much does Paula weigh? 2a..................... ■■

b What is their total weight? b...................... ■■

3 Sally can type W words per minute. David can type twice as fast as Sally. Vicky can type seven words per minute faster than David.

a How many words per minute can David type? 3a..................... ■■

b How many words per minute can Vicky type? b...................... ■■

c How many words can Sally type in six minutes? c ...................... ■■

d How many words can Vicky type in six minutes? d...................... ■■

4 A room is L metres long and W metres wide.

a What is the area? 4a..................... ■■

b What is the perimeter? b...................... ■■

5 Martin buys B books at £10 each. What is the total cost? 5....................... ■■

6 Mandy can run one kilometre in M minutes. James takes N minutes less. How long does James take? 6....................... ■■

7 Bananas cost x pence per kilogram.

a What is the cost of B kilograms of bananas? 7a..................... ■■

b How many kilograms can be bought with Y pence? b...................... ■■

8 What is the cost of V videos at £P each? 8....................... ■■




42 Writing in algebra – 2

14

Given a = 0, b = 1, c = 2, d = 3, e = 4, work out the following. Show your working.

1 d + e 1....................... ■■

2 de 2....................... ■■

3 d – e 3....................... ■■

4 ad + bc 4....................... ■■

5 c + 3de 5....................... ■■

6 5b + 3a 6....................... ■■

7 d(b + c) 7 ....................... ■■

8 cd(a + b + c) 8 ....................... ■■

9 (d + e)c 9....................... ■■

10 e(3d + 2c) 10..................... ■■

11 y = 3(A + B) Find y when A = 4 and B = 7. 11..................... ■■

12 A = B – C

a Find A when B = 8 and C = 2. 12a................... ■■

b Find A when B = -6 and C = -3. b ................... ■■

c Find B when A = -8 and C = 5. c .................... ■■

13 A = B + CD + E

Find A when B = 12, C = 8, D = 3, E = 2. 13..................... ■■




43 Using algebra – 1

15

Given a = 0, b = 1, c = 2, d = 3, e = 4, work out the following (show your working):

1 cd 1....................... ■■

2 cde 2....................... ■■

3 c + d + e 3....................... ■■

4 abc 4....................... ■■

5 ad + ce 5....................... ■■

6 c(d + e) 6....................... ■■

7 d(c – e) 7....................... ■■

8 cd(a + c) 8 ....................... ■■

9 (c + d)e 9....................... ■■

10 d + 3ce 10..................... ■■

11 A = 2(B – C) Find A when B = 3 and C = 8. 11..................... ■■

12 C = A – B

a Find C when A = 10 and B = 4. 12a................... ■■

b Find A when C = 7 and B = 1. 12b................... ■■

c Find B when C = -3 and A = -7. 12c ................... ■■

13 A = BC

D - E

Find A when B = 10, C = 6, D = 8 and E = 5. 13..................... ■■




44 Using algebra – 2

15

Solve these equations:

1 x + 4 = 10 2 x – 3 = 7 1....................... ■■

2....................... ■■

3 4y = 24 4 8a = 27 3....................... ■■

4....................... ■■

5 -5a = 17 6 -8y = -22 5....................... ■■

6....................... ■■

7 c = 8 8 a = -12 7....................... ■■4 3

8....................... ■■

9 3x – 2 = 37 10 4a – 5 = -8 9....................... ■■

10..................... ■■

11 8a – 7 = 3a + 15 12 6a – 5 = 18 - 2a 11..................... ■■

12..................... ■■

13 x + 1 = 6 14 3x = 21 13..................... ■■3 5

14..................... ■■




45 Rules: Equations – 1

14

Solve these equations:

1 a + 3 = 8 1....................... ■■

2 a - 5 = 3 2....................... ■■

3 6a = 39 3....................... ■■

4 -5a = 42 4....................... ■■

5 -4a = -47 5....................... ■■

6 c5 = 20 6....................... ■■

7 d3 = 12 7....................... ■■

8 4x + 3 = 29 8....................... ■■

9 8a - 6 = 3a + 20 9....................... ■■

10 4y + 10 = 6y + 2 10..................... ■■

11 6a + 3a - 5 = 7a - 23 11..................... ■■

12 6a - 4a + 5 = 8 - 2a 12..................... ■■

13 a3 + 2 = 14 13..................... ■■

14 2a5 = 20 14..................... ■■




46 Rules: Equations – 2

14


1 I think of a number. I double it, then add 6. The answer is 20. Use N for the number.

a Write an equation to show this. 1a.................................... ■■

b Solve the equation. Show your working. b.................................... ■■

2 Mr Hammond buys D desks at £18 each. He spends £414 in total.

a Write an equation to show this. 2a.................................... ■■

b Solve the equation. Show your working. b.................................... ■■

3 A gas bill is calculated by the formula:

gas bill = £25 standing charge + 18 pence per unit used

Let B be the gas bill and U the number of units used.

a Complete the formula £B = 3a.................................... ■■

b Use the formula to calculate the cost if U = 257 b.................................... ■■

c Calculate the number of units used if £B = £83.32 c .................................... ■■



47 Writing equations – 1

7

£( + )

1 I think of a number. I multiply by 3, then take away 4. The answer is 17. Use N for the number.

a Write an equation to show this. 1a....................................... ■■

b Solve the equation. Show your working. b........................................ ■■

2 Mrs Roberts buys c chairs at £15 each. She spends £105 in total.

a Write an equation to show this. 2a....................................... ■■

b Solve the equation. Show your working. b........................................ ■■

3 The cost of hiring a car is £30 plus 25 pence per mile. Let c be the cost and m be the number of miles.

a Complete this formula: 3a £c = £( + ) ■■

b Use the formula to calculate the cost if m = 286. b....................................... ■■

c Calculate the number of miles covered if £c = £120.75. c ....................................... ■■




48 Writing equations – 2

7


1 x3 = 200

Find the value of x correct to one decimal place using trial and improvement methods. 1....................... ■■

2 x2 + 5x = 90





49 Trial and improvement – 1

2

You must show all your working.

1 x2 - 3x = 116


2 x3 + 3x = 130





50 Trial and improvement – 2

2

Give the answer to three significant figures where appropriate.

1 a2 = 30 1....................... ■■

2 c2 - 5 = 75 2....................... ■■

3 √x = 18 3....................... ■■

4 √x = 0.2 4....................... ■■

5 6a + 3(4a - 5) = 18 5....................... ■■

6 4(c - 3) = 6(c - 12) 6....................... ■■

7 5a - 4(2a - 5) = 3(2a + 1) 7....................... ■■

8 0.3a + 6 = 0.7a - 20 8....................... ■■

9 34

x + 2 = 18 9....................... ■■

10 y8 + 2 = 16 10..................... ■■

11 8y = 5 11..................... ■■

12 3y - 4 = 8 12..................... ■■




51 Harder equations

12

In each question, make Y the subject.

1 √Y = x 1....................... ■■

2 Y2 = x 2....................... ■■

3 A = Y + B 3....................... ■■

4 C = 3Y + 2A 4....................... ■■

5 6A = 4C - Y 5....................... ■■

6 5A = 3C - 4Y 6....................... ■■

7 2A = 3Y4 7....................... ■■

8 5A = 3YC 8....................... ■■

9 6A = 8 - 3Y 9....................... ■■

10 5C = 4 + 3Y 10..................... ■■

11 Y2C = A 11..................... ■■

12 A√Y = B 12..................... ■■

13 Y2

A = C 13..................... ■■

14 4C = AY 14..................... ■■

15 5A = 3C2Y 15..................... ■■

16 A = Y(C + D) 16..................... ■■




52 Rewriting formulae

16

In each question, find the value of y correct to six significant figures where appropriate.

a = 5.6 b = 57 c = -2.3 d = 5.237 e = -79

1 y = 3a - 4b2d 1 .............................. ■■

2 y = 4a(bd + 3)de 2 .............................. ■■

3 y = a√ bdc + a 3 .............................. ■■

4 y = √ 5cea + c 4 .............................. ■■

5 y = √ a + b + c 5 .............................. ■■

6 y = 5a + 3b - 2c 6 .............................. ■■

7 y = √a + √b 7 .............................. ■■

8 y = a2 + c2

b5 8 .............................. ■■




53 Using algebraic formulae

8

4d - 3e

d + e

( )

( )

( )

Simplify:

1 5a3 x 3a6 1 ........................................... ■■

2 4a3c2 x 3a5c 2 ........................................... ■■

3 8a4 x 4cd2 3 ........................................... ■■

4 (a3)4 4 ........................................... ■■

5 8a8c4 ÷ 4a2c 5 ........................................... ■■

Expand:

6 7(3a - 4) 6 ........................................... ■■

7 2y3(4y2 + 6y) 7 ........................................... ■■

8 -3a(4a - 3c2) 8 ........................................... ■■

9 2a3(3a4 + 5a2) 9 ........................................... ■■

10 (4a + 2) (3a - 5) 10 ......................................... ■■

11 (5a - 3) (2a + 6) 11 ......................................... ■■

12 (6a - 4) (5a - 2) 12 ......................................... ■■

13 (3a - 2)2 13 ......................................... ■■




54 Expansion of brackets

13

Factorise:

1 10a + 8 1.............................................. ■■

2 12a - 3c 2.............................................. ■■

3 10a - 8c 3.............................................. ■■

4 25a - 20c + 15 4.............................................. ■■

5 3a4 + 2a3 5.............................................. ■■

6 6a5 + 15a3 6.............................................. ■■

7 10a5 + 4a 7.............................................. ■■

8 7a2b + 14ab 8.............................................. ■■

9 20a3c2 - 25a4c 9.............................................. ■■

10 40acd - 30a2d 10............................................ ■■

11 12a4 + 8a2 + 4ad 11............................................ ■■

12 6a6 + 4c6 + 2d3 12............................................ ■■




55 Factorisation

12

1 Give the coordinates of the points shown.

A=..................... ■■

B=..................... ■■

C=..................... ■■

D=..................... ■■

E= ..................... ■■

Mark these points on the graph:

V = (1, 5) V ■■

W = (5, 4) W ■■

X = (2, 3) X ■■

Y = (4, 2) Y ■■

Z = (3, 1) Z ■■




56 Coordinates

10

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8

Ax

Bx

Cx

Dx

Ex

5

4

3

2

1

00 1 2 3 4 5

Which letters represent the following lines?

1 x = 0 1....................... ■■

2 y = 0

3 y = x 2....................... ■■

4 y = -x

5 y = 3 3....................... ■■

6 y = -3

7 x = 3 4....................... ■■

8 x = -3

5....................... ■■

6....................... ■■

7....................... ■■

8....................... ■■

9 Complete this table of values and draw the graph of y = x2 – 3.

Table ................ ■■

Graph ............... ■■




57 Drawing lines – 1

10

-5 -4 -3 -2 -1 0 1 2 3 4 5

5

4

3

2

1

-1

-2

-3

-4

-5

y

x

A

B

C

DE F G H

-4 -3 -2 -1 1 2 3 40

14

12

10

8

6

4

2

-2

-4

x -4 -3 -2 -1 0 1 2 3 4

y

Which letters represent the following lines?

1 y = -2 1................. ■■

2 x = -2 2................. ■■

3 y = 0 3................. ■■

4 x = 0 4................. ■■

5 y = x 5................. ■■

6 y = -x 6................. ■■

7 y = x + 3 7................. ■■

8 y = -x + 3 8................. ■■

9 Complete this table of values and draw the graph of y = 1/2 x2 – 4.

Table .......... ■■

Graph ......... ■■




58 Drawing lines – 2

10

5

4

3

2

1

1 2 3 4 50

-1-1-2-3-4-5

-2

-3

-4

-5

A x

F

y

C

D

B

E

H

G

x -4 -3 -2 -1 0 1 2 3 4

y

4

3

2

1

1 2 3 40

-1-1-2-3-4

-2

-3

-4

x

y

This graph shows the journeys made by a cyclist and a runner.

1 a What time did the runner and cyclist meet? 1a .................................................. ■■

b How far were they from Stoke? b .................................................. ■■

2 How many times did the runner stop? 2 .................................................... ■■

3 What time did the cyclist start his journey? 3 .................................................... ■■

4 a Between which times did the runner travel fastest? 4a .................................................. ■■

b How did you decide? b .................................................. ■■

5 How long did the cyclist stop during his journey? 5 .................................................... ■■

6 Where did the cyclist finish his journey? 6 .................................................... ■■

7 How far is it from Stoke to Manchester? 7 .................................................... ■■

8 What was the speed of the runner at:

a 10.00? 8a .................................................. ■■

b 12.00? b .................................................. ■■

9 What was the speed of the cyclist at:

a 10.30? 9a .................................................. ■■

b 14.30? b .................................................. ■■




59 Speed, time and distance graphs

13

0

10

20

30

Manchester

40

50

09.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00

Dis

tan

ce (

kilo

met

res)

Time

Cyclist

Runner

Stoke

Solve these inequalities:

1 8x ≤ 32 1................................ ■■

2 3x - 7 > 11 2................................ ■■

3 x2 < 25 3................................ ■■

4 5 < 3x - 1 < 23 4................................ ■■

5 -3x ≤ 15 5................................ ■■

6 -4x > -32 6................................ ■■




60 Inequalities

6

Measure each angle.

a....................... ■■

b....................... ■■

c ....................... ■■

d....................... ■■

e ....................... ■■

f........................ ■■




61 Using a protractor – 1

6

a

c

d

e

b

f

Measure each angle.

a....................... ■■

b....................... ■■

c ....................... ■■

d....................... ■■

e ....................... ■■

f........................ ■■




62 Using a protractor – 2

6

a

b

c

d

e

f

Give the special names of these angles:

a....................... ■■

b....................... ■■

c ....................... ■■

d....................... ■■

e ....................... ■■

f........................ ■■

g....................... ■■

h....................... ■■




63 Angles – 1

8

a

b

c

d

e

g

h

f

Give the special names of these angles:

1 ..................................... ■■

2 ..................................... ■■

3 ..................................... ■■

4 ..................................... ■■

5 ..................................... ■■




64 Angles – 2

5

1 2

3 4

5

Find the missing angles in these diagrams:

1 a= ................ ■■

2 b= ................. ■■

c= ................. ■■

3 d= ................ ■■

e= ................. ■■

4 f= ................. ■■

g= ................. ■■

h= ................. ■■

5 i= .................. ■■

6 j= .................. ■■

k= ................. ■■

7 l= .................. ■■

m= ................ ■■

n= ................. ■■

8 o= ................. ■■




65 Intersecting and parallel lines – 1

15

70o

a

130o

b c

d

e70o

h

f

g

35o

28o

i

72o

j

k

65o

m n

l112o

o

1

2

3

4

5

6

7

8

Find the missing angles in these diagrams:

1 a=............................ ■■

b=............................ ■■

2 c= ............................ ■■

3 d= ........................... ■■

4 e= ............................ ■■

5

5 f=............................. ■■

g= ............................ ■■

6 h=............................ ■■

7 i=............................. ■■

j= ............................. ■■

k=............................ ■■

l=............................. ■■

m=........................... ■■

n=............................ ■■

o=............................ ■■8 Look at question 7.

a What is the special name used to describe angles k and o? 8a............................... ■■

b What is the special name used to describe angles k and m? b................................ ■■




66 Intersecting and parallel lines – 2

17

80°

a b

c

120°

130°

d70°

e

1 2

3 4

g

75° 35°

f

50°

80°

h

65°

i j

k

l m

no

6 7

Calculate: a the exterior angle

b the interior angle

c the sum of the interior angles of the following regular polygons(you must show all of your working).

1 A regular nine-sided polygon.

1a..................... ■■

b..................... ■■

c ..................... ■■

2 A regular twelve-sided polygon.

2a..................... ■■

b..................... ■■

c ..................... ■■

3 Each exterior angle of a regular n-sided polygon is 12o. How many sides does the polygon have?

3....................... ■■

4 Each interior angle of a regular n-sided polygon is 170o. How many sides does the polygon have?

4....................... ■■




67 Regular polygons – 1

8

Calculate: a the exterior angle

Calculate: b the interior angle

Calculate: c the sum of the interior angles of the following regular polygons (you must show all of your working).

1 A regular pentagon.

1a..................... ■■

b...................... ■■

c ...................... ■■

2 A regular ten-sided polygon.

2a..................... ■■

b...................... ■■

c ...................... ■■

3 Each exterior angle of a regular n-sided polygon is 15°. 3 ....................... ■■How many sides does the polygon have?

4 Each interior angle of a regular n-sided polygon is 168°. 4 ....................... ■■




68 Regular polygons – 2

8

What are the bearings of:

1 B from Y? 1....................... ■■

2 B from R? 2....................... ■■

3 Y from C? 3....................... ■■

4 Y from S? 4....................... ■■

5 Y from R? 5....................... ■■

6 R from L? 6....................... ■■

7 R from Y? 7....................... ■■

8 S from B? 8....................... ■■

9 S from Y? 9....................... ■■

10 L from S? 10..................... ■■

11 L from B? 11..................... ■■

12 C from S? 12..................... ■■




69 Bearings

12

x C

xL

xR

N

xY

xB

x SKey

L is a lighthouse

C is a coastguard station

R is a radio mast

B is a buoy

Y is a yacht

S is a ship


1 ABCD is a square. Complete the diagram.

■■

2 The shape EFGH is turned and moved to form the shape E’F’G’H’. E’F’ are shown. Complete the diagram and mark the points G’H’.

■■

3 HIJK is a rectangle. Complete the diagram.

■■

4 The shape LMNO is turned over and moved to form the shape L’M’N’O’. L’M’ are shown. Complete the diagram and mark the points N’O’.

■■



70 Common 2-D shapes

4

A

B

C

I

J

H

G

H

E

F

L M

N

O

L'

M'

E' F'


1 This is a rhombus. Write two facts about the sides.

1 ....................................... ■■

......................................... ■■

2 This is a parallelogram. Complete the diagram.

2 ■■

3 This is a description of a quadrilateral: ‘The quadrilateral has four equal angles.’ Name the quadrilateral. 3 ....................................... ■■

4 Give the order of rotational symmetry for the following quadrilaterals. Tick the appropriate box.

a

■■ ■■ ■■ ■■ 4a ■■

b

■■ ■■ ■■ ■■ b ■■

c

■■ ■■ ■■ ■■ c ■■



71 Properties of quadrilaterals – 1

7

No rotational symmetry

Order2

Order3

Order4

1 This is a parallelogram.

Write two facts about the sides.

1....................................... ■■

......................................... ■■

2 This is a rhombus. Complete the diagram.

2 ■■

3 This is a description of a quadrilateral:

‘The quadrilateral has one pair of parallel lines’.

Name the quadrilateral. 3....................................... ■■

4 Give the order of rotational symmetry for the following quadrilaterals. Tick the appropriate box.

No rotational order order ordersymmetry 2 3 4

a kite ■■ ■■ ■■ ■■ 4a ■■

b trapezium ■■ ■■ ■■ ■■ b ■■

c square ■■ ■■ ■■ ■■ c ■■

d rectangle ■■ ■■ ■■ ■■ d ■■

e rhombus ■■ ■■ ■■ ■■ e ■■

f parallelogram ■■ ■■ ■■ ■■ f ■■




72 Properties of quadrilaterals – 2

10


Draw the axes of symmetry on these shapes. If there is no axis of symmetry, write ‘none’ in the shape.

1 rhombus

■■

2 parallelogram

■■

3 trapezium

■■

4 rectangle

■■

5 This triangle has three equal sides.

a Name the triangle. 5a ................................ ■■

b What is the value of x? b ................................ ■■

6 This triangle has two equal sides.

a Name the triangle. 6a ................................ ■■

b What is the value of y? b ................................ ■■

c What is the value of z? c................................. ■■



73 Properties of quadrilaterals and triangles – 1

9

xo

80o

y

z

Draw the axes of symmetry of these shapes:

1 Rectangle ■■

2 Square ■■

3 Kite ■■

Name these triangles:

4 4 ........................................... ■■

5 5 ........................................... ■■




74 Properties of quadrilaterals and triangles – 2

5

1

2

3

Here are some rectangles.

1 Rectangle A is congruent to 1....................... ■■

2 Rectangle D is congruent to 2....................... ■■

3 Rectangle F is congruent to 3....................... ■■

4 Rectangle K is congruent to 4....................... ■■

5 Rectangle J is congruent to 5....................... ■■

6 Rectangle G is congruent to 6....................... ■■




75 Congruent shapes

6

A

B C

D

E

F

G

H

I

J

KL

If a shape does not have rotational symmetry, write ‘none’. If a shape does have rotational symmetry, write the order, eg order 4.

1

1....................... ■■

2

2....................... ■■

3

3....................... ■■

4

4....................... ■■

5

5....................... ■■

6

6....................... ■■




76 Rotational symmetry – 1

6

If a shape does not have rotational symmetry, write ‘none’. If a shape does have rotational symmetry, write the order, eg order 4.

1 1 ...........................................

............................................. ■■

2 2 ...........................................

............................................. ■■

3 3 ...........................................

............................................. ■■

4 4 ...........................................

............................................. ■■

5 5 ...........................................

............................................. ■■




77 Rotational symmetry – 2

5


a Draw the axes of symmetry on these shapes.

b Name the shapes.

1

1a ■■

b ........................................ ■■

2

2a ■■

b ........................................

......................................... ■■

3

3a ■■

b ........................................ ■■

4

4a ■■

b ........................................ ■■



78 Symmetry of 2-D shapes – 1

8

a Draw the axes of symmetry of these shapes.

b Name the shapes.

1 1a ■■

b .......................... ■■

2 2a ■■

b .......................... ■■





4

The dotted lines are axes of symmetry. Complete the shapes.

1

■■

2

■■

3

■■

4

■■





4

The dotted lines are mirror lines. Reflect the following shapes in the mirror lines. You may use tracing paper.

1

1 ■■

2

2 ■■

3

3 ■■

4

4 ■■

5

5 ■■

6

6 ■■




81 Reflection

6


Draw the enlargements and give the coordinates of the enlargements.

New coordinates

1 Enlarge triangle T by a scale factor of 3. 1 A’ ..................... ■■The centre of enlargement is the point (11,1). B’...................... ■■Label the new triangle A’B’C’. C’ ..................... ■■

2 Enlarge rectangle R by a scale factor of 2. 2 D’ ..................... ■■The centre of enlargement is the point (11,4). E’...................... ■■Label the new rectangle D’E’F’G’. F’...................... ■■

G’..................... ■■

3 Enlarge square S by a scale factor of 2. 3 H’ ..................... ■■The centre of enlargement is the point (11,11). I’ ...................... ■■Label the new square H’I’J’K’. J’ ...................... ■■

K’ ..................... ■■



82 Enlargement – 1

11

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

01 2 3 4 5 6 7 8 9 10 11 12

S

R

T

H I

JK

D E

FG

A

B C

Draw the enlargements and give the coordinates of the enlargements.

1 Enlarge rectangle R by a scale factor of 3. 1A‘=.................. ■■

The centre of enlargement is the point (1, 2). B‘=................... ■■

Label the new rectangle A’ B’ C’ D’. C‘=................... ■■

D‘= .................. ■■

2 Enlarge triangle T by a scale factor of 2. 2E‘= .................. ■■

The centre of enlargement is the point (3, 10). F‘= ................... ■■

Label the new triangle E’ F’ G’. G‘= .................. ■■

3 Enlarge triangle T by a scale factor of 3. 3E”= ................. ■■

The centre of enlargement is the point (6, 3) F”= .................. ■■

Label the new triangle E” F” G”. G”=.................. ■■





10

01

1

2 3 4 5 6 7 8 9 10 11 12

2

3

4

5

6

7

8

9

10

11

12

13

14

15

R

TB

E

F

GC

A D

1 B is an enlargement of A.

a What are the coordinates of the centre of enlargement? 1a..................... ■■

b What is the scale factor of the enlargement? b..................... ■■

2 C is an enlargement of A.



3 D is an enlargement of A.



4 E is an enlargement of F.







8

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15

E

AB

C

D

F

You must show any lines you draw to find the answers.

1 B is an enlargement of A.


b What is the scale factor of the enlargement? b...................... ■■

2 A is an enlargement of C.



3 D is an enlargement of E.



4 F is an enlargement of E.







8

01

1

2 3 4 5 6 7 8 9 10 11 12 13 14 15

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

A

B C

D

E

F

1 Enlarge the triangle T by a scale factor of 1/2.

Centre of enlargement is the point (11, 10). 1A’=.................. ■■

B’= .................. ■■

C’= .................. ■■

2 Enlarge the rectangle R by a scale factor of 1/3.

Centre of enlargement is the point (16, 17). 2D’=.................. ■■

E’= ................... ■■

F’= ................... ■■

G’= .................. ■■




86 Enlargement by a fractional scale factor

7

01

1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

A B

CD E

G F

T

R

Describe the translation that moves:

1 A to B 1................................................ ■■

2 A to D 2................................................ ■■

3 C to A 3................................................ ■■

4 C to B 4................................................ ■■

5 B to C 5................................................ ■■

Translate the triangle PQR using the following instructions. Draw the shape and give the new coordinates of PQR.

6 Two units right, one unit up. 6P ..................... ■■Q..................... ■■R ..................... ■■

7 Three units right, five units down. 7P ..................... ■■Q..................... ■■R ..................... ■■

8 Four units left, one unit up. 8P ..................... ■■Q..................... ■■R ..................... ■■

9 Seven units left, four units down. 9P ..................... ■■Q..................... ■■R ..................... ■■




87 Translations

17

1

1

-1-1-2-3-4-5-6-7-8 2 3 4 5 6 7 8

2

3

4

5

-2

-3

-4

-5

y

x

C

B

A

DP

P

QR


1 This is a car speedometer. It shows the speed in kilometres per hour. What speed is shown?

1 .................................. ■■

2 Which of these units would you use to measure the capacity of water in a bath: litres, millilitres, centilitres?

2 .................................. ■■

3 Which of these units would you use to measure the weight of a full suitcase: grams, kilometres, litres, kilograms, metres, tonnes?

3 .................................. ■■

4 This giraffe is standing next to Mr Green. Guess the height of:

a Mr Green 4a......................metres ■■

b the giraffe. b......................metres ■■



88 Metric units of measure

5

0

10

20

30 40 50

60

70

80

Here are some measurements given in imperial units. Convert the imperial units to metric units.

1 A ruler is 6 inches long.

What is this in centimetres? 1....................... ■■

2 A cat is 3 feet long.


3 A cake weighs 4 pounds.

What is this in kilograms? 3....................... ■■

4 The distance from Poole to Winchester is 40 miles. How many kilometres is this?

4....................... ■■

5 A dog weighs 2 stone.

What is this in kilograms? [14 pounds = 1 stone] 5....................... ■■

6 A girl is 4 feet 10 inches tall.

What is this in centimetres? [12 inches = 1 foot] 6....................... ■■

7 A petrol car holds 4 gallons.

How many litres is this? 7....................... ■■

8 A tank holds 10 gallons.





89 Rough metric equivalents of imperial units – 1

8

Here are some measurements given in imperial units. Convert the imperial units to metric units.

1 A book is 6 inches wide and 8 inches long.

a The metric width is 1a..................... ■■

b The metric length is b...................... ■■

2 A boy is 5 feet tall.

How many centimetres is this? 2....................... ■■

3 My father travels 20 miles to work.

How many kilometres is this? 3....................... ■■

4 A recipe requires 4 ounces of sugar.

How many grams is this? 4....................... ■■

5 An encyclopaedia weighs 6 pounds.

How many kilograms is this? 5....................... ■■

6 The petrol tank in a car holds 12 gallons.


7 A man is 5 feet 8 inches tall.





90 Rough metric equivalents of imperial units – 2

8

1 Convert 84 millimetres into centimetres 1....................... ■■

2 Convert 236 centimetres into metres 2....................... ■■

3 Convert 3.4 kilometres into metres 3....................... ■■

4 Convert 1.2 kilograms into grams 4....................... ■■

5 Convert 3720 grams into kilograms 5....................... ■■

6 Convert 0.38 tonnes into kilograms 6....................... ■■

7 Convert 1.8 centilitres into millilitres 7....................... ■■

8 Convert 128 millilitres into litres 8....................... ■■

9 Convert 0.173 litres into millilitres 9....................... ■■

10 Convert 3.7 kilometres into metres 10..................... ■■

11 Convert 38 centimetres into metres 11..................... ■■

12 Convert 0.28 centimetres into millimetres 12..................... ■■

13 Convert 0.7 metres into centimetres 13..................... ■■

14 Convert 0.32 tonnes into kilograms 14..................... ■■

15 Convert 28 grams into kilograms 15..................... ■■

16 Convert 371 kilograms into tonnes 16..................... ■■

17 Convert 0.08 kilograms into grams 17..................... ■■

18 Convert 0.3 litres into millilitres 18..................... ■■

19 Convert 0.32 litres into centilitres 19..................... ■■

20 Convert 2.81 centilitres into millilitres 20..................... ■■




91 Converting one metric unit to another – 1

20

1 Convert 382 millimetres into centimetres 1....................... ■■

2 Convert 47 centimetres into metres 2....................... ■■

3 Convert 7.2 kilometres into metres 3....................... ■■

4 Convert 7.4 kilograms into grams 4....................... ■■

5 Convert 873 grams into kilograms 5....................... ■■

6 Convert 0.78 tonnes into kilograms 6....................... ■■

7 Convert 3.8 centilitres into millilitres 7....................... ■■

8 Convert 478 millilitres into litres 8....................... ■■

9 Convert 0.81 litres into millilitres 9....................... ■■

10 Convert 0.08 kilometres into metres 10..................... ■■

11 Convert 784.6 centimetres into metres 11..................... ■■

12 Convert 0.8 centimetres into millimetres 12..................... ■■

13 Convert 3.24 metres into centimetres 13..................... ■■

14 Convert 0.071 tonnes into kilograms 14..................... ■■

15 Convert 347.8 grams into kilograms 15..................... ■■

16 Convert 3684 kilograms into tonnes 16..................... ■■

17 Convert 0.3 kilograms into grams 17..................... ■■

18 Convert 3.8 litres into millilitres 18..................... ■■

19 Convert 0.78 litres into centilitres 19..................... ■■

20 Convert 5.3 centilitres into millilitres 20..................... ■■

21 Convert 274 millilitres into centilitres 21..................... ■■

22 Convert 0.03 kilometres into centimetres 22..................... ■■

23 Convert 0.007 tonnes into grams 23..................... ■■

24 Convert 2 kilometres into centimetres 24..................... ■■

25 Convert 3.62 metres into millimetres 25..................... ■■

92 Converting one metric unit to another – 2



25



Estimate the following using metric units:

1 The height of a classroom door 1 ................................ ■■

2 The weight of a newborn baby 2 ................................ ■■

3 The length of your calculator 3 ................................ ■■

4 The weight of your ruler 4 ................................ ■■

5 The capacity of a teacup 5 ................................ ■■

6 The capacity of a teaspoon. 6 ................................ ■■

Which metric unit would you use to measure the following:

7 The length of your bedroom 7 ................................ ■■

8 The weight of a ship 8 ................................ ■■

9 The capacity of a glass 9 ................................ ■■

10 The weight of a pair of spectacles 10 .............................. ■■

11 The capacity of a bath 11 .............................. ■■

12 The distance from London to Manchester 12 .............................. ■■

13 The length of a postcard 13 .............................. ■■

14 The height of a giraffe? 14 .............................. ■■

15 Miss Jones is standing by a house. Estimate the height of the house. 15 .............................. ■■



93 Making sensible estimates – 1

15

Estimate the following (use metric units):

1 Your weight 1 ................................... ■■

2 Your height 2 ................................... ■■

3 The length of your pencil 3 ................................... ■■

4 The weight of your pencil 4 ................................... ■■

5 The capacity of a can of cola 5 ................................... ■■

6 The capacity of a large bottle of lemonade 6 ................................... ■■

Which metric units would you use to measure the following:

7 The distance from London to New York? 7 ................................... ■■

8 The weight of a fully loaded lorry? 8 ................................... ■■

9 The capacity of a wine glass? 9 ................................... ■■

10 The weight of a dog? 10 ................................. ■■

11 The capacity of a swimming pool? 11 ................................. ■■

12 The weight of a packet of chewing gum? 12 ................................. ■■

13 The length of a pencil? 13 ................................. ■■

14 The height of a tree? 14 ................................. ■■

15 The length of a fly? 15 ................................. ■■

16 Mr Roberts is standing by an elephant. Estimate the height of the elephant. 16 ................................. ■■

94 Making sensible estimates – 2



16


1 A train journey started at 16.23 and finished at 18.07.

a How long did the journey take in hours and minutes? 1a ............hours

..................mins ■■

b How long did the journey take in minutes? b .............mins ■■

2 A commercial break had three adverts. Advert 1 lasted for 1 minute 8 seconds, advert 2 lasted for 48 seconds, advert 3 lasted for 1 minute 27 seconds. What was the total length of the commercial break? 2................mins

...................secs ■■

3 A bus journey took 3 hours 17 minutes. The journey finished at 16.13. What time did the journey start? 3....................... ■■

4 A train left Glasgow at 22.52 on Monday and arrived in London at05.27 on Tuesday. How long did the journey take? 4 ..............hours

..................mins ■■

5 A car journey started at 07.48 and lasted for 17 minutes. What time did the journey finish? 5....................... ■■




95 Time – 1

6

1 A train left Edinburgh at 07.28. It arrived in London at 16.05. How long did the journey take? 1................................................ ■■

2 A plane left London at 21.47 on Monday and arrived in New York 6 hours 52 minutes later. What was the time in London when the plane landed in New York? 2................................................ ■■

3 A car travelled from Liverpool to Ipswich. The journey took 4 hours 47 minutes. The car arrived in Ipswich at 17.34. What time did the car leave Liverpool? 3................................................ ■■

4 A train travels 246 kilometres at an average speed of 97 kilometres per hour. Calculate the time taken:

a to the nearest minute 4a ............................................. ■■

b to the nearest second. b .............................................. ■■

5 A car travels 89 kilometres at an average speed of 67 kilometres per hour. Calculate the time taken:

a to the nearest minute 5a ............................................. ■■

b to the nearest second. b .............................................. ■■

6 How many seconds are there in one day? 6................................................ ■■




96 Time – 2

8

1 A train travels 568 kilometres in 7 hours 28 minutes. Calculate the average speed, correct to three significant figures. 1 .................................. ■■

2 A plane travels 826 kilometres in 2 hours 37 minutes. Calculate the average speed, correct to three significant figures. 2 .................................. ■■

3 A car travels at an average speed of 78 kilometres per hour for 3 hours 42 minutes. Calculate the distance travelled. 3 .................................. ■■

4 A car travels at a speed of 56 kilometres per hour for 48 minutes. Calculate the distance travelled. 4 .................................. ■■

5 A liquid has a volume of 68.3 cm3 and a mass of 78.5 g. Calculate the density. 5 .................................. ■■

6 A car travels at a speed of 12.3 metres per second. Calculate this speed in kilometres per hour. 6 .................................. ■■

7 The density of a block of wood, volume 38.4 cm3 was 0.72 g/cm3. Calculate the mass. 7 .................................. ■■




97 Compound measures

7

1 Find: a the perimeter; b the area of each shape. The dots are 1 cm apart.

A a ................cm ■■

b.................cm2 ■■

B a ................cm ■■

b.................cm2 ■■

C a ................cm ■■

b.................cm2 ■■

D a ................cm ■■

b.................cm2 ■■

E a ................cm ■■

b.................cm2 ■■

2 Find the volumes of the following shapes (each small cube has a volume of 1 cm3):

2a...............cm3 ■■

b ..............cm3 ■■

c...............cm3 ■■

d ..............cm3 ■■




98 Perimeter, area and volume

14

A

B

C

D

E

ab

cd

1 Find: a the area; b the perimeter of a square, side 8 cm. 1a...............cm2 ■■

b ................cm ■■

2 Find: a the area; b the perimeter of this rectangle: 2a...............cm2 ■■

b ................cm ■■

4 cm

9 cm

3 Find the area of this triangle. 3.................cm2 ■■

4 Find the volume of this cuboid. 4.................cm3 ■■

5 The volume of a cuboid is 80 cm3. The area is 20 cm2. Find the height. 5 ..................cm ■■

6 The area of this triangle is 40 cm2. Find x. 6 ..................cm ■■




99 Calculating length, area and volume – 1

8

12 cm

15 cm 20 cm

5 cm

12 cm

x

10 cm


1 Find:

a the area 1a................................ ■■

b the perimeter of a square, side 6 cm. b................................. ■■

2 For the triangle below, find:

a the area 2a................................ ■■

b the perimeter. b................................. ■■

3 Find the area of this trapezium. 3.................................. ■■

4 The volume of this cuboid is 240 cm3. Find:

a the missing side. 4a................................ ■■

b the total surface area. b................................. ■■

5 The area of this triangle is 60 cm2. Find x. 5 .................................. ■■

6 Find the volume of a cuboid, length 80 cm, width 70 cm, height 1.2 m. 6.................................. ■■




9

9 cm

12 cm

15 cm

8 cm

6 cm11 cm

8 cm6 cm

?

x

12 cm


Find the volume of these prisms:

1

1 ..................m3 ■■

2

2.................cm3 ■■

3

3 ..................m3 ■■

4

4.................cm3 ■■




4

4 m6 m

7 m

8 cm

3 cm

2 cm

9 cm

4 cm

2 cm

8 m

6 m

5 m

3 m

2 m

28 cm

36 cm

50 cm18 cm

5 cm

Find the volume of these prisms:

1 1 ................................... ■■

2 2 ................................... ■■

3 3 ................................... ■■

4 4 ................................... ■■





4

6 cm

4 cm

10 cm

5 cm

12 cm

12 cm

12 cm

12 cm

8 cm

8 cm

8 cm

2 cm

4 cm

0.4 m

9 cm

8 cm

Find: a the perimeter; b the area of these shapes:

1

1a ................cm ■■

b ..............cm2 ■■

2

2a ................cm ■■

b ..............cm2 ■■

3 This is a diagram of a swimming pool with a concrete path all the way around. The pool is 20 m long and 16 m wide. The path is 1.5 m wide.

Find the area of the path. 3 ..................m2 ■■





5

Path

Pool

20 m

16 m

1.5 m

3 cm

6 cm 5 cm

3 cm

5 cm

4 cm

3 cm

2 cm

6 cm4 cm

10 cm

Find:

a the perimeter

b the area of these shapes.

1 1a..................... ■■

b...................... ■■

2 2a..................... ■■

b...................... ■■

3 This is a diagram of a lawn with a concrete path, width 3 m, all the way around. The lawn is 8 m long and 6 m wide.

a Find the area of the path. 3a..................... ■■

b The path is made of concrete 5 cm deep. Find the volume of concrete. b...................... ■■





6

3 cm

7 cm

6 cm

9 cm

16 cm

4 cm

11 cm

5 cm

8 cm

Lawn

Path

a, b, c and d are lengths.

State whether each formula gives a length, area, volume or none of these.

1 3a + 6c 1....................... ■■

2 8ab - 2cd 2....................... ■■

3 a2b + cd 3....................... ■■

4 abc 4....................... ■■

5 abcd2a 5....................... ■■

6 a3 + bcd 6....................... ■■

7 3ab - 2c2 7....................... ■■

8 a2c2d 8....................... ■■

9 a3+ c2 9....................... ■■

b

1013 ab + c2 10..................... ■■

11 11..................... ■■

12 cd2 + ab 12..................... ■■




105 Formulae for length, area and volume

12

3ab2c

Find: a the circumference; b the area of these circles. Use π = 3.14

1 Circle radius 8 cm.

1a..................... ■■

b..................... ■■

2 Circle diameter 7.8 cm.

2a..................... ■■

b..................... ■■

3 Circle radius 0.6 m.

3a..................... ■■

b..................... ■■

4 Circle diameter 7.32 m.

4a..................... ■■

b..................... ■■

5 Find the volume of this cylinder radius 7 mm, height 1.2 cm. Give your answer in cm3.

5.................cm3 ■■

6 Find the radius of a circle, circumference 72 cm. 6....................... ■■

7 Find the diameter of a circle, circumference 27 cm. 7....................... ■■

8 Find the height of a cylinder, volume 300 cm3, radius 8 cm. 8....................... ■■




106 Circle formulae – 1

12

For each circle below, find:

a the circumference

b the area.

1 Circle radius 4 cm.

1a ............................................. ■■

b .............................................. ■■


2a ............................................. ■■

b .............................................. ■■

3 Circle radius 2.2 cm.

3a ............................................. ■■

b .............................................. ■■


4a ............................................. ■■

b .............................................. ■■

Give your answers correct to three significant figures.

5 Find the volume of a cylinder, radius 65 cm, height 1.4 m. 5 ............................................... ■■

6 Find the radius of a circle, circumference 85 cm. 6 ............................................... ■■

7 Find the diameter of a circle, area 200 cm2. 7 ............................................... ■■

8 Find the radius of a cylinder, volume 80 cm3, height 12 cm. 8 ............................................... ■■




107 Circle formulae – 2

12

Find the missing side.

Give your answer correct to three significant figures.

1 1....................... ■■

2 2....................... ■■

3 3....................... ■■

4 4....................... ■■

5 A ladder is 6 m long. It is 3 m from the foot of a wall. How far does the ladder reach up the wall? 5....................... ■■

6 This is a circle, radius 8 cm. O is the centre of the circle. Calculate the length AB. 6....................... ■■




108 Pythagoras’ theorem

6

6.8 cm

4.7 cm

6.4 cm

8.7 cm

5.9 cm

7.8 cm

8.3 cm4.6 cm

8 cm

O

A B

5 cm

1 Construct the locus of the point A such that the locus is always 2 cm from the point A. 1 ■■

2 Construct the locus of a point that is always 1 cm from the line AB.

Show all construction lines. 2 ■■

3 XY and XZ are two straight roads. A helicopter flies from X between the two roads such that it is always equidistant from the two roads. Plot the flight of the helicopter. 3 ■■

Show all construction lines.

4 A goat is tethered to the L shaped rail and moves so that it is always 2 m away from the rail.

Using a scale of 1 cm represents 1 m, construct the locus of the goat’s path. 4 ■■




109 Locus

4

A

A B

.

Y

X

Z


1 State one advantage and one disadvantage of asking this question:

‘Why do you like school?’

Advantage

.................................................................................................................

................................................................................................................. 1 ■■

Disadvantage

.................................................................................................................

................................................................................................................. ■■

2 Look at this question: ‘Do you eat a lot of chocolate each week?’

Do you think this is a good question?

If yes, say why.

.................................................................................................................

................................................................................................................. 2 ■■

If no, say why and try to improve the question.

.................................................................................................................

................................................................................................................. ■■

3 State one advantage and one disadvantage of asking this question:

‘What is your favourite type of film? Tick one box.’

comedy

science fiction

romance

Advantage

................................................................................................................. 3 ■■

.................................................................................................................

Disadvantage

.................................................................................................................

................................................................................................................. ■■



110 Designing questionnaires – 1

6

1 A class of 16 year old students were asked to find out the favourite music of teachers at their school.Dawn asked this question to 20 teachers.

‘Choose your favourite music from this list:’

Dawn stated: ‘The favourite music of 90% of teachers is pop’.

Is Dawn’s statement justified? Answer yes or no. ......................... ■■

If so, explain why.

If not, explain why not.

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................ ■■

Look at the questions below.

a Criticise the questions.

b Suggest a better way to ask the questions.

2 How much do you like sport?

Criticism ■■

........................................................................................................................................................

........................................................................................................................................................

Better question ■■

........................................................................................................................................................

........................................................................................................................................................

3 How much chocolate do you eat?

Criticism ■■

........................................................................................................................................................

........................................................................................................................................................

Better question ■■

........................................................................................................................................................

........................................................................................................................................................




111 Designing questionnaires – 2

6

Pop

Folk

Heavy rock

18

0

2

Favourite music Frequency

How could you test these hypotheses?

Choose from experiment, observation or questionnaire.

1 Boys’ favourite television channel is BBC1. 1............................................. ■■

2 A drawing pin thrown into the air will land point up more than point down. 2............................................. ■■

3 Most girls wear trousers in school. 3............................................. ■■

4 Most teachers own a car. 4............................................. ■■

5 If an egg is dropped on a hard surface, it will not break. 5............................................. ■■

6 The most popular school subject is Maths. 6............................................. ■■

7 Boys can throw a cricket ball farther than girls can. 7............................................. ■■

8 The most popular music is pop. 8............................................. ■■

9 Boys can thread a needle faster than girls. 9............................................. ■■

10 Most girls own a bicycle. 10........................................... ■■




112 Hypotheses

10

1 These are the ages of pupils at a chess club:

12 12 14 16 13 12 13 14 12 13 12 16 12 13 12 13 16 14 15 13

Complete the table below to show this information.

Age Tally Frequency

12 1....................... ■■

13 ......................... ■■

14 ......................... ■■

15 ......................... ■■

16 ......................... ■■

Total

2 These are the numbers of pins in some boxes:

403 410 407 425 437 416 408 432

404 406 421 408 427 430 416 412

Complete the table below to show this information.

Number Tally Frequency

of pins

400-409 2....................... ■■

410-419 ......................... ■■

420-429 ......................... ■■

430-439 ......................... ■■

Total




113 Frequency tables

9

1 This frequency diagram shows the weights of some boxers in a gym:

a How many boxers were between 50 kg and 60 kg? 1a..................... ■■

b How many boxers were between 70 kg and 80 kg? b..................... ■■

c How many boxers were between 80 kg and 110 kg? c ..................... ■■

d How many boxers were under 80 kg? d .................... ■■

e How many boxers were in the gym? e..................... ■■

2 This frequency diagram shows the heights of some trees in an orchard:

a How many trees were between 4 m and 6 m? 2a..................... ■■

b How many trees were between 6 m and 10 m? b..................... ■■

c How many trees were over 4 m? c ..................... ■■

d How many trees were in the orchard? d .................... ■■




114 Frequency diagrams

9

6

5

4

3

2

1

0

Freq

uen

cy

50 60 70 80 90 100 110Weight (kilograms)

8

6

4

2

0

Freq

uen

cy

0 2 4 6 8 10Height (metres)

This is a line graph. It shows the height of a plane above sea level during a flight.

Draw lines on the graph to show how you found the answers.

1 What was the height of the plane at 13.30? 1....................... ■■

2 What was the height of the plane at 14.00? 2....................... ■■

3 a What was the greatest height the plane reached? 3a..................... ■■

b What time did it reach this height? b..................... ■■

4 The plane was at a height of 3000 m on two occasions.

a When was the first time? 4a..................... ■■

b When was the second time? b..................... ■■

5 What time did the plane take off? 5....................... ■■

6 What time did the plane land? 6....................... ■■




115 Line graphs

8

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

Hei

gh

t (m

etre

s)

13.00 13.30 14.00 14.30 15.00 15.30 16.00 16.30

Time


This graph shows the exchange rate for £ and $.

Draw lines on the graph to show how you found your answers.

1 How many $ will Dave receive for £5? 1....................... ■■

2 How many £ will Sally receive for $9? 2....................... ■■

3 How many $ will Joe receive for £300? 3....................... ■■

4 Marie wants $1000. How many £ will this cost? 4....................... ■■

5 Which is worth more: $7 or £4? 5....................... ■■

6 12 inches = 1 foot

1 inch = 2.5 centimetres

Use this information to complete this table:

3 feet = ...................inches ■■

........................cm ■■

48 inches = .......................feet ■■

........................cm ■■

150 centimetres = .......................feet ■■

...................inches ■■



116 Using and drawing conclusions from graphs – 1

11

8

7

6

5

4

3

2

1

0

£

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14$

Feet Inches Centimetres

3

48

150

This is a graph for changing inches into centimetres.

Draw lines on the graph to show how you found your answers.

1 A pencil is 5 inches long. What is this in centimetres? 1....................... ■■

2 A bottle is 6 inches high. What is this in centimetres? 2....................... ■■

3 A box is 7.5 centimetres tall. What is this in inches? 3....................... ■■

4 A man is 6 feet tall (12 inches = 1 foot). What is his height in centimetres? 4....................... ■■

5 A table is 1 metre high. What is this in inches? 5....................... ■■

6 A garden gnome is 20 inches high. What is this in centimetres? 6....................... ■■

7 The height of horses is measured in hands (1 hand = 4 inches).

Complete this table:

Bere ...............inches ■■

...................cms ■■

Charlie ...............hands ■■

...................cms ■■

Deva ...............hands ■■

...............inches ■■



12


117 Using and drawing conclusions from graphs – 2

1

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15

2

3

4

5

6

Inch

es

Centimetres

Bere

Charlie

Deva

16

60

130

Name Hands Inches Centimetres


1 This data shows the height of 20 people. The height is in centimetres.

a Complete this frequency table.

168 181 168 173 176 Height in cm Tally Frequency

183 175 184 178 182 160 - under 170 ■■

187 194 170 162 173 170 - under 180 ■■

179 182 190 191 171 180 - under 190 ■■

190 - under 200 ■■

b Show this information in a frequency diagram.

■■

■■

■■

■■

2 The following are the times (in minutes) taken to complete a Maths homework.

a Complete this frequency table.

■■

■■

■■

■■

b Show this information ■■in a frequency diagram. ■■

■■

■■



118 Frequency tables and frequency diagrams – 1

16

9

8

7

6

5

4

3

2

1

0160 170 180 190 200

Height (cms)

Freq

uen

cy

48

44

17

42

37

29

41

23

33

30

27

19

31

36

Minutes

10 - under 20

20 - under 30

30 - under 40

40 - under 50

Tally Frequency

5

4

3

2

1

0

10 20 30 40 50Time (minutes)

Freq

uen

cy


This data shows the weight of 20 people. The weight is in kilograms.

1 a Complete this frequency table:

■■

■■

■■

■■


■■

■■

■■

■■

The following are the times (in seconds) taken to thread a needle.

■■

■■

■■

2a Complete this frequency table: ■■

■■


■■

■■

■■

■■



119 Frequency tables and frequency diagrams – 2

18

57

73

58

74

88

68

74

75

75

60

65

72

64

78

62

67

81

59

79

88

50 – under 60

60 – under 70

Tally FrequencyKilograms

9

8

7

6

5

4

3

2

1

050 60 70 80 90

Weight (kilograms)

Freq

uen

cy

18 22 14 12 3 16 8 13

7 10 19 14 4 7 12 16

0 – under 5

5 – under 10

Tally FrequencySeconds

5

6

4

3

2

1

05 10 15 20 25

Number of seconds

Freq

uen

cy

1 This table shows the distances 20 amateur golfers and 20 professional golfers hit a golf ball:

a Present the data in this frequency polygon.Use a dotted line for amateurs, a solid line for professionals.

Amateur Professional

Amateur ■■

Professional ■■

b Compare the distributions and comment on your findings.

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................ ■■




120 Comparing the data

3

150 – under 175

175 – under 200

200 – under 225

225 – under 250

250 – under 275

275 – under 300

2

3

6

5

3

1

0

0

2

8

7

3

Amateurs ProfessionalsDistance (yards)

8

7

6

5

4

3

2

1

0

150 175 200 225 250 275 300

Distance (yards)

Freq

uen

cy

Find: a the median; b the mode of these numbers:

1 5, 7, 8, 8, 6 1a..................... ■■

b..................... ■■

2 2, 6, 4, 6, 1, 6 2a..................... ■■

b..................... ■■

3 5, 8, 5, 3, 8, 2, 6, 8, 9, 2 3a..................... ■■

b..................... ■■

4 3, 7, 7, 2, 4, 7, 2 4a..................... ■■

b..................... ■■

5 These are the weights, in grams, of some oranges:

200, 250, 230, 230, 260, 250, 260, 210, 260

Find: a the median; b the mode. 5a..................... ■■

b..................... ■■

6 The median of these numbers is 6.5. Find the value of x.

9, 3, 7, 8, 5, x 6....................... ■■

7 The mode of these numbers is 2. Find the median.

2, 2, 8, 3, 8, x 7....................... ■■




121 Median and mode – 1

12

Find:a the median

b the mode of these numbers:

1 6, 8, 10, 6, 12 1a..................... ■■

b...................... ■■

2 3, 5, 7, 8, 7, 4, 8, 5, 7, 2, 3 2a..................... ■■

b...................... ■■

3 3, 6, 4, 6, 1, 2 3a..................... ■■

b...................... ■■

4 5, 4, 5, 7, 9, 8, 5, 8 4a..................... ■■

b...................... ■■

5 These are the heights in centimetres of some roses:

18, 25, 17, 24, 18, 24, 15, 24, 16, 24

Find: a the median; b the mode. 5a..................... ■■

b...................... ■■

6 The median of these numbers is 6. Find the value of x.

x, 8, 7, 4, 9, 3 6....................... ■■

7 The mode of these numbers is 7. Find the value of x.

5, 7, 5, 4, 7, 3, x 7....................... ■■




122 Median and mode – 2

12

In the following lists of numbers, find: a the mean

b the range.

1 12, 15, 13, 21, 17, 20, 17, 18 1a..................... ■■

b..................... ■■

2 7, 10, 8, 6, 8 2a..................... ■■

b..................... ■■

3 28, 21, 24, 24 3a..................... ■■

b..................... ■■

4 17, 15, 3, 15, 2, 6, 4, 8, 6, 13 4a..................... ■■

b..................... ■■

5 The mean age of four boys is 7. A new boy joins the group and the mean age increases to 8. What is the age of the new boy? 5....................... ■■

6 This table shows the number of bottles of milk delivered to some houses in a street:

Find the mean.

6....................... ■■

7 This table shows the number of radios in 20 houses:

Find the mean.

7....................... ■■




123 Mean and range – 1

11

Bottles of milk

Numberof houses

0 1 2 3

3 2 8 3

Radios

Numberof houses

0 1 2 3 4 5

2 3 5 4 5 1

Find:

a the mean

b the range of the following lists of numbers:

1 3, 7, 12, 8, 6 1a..................... ■■

b...................... ■■

2 14, 28, 17, 41 2a..................... ■■

b...................... ■■

3 16, 25, 14, 38, 52, 18, 26, 30 3a..................... ■■

b...................... ■■

4 12, 52, 8, 36, 43, 51, 47, 28, 27, 36 4a..................... ■■

b...................... ■■

5 The mean of five numbers is 8. The numbers are 8, x, 7, 12, 4. Find x. 5 ....................... ■■

6 This table shows the number of loaves of bread delivered to some houses in a street:

Find the mean. 6....................... ■■




124 Mean and range – 2

10

Loaves

Number of houses

0

2

1

3

2

5

3

4

4

2

1 This table shows the scores of two teams of golfers. Each team had two members. (Low scores are better than high scores.)

Use the range and mean to compare the two teams.

Compare the scores:

............................................................................................. European team

............................................................................................. Range............... ■■

............................................................................................. Mean................ ■■

............................................................................................. American team

............................................................................................. Range............... ■■

............................................................................................. Mean................ ■■

............................................................................................. Comparison ■■

2 This table shows the time taken by ten boys and ten girls to run 100 metres. The time is in seconds.

Use the range and mean to compare the times taken by the men and women.

Compare the times:

............................................................................................. Boys

............................................................................................. Range............... ■■

............................................................................................. Mean................ ■■

............................................................................................. Girls

............................................................................................. Range............... ■■

............................................................................................. Mean................ ■■

............................................................................................. Comparison ■■




125 Comparing two sets of data – 1

10

European team American team

68 65 82 69

72 71 70 72

67 69 75 72

74 72 70 72

Boys Girls

12 18 15 20 18

10 12 11 13 14

18 17 16 20 16

21 16 18 17 18

1 This table shows the number of fish caught by two fishing teams. Each team had ten members.

Use the range and mean to compare the two teams.

Team A Range............... ■■Mean................ ■■

Team B Range............... ■■Mean................ ■■

Comparison:

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................ ■■

2 This table shows the time taken by eight men and eight women to thread a needle. The time is in seconds:

Use the range and the mean to compare the times taken by the men and women.

Men Range............... ■■Mean................ ■■

Women Range............... ■■Mean................ ■■

Comparison:

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................

........................................................................................................................................................ ■■



10


126 Comparing two sets of data – 2

Team A

3

8

5

7

8

0

0

9

9

8

Team B

6

8

7

6

5

5

4

5

7

4

Men

36

51

54

48

4

17

38

31

Women

6

21

10

16

15

11

12

9

1 This table shows the number of people using a swimming pool over a period of 200 days:

a What is the modal class? 1a..................... ■■

b Estimate the median. b...................... ■■

2 This table shows the number of packs of crisps sold each day over a period of one year:

a What is the modal class? 2a..................... ■■

b Estimate the median. b...................... ■■




127 Grouped data

4

Number of people

Frequency

50 – 99

23

100 – 149

78

150 – 199

67

200 – 249

32

Number of packetsof crisps sold

Frequency

100 – 199

9

200 – 299

15

300 – 399

110

400 – 499

189

500 – 599

42

Ten boys attended an adventure centre. They received marksout of ten for each activity.

a Complete these scatter diagrams.

b Describe the relationship shown by each scatter diagram. Choose from: positive correlation, negative correlation, no correlation.

1

This scatter diagram shows:

..................................... Diagram ■■

..................................... Relationship ■■

2


..................................... Diagram ■■

..................................... Relationship ■■

3


..................................... Diagram ■■

..................................... Relationship ■■




128 Scatter diagrams – 1

6

Boy

Climbing

Football

Cricket

Chess

Adam

3

8

6

3

Barry

5

6

4

5

Carl

1

7

4

4

Dave

10

5

3

6

Ewan

6

6

5

4

Fred

10

4

2

9

George

10

9

7

1

Harry

1

8

7

2

Ian

9

9

6

2

John

1

3

1

10

10

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10

Cricket

Ch

ess

10

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10

Cricket

Foo

tba

ll

10

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10

Chess

Cli

mb

ing

Ten girls took some tests. They received marks out of ten.

a Complete these scatter diagrams.

b Describe the relationship shown by each scatter diagram.

1 1a ■■

b...................... ■■

2 2a ■■

b...................... ■■

3 3a ■■

b...................... ■■



6


129 Scatter diagrams – 2

Test 1 Maths

Test 2 Physics

Test 3 Archery

Test 4 Cooking

1

1

9

2

Girl 1

3

3

7

4

2

8

6

2

8

3

1

2

8

10

4

7

7

3

3

5

9

8

1

2

6

5

4

5

10

7

9

9

2

4

8

4

3

6

7

9

2

1

10

8

10

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10Maths

Arc

her

y

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10Maths

Co

oki

ng

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10Maths

Phys

ics

1 This table shows the hours of sunshine and millimetres of rain on the 3rd October in ten towns:

a Complete this scatter diagram. ■■

b Draw a line of best fit. ■■

c Describe the relationship shown by the scatter graph. ......................................................... ■■

d Use the line of best fit to answer the following:

i Town K has 3 millimetres of rain. Estimate the hours of sunshine. di...................... ■■

ii Town L has 1.5 millimetres of rain. Estimate the hours of sunshine. ii ...................... ■■

iii Town M has 5 millimetres of rain. Estimate the hours of sunshine. iii ..................... ■■

iv Town N has 10 hours of sunshine. Estimate the number of millimetres of rain. iv ..................... ■■

v Town O has 3 hours of sunshine. Estimate the number of millimetres of rain. v ...................... ■■




130 Line of best fit

8

Sunshine (hours)

Rain (mm)

9

1

Town A

1

7

B

2

6

C

10

1

D

1

6

E

4

5

F

8

2

G

7

3

H

5

5

I

7

4

J

01 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

Sunshine (hours)

Ra

in (

mm

)

1 This pie chart shows the sports activities chosen by the pupils in Year 10:

a How many pupils chose hockey?

1a..................... ■■

b What is the angle for swimming?

b..................... ■■

c How many pupils chose football?

c ..................... ■■

d What is the angle for football?

d .................... ■■

e How many pupils are in Year 10?

e..................... ■■

2 This pie chart shows the most popular hobbies of 90 men:

a How many men chose golf?

2a..................... ■■

b How many men chose tennis?

b..................... ■■

c What is the angle for bowls?

c ..................... ■■

d What is the angle for fishing?

d .................... ■■

e How many men chose fishing?

e..................... ■■




131 Understanding pie charts – 1

10

Hockey

Tennis

14 pupils

Swimming

22 pupils

Football

36o

84o

120o

Fishing

Golf

Bowls

Tennis

48o

10 men

1 This pie chart shows the number of television sets in some houses:

a How many houses had three televisions? 1a..................... ■■

b What is the angle for ‘no television’? b...................... ■■

c How many houses had two televisions? c ...................... ■■

d What is the angle for two televisions? d...................... ■■

2 This pie chart shows the favourite music of the teachers in a school:

a How many teachers chose classical? 2a..................... ■■

b What is the angle for pop? b...................... ■■

c How many teachers were asked? c ...................... ■■

d How many teachers chose heavy rock? d...................... ■■

e What is the angle for heavy rock? e ...................... ■■




132 Understanding pie charts – 2

9

144°

81°

1 television16 houses

2 housesno televisions

2 televisions3 televisions

Classical

Heavy rock

Pop7 teachers

Country5 teachers 75°

135°

1 40 people were asked to name their favourite type of film.

8 chose romance.

6 chose science fiction.

12 chose westerns.

The rest chose comedy.

Show this information on this pie chart:

Angle size

romance ......................... ■■

science fiction ......................... ■■

westerns ......................... ■■

comedy ......................... ■■

2 120 people were asked to name their favourite colour. The results are shown.

Put this information onto this pie chart:

Angle size

Red 52 ......................... ■■

Blue 28 ......................... ■■

Yellow 16 ......................... ■■

Grey 14 ......................... ■■

Pink 10 ......................... ■■




133 Drawing pie charts – 1

9

1 72 people attended a show. There were 26 men, 21 women, 17 boys and 8 girls. Show this information in a pie chart. Label each sector and show the angle.

Angle size

Men.................. ■■

Women............. ■■

Boys.................. ■■

Girls .................. ■■

2 A farm had 60 animals. There were 16 cows, 10 horses, 20 pigs and 14 sheep. Show this information in a pie chart. Label each sector and show the angle.

Angle size

Cows ................ ■■

Horses............... ■■

Pigs................... ■■

Sheep ............... ■■




134 Drawing pie charts – 2

8


1 A six-sided die is shaken. What is the probability of the following? Choose from: certain, likely, even, unlikely, impossible.

a shaking a 3 1a ................................... ■■

b shaking an odd number b ................................... ■■

c shaking an 8 c.................................... ■■

d shaking a number less than 6 d ................................... ■■

e shaking a number less than 10 e ................................... ■■

f shaking a 3 or a 4 f .................................... ■■

g shaking a 1, 2, or 3 g ................................... ■■

h shaking a 2, 3, 4 or 5 h ................................... ■■

2 A six-sided die is shaken. What is the probability of the following. Choose from: less than even, even or more than even. Write ‘less’, ‘even’ or ‘more’ in the answer column.

a shaking an odd number 2a ................................... ■■

b shaking a 5 b ................................... ■■

c shaking a 3 or 4 c.................................... ■■

d shaking a number greater than 1 d ................................... ■■

e shaking a 3, 4, 5 or 6 e ................................... ■■



135 Probability

13

Show the probability of the following events on the probability scales using an arrow

1 Throwing a six-sided die and getting an even number.

1 ....................... ■■2 Throwing a six-sided die and getting an 8.

2....................... ■■3 Tossing a coin and the coin landing on its edge.

3....................... ■■4 Throwing a six-sided die and getting more than 1.

4....................... ■■5 Tossing a coin and getting a head.

5....................... ■■6 Throwing a six-sided die and getting a 4.

6....................... ■■7 Here is a bag of counters:

R = Red

B = Blue

Y = Yellow

One counter is selected.

a Show the probability of a red.

7a..................... ■■b Show the probability of a blue.

b..................... ■■c Show the probability of a yellow.

c ..................... ■■




136 The probability scale – 1

9

1012

RR

RY

BB

BB

1012

1012

1012

1012

1012

1012

1012

1012

Show the probability of the following events on the probability scales using an arrow.

1 Tossing a coin and getting a tail.

■■

2 Throwing a die and scoring less than 6.

■■

3 Throwing a die and scoring 6.

■■

4 Choosing a red counter from a full bag of red counters.

■■

5 Here is a bag with 2 black, 5 red and 9 yellow counters.

One counter is selected.

a Show the probability of choosing a black counter.

■■

b Show the probability of choosing a red counter.

■■

c Show the probability of choosing a yellow counter.

■■




137 The probability scale – 2

7

1012

1012

1012

1012

RR

R

RR

YY

YY

YY

Y

YY

BB B = Black

R = RedY = Yellow

1012

1012

1012

How would you decide the probability of each of the following? Choose: A equally likely outcomes, or B experimental evidence. Write A or B in the answer column.

1 Three coins are tossed one hundred times. How many times do they all land heads? 1....................... ■■

2 A dice are thrown. What proportion of times is 5 scored? 2....................... ■■

3 Dave and John compete in a snooker match. What proportion of times will Dave win? 3....................... ■■

4 Three boys throw a javelin. Who throws farthest? 4....................... ■■

5 A drawing pin is dropped onto the floor. What is the probability that it lands point up? 5....................... ■■

6 A football team can win, lose or draw a match. Is there an equal chance of each? Explain your answer. 6 ....................... ■■

Explanation:

.........................................................................................

.........................................................................................

.........................................................................................

.........................................................................................

.........................................................................................

.........................................................................................

.........................................................................................




138 Justifying probabilities – 1

6

How would you decide the probability of each of the following?

Choose equally likely outcomes or experimental evidence.

1 A golfer tries to hole putts from four yards. 1 .....................................

What proportion go in the hole? ....................................... ■■

2 Eggs are dropped from a height of two metres. 2 .....................................

What proportion will crack? ....................................... ■■

3 Numbers are chosen at random from the numbers 1 to 10. 2 .....................................

What proportion will be odd numbers? ....................................... ■■

4 This spinner is spun.

4 .....................................

What proportion of spins will land on blue? ....................................... ■■

5 A train can arrive early, on time or late.

Is there an equal chance of each? Explain your answer.

..........................................................................................................................................................

.......................................................................................................................................................... ■■

6 There are 11 players in a cricket team.

They decide to choose a captain by putting their names in a hatand selecting one name.

Is there an equal chance of each player being selected?

Explain your answer.

..........................................................................................................................................................

.......................................................................................................................................................... ■■



6


139 Justifying probabilities – 2

Green

Black

Red Blue

Write all answers in fractions.

1 A bag contains 7 red discs,

2 blue discs and 1 yellow disc.

What is the probability of choosing:

a a red disc? 1a..................... ■■

b a blue disc? b..................... ■■

c a yellow disc? c ..................... ■■

d a green disc? d .................... ■■

e a red or a blue disc? e..................... ■■

f a red or a yellow disc? f ..................... ■■

g a blue or a yellow disc? g..................... ■■

h a red or blue or yellow disc? h..................... ■■

2 A bag contains 6 white discs, 3 pink discs,

5 blue discs and 2 red discs.


a a white disc? 2a..................... ■■

b a red disc? b..................... ■■

c a red or a pink disc? c ..................... ■■

d a white or a pink or a blue disc? d .................... ■■

e a yellow disc? e..................... ■■

f a white or a pink or a blue or a red disc? f ..................... ■■

g a red or a blue or a white disc? g..................... ■■

h a red or a blue disc? h..................... ■■




140 Probability: Or

16

Y

BBR

RR

R

RR

R

B

BP R

W

R

B

B

BP

PW

W WW

W

1 Ann, Barbara and Carolyn compete in a race.

Show all of the possible results. The first is done for you. A B C......................... ■■

......................... ■■

......................... ■■

......................... ■■

......................... ■■

2 A four sided spinner is spun twice. The numbers are multiplied together and recorded in a table. Complete the table.

■■

Use your table to answer these questions:

a What is the probability of a score of 6? 2a..................... ■■

b What is the probability of a score of more than 11? b..................... ■■

c What is the most likely total? c ..................... ■■

3 The probability of a new car having at least one fault is 0.78.

a What is the probability that a car has no faults? 3a..................... ■■

b A car manufacturer produces 400 cars. How many would you expect to have at least one fault? b..................... ■■




141 Probability: Examination-type questions

11

1

3

2 4 1

2

3

4

1+ 2 3 4

1st spin

2nd

spi

n

1 A coin was tossed by Mandy and Paul. Their results are shown below:

a Do the results indicate the coin is biased? Explain.

........................................................................................................................................................

........................................................................................................................................................ ■■

b Is Mandy correct in saying ‘The coin will produce more tails than heads’?Explain your answer.

........................................................................................................................................................

........................................................................................................................................................ ■■

2 A shoe manufacturer decided to make 200 000 pairs of trainers for men. The manufacturer neededto know how many pairs of trainers of each size to produce. A survey of men buying trainers in ashoe shop was carried out. 500 men were surveyed. Their shoe sizes are shown below:

Use the survey results to decide how many pairs of each size should be made.

Size 6............................ ■■

Size 7............................ ■■

Size 8............................ ■■

Size 9............................ ■■

Size 10.......................... ■■

Size 11.......................... ■■

Size 12.......................... ■■




142 Estimation of probability by experiment

9

Mandy

Paul

Heads

3

246

Tails

7

254

Size

Number of men

6

5

7

35

8

86

9

102

10

160

11

84

12

28

1 A bag contains 6 yellow discs, 5 black discs and 4 white discs.


a a yellow disc? 1a..................... ■■

b a black disc? b...................... ■■

c a white disc? c ...................... ■■

d a yellow or a black disc? d...................... ■■

e a yellow or a white disc? e ...................... ■■

f a yellow or a white or a black disc? f....................... ■■

g a green disc? g...................... ■■

2 A bag contains 4 red discs, 3 blue discs, 2 white discs and 1 yellow disc.


a a red disc? 2a..................... ■■

b a white disc? b...................... ■■

c a red or a white disc? c ...................... ■■

d a blue or a red or a yellow disc? d...................... ■■

e a white or a yellow disc? e ...................... ■■

f a white or a yellow or a blue disc? f....................... ■■

g a purple disc? g...................... ■■




143 Probability: And/or

14

WW

W

WY

Y

YY

Y

Y

B

B

B

B

B B = BlackW = WhiteY = Yellow

R

R

R

RY

BBB B = Blue

R = RedW = WhiteY = Yellow

W

W

Two-Tier GCSE Mathematics Homework · 2015-04-15 · Two-Tier GCSE Maths Homework Pack 1:...

Documents

Transcript of Two-Tier GCSE Mathematics Homework · 2015-04-15 · Two-Tier GCSE Maths Homework Pack 1:...