Revision Guide answers

1

Cambridge CheCkpoint mathematiCs revision guide For the Cambridge seCondary 1 test Answers

1 Place value, ordering and rounding

Check your understanding 1.11 623 < 652

2 3108 < 3112

3 0.235 > 0.215

4 9740 < 12 350

5 13.226 > 12.895

Check your understanding 1.2 1 3620 2 1370

3 122 000 4 140

5 180 6 60 000

7 740 000 8 3000

9 540 10 13 000

Check your understanding 1.3 1 2530

2 4800

3 90

4 260

5 300

6 6820

7 12 400 people.

8 $123 000

Check your understanding 1.4 1 18.6 2 304.8

3 8.07 4 28.222

5 61.46 6 72.20

7 3.142 8 1.4

9 0.07 10 7.071

Check your understanding 1.5 1 3.1 2 156.1

3 166 4 154 300

5 16 300 6 900

7 2520 8 0.0032

9 0.010 10 1

Check your understanding 1.6 1 200 × 40 = 8000

2 50 × 20 = 1000

3 2000 ÷ 50 = 40

4 600 ÷ 30 = 20

5 70 × 20 = 1400 g

6 500 ÷ 20 = 25

7 60 ÷ 4 = 15

8 40 000 ÷ 200 = 200

9 $600 000 ÷ 30 = $20 000

10 20 × 10 = 200

Cambridge Checkpoint Mathematics Revision Guide 1 © Hodder & Stoughton Ltd 2013


l ANSWERS

Spotlight on the test (page 5)1 a) 7325 > 7236

b) 20 × 1000 = 200 × 100c) 29 × 59 < 31 × 61d) 40 000 ÷ 100 > 400 ÷ 10

2 10 000

3 9285

4 a) 15.604 b) 15.6

5 a) 300 and 20b) 300 × 20 = 6000

6 a) 365 days in a year, 24 hours in a day, 60 minutes in an hour, 60 seconds in a minute

b) 8000 c) 4000 d) 30 million

2 Integers, powers and roots

Check your understanding 2.1 1 a) (+5) = 5 b) (+7) = 7 c) (+1) = 1

2 a) (–7) = –7 b) (–4) = –4 c) (–2) = –2

3 a) (+4) = +4 b) (–2) = –2 c) (–7) = –7

4 a) (–10) = –10 b) (–2) = –2 c) (–1) = –1

5 a) (–0.4) = –0.4 b) (–1.6) = –1.6 c) 0

6 a) (+0.7) = 0.7 b) (–4.0) = –4.0c) (+4.1) = 4.1

7 a) (+14.4) = 14.4 b) 0 c) (–3.9) = –3.9

8 (–4), (–3), (+6)

9 (–10), (–5), (–1), (+2)

10 (–10), (–8), (–5), (+1)

Check your understanding 2.21 a) 12, 15 b) 10, 15 c) 11, 13, 17

2 5

3 6

4 a) 37 b) 41, 43, 47c) No – 51 is 3 × 17 d) 8

Check your understanding 2.31 a) –14 b) –12 c) 18 d) 18

2 a) –5 b) –4 c) 2 d) –15

3 a) –48 b) –4 c) 36 d) 10

Check your understanding 2.41 a) 32 × 5

b) 22 × 11 c) 23 × 32 d) 22 × 32 × 5

2 14

3 315

4 a) 120 = 23 × 3 × 5 and 144 = 24 × 32 b) 24

5 a) 75 = 3 × 52 and 120 = 23 × 3 × 5 b) 600

Check your understanding 2.51 a) 121 b) 216 c) 12 d) 4

2 a) 81 b) 512 c) 17 d) 9

3 a) 169 b) 125 c) 19 d) 3

4 343

5 102 = 100 and 112 = 121. 105 does lie between these values, so its square root lies between 10 and 11.

6 52 = 25, 62 = 36, 72 = 49 and 36 < 43 < 49 so Anton is right.

Cambridge Checkpoint Mathematics Revision Guide 1 © Hodder & Stoughton Ltd 2013 3

ANSWERS l


3 43 4 22

5 512 6 4–1

7 812 8 56

9 45 10 101 or just 10

11 65 12 73

13 39 14 1

15 3 16 –3

Check your understanding 2.71 34 2 64

3 11 4 2

5 77 6 29

7 15 8 3

9 8 10 4

Spotlight on the test (page 12) 1 a) 24 b) 20 c) 23

2 260 ºC

3 25 July

4 a) Wednesday b) 6 ºC

5 a) 72 = 49, 82 = 64 and 49 < 60 < 64b) 73 = 343 and 83 = 512; 250 does not lie

between these values.

6 a) a = 4 b) b = –3 c) c = 0

7 41

8 a) 512 b) 28 c) 1

9 46

10 12

3 Expressions, equations and formulae

Check your understanding 3.11 expression 2 formula

3 equation 4 expression

5 formula 6 expression

7 formula 8 expression

9 equation 10 formula

Check your understanding 3.21 x9 2 y4

3 z6 4 x7

5 y4 6 1

7 y3 8 z9

9 m–2 10 z2

Check your understanding 3.3 1 2x + 8 2 3x + 6

3 10x – 5 4 7a + 35

5 20b – 30 6 12x + 8y

7 2x – 6y 8 8x + 12y

9 18a – 27b 10 20b + 50

11 9x + 14 12 5x + 4

13 44x + 17 14 17y – 5

15 3x + 3y 16 2x + 6

17 9m 18 4n – 5

19 16k + 5 20 p + 3


l ANSWERS

Check your understanding 3.4 1 7(x + 3)

2 2(2y + 5)

3 5(z – 4)

4 3(3x + 5)

5 5(3y – 5)

6 x(x + 7)

7 3y(y – 3)

8 5y(2y + 5)

9 3z(4z – 5)

10 2x(2y – 5)

Check your understanding 3.5

1 b = Vac

2 m = y – cx

3 r = C2p

4 T = PVR

5 h = √–W8

–

6 n = u – 2a

7 a = u – n2

8 a = Fm

9 r = √–Ap

–

10 u = √v2 – 2as


1 58

2 5x8

3 720

4 7x20

5 5y21

6 a5

7 17b30

8 7c20

9 5x + 128

10 5y + 228

11 12x – 520

12 112x

Spotlight on the test (page 17) 1 a) expression

b) formulac) equation

2 4x2 + 20x

3 2x2 – 5x – 3

4 2m(3m + 4n)

5 a) y7 b) x5 c) z8

6 s = v2 – u2

2a

7 x = y – 93

8 a) B and E b) A, C and D

9 7x8

10 3x + 110


ANSWERS l

4 Shapes, congruency and geometric reasoning

Check your understanding 4.11 Congruent – ASA

2 Not congruent

3 Congruent – SAS

4 Congruent – RHS

5 Annie is wrong – the shapes are similar but not congruent.

Check your understanding 4.21 Two lines of symmetry, and rotation

symmetry of order 2.

2 No lines of symmetry, and rotation symmetry of order 2.

3 One line of symmetry, no rotation symmetry.


5 One line of symmetry, no rotation symmetry.


7 More than one plane of symmetry.

8 No plane of symmetry.

9 More than one plane of symmetry.

Check your understanding 4.3Interior/exterior angles in polygons

1 a) 6 b) 60° c) 120°

2 36°

3 140°

4 24 sides

5 45 sides

Spotlight on the test (page 21)1 Congruent – SSS

2 Congruent – RHS

3 Not congruent

4

5 a) Order 4b) No reflection symmetry

6 x = 150° and y = 30°


l ANSWERS

5 Measures and motion

Check your understanding 5.11 a) 160 cm b) 2.5 litres c) 3500 grams

2 a) 3.5 m b) 750 ml c) 0.65 kg

3 72 km

4 15 cm

5 190 miles

6 15 kg

Check your understanding 5.21 115 km per hour

2 8 m per second

3 16 miles per hour

4 a) 1000 m or 1 kmb) 60 km per hour

5 a) A 3.6 m/h, B 3.8 m/h, C 3.4 m/h, D 3.3 m/h

b) Snail B is the fastest.

Check your understanding 5.31 A 60 km h–1, B 0, C 20 km h–1, D 180 km h–1,

E 8 m s–1, F 4 m s–1, G 2 m s–1.

2 a) 48 km h–1 b) 30 minutes c) 32 km h–1

Check your understanding 5.41 a) 70 litres

b) 10 litresc) The minibus stopped for half an hourd) The minibus stopped to refuel

2 a) A b) $14 000c) $6000d) 2009

Spotlight on the test (page 26)1 7.5 kg

2 325 cm

3 25 miles

4 a) S travels at 100 km per hour, so is breaking the rule.

T travels at just under 90 km per hour so is not breaking the rule.

b) Train T passes train S which is stationary but travelling in the opposite direction.

5 a) Downb) 20 minutesc) 1520

6 Planning, collecting and displaying data

Check your understanding 6.11 Discrete.

2 Continuous.

3 Continuous.

4 Discrete.

5 Continuous.

Check your understanding 6.21 Better to replace with (for example) more

than 5 times a week, 2 to 4 times a week, and fewer than 2 times a week.

2 No improvement needed.

3 $10 and $20 are members of two different categories – ambiguous.


ANSWERS l

Check your understanding 6.31 a) 13 b) 43 c) 43 – 8 = 35

2 4 8 Key 7 1 = 71

5 3 7

6 2 5 8

7 1 1 4 4

8

9 3

Check your understanding 6.41 a) Time t, in seconds Frequency

12 ≤ t < 13 2

13 ≤ t < 14 5

14 ≤ t < 15 3

15 ≤ t < 16 1

16 ≤ t < 17 1

b)

011 13 15 17

2

4

6

Time (s)

Freq

uenc

y

2 Categorical data: a pie chart would be suitable (or a bar chart).

Spotlight on the test (page 30)1 Remove overlapping options, that is 1–5,

6–10, 11–15, >15 Allow option to reply 0.

2 a) 1 2 3 3 5 8 9

2 1 4 7 key 1 9 = 19

3 1 6

4

5 2

b) 52 is very different from the rest.

3 a) Age n of child, in years Frequency

5 ≤ n < 10 4

10 ≤ n < 15 7

15 ≤ n < 20 9

20 ≤ n < 25 8

25 ≤ n < 30 5

b)

0 10 20 30

2

4

6

8

10

Age (years)

Freq

uenc

y

c) A pie chart is unsuitable as this is not categorical data.

7 Equations, functions and inequalities

Check your understanding 7.1 1 x = 7 2 x = 8

3 x = 17 4 x = 0.5

5 x = 10 6 x = 3

7 x = 1 8 x = 5

9 x = 1 10 x = 4

11 x = 4 12 x = 3

13 x = 5 14 x = 8

15 x = 2 16 x = 2

Check your understanding 7.21 x = 3, y = 1 2 x = 4, y = 2

3 x = 6, y = 3 4 x = 3, y = –1

5 x = 7, y = 3 6 x = 6, y = 4

7 x = 2, y = –1 8 x = 1, y = 1

9 x = 3, y = –2 10 x = 7, y = 0


l ANSWERS

Check your understanding 7.31 a) 3x – 10 = 2(x + 1), b) x = 12, c) 26 by 48

2 a) y + y – 6 + 2y – 2 = 40, b) y = 12

3 a) 3x – 2 + 4x + 2 + x + 7 = 39, b) x = 4, c) 10, 18, 11

4 a) C = 12n + 10, b) nine people

Check your understanding 7.4 1 x < 4

2 x ≤ 6

3 y < 5

4 x ≤ 4

5 x ≤ 1

6 x < 4

7 x < 5

8 x ≤ 7

9 4 6 108 12

10 2 4 86

11 2 4 86

12 2 4 6

13 3, 4, 5, 6 and 7

14 3, 4, 5, 6 and 7

15 2, 3, 4, 5, 6, 7, 8 and 9

16 19

Check your understanding 7.5 1 x2 + 7x + 12 2 y2 + 8y + 12

3 x2 – 5x – 14 4 y2 + y – 20

5 x2 – 9x – 22 6 x2 – 36

7 y2 – 9 8 y2 + 5y + 6

9 2x2 + x – 1 10 2x2 – x – 6

11 3x2 – 5x + 2 12 3x2 + 8x – 3

13 4x2 + 8x + 3 14 6x2 – 7x – 3

15 6x2 + 13x + 6 16 9x2 – 4

Spotlight on the test (page 36)1 x = 3

2 x = 5, y = 1

3 10y + 30

4 x = 3 so shape A has side 8 and shape B side 6

5 1, 2 and 3

6 a) 6 < x ≤ 10

b) 6 8 10

7 x2 + 2x – 15

8 6x2 + 7x – 3


ANSWERS l

8 Measurement and construction

Check your understanding 8.1 This is a construction exercise, so there are no numerical solutions.

1

5 cm

7 cm

4 cm

2

6 cm

9 cm

5 cm

3

8 cm

Spotlight on the test (page 38)

1

5 cm

2

4 cm 3 cm

5 cm

3

4 cm

7 cm

6 cm


l ANSWERS

4

5 cm

5 cm

5 cm

5 cm

5 cm

5 cm

5 The correct order of instructions is:l Draw two straight lines BA and BC meeting at a point B.l Use compasses to draw the arc DE centred on B.l Use compasses to draw two arcs (with the same radii) centred on D and E.l The two arcs centred on D and E cross each other (intersect) at F.l Use a ruler to draw a straight line passing through B and F.

9 Pythagoras’ theorem

Check your understanding 9.11 13 cm 2 17 cm

3 12.5 cm 4 2.5 cm

5 11.4 cm 6 8.5 cm

7 9.9 cm 8 41 cm

Check your understanding 9.21 1.5 cm 2 7.5 cm

3 8 cm 4 20 cm

5 6.2 cm 6 8.0 cm

7 5.6 cm 8 6 cm

Spotlight on the test (page 40)1 a = 13.6 cm b = 5.2 cm

c = 13 cm d = 11.6 cm

2 j = 12 cm k = 20 cm


ANSWERS l

10 Transformations

Check your understanding 10.11 Centre (0, 1) scale factor × 3

2 Scale factor × 4

Check your understanding 10.21 a) Translation [ 4

2 ]b) Reflection in line y = –1 c) Rotation 90° anticlockwise, about O.

2 Rotation 180° about O.

Spotlight on the test (page 44)1

0

2

4

6

8

2 4 6 8 10

S

R

2 a) b)

c) 180° rotation about (5, 1)

3 Enlargement by scale factor ×6, centre (0, 3).

0

2

4

6

–6

–4

–2

2

A

B

T

4 6–6 –4 –2


l ANSWERS

11 Averages and spread

Check your understanding 11.11 a) 15.6

b) 7

2 Mean 19.5, median 18, mode 17 and range 15

3 a) 15 b) 0 c) median

Check your understanding 11.21 Mean = 1.875

2 a) Mean = 61.5 mmb) Modal class is 60 < t ≤ 90

Check your understanding 11.31 The average age of both clubs is similar. The spread of the ages is much smaller in

the squash club.

Spotlight on the test (page 48)1 a) 14.5 years b) 15.5 years

c) 16 years d) 7 years e) Decrease, as 13 < 14.5

2 3, 3, 7, 8, 10

3 a) 29 b) 36c) Mr Hindocha’s class has done better – they

have a higher median score.

12 Processing and presenting data


60°

84°216°

brown

blond

black

2

144°

126°

90°

cinema

station

mall

0

1

2

3

4

5

6

7

8

9

station cinema mall


ANSWERS l

Check your understanding 12.21 A – 3 B – 1 C – 2

2 C

Spotlight on the test (page 52)1

90°

120°150°

coaches

cars

lorries

2

40°

60°

60°200°

gold

silver

bronze

no award

3 a)

4

0 84 12 16 20

8

12

16

20

Maths

Engl

ish

b) Positive correlationc) Chloe might have scored 18 in Maths (or 17, or 19, depending

on how you judge the correlation graph).


l ANSWERS

13 Fractions, decimals and percentages

Check your understanding 13.11 a) 2

3 b) 23

24 c) 17

20 d) 5

6

2 a) 14 b) 1

5 c) 17

30 d) 1

4

3 a) 5 34 b) 1 1

2 c) 8 7

12 d) 1 1

6

4 a) 211 b) 2

3 c) 4

15 d) 5

12

5 a) 9 13 b) 10 1

2 c) 4

5 d) 1 1

3

Check your understanding 13.21 80% 2 85%

3 180 4 276

5 $102 6 $37


1 1320

2 112

3 80%

4 60

5 $510

6 a) 1.65 b) $9.90 c) $8.00

14 Sequences, functions and graphs

Check your understanding 14.11 a) 11, 13, rule 2n – 1

b) 16, 22, not arithmeticc) 37, 41, rule 4n + 17 d) 7, 6, rule 12 – n

2 2, 7, 22, 67

3 5, 8, 13

Check your understanding 14.21 a) y = x + 1 b) y = 3x + 2 c) y = 5 – x

Spotlight on the test (page 59)1 A = R, B = P, C = S, D = Q

2 a) 3n + 4 b) 154

3 A = 2, B = 3, C = 1

4 y = 3x + 4


ANSWERS l

15 Angle properties

Check your understanding 15.11 a = 40°, b = 140°, c = 100°, d = 40°

2 p = 30°, q = 30°, r = 80°, s = 140°

3 t = 61°

Check your understanding 15.21 a = 72° (alternate), b = 130° (corresponding),

c = 120° (alternate), d = 60° (angles on a straight line), e = 51° (alternate), f = 129° (angles on a straight line), g = 115° (corresponding), h = 82° (alternate)

2 a) Alternate b) Corresponding

3 a = 86° (alternate), b = 41° (alternate)

Check your understanding 15.31 w = 44°, x = 80°, y = 53°, z = 80°

2 40°

3 135°

4 57 + 63 + 70 = 190° not 180° as it should be for a triangle

Spotlight on the test (page 63)1 x = 51°, y = 132°

2 Alternate

3 a = 44°, b = 81°, c = 60°, d = 39°, e = 141°, f = 103°, g = 77°, h = 38°, i = 142°, h = 38°

16 Area, perimeter and volume

Check your understanding 16.11 28 cm2

2 14 cm2

3 12 cm2

4 4 cm2

5 45 cm2

6 8 cm2

Check your understanding 16.21 70 cm2

2 48 cm2

3 40 cm2

4 75 cm2

Check your understanding 16.31 A yes, B no, C yes, D yes, E no

2

6 cm

6 cm

3 cm

3 cm

3 cm

Check your understanding 16.41 6 + 6 + 30 + 40 + 50 = 132 cm2

2 2 × (24 + 36 + 54) = 228 cm2

Check your understanding 16.51 72 cm2, 70 cm2

2 x = 20, y = 8


l ANSWERS

Check your understanding 16.61 550 mm2

2 60 000 cm3

3 12 m2

4 0.0075 m3

5 a) 600 cm2 b) 0.06 m2

6 1 000 000 000

Spotlight on the test (page 69)1 a) 28 cm b) 36 cm2

2 a) Cuboid

b)

4 cm

2 cm

3 cm

2 cm

3 cm

2 cm

c) 2 × (12 + 6 + 8) = 52 cm2

d) 24 cm3

3 25 000 mm2

4 a)

4 cm6 cm

6 cm

6 cm

10 cm

10 cm

8 cm 10 cm

b) 24 + 24 + 24 + 32 + 40 = 144 cm2

17 Ratio and proportion

Check your understanding 17.11 a) 4:7 b) 3:4 c) 7:11 d) 5:6

2 60 cm and 100 cm

3 80 birch and 120 beech

Check your understanding 17.21 40 minutes

2 120 minutes

3 334 hours

4 6 days

5 8 hours

Check your understanding 17.31 45 kilometres

2 12.5 kg

3 $192

4 $875

Spotlight on the test (page 72)1 4 : 5 2 $80

3 a) 36 4 a) €300 b) 6 b) £375

5 9 hours 6 720 g

7 32 minutes 8 $7.68


ANSWERS l

18 Formulae, functions and graphs

Check your understanding 18.11 24 2 1300

3 23 4 50

5 17 6 120

7 4 8 5

9 5 10 28

Check your understanding 18.21 1.5 2 8.1

3 2.8 4 0.9

5 3.7 6 1.6

7 2.6 8 0.3

9 2.7 10 3.1

Check your understanding 18.31 a) y = 3x + 4 gradient 3 intercept 4

b) y= 3x gradient 3 intercept 0c) y = –4x + 2 gradient –4 intercept 2

2 a) y = 2x + 43 gradient 2 intercept 4

3

b) y = 14 x – 3

4 gradient 1

4 intercept – 3

4

c) y = – 32× + 6 gradient – 3

2 intercept 6

3 a) y = –x + 10 gradient –1 intercept 10

b) y = 34 x + 5

4 gradient 3

4 intercept 5

4

c) y = – 43 x + 1

3 gradient – 4

3 intercept 1

3

Check your understanding 18.41 a) Plan B

b) Plan Bc) 400

Spotlight on the test (page 77)1 a) 27

b) 9

2 a) 600 b) 5

3 4.1

4 a) y = 1.2x – 3 b) 1.2 c) –3

5 a) T b) Q and R c) S

6 a) B b) A c) 8 secondsd) B, because after 500 m it is in front and

going faster.


l ANSWERS

19 Bearings and drawings

Check your understanding 19.11 168 cm (1.68 m)

2 24 mm

3 1 : 50 000

4 10.5 cm

5 250 m

Check your understanding 19.21 A 074°, B 118°, C 198°, D 249°, E 295°,

F 352°.

Check your understanding 19.31 A B

D C

Flowerbed

Gravel path

2

RM

Spotlight on the test (page 81)1 11.24 m

2 b) 8.9 m

3 10

8

6

4

2

0 2 4 6 8 10

V

BA

b) 5 km c) 7.1 km d) 1 : 100 000


ANSWERS l

20 Circles, cylinders and prisms

Check your understanding 20.11 Area 28.3 cm2, circumference 18.8 cm.

2 Area 78.5 cm2, circumference 31.4 cm.

3 Area 113 cm2, circumference 37.7 cm.



6 Area 38.5 cm2, circumference 22.0 cm.

Check your understanding 20.21 CSA = 251 cm2, volume = 628 cm3.

2 CSA = 528 cm2, volume = 1850 cm3.

3 CSA = 94.2 cm2, volume = 141 cm3.

4 CSA = 50.3 cm2, volume = 101 cm3.

5 452 cm3. 6 138 cm2.

Check your understanding 20.31 Area of cross-section = 16 cm2,

volume = 160 cm3.

2 Area of cross-section = 9 cm2, volume = 72 cm3.

Spotlight on the test (page 85)1 a) 56.5 cm b) 254 cm2

2 a) 8 cm b) 41.1 cm2 (25.1 + 16)

3 a) 251 cm3 b) 126 cm2

4 a) 24 cm2 b) 96 cm3

21 Probability

Check your understanding 21.11 1

4 2 2

5

3 12100 (=

325 or 0.12) 4 0.1

5 a) 0.4 b) 0.8 c) 2

Check your understanding 21.21 a) H H

(H, H) (H, T)

(T, H)

H

T (T, T)

b) 14 (= 0.25)


1 a) 40100 = 0.4 b)

60100 = 0.6

2 0.8

3 a) 8 b) 4

4 a) 0.2 b) 0.65 c) 6

5 218 =

19

2 a) 1 1 2 3 4 5 62 2 4 6 8 10 123 3 6 9 12 15 184 4 8 12 16 20 245 5 10 15 20 25 306 6 12 18 24 30 36

1 2 3 4 5 6 b) 436 =

19


l ANSWERS

22 Written and mental arithmetic methods


3 4617 4 5632

5 18 872 6 2233

7 29 172 8 8760

9 50.24 10 60.68

11 178.2 12 43.5

13 1.44 14 0.12

15 163.2 16 14.62

Spotlight on the test (page 90)1 a) 4.5

b) 550

2 70

3 101.52

23 Problem solving

P1 12 m

P2 5, 5, 6, 7, 8

P3 Snail D (their distances per minute are 48, 45, 42, 51, 36 cm)

P4 12.6 cm

P5 a) 16.6 b) 6

P6 10 beads

P7 n = 15

P8 253 (since 235 is not a multiple of 11)

P9 31.8 m

P10 No: 182 + 302 = 1224 but 352 = 1225

P11 69, 101 and 1037

P12 a) 6x – 60 = 180b) 40°, 90°, 50°c) right-angled triangle

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Revision Guide answers