Autumn Assessment
Year 9
Mathematics
Higher: No calculator allowed
Time allowed: 45 minutes
First name
Middle name
Last name
Date of birth
Day
Month
Teacher
These assessments have been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
Year
Diagram not drawn accurately.
1
10 cm
6 cm
12 cm
8 cm
Work out the volume of the prism.
cm3
2 marks
Work out the surface area of the prism.
cm2
3 marks
Page 2 of 16
3
Rearrange 4x + 2y = 12 to make y the subject.
2 marks
State the gradient of the straight line with equation 4x + 2y = 12
1 mark
Page 4 of 16
4
x
1
2
5
10
40
y
100
50
20
10
2.5
Tick the correct statement.
x is directly proportional to y
x is inversely proportional to y
x is neither directly nor inversely proportional to y
1 mark
Work out the value of y when x = 4
y=
1 mark
Page 5 of 16
5
Solve the inequality
2(3m + 4) > 7m
2 marks
Page 6 of 16
6
Here is a linear graph.
y
5
4
3
2
1
-10
-8
-6
-4
-2
0
x
2
4
6
8
10
-1
-2
-3
-4
-5
Find the gradient of the line.
2 marks
Write down the equation of the line.
1 mark
Page 7 of 16
7
The volume of a cone is given by the formula V = 13 πr2h.
Find the volume of the cone, giving your answer in terms of π.
12 cm
13 cm
5 cm
cm3
2 marks
Page 8 of 16
8
Use a ruler and pair of compasses to construct a perpendicular
from the point A to the line segment BC.
You must show all your construction lines.
.A
C
B
2 marks
9
Make b the subject of the formula a2 + b2 = c2
2 marks
Page 9 of 16
10
Amir is investigating the difference between the products of the numbers
in the opposite corners of a 2 by 3 rectangle placed on a hundred square.
1
2
3
4
5
6
7
8
9
10
11 12 13 14 15 16 17 18 19 20
22 x 14 = 308
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
12 x 24 = 288
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
308 – 288 = 20
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 70
Amir calls the top left number in his rectangle x.
Write expressions to complete the rectangle.
x
x+1
x + 11
1 mark
Page 10 of 16
It doesn’t matter
where I place this
rectangle on a hundred square.
The difference between
the products of the numbers
in the opposite corners
will always be 20
Show that Amir is correct.
2 marks
Page 11 of 16
11
ABCD is the plan view of a garden.
A tree is to be planted so that it is more than 5 m away from D,
and closer to CD than BC.
Shade the region where the tree could be planted.
You must use a ruler and a pair of compasses.
Show all your construction lines.
A
B
D
C
Scale 1 cm stands for 1 m.
3 marks
Page 12 of 16
12
The line y = 3x + 7 is perpendicular to the line y = 4 – 13 x
Is the statement true or false? Circle your answer.
True
False
Explain your reasoning.
1 mark
13
The volume of a cylinder of height 8 cm is 72π cm3
Find the radius of the cylinder.
cm
2 marks
Page 13 of 16
14
Determine whether the triangles are congruent.
7 cm
97°
70 mm
42°
41°
41°
Diagrams not drawn accurately.
3 marks
Page 14 of 16
15
Find the range of values of x for which the fraction is improper.
7 – 5x
3x + 4
3 marks
Page 15 of 16
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Please do not write on this page.
Page 16 of 16
Spring Assessment
Year 9
Mathematics
Higher: No calculator allowed
Time allowed: 45 minutes
First name
Middle name
Last name
Date of birth
Day
Month
Teacher
These assessments have been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
Year
1
A waste paper basket is an open cylinder of height 30 cm
and diameter 20 cm.
30 cm
20 cm
Find the total surface area of the waste paper basket.
Give your answer in terms of π.
cm2
3 marks
Page 2 of 12
2
Ms Kowal invests £6000 in a simple interest account.
After 5 years her investment has earned £450 interest.
What rate of interest does the account pay?
%
3 marks
Ms Smith invests £6000 in an account that pays 3.5% compound
interest account.
Which calculation works out the value of her investment after 5 years?
Circle your answer
6000 × 1.053.5
6000 × 1.355
6000 × 1.53.5
6000 × 1.0355
1 mark
Page 3 of 12
3
Value Added Tax (VAT) is charged at 20% on watches.
The amount of VAT charged on a watch is £180
Find the total cost of the watch.
£
2 marks
Page 4 of 12
G
F
4
65°
E
56°
D
Diagram NOT
accurately drawn
x
A
B
C
Work out the size of the angle marked x.
Give a reason for each stage of your working.
°
3 marks
Page 5 of 12
y
5
7
6
5
4
P
3
2
1
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
x
-1
-2
-3
-4
-5
-6
-7
Shape P is reflected in the line x = −1 to give shape Q.
Shape Q is reflected in the line the x-axis to give shape R.
Describe fully the single transformation that maps shape P
onto shape R.
3 marks
Page 6 of 12
6
A car costs £15 000 when new.
The car loses 20% of its value its first year and 10% of its value
every year after that.
Work out the value of the car after 2 years.
£
3 marks
A van costs £20 000 when new.
After 2 years the van is worth £13 000
What percentage of its value has the van lost?
%
2 marks
Page 7 of 12
7
The kinetic energy K of an object mass m travelling at velocity v is
given by the formula
K = 12_ mv2
Find the value of K when m = 10 and v = 4
2 marks
Rearrange the formula to make m the subject.
2 marks
Page 8 of 12
8
a is a prime number.
b is an even number.
Are the statements always true, sometimes true or never true?
Circle your answers.
ab is odd
Always
True
Sometimes
True
Never
True
1 mark
a(b + 1) is even
Always
True
Sometimes
True
Never
True
1 mark
9
Show that the line with equation 4x + 2y = 10 is parallel to the
line with equation y = 6 − 2x.
2 marks
Page 9 of 12
10
Using a ruler and a pair of compasses, construct an angle of
60° from the point A.
A
x
2 marks
11
Work out
1.6 × 106 ÷ 4.8 × 105
Give your answer as a mixed number.
2 marks
Page 10 of 12
12
Show that √0.25 is a rational number.
2 marks
13
ABCDEFGH is a cuboid.
H
E
D
A
G
F
C
B
AB = 12 cm, BC = 5 cm and CG = 5 cm.
Show that AG < 14 cm.
4 marks
Page 11 of 12
14
PQRS represents the rectangular side of a box.
M id the midpoint of RS.
The box is rotated clockwise about point P until Q meets the ground.
Draw the new position of PQRS and the locus of the point M
as the box rotates about P.
R
Q
M
S
Ground
P
3 marks
END OF TEST
Page 12 of 12
Autumn Assessment
Year 10
Mathematics
Paper 3 (Non-Calculator)
Higher Tier
Surname
Other names
You should have:
A pen, pencil, ruler and an eraser.
Tracing paper may be used.
Information
•
•
•
•
•
•
•
The total mark for this paper is 50
The marks for each question are shown in brackets.
Answer all questions in the spaces provided – there may be more space than you need.
You must show all your working.
Diagrams are not accurately drawn, unless otherwise indicated.
Calculators may not be used.
Check your answers if you have time at the end.
This assessment has been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
1
a) Work out 62 +
81
53 × 97
b) Estimate the value of
22
(2 marks)
You must show all your working.
(2 marks)
Page 2 of 16
© White Rose Maths 2020
2
Here are the maximum daily temperatures in a town over one week.
−2°C
5°C
0°C
−7°C
4°C
3°C
2°C
Find the range of the maximum daily temperatures.
(2 marks)
3
a) Expand and simplify (x − 7) (x + 4)
(2 marks)
b) Simplify 5a2 × 6a–1
(2 marks)
Page 3 of 16
© White Rose Maths 2020
4
a) Work out
5 3
–
7 5
(2 marks)
b) i) Write 6.3 × 10–4 as a decimal number.
1.8 × 10
3 × 102
Give your answer in standard form.
ii) Find the value of
7
(1 mark)
(2 marks)
Page 4 of 16
© White Rose Maths 2020
5
A company gives a bonus to two salespeople, Miss Xu and Ms Trent, in the ratio of the
sales they make in January.
Miss Xu made sales of £24 000 in January.
Ms Trent made sales of £30 000 in January.
a) Write the ratio that will be used to share the bonus in its simplest form.
(1 mark)
b) The total bonus is £5850
How much will each person receive?
Miss Xu receives
Ms Trent receives
(3 marks)
Page 5 of 16
© White Rose Maths 2020
6
a) Complete the table of values for y = 2x – 3
x
–1
0
y
1
2
3
–3
4
3
(2 marks)
b) On the grid, draw the graph of y = 2x – 3
y
6
5
4
3
2
1
–1
0
–1
1
2
3
4
x
–2
–3
–4
–5
–6
(2 marks)
Page 6 of 16
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7
Triangle A is shown on the grid.
y
10
9
8
7
6
5
A
4
3
2
1
0
0
1
2
3
4
5
On the grid, translate A by the vector
(–14 )
6
7
8
9
10
x
(2 marks)
Page 7 of 16
© White Rose Maths 2020
8
13x + 1
11x + 9
x
a) Explain why 13x + 1 = 11x + 9
(1 mark)
b) Solve 13x + 1 = 11x + 9
(2 marks)
c) Use your answer to part b) to work out the perimeter of the triangle.
units
(2 marks)
Page 8 of 16
© White Rose Maths 2020
9
Here is an inequality, in x, shown on a number line.
x
–4
–3
–2
–1
0
1
2
3
4
5
Write the inequality.
(2 marks)
Page 9 of 16
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10 Solve the simultaneous equations.
3x + 2y = 4
4x + 5y = 17
x=
y=
(4 marks)
Page 10 of 16
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11 A logo consists of two right-angled triangles joined together as shown.
Find the perimeter of the logo.
17 cm
9 cm
12 cm
(3 marks)
Page 11 of 16
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12 Enlarge the triangle by a scale factor of –2, centre (–2, 0).
y
10
8
6
4
2
–14
–12
–10
–8
–6
–4
–2
0
2
4
6
8
10
12
14
x
–2
–4
–6
(3 marks)
Page 12 of 16
© White Rose Maths 2020
13 Two similar plant pots are shown.
10 cm
15 cm
When the smaller plant pot is full, it holds 0.8 litres of compost.
Calculate how many litres of compost the larger pot holds when it is full.
(2 marks)
Page 13 of 16
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14 Find the values of x for which x2 + 2x − 15 < 0
(3 marks)
Page 14 of 16
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Please do not write on this page.
Page 16 of 16
© White Rose Maths 2020
Autumn Assessment
Year 10
Mathematics
Paper 4 (Calculator)
Higher Tier
Surname
Other names
You should have:
A pen, pencil, ruler, eraser and a scientific calculator.
Tracing paper may be used.
Information
•
•
•
•
•
•
The total mark for this paper is 50
The marks for each question are shown in brackets.
Answer all questions in the spaces provided – there may be more space than you need.
You must show all your working.
Diagrams are not accurately drawn, unless otherwise indicated.
Check your answers if you have time at the end.
This assessment has been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
1
a) Use your calculator to work out
37.6 × 12.9
17.2 – 5.6
Write all the digits on your calculator display.
(1 mark)
b) Write your answer to part a), correct to 1 significant figure.
(1 mark)
2
Solve the equation 0.4x – 1.8 = 7.3
(2 marks)
Page 2 of 16
© White Rose Maths 2020
3
A restaurant owner is buying plates.
A box of plates costs £87.50
She buys 6 boxes.
She gets a discount of 7% on her order.
Work out the total cost of the order after the discount.
(3 marks)
Page 3 of 16
© White Rose Maths 2020
4
Filip is on holiday in Germany
He buys a guidebook for 25 euros.
In the UK, the same guidebook costs £15
The exchange rate is £1 = €1.09
Work out the difference between the cost of the guidebook in Germany
and the cost of the guidebook in the UK.
(3 marks)
Page 4 of 16
© White Rose Maths 2020
5
Find the next term in each sequence.
a)
12
10.8
9.6
8.4
(1 mark)
b)
1
5
25
125
(1 mark)
6
A dice is biased so the probability it lands on 4 is 0.2
a) What is the probability that the dice does not land on 4?
(1 mark)
b) Aisha is going to roll the dice 300 times.
Work out an estimate for the number of times the dice will land on 4
(2 marks)
Page 5 of 16
© White Rose Maths 2020
7
y
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
x
On the grid, enlarge the shape by a scale factor of 2, centre (0, 0).
(3 marks)
Page 6 of 16
© White Rose Maths 2020
8
E
18 cm
B
6.5 cm
A
5 cm
C
D
12 cm
F
Triangles ABC and DEF are similar.
AB = 6.5 cm
AC = 5 cm
EF = 18 cm
DF = 12 cm
a) Work out the length of DE.
(2 marks)
b) Work out the length of BC.
(2 marks)
Page 7 of 16
© White Rose Maths 2020
9
P
B
Q
A
73°
D
R
x
C
S
AQB, CRD and PQRS are straight lines.
AB is parallel to CD.
Angle AQR = 73°.
Work out the value of x.
Give reasons for your answer.
(3 marks)
Page 8 of 16
© White Rose Maths 2020
10 a)
P
6.4 cm
43°
R
Q
Work out the length of PQ.
Give your answer correct to 3 significant figures.
(2 marks)
b)
12 cm
4.5 cm
x
Calculate the value of x.
Give your answer correct to 1 decimal place.
(2 marks)
Page 9 of 16
© White Rose Maths 2020
11 The graphs of the straight lines y = 2x – 3 and x + y = 3 have been drawn on the grid.
y
y = 2x – 3
4
3
2
1
–4
–3
–2
–1
0
–1
1
2
3
4
x
x+y=3
–2
–3
–4
Use the graphs to solve the simultaneous equations.
y = 2x – 3
x+y=3
x=
y=
(2 marks)
Page 10 of 16
© White Rose Maths 2020
12 The areas of two squares are in the ratio 9 : 16
a) Complete the statement with a fraction.
The area of the smaller square is
larger square.
of the area of the
(1 mark)
b) The area of the larger square is 144 cm2
Find the perimeter of the smaller square.
(2 marks)
Page 11 of 16
© White Rose Maths 2020
13 The diagram shows parallelogram ABCD.
A
B
E
D
C
The diagonals of ABCD meet at point E.
Find three different pairs of congruent triangles in the diagram and complete
the sentences.
Triangle
is congruent to triangle
Triangle
is congruent to triangle
Triangle
is congruent to triangle
(2 marks)
Page 12 of 16
© White Rose Maths 2020
14 The diagram shows a cuboid.
HG = 3 cm, AE = 5 cm and EH = 7 cm.
B
C
A
D
5 cm
F
G
3 cm
E
H
7 cm
Work out the length of AG.
(3 marks)
Page 13 of 16
© White Rose Maths 2020
16 Solve the simultaneous equations.
y=x+2
x2 + y2 = 10
Show clear algebraic working.
x=
y=
(4 marks)
Page 15 of 16
© White Rose Maths 2020
Spring Assessment
Year 10
Mathematics
Paper 3 (Non-Calculator)
Higher Tier
Surname
Other names
You should have:
A pen, pencil, ruler and an eraser.
Tracing paper may be used.
Information
•
•
•
•
•
•
•
The total mark for this paper is 50
The marks for each question are shown in brackets.
Answer all questions in the spaces provided – there may be more space than you need.
You must show all your working.
Diagrams are not accurately drawn, unless otherwise indicated.
Calculators may not be used.
Check your answers if you have time at the end.
This assessment has been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
1
Translate shape A by the vector
(–87 ).
y
10
9
8
7
6
5
4
A
3
2
1
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0
–1
1
2
3
4
5
6
7
8
9 10
x
–2
–3
–4
–5
–6
–7
–8
–9
–10
(2 marks)
2
Mrs Trent buys some furniture.
The total cost of the furniture is £7000 plus VAT at 20%.
She pays a deposit of £3000 and pays the rest in 12 equal monthly payments.
Work out the amount of each monthly payment.
(3 marks)
Page 2 of 16
© White Rose Maths 2021
3
ξ = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
A = { 1, 3, 6, 9 }
B = { 3, 5, 6, 8 }
a) Complete the Venn diagram to represent this information.
ξ
A
B
(3 marks)
A number is chosen at random from the universal set ξ.
b) Find the probability that the number is in the set A ∩ B.
(1 mark)
Page 3 of 16
© White Rose Maths 2021
6
The diagram shows the relative position of two boats.
N
×
boat A
×
boat B
a) Find the bearing of boat B from boat A.
(1 mark)
The scale of the diagram is 1 cm represents 3 km.
b) Work out the actual distance between the two boats.
(2 marks)
A third boat, C, is 12 km due east of boat A.
c) On the diagram, show the position of boat C.
(2 marks)
Page 5 of 16
© White Rose Maths 2021
7
Ron has two fair spinners split into equal sections.
spinner A
5
1
2
4
3
spinner B
4
1
3
2
Spinner A can land on 1, 2, 3, 4 or 5
Spinner B can land on 1, 2, 3 or 4
Ron spins both spinners.
a) Complete the probability tree diagram.
Spinner A
Spinner B
lands on an
even number
lands on an
even number
lands on an odd
number
lands on an
even number
lands on an odd
number
lands on an odd
number
(2 marks)
b) Work out the probability that exactly one spinner lands on an even number.
(2 marks)
Page 6 of 16
© White Rose Maths 2021
11
A
10 cm
diagram not
drawn accurately
C
B
12 cm
5 cm
E
D
a) Show that triangles ABC and ADE are similar.
(2 marks)
b) Work out the length of DE.
(2 marks)
Page 9 of 16
© White Rose Maths 2021
12 There are 10 counters in a bag.
6 of the counters are red and 4 of the counters are green.
Two counters are taken at random from the bag.
Work out the probability that the two counters are different colours.
(4 marks)
Page 10 of 16
© White Rose Maths 2021
13 Given that x2 : 5x + 12 = 1 : 2, find the possible values of x.
(4 marks)
Page 11 of 16
© White Rose Maths 2021
15 Triangle ABC is an isosceles triangle with
ABC =
ACB.
A
M
N
B
C
M and N are points on AB and AC such that AM = AN.
Prove that triangle ABN is congruent to triangle ACM.
(4 marks)
Page 13 of 16
© White Rose Maths 2021
BLANK PAGE
Please do not write on this page.
Page 14 of 16
© White Rose Maths 2021
Spring Assessment
Year 10
Mathematics
Paper 4 (Calculator)
Higher Tier
Surname
Other names
You should have:
A pen, pencil, ruler, eraser and a scientific calculator.
Tracing paper may be used.
Information
•
•
•
•
•
•
The total mark for this paper is 50
The marks for each question are shown in brackets.
Answer all questions in the spaces provided – there may be more space than you need.
You must show all your working.
Diagrams are not accurately drawn, unless otherwise indicated.
Check your answers if you have time at the end.
This assessment has been designed by White Rose Maths.
For more information, please visit www.whiterosemaths.com
1
a) Solve the equation 4(2 + 5x) = 90
(3 marks)
b) Solve the inequality –8y < 196
(2 marks)
Page 2 of 12
© White Rose Maths 2021
2
A bag contains red and blue counters in the ratio 3 : 4
What percentage of the counters in the bag are red?
(2 marks)
3
The table shows the probability of a biased dice landing on each number.
Outcome
1
2
3
4
5
6
Probability
0.05
0.43
0.17
0.09
0.16
0.1
Eva rolls the dice 700 times.
Work out an estimate for the number of times the dice will land on 2
(2 marks)
Page 3 of 12
© White Rose Maths 2021
4
Mr Hall goes on holiday to Switzerland.
He wants to buy £650 worth of Swiss francs.
Mr Hall receives all the money in 20 franc notes.
The exchange rate is £1 = 1.19 francs.
How many 20 franc notes will he receive?
(3 marks)
5
Ms Rose invests £2500 for 4 years in a savings account.
The account pays 3% per annum compound interest.
How much interest will Ms Rose earn over the 4 years?
(3 marks)
Page 4 of 12
© White Rose Maths 2021
6
The ratio of mugs to cups in a cafe is 5 : 3
The ratio of cups to glasses in the cafe is 6 : 11
There are 190 mugs in the cafe.
How many glasses are there?
(3 marks)
7
A bodybuilder has lost 14% of his mass for a competition.
His mass is now 103.2 kg.
Work out the mass of the bodybuilder before the competition.
(2 marks)
Page 5 of 12
© White Rose Maths 2021
8
17 mm
Find the area of the sector.
Give your answer to 3 significant figures.
(2 marks)
9
One of the two solutions of a quadratic equation is x = –6
The quadratic equation is x2 + bx + 12 = 0, where b is an integer.
Find the other solution of the equation.
You must show all your working.
(3 marks)
Page 6 of 12
© White Rose Maths 2021
14 Shade the region defined by the following inequalities.
x ≥ –2
y≥1
x+y≤3
y
4
3
2
1
–3
–2
–1
0
1
2
3
4
x
–1
–2
–3
(3 marks)
Page 10 of 12
© White Rose Maths 2021
15 a) Two cones, X and Y, are mathematically similar.
The height of cone X is 10 cm and the height of cone Y is 12 cm.
The volume of cone X is 800 cm3
Calculate the volume of cone Y.
(3 marks)
b) Square A has sides of length a cm.
Square B has sides of length b cm.
The area of square B is 44% greater than the area of square A.
Work out the ratio a : b.
(2 marks)
Page 11 of 12
© White Rose Maths 2021
16 The diagram shows a triangular prism.
F
E
C
D
20 cm
B
32°
A
20 cm
The base, ABCD, of the prism is a square of side length 20 cm.
Angle ABE and angle CBE are right angles.
Angle EAB = 32°
P is the point on DA such that DP : PA = 3 : 2
Calculate the size of the angle between EP and the base of the prism.
Give your answer correct to 1 decimal place.
(4 marks)
Page 12 of 12
© White Rose Maths 2021