Year 8 · Key Stage 3 · free KS3 maths weekly check

Weekly check: Year 8 whole year

20 mixed questions from 20 Year 8 topics, 50 marks. It covers the whole of Year 8.

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The questions

It takes 8 bricklayers 15 days to build a wall.

Work out how many days it would take 12 bricklayers to build the same wall.
State one assumption you have made.

3 marks

Show answer

a) 10 days b) All the bricklayers work at the same rate

See the working

a)
Total work in worker-days
8 × 15=120
Share the work between 12 bricklayers
120 ÷ 12=10
10 days
b)
All the bricklayers work at the same rate

The diagram shows a sector of a circle with radius 9 cm and angle 100°.

Work out the area of the sector. Give your answer correct to 1 decimal place.

2 marks

Show answer

70.7 cm²

See the working

Fraction of the circle = 100360
Area = 100360 × π × 92
= 70.68...
70.7 cm2

At midnight the temperature in York was −4 °C.

By 4 am the temperature had fallen by 5 °C.

By 10 am the temperature had risen by 8 °C from its 4 am value.

Work out the temperature at 10 am.

2 marks

Show answer

-1°C

See the working

4 am: fallen by 5

-4 - 5	=	-9 °C
		10 am: risen by 8
-9 + 8	=	-1 °C

-1 °C

A block of pine wood has a volume of 240 cm³.

The density of the pine wood is 0.65 g/cm³.

Work out the mass of the block.

2 marks

Show answer

156 g

See the working

Mass	=	density × volume
Mass	=	0.65 × 240
Mass	=	156

156 g

The points A, B, C and D are shown on the grid.

Write down the coordinates of A and B.
Write down the coordinates of C and D.

2 marks

Show answer

a) A (3, 4), B (-2, 3) b) C (-4, -1), D (2, -3)

See the working

a)
across first, then up or down
A: 3 right, 4 up
A (3, 4)
B: 2 left, 3 up
B (-2, 3)
b)
C: 4 left, 1 down
C (-4, -1)
D: 2 right, 3 down
D (2, -3)

Ben wants to work out the perimeter of a square with sides of length 6 cm.

Ben writes:

perimeter = 6 × 6 = 36 cm

Explain the mistake Ben has made.

2 marks

Show answer

6 × 6 gives the area of the square, not the perimeter. The perimeter is 4 × 6 = 24 cm.

See the working

6 × 6 is the area

Area	=	6 × 6
Area	=	36 cm²
		Perimeter: add all 4 sides
Perimeter	=	6 + 6 + 6 + 6
Perimeter	=	4 × 6
Perimeter	=	24 cm

He found the area, not the perimeter (24 cm)

A garden pond is a cuboid 2.5 m long, 1.2 m wide and 0.6 m deep.

The pond is filled with water from a hose. Water flows from the hose at 15 litres per minute.

Work out how long it takes to fill the pond. Give your answer in hours.

1 m³ = 1000 litres

3 marks

Show answer

2 hours

See the working

volume = length × width × depth

V	=	2.5 × 1.2 × 0.6
V	=	1.8 m³
1.8 × 1000	=	1800 litres
1800 ÷ 15	=	120 minutes

2 hours

By rounding each number to 1 significant figure, work out an estimate for

(587 + 214) ÷ 3.9

2 marks

Show answer

200

See the working

Round to 1 significant figure
587 ≈ 600
214 ≈ 200
3.9 ≈ 4
(600 + 200) ÷ 4=800 ÷ 4
=200
200

The stem and leaf diagram shows the masses, in grams, of some tomatoes.

Stem	Leaves
2	1 4 6
3	0 2 5 8
4	3 7

Key: 2 | 1 = 21 grams

Find the range of the masses.

2 marks

Show answer

26 grams

See the working

Smallest: 21 g

Largest: 47 g

Range	=	largest - smallest
Range	=	47 - 21
Range	=	26

26 grams

A bag contains 4 red counters and 6 blue counters. Isla takes a counter at random and does not put it back. She then takes a second counter at random.

Explain why the colour of the second counter is not independent of the colour of the first counter.
Complete the probability tree diagram.
Work out the probability that both counters are red.

4 marks

Show answer

a) not replaced, so the second probabilities depend on the first counter b) 410, 610; 39, 69; 49, 59 c) 215

See the working

a) no replacement
the counters left depend on the first pick
dependent events
b) first pick out of 10
red 410, blue 610
after red: 3 red, 6 blue left
red 39, blue 69
after blue: 4 red, 5 blue left
red 49, blue 59
R 410, B 610; after R: R 39, B 69; after B: R 49, B 59
c) multiply along the branches
P(R, R)=410 × 39
P(R, R)=1290
=215
215

Work out the size of each interior angle of a regular decagon.

3 marks

Show answer

144°

See the working

A decagon has 10 sides

Sum	=	(n - 2) × 180°
Sum	=	(10 - 2) × 180°
Sum	=	1440°
Each angle	=	1440° ÷ 10
Each angle	=	144°

144°

n is an integer.

−2 < n ≤ 3

Write down all the possible values of n.

2 marks

Show answer

-1, 0, 1, 2, 3

See the working

-2 < n ≤ 3
< means -2 is not included
≤ means 3 is included
-1, 0, 1, 2, 3

Amara bakes cakes. Each cake needs 214 cups of flour.

How many cups of flour does she need for 3 cakes? Give your answer as a mixed number.
Amara has 10 cups of flour. Work out how many whole cakes she can make, and how much flour she has left over.

4 marks

Show answer

a) 6 34 cups b) 4 cakes with 1 cup left over

See the working

a)
214 = 94
94 × 3 = 274
= 634
634 cups
b)
10 ÷ 94 = 10 × 49
= 409 = 449
Only whole cakes count
4 cakes use 4 × 94 = 9 cups
10 - 9 = 1
4 cakes, 1 cup left over

The diagram shows triangle PQR and triangle XYZ.

Are the two triangles congruent? Give a reason for your answer.

2 marks

Show answer

Yes - two angles and the side between them are equal (ASA)

See the working

PQ = XY = 6 cm
Angle P = angle X = 50°
Angle Q = angle Y = 70°
The 6 cm side is between the two angles in both
Yes, congruent (ASA)

The table shows information about the time, t minutes, that 30 customers waited at a garage.

Time (t minutes)	Frequency
0 < t ≤ 10	4
10 < t ≤ 20	9
20 < t ≤ 30	12
30 < t ≤ 40	5

Work out an estimate for the mean waiting time.

3 marks

Show answer

21 minutes

See the working

Use the midpoint of each class

Midpoints: 5, 15, 25, 35

Midpoint × frequency

5 × 4	=	20
15 × 9	=	135
25 × 12	=	300
35 × 5	=	175
		Total
20 + 135 + 300 + 175	=	630
		Divide by the total frequency
Mean	=	630 ÷ 30
Mean	=	21

21 minutes

Make x the subject of the formula

5(x + 2y) = w + 3x

3 marks

Show answer

x = w - 10y2

See the working

	5(x + 2y)	=	w + 3x
			Expand the bracket
	5x + 10y	=	w + 3x
-3x	2x + 10y	=	w	-3x
-10y	2x	=	w - 10y	-10y
÷2	x	=	w - 10y2	÷2

x = w - 10y2

Draw a straight line 10 cm long. Mark a point P about 4 cm above the line.

Using a ruler and compasses only, construct the perpendicular from P to the line.

You must show all your construction lines.

2 marks

Show answer

An arc from P crossing the line at two points, then arcs of equal radius from those two points crossing below the line; the line from P through that crossing point is perpendicular to the original line

See the working

Arc from P crossing the line twice
Crossing points X and Y
Same radius: arcs from X and Y
Arcs cross below the line
Join P to that crossing point
The line from P meets the line at 90°

Find the highest common factor (HCF) of 54 and 90

2 marks

Show answer

See the working

Prime factors of each

54	=	2 × 3 × 3 × 3
90	=	2 × 3 × 3 × 5
		Primes in both: 2, 3, 3
HCF	=	2 × 3 × 3
HCF	=	18

The line AB is perpendicular to the line CD. They cross at O. The straight line EF also passes through O.

Angle BOE = 27°.

Work out the size of angle x. Give a reason.
Work out the size of angle y. Give a reason.

3 marks

Show answer

a) 63° (AB and CD are perpendicular, so angle BOC = 90°) b) 63° (vertically opposite to x)

See the working

a) Perpendicular, so angle BOC = 90°

x	=	90 - 27
x	=	63

x = 63°

b) Vertically opposite angles are equal

y	=	x
y	=	63

y = 63°

Write 7⁴ × 7³ as a single power of 7
Write 12⁹ ÷ 12⁴ as a single power of 12

2 marks

Show answer

a) 7⁷ b) 12⁵

See the working

Multiplying: add the powers

7⁴ × 7³	=	7^{4 + 3}
	=	7⁷

7⁷

Dividing: subtract the powers

12⁹ ÷ 12⁴	=	12^{9 - 4}
	=	12⁵

12⁵

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Every question here is original and written by Robinson Tuition, drawn from the Year 8 topic worksheets. It follows the Key Stage 3 programme of study.

8 × 15	=	120
		Share the work between 12 bricklayers
120 ÷ 12	=	10

Weekly check: Year 8 whole year

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