Year 7 · Key Stage 3 · free KS3 maths weekly check

Weekly check: Year 7 part 3

20 mixed questions from 7 Year 7 topics, 51 marks. It covers area and perimeter to volume of prisms, the last third of the year in the order schools usually teach it.

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The questions

At A, draw an angle of 65° above the line AB.
At C, draw an angle of 270° measured anticlockwise from the line CD (a three-quarter turn).

2 marks

Show answer

a) a line from A at 65° to AB b) a line from C straight down, making a reflex angle of 270° with CD

See the working

a) protractor centre on A, 0° along AB
mark 65°, then join to A
angle of 65° drawn at A
b) 270° = 3 × 90°
three right angles anticlockwise from CD
the new arm points straight down
reflex angle of 270° at C

A regular octagon has sides of length 7 cm. Work out its perimeter.
Work out the perimeter of the pentagon in the diagram.
A regular hexagon has a perimeter of 45 cm. Work out the length of one side.

3 marks

Show answer

a) 56 cm b) 26 cm c) 7.5 cm

See the working

a) 8 equal sides

8 × 7

56 cm

b) add all 5 sides

8 + 4 + 5.5 + 5 + 3.5

26 cm

c) 6 equal sides

45 ÷ 6

7.5

7.5 cm

There are 200 pupils in Year 7 at Hillside School.

Jamal asks 50 of the Year 7 pupils how they get to school. 30 of them say they walk.

Estimate how many of the 200 Year 7 pupils walk to school.
Jamal asked the 50 pupils as they arrived through the main gate, which is next to the bus stop. Give one reason why his estimate might not be good for the whole of Year 7.

3 marks

Show answer

a) 120 b) The sample is biased: pupils who use the bus stop gate are over-represented, so it may not represent all of Year 7

See the working

a) fraction of the sample who walk
3050=35
use the same fraction of the population
200 ÷ 5=40
3 × 40=120
about 120 pupils
b)
he only asked pupils at the gate by the bus stop
the sample may not represent all of Year 7

A cuboid has a volume of 180 cm³.

The base of the cuboid measures 6 cm by 5 cm.

Work out the height of the cuboid.

3 marks

Show answer

6 cm

See the working

	Base area	=	6 × 5
	Base area	=	30 cm²
	V	=	base area × height
	30 × h	=	180
÷30	h	=	6	÷30

6 cm

150 students travel to school by bus, by car or by walking.

The two-way table shows some information.

	Bus	Car	Walk	Total
Year 7	24		30	80
Year 8		18
Total	55			150

Complete the two-way table.

3 marks

Show answer

Year 7 Car) 26 Year 8 Bus) 31 Year 8 Walk) 21 Year 8 Total) 70 Car Total) 44 Walk Total) 51

See the working

Year 7 Car	=	80 - 24 - 30
Year 7 Car	=	26

Year 7 Car: 26

Year 8 Total	=	150 - 80
Year 8 Total	=	70

Year 8 Total: 70

Year 8 Bus	=	55 - 24
Year 8 Bus	=	31

Year 8 Bus: 31

Year 8 Walk	=	70 - 31 - 18
Year 8 Walk	=	21

Year 8 Walk: 21

Car Total	=	26 + 18
Car Total	=	44

Car Total: 44

Walk Total	=	30 + 21
Walk Total	=	51

Walk Total: 51

Check

55 + 44 + 51 = 150

Three angles meet at a point. Two of the angles are 145° and 118°. The third angle is x°.

Work out the value of x. Give a reason for your answer.

2 marks

Show answer

x = 97 (angles around a point add up to 360 degrees)

See the working

Angles around a point add to 360°

	x + 145 + 118	=	360
	x + 263	=	360
-263	x	=	97	-263

x = 97

Angles around a point add up to 360°

The diagram shows five quadrilaterals, labelled A, B, C, D and E, drawn on a centimetre grid.

Write down the letters of the pair of congruent quadrilaterals.
Write down the mathematical name of quadrilateral A.

2 marks

Show answer

a) A and C b) parallelogram

See the working

a)
A: sides 4 across, slant 1 across 2 up
C: sides 4 up, slant 2 across 1 up
Same shape and size, C is A turned
A and C
b)
2 pairs of parallel sides
No right angles
parallelogram

A rectangle has length 9 cm and width 4 cm.

Work out the area of the rectangle.
Work out the perimeter of the rectangle.

2 marks

Show answer

a) 36 cm² b) 26 cm

See the working

Area	=	length × width
Area	=	9 × 4
Area	=	36

36 cm²

Perimeter	=	9 + 4 + 9 + 4
Perimeter	=	26

26 cm

A rectangle is made from three identical squares placed side by side in a row.

The perimeter of the rectangle is 48 cm.

Work out the area of the rectangle.

3 marks

Show answer

108 cm²

See the working

Each square has side s

Rectangle: 3s long, s wide

	Perimeter	=	3s + s + 3s + s
	Perimeter	=	8s
	8s	=	48
÷8	s	=	6	÷8
	Length	=	3 × 6
	Length	=	18 cm

Rectangle is 18 cm by 6 cm

Area	=	18 × 6
Area	=	108

108 cm²

Here are three scatter graphs, A, B and C.

For each graph, write down the type of correlation it shows.

3 marks

Show answer

A) positive B) negative C) no correlation

See the working

uphill = positive, downhill = negative, no pattern = none
A positive
B negative
C no correlation

Here is a triangular prism.

Write down the number of faces of a triangular prism.
Write down the number of edges of a triangular prism.

2 marks

Show answer

a) 5 b) 9

See the working

2 triangles + 3 rectangles

2 + 3

3 on the front end, 3 on the back end

3 joining the two ends

3 + 3 + 3

Part of a bus timetable is shown.

	Bus A	Bus B	Bus C
Bus station	07:40	08:05	08:35
Park Road	07:52	08:17	08:47
Library	08:03	08:28	08:58
School	08:15	08:40	09:10

How long does Bus B take to go from the bus station to school?
Maya gets on at Park Road. She must be at school by 08:30. Which is the latest bus she can catch?
Ollie arrives at the Library stop at 08:10. How long does he have to wait for the next bus?

3 marks

Show answer

a) 35 minutes b) Bus A, leaving Park Road at 07:52 c) 18 minutes

See the working

a) Bus B column
08:05 to 08:40
40 - 5=35
35 minutes
b) arrival times at school
Bus A 08:15    Bus B 08:40 (too late)
Bus A at 07:52
c) next bus at the Library after 08:10
Bus B at 08:28
28 - 10=18
18 minutes

The diagram shows line AB above a ruler marked in centimetres and millimetres. Write down the length of AB to the nearest millimetre.
Use a protractor to measure angle DEF.

2 marks

Show answer

a) 6.3 cm (63 mm) b) 137°

See the working

a) A is at 1 cm, B is at 7.3 cm
7.3 - 1=6.3
6.3 cm = 63 mm
b) centre on E, 0° along ED
obtuse, so more than 90°
137°

A box of chocolates is a triangular prism.

The triangle at the end has a base of 10 cm and a height of 6 cm. The box is 15 cm long.

Work out the volume of the box.

2 marks

Show answer

450 cm³

See the working

Area of the triangle

A	=	12 × 10 × 6
	=	30 cm²
		Volume = area × length
V	=	30 × 15
	=	450

450 cm³

The table shows the number of children in each of 20 families.

Number of children	Frequency
0	3
1	8
2	6
3	3

Work out the mean number of children per family.

3 marks

Show answer

1.45

See the working

Number × frequency for each row

0 × 3	=	0
1 × 8	=	8
2 × 6	=	12
3 × 3	=	9
		Total number of children
0 + 8 + 12 + 9	=	29
		Divide by the number of families
Mean	=	29 ÷ 20
Mean	=	1.45

1.45

Ayesha has a cube of modelling clay with edges of 6 cm.

She reshapes all of the clay into a cuboid. The cuboid is 8 cm long and 3 cm wide.

Work out the height of the cuboid.

3 marks

Show answer

9 cm

See the working

Volume of the cube

	V	=	6 × 6 × 6
		=	216 cm³
			Same volume for the cuboid
	8 × 3 × h	=	216
	24h	=	216
÷24	h	=	9	÷24

9 cm

The pictogram shows the number of cars washed at a garage on Friday and Saturday.

Key: ● represents 6 cars

Work out how many more cars were washed on Saturday than on Friday.

2 marks

Show answer

See the working

1 circle = 6 cars

Friday: 312 circles

3.5 × 6	=	21 cars
		Saturday: 5 circles
5 × 6	=	30 cars
30 - 21	=	9

9 more cars

Find the median of these numbers.
14 9 21 11 17 9 12
Here are the heights, in cm, of six pupils. Find the median height.
152 147 160 155 149 158

3 marks

Show answer

a) 12 b) 153.5 cm

See the working

a) put them in order first
9, 9, 11, 12, 14, 17, 21
7 numbers, so the middle is the 4th
12
b) in order
147, 149, 152, 155, 158, 160
two middle values
(152 + 155) ÷ 2=153.5
153.5 cm

The scatter graph shows the number of hours of sunshine and the number of visitors to a country park on each of 10 days.

Describe the correlation shown by the scatter graph.
On another day there were 7.5 hours of sunshine. By drawing a line of best fit, estimate the number of visitors to the park on this day.

3 marks

Show answer

a) positive correlation b) approximately 160 (accept 150-175)

See the working

a)
Points go up from bottom left to top right
Positive correlation
b)
Draw a line of best fit
Ruled line through the middle of the points
Go up from 7.5 hours to the line
Go across to the visitors axis
Reading: about 159
About 160 visitors (accept 150 to 175)

A group of Year 7 pupils and a group of Year 8 pupils did the long jump.

	Median	Range
Year 7	2.9 m	1.2 m
Year 8	3.3 m	0.8 m

Make two comparisons between the long jumps of the two year groups.

2 marks

Show answer

Year 8 jumped further on average (higher median). Year 8 were more consistent (smaller range).

See the working

compare the average
3.3 m > 2.9 m
on average Year 8 jumped further
compare the spread
0.8 m < 1.2 m
Year 8 were more consistent

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition, drawn from the Year 7 topic worksheets. It follows the Key Stage 3 programme of study.

3050	=	35
		use the same fraction of the population
200 ÷ 5	=	40
3 × 40	=	120

Weekly check: Year 7 part 3

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