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Year 9 · Key Stage 3 · free KS3 maths weekly check

Weekly check: Year 9 whole year

20 mixed questions from 20 Year 9 topics, 50 marks. It covers the whole of Year 9.

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The questions

1

The diagram shows the graph of y = x2 - 2x - 3

  1. Write down the coordinates of the point where the graph crosses the y-axis.
  2. Write down the solutions of x2 - 2x - 3 = 0
  3. Write down the coordinates of the turning point of the graph.
−3−2−112345−5−4−3−2−1123456Oxy
3 marks
Show answer
a) (0, -3) b) x = -1 and x = 3 c) (1, -4)
See the working

a)

Crosses the y-axis where x = 0

y=02 - 2 × 0 - 3
y=-3

(0, -3)

b)

Where the curve crosses the x-axis

x = -1

x = 3

c)

Halfway between the roots

x=-1 + 32
x=1
y=12 - 2 × 1 - 3
y=-4

(1, -4)

2

At the school tuck shop:

2 cookies and 1 drink cost £2.30
1 cookie and 1 drink cost £1.60

Work out the cost of one cookie and the cost of one drink.

3 marks
Show answer
cookie 70p, drink 90p
See the working

Work in pence

2c + d=230
c + d=160
Subtract the equations
c=70
70 + d=160
-70d=90-70

Check: 140 + 90 = 230

Cookie 70p, drink 90p

3

5 miles is about 8 kilometres.

  1. A school fun run is 12 km long. Work out about how many miles this is.
  2. A road sign says London is 25 miles away. Work out about how many kilometres this is.
2 marks
Show answer
a) 7.5 miles b) 40 km
See the working

a)

12 ÷ 8=1.5
1.5 × 5=7.5

7.5 miles

b)

25 ÷ 5=5
5 × 8=40

40 km

4

The table shows the heights, in centimetres, of 30 students.

Height (h cm)Frequency
140 < h ≤ 1506
150 < h ≤ 16011
160 < h ≤ 1709
170 < h ≤ 1804

Draw a frequency polygon for this information.

140150160170180024681012Height (cm)Frequency
2 marks
Show answer
Points at (145, 6), (155, 11), (165, 9), (175, 4) joined with straight lines
See the working

Find the midpoint of each class

140 + 1502=145
150 + 1602=155
160 + 1702=165
170 + 1802=175

Plot (midpoint, frequency)

(145, 6) (155, 11) (165, 9) (175, 4)

Join with straight lines

Do not join last point to first

Points (145, 6), (155, 11), (165, 9), (175, 4) joined

5

A trapezium has parallel sides of length 8 cm and 14 cm.

The area of the trapezium is 66 cm2.

Work out the perpendicular height of the trapezium.

2 marks
Show answer
6 cm
See the working

Area = (a + b)2 × h

8 + 142 × h=66
11h=66
÷11h=6÷11

6 cm

6

The diagram shows a right-angled triangle.

Work out the length x.

4.5 cm6 cmxDiagram NOT accurately drawn
2 marks
Show answer
7.5 cm
See the working
x2=4.52 + 62
x2=20.25 + 36
x2=56.25
√x=√56.25√
x=7.5

7.5 cm

7
  1. Write each of these in the correct algebraic way.
    (i)  a × 4 × b     (ii)  m ÷ 3     (iii)  y × y × 5
  2. Simplify  5p + 3q − 2p + q
3 marks
Show answer
a) 4ab, m3, 5y2 b) 3p + 4q
See the working

a) Number first, no × signs

(i)

4ab

(ii)

m3

(iii)

5y2

b) Collect like terms

5p - 2p = 3p

3q + q = 4q

3p + 4q

8

A straight line has gradient -2 and passes through the point (3, 1).

Find the equation of the line.

3 marks
Show answer
y = -2x + 7
See the working
y=-2x + c
Substitute (3, 1)
1=-2 × 3 + c
1=-6 + c
+6c=7+6

y = -2x + 7

9
  1. Write 82 as a power of 2.
  2. Write 43 × 25 as a single power of 2.
  3. Write 94 ÷ 27 as a single power of 3.
4 marks
Show answer
a) 26 b) 211 c) 35
See the working

a) 8 = 23

82=(23)2
(23)2=26

26

b) 4 = 22

43=(22)3
=26
26 × 25=211

211

c) 9 = 32 and 27 = 33

94=(32)4
=38
38 ÷ 33=35

35

10

Solve 3(x + 4) = 27

2 marks
Show answer
x = 5
See the working
3(x + 4)=27
÷3x + 4=9÷3
-4x=5-4

x = 5

11

Work out 49 × 310

Give your answer as a fraction in its simplest form.

2 marks
Show answer
215
See the working

Multiply tops, multiply bottoms

49 × 310=4 × 39 × 10
49 × 310=1290
Divide top and bottom by 6
1290=215

215

12

A taxi charges £4 plus £2 for every mile.

Leo has £15. He travels m miles.

  1. Write an inequality in m to show that Leo cannot spend more than £15.
  2. Solve your inequality to find the greatest whole number of miles Leo can travel.
3 marks
Show answer
a) 4 + 2m ≤ 15 b) 5
See the working

a) £4 plus £2 for each of m miles

4 + 2m ≤ 15

b)

4 + 2m≤15
-42m≤11-4
÷2m≤5.5÷2

greatest whole number up to 5.5

5 miles

13

Triangle A has vertices at (1, 1), (3, 1) and (1, 4).

Triangle B has vertices at (5, −1), (7, −1) and (5, 2).

Describe fully the single transformation that maps triangle A onto triangle B.

2 marks
Show answer
Translation by the vector (4, -2): 4 right and 2 down.
See the working

Compare matching vertices

(1, 1) → (5, -1): +4 in x, -2 in y

(3, 1) → (7, -1): +4 in x, -2 in y

(1, 4) → (5, 2): +4 in x, -2 in y

Same size, same way up

Translation by the vector (4, -2)

14

The price of a jacket is reduced by 10%.

The reduced price is £63.

Work out the price of the jacket before the reduction.

2 marks
Show answer
£70
See the working
100% - 10%=90%
£63 is 90%
10%=63 ÷ 9
10%=7
100%=7 × 10
100%=70
Check
70 × 0.9=63

£70

15

A taxi company shows its fares on a graph of cost against distance.

The graph is a straight line through (0, 3) and (10, 18), where cost is in pounds and distance is in miles.

  1. Write down the fixed charge for any journey.
  2. Work out the cost per mile.
  3. Work out the fare for a journey of 6 miles.
01234567891002468101214161820Distance (miles)Cost (£)
3 marks
Show answer
a) £3 b) £1.50 c) £12
See the working

a)

Cost when distance = 0

Line crosses the cost axis at 3

£3

b)

Gradient=18 - 310 - 0
Gradient=1510
Gradient=1.5

£1.50 per mile

c)

Fare=3 + 6 × 1.50
Fare=3 + 9
Fare=12

£12

16

The passcode for a tablet is a 4 digit number.

The first digit cannot be 0.

Digits may repeat.

  1. Work out the number of different passcodes that are possible.
  2. Ruby does not know the passcode. She types one 4 digit number at random, with a non-zero first digit. Write down the probability that Ruby types the correct passcode.
3 marks
Show answer
a) 9000 b) 19000
See the working

a)

first digit: 1 to 9, so 9 choices

other digits: 0 to 9, so 10 choices

9 × 10 × 10 × 10=9000

9000

b)

1 correct code out of 9000

P(correct)=19000

19000

17
  1. There are 32 pupils in a Year 9 class. 12 of them walk to school. What fraction of the class walk to school? Give your answer in its simplest form.
  2. Write 40 minutes as a fraction of 2 hours. Give your answer in its simplest form.
2 marks
Show answer
a) 38 b) 13
See the working

a)

1232=38

38

b)

same units first

2 hours=120 minutes
40120=13

13

18

Meera says

"Every multiple of 5 ends in the digit 5."

Give an example to show that Meera is wrong.

2 marks
Show answer
Any multiple of 5 ending in 0, e.g. 10
See the working

Multiples of 5

5, 10, 15, 20, ...

2 × 5=10

10 ends in 0, not 5

10 is a multiple of 5 ending in 0

19

A number y is 0.08, correct to 1 significant figure.

Complete the error interval for y.

....... ≤ y < .......

2 marks
Show answer
0.075 ≤ y < 0.085
See the working

1 sf of 0.08 is the nearest 0.01

Half of 0.01 is 0.005

Lower bound=0.08 - 0.005
Lower bound=0.075
Upper bound=0.08 + 0.005
Upper bound=0.085

0.075 ≤ y < 0.085

20

The cross-section of a triangular prism is a right-angled triangle with base 3 cm, height 4 cm and hypotenuse 5 cm.

The length of the prism is 10 cm.

Work out the total surface area of the prism.

3 cm4 cm10 cm5 cm
3 marks
Show answer
132 cm²
See the working

Two triangle ends

A=12 × b × h
A=12 × 3 × 4
A=6
2 × 6=12
Three rectangles
3 × 10=30
4 × 10=40
5 × 10=50
Add all the faces
SA=12 + 30 + 40 + 50
SA=132

132 cm²

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Every question here is original and written by Robinson Tuition, drawn from the Year 9 topic worksheets. It follows the Key Stage 3 programme of study.

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