CHECKPOINT MATHEMATICS/1112/02 2019

SOLUTION TO APRIL 2019 – PAPER 2

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CHECKPOINT MATHEMATICS/1112/02 2019

Solution Marks Notes

S1 25 × 1.8 + 32 1

(a)

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= 45 + 32

= 77 °F

(b)

S2 142 + 29 1

3×22 + 7 Back to QUICK ACCESS GRID

256 + 29

= 3×4 + 7 1 Note:

285

= 12 + 7 The answer can be worked out in a single

285 step using the calculator.

= 19

= 15 Back to QUICK ACCESS GRID

S3

1 P (Mike arrives late to school)

15 3

= 20 = 4

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CHECKPOINT MATHEMATICS/1112/02 2019

Solution Marks Notes

S4 248 675 1

(a) = 249 000 to the nearest thousand

(b) 52.747 square kilometres 1 number in the second decimal place (4) < 5

= 52.7 square kilometres

∴ number in the first decimal place remains

S5 unchanged.

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2

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CHECKPOINT MATHEMATICS/1112/02 2019

Solution Marks Notes

S6 1

(a)

(b)

Line = 2 shown on the grid in red 1

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CHECKPOINT MATHEMATICS/1112/02 2019

Solution Marks Notes

S7 Diameter of the pond in the scale 1 1 cm → 2 m

(a) drawing = 3.1 cm

3.1 cm → 3.1 × 2 m = 6.2 m

Diameter of the pond in real life

= 6.2 metres

(b)

Length of the shed in the scale drawing 1 2 m → 1 cm

= 1.5 cm 3 m → 3 ÷ 2 cm = 1.5 cm

4 m → 4 ÷ 2 cm = 2 cm

Width of the shed in the scale drawing

= 2 cm

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Solution Marks Notes

S8 Total distance Carlos swims 2 1000 m = 1 km

(a) To convert m to km → divide by 1000

= 90 × 25 m

= 2250 m 2250 m = 2250 ÷ 1000 km = 2.250 km

= 2.250 km

(b) number of lengths Carlos swims on his 2

front

4

= 4 + 1 × 90

4

= 5 × 90

= 72

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S9

(a)

1

(b)

= –2 1 solution to the simultaneous equations

= –3 = co-ordinates of point of intersection of

the two lines

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Solution Marks Notes

S10 S = a × b × ÷ 2 2

(a)

S =

(b) × 7.6 × 9.22 2 2

V = 8 = 252.6 cm3 V= 8

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S11

(a)

(b) = 5.7 1

1 56 – 55.29 = 0.71

56.84 – 56 = 0.84

∴ 55.29 is closer to 56 than 56.84

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Solution Marks Notes

S12

(a)

(b) 1 Blessy is older than Manjit.

< ∴ Blessy’s age > Manjit’s age

1 Anastasia is less than half the age of Blessy.

Anastasia’s age < ½ of Blessy’s age

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S13 Number of runners that take less than 1 2 1 hour = 60 minutes

hour = 20 + 15 + 10 = 45

Percentage of runners that take less than

1 hour

45

= 85 × 100

= 52.9%

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Solution Marks Notes

S14

2

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S15

(a)

Data shown by red cross on graph 1

(b) 8.75 seconds (approximately) 1 time deduced from the line of best fit;

values in the range of 8 – 9 seconds will be

acceptable

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Solution Marks Notes

S16

0.075 km 7.6 m 77 cm 780 mm

75 m 7.6 m 0.77 m 0.78 m

0.77 m 0.78 m 7.6 m 75 m

77 cm 780 mm 7.6 m 0.075 km

smallest largest

2 To compare the lengths, it is essential to

express them using the same units.

To convert:

km to m → multiply by 1000

cm to m → divide by 100

mm to m → divide by 1000

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S17 Chen earned a bonus ✔ 2 total distance

Average speed = total time

Total distance covered by Chen on his Total distance = average speed × total time

last journey

= 61 × 4.5

= 274.5 km

Distance covered per litre of fuel

274.5

= 96

= 2.859375 km/

2.859375 km/ > 2.8 km/

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Solution Marks Notes

S18

1 2.3 kilograms = 2.3 × 1000 g = 2300 g

0.3 litres = 0.3 × 1000 ml = 300 ml

150 ml < 300 ml

150 ml < 0.3

5 metres = 5 × 1000 mm = 5000 mm

5000 millimetres = 5 metres

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S19 1 2 Area of a trapezium

Area of the trapezium = 2 × (a + b) × 6 1

1

2 × (a + b) × 6 = 30 = 2 × (sum of parallel sides) × height

Other possible values of a and b in cm:

(a + b) × 3 = 30 ab

30 19

28

(a + b) = 3 37

a + b = 10 cm

a = 4 cm

b = 6 cm

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S20 Solution Marks Notes

% of children in film A audience 2 To convert a fraction to percentage

11 ↓

= 11+19 × 100 Multiply the fraction by 100

11

= 30 × 100

= 36.7

% of children in film B audience

5

= 5+7 × 100

5

= 12 × 100

= 41.7

∴ Film B has the greater proportion of

children in the audience.

Film B ✔

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Solution Marks Notes

S21 3

Area of the square = 82 = 64 cm2

Area of the square covered by the star

= 40% of 64 cm2

40

= 100 × 64

= 25.6 cm2

Width of the rectangle = 8 cm

60

60% of 8 cm = 100 × 8 = 4.8 cm

Length of the rectangle

= 8 + 4.8 = 12.8 cm

Area of the rectangle

= 12.8 × 8

= 102.4 cm2

% of the rectangle that the star covers

25.6

= 102.4 × 100

= 25%

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Solution Marks Notes

S22 4200 cm3 54 000 mm3 45 litres 52 000 m

4200 cm3 54 cm3 45 000 cm3 52 000 cm3

52 000 cm3 → largest measurement

1 To compare the measurements, it is

essential to express them using the same

units.

To convert:

mm3 to cm3 → divide by 1000

litres to cm3 → multiply by 1000

1 cm3 = 1m

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Solution Marks Notes

S23

Age Number of Can Cannot % of people

remember that can

11 to 20 people tested remember remember

21 to 30 4 80

31 to 40 20 16 6 70

20 14 14 65

40 26

Yes No ✔ 2

Reason:

As age increases, the percentage of

people that can remember decreases.

This indicates that younger people can

remember better than older people.

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Solution Marks Notes

S24 Volume of the cube = 33 = 27 cm3 3 Volume of a cube = side3

Volume of the cuboid Volume of a cuboid

= 1.2 × 100 × 30 × 50 = length × width × height

= 180 000 cm3

Number of cubes that fit inside the box Length of the cuboid = 1.2 m = 1.2 × 100 cm

180 000 180 000

= 27 27 = 6666.7

= 6666

∴ number of cubes that fit completely

inside the box = 6666

S25 Back to QUICK ACCESS GRID

√ . = +3.5 and –3.5 1

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