Test Your Level | British Curriculum

Question 1

Cambridge Primary 1

Which set shows 2 objects?

Explanation
The picture has exactly 2 objects.

Question 2

Cambridge Primary 1

What shape is shown?

Explanation
A rectangle has four sides, with opposite sides the same length.

Question 3

Cambridge Primary 1

Which pair has the same length?

Explanation
Equal numbers of units mean the same length.

Question 4

Cambridge Primary 1

Which subtraction sentence equals 13?

Explanation
Eighteen minus five equals thirteen.

Question 5

Cambridge Primary 1

Complete the subtraction: 5 - __ = 3

Explanation
Five minus two equals three.

Question 6

Cambridge Primary 2

Which number is odd?

Explanation
37 is odd because it cannot be shared into pairs exactly.

Question 7

Cambridge Primary 2

A farmer has 24 eggs. He puts 6 eggs in each box. How many boxes can he fill?

Explanation
24 divided by 6 equals 4.

Question 8

Cambridge Primary 2

Round 46 to the nearest 10.

Explanation
46 is closer to 50 than 40.

Question 9

Cambridge Primary 2

Which number is 10 more than 63?

Explanation
Adding 10 to 63 gives 73.

Question 10

Cambridge Primary 2

Which number is even?

Explanation
28 is even because it can be shared into pairs exactly.

Question 11

Cambridge Primary 3

Which fraction is greater?

Explanation
\(\frac{1}{2}=\frac{4}{8}\), which is greater than \(\frac{3}{8}\).

Question 12

Cambridge Primary 3

There are 5 bags with 12 marbles in each bag. 8 marbles are lost. How many are left?

Explanation
5 x 12 = 60 marbles. 60 - 8 = 52.

Question 13

Cambridge Primary 3

What is one third of 24?

Explanation
24 divided by 3 equals 8.

Question 14

Cambridge Primary 3

There are 96 stickers shared equally among 8 children. How many stickers does each child get?

Explanation
96 divided by 8 equals 12.

Question 15

Cambridge Primary 3

What is 506 - 179?

Explanation
506 - 180 = 326, then add 1 back to get 327.

Question 16

Cambridge Primary 4

A recipe needs 250 g of flour for one cake. How much flour is needed for 5 cakes?

Explanation
250 g x 5 = 1250 g.

Question 17

Cambridge Primary 4

What is 12.5 - 4.86?

Explanation
Write 12.5 as 12.50. Then 12.50 - 4.86 = 7.64.

Question 18

Cambridge Primary 4

Which fraction is equivalent to \(\frac{3}{6}\)?

Explanation
\(\frac{3}{6}\) simplifies to \(\frac{1}{2}\).

Question 19

Cambridge Primary 4

A train leaves at 09:35 and arrives at 10:20. How long is the journey?

Explanation
From 09:35 to 10:00 is 25 minutes, then 20 more minutes gives 45 minutes.

Question 20

Cambridge Primary 4

A ribbon is 2.4 m long. It is cut into 4 equal pieces. How long is each piece?

Explanation
2.4 divided by 4 equals 0.6 m.

Question 21

Cambridge Primary 5

What type of angle is 90 degrees?

Explanation
A right angle is 90 degrees.

Question 22

Cambridge Primary 5

Which is smaller?

Explanation
0.25 is 25%, which is smaller than 30%.

Question 23

Cambridge Primary 5

Which fraction is equivalent to 15/20?

Explanation
Divide 15 and 20 by 5 to get 3/4.

Question 24

Cambridge Primary 5

Convert 3:45 pm to 24-hour time.

Explanation
Add 12 to the hour for pm times after noon.

Question 25

Cambridge Primary 5

Use the model. What is the greatest common factor of 12 and 18?

Explanation
The common factors are 1, 2, 3 and 6, so the greatest is 6.

Question 26

Cambridge Primary 6

Find the highest common factor of 54 and 72.

Explanation
18 divides both 54 and 72, and no larger listed number does.

Question 27

Cambridge Primary 6

A car travels 150 km in 2.5 hours. What is its average speed?

Explanation
Speed is distance divided by time: \(150\div2.5=60\).

Question 28

Cambridge Primary 6

A triangle has angles 54 degrees and 67 degrees. Find the third angle.

Explanation
Angles in a triangle total 180 degrees. 180-54-67=59.

Question 29

Cambridge Primary 6

Which value is equivalent to 0.04?

Explanation
0.04=4 hundredths, which is 4%.

Question 30

Cambridge Primary 6

What is the next term: 3, 7, 15, 31, __?

Explanation
Each term doubles then adds 1: 31 doubled plus 1 is 63.

Question 31

Cambridge Lower Secondary 7

What is the probability of rolling an even number on a fair six-sided die?

Explanation
The even outcomes are 2, 4 and 6, so 3 out of 6.

Question 32

Cambridge Lower Secondary 7

Which is the median of 4, 9, 11, 12, 19?

Explanation
The middle value is 11.

Question 33

Cambridge Lower Secondary 7

Simplify 6a+4a-3a.

Explanation
Combine like terms: 6a+4a-3a=7a.

Question 34

Cambridge Lower Secondary 7

Find the circumference of a circle with radius 5 cm, using \(\pi=3.14\).

Explanation
Circumference is \(2\pi r=2\times3.14\times5=31.4\).

Question 35

Cambridge Lower Secondary 7

Simplify \(\frac{24}{36}\).

Explanation
Divide numerator and denominator by 12.

Question 36

Cambridge Lower Secondary 8

Calculate \(\frac{3}{5}\div\frac{6}{7}\).

Explanation
Divide by multiplying by the reciprocal: \(\frac{3}{5}\times\frac{7}{6}=\frac{21}{30}=\frac{7}{10}\).

Question 37

Cambridge Lower Secondary 8

Factorise x²+7x.

Explanation
Both terms share a factor of x.

Question 38

Cambridge Lower Secondary 8

Find the midpoint of (2, 7) and (8, 1).

Explanation
Average the coordinates: (2+8)/2=5, (7+1)/2=4.

Question 39

Cambridge Lower Secondary 8

A £240 item is discounted by 15%. What is the sale price?

Explanation
15% of 240 is 36, so the sale price is 240 - 36 = 204.

Question 40

Cambridge Lower Secondary 8

Solve 4(x-2)=20.

Explanation
Divide by 4 to get x-2=5, so x=7.

Question 41

Cambridge Lower Secondary 9

Solve \(\frac{x+4}{3}=2x-1\).

Explanation
Multiply by 3: x+4=6x-3. Then 7=5x, so \(x=\frac{7}{5}\).

Question 42

Cambridge Lower Secondary 9

Calculate \(\frac{6.3\times10^5}{2.1\times10^2}\).

Explanation
Divide 6.3 by 2.1 to get 3 and subtract powers: 10⁵/10²=10³.

Question 43

Cambridge Lower Secondary 9

A cube has side 6 cm. What is its total surface area?

Explanation
A cube has 6 square faces. Each is 6²=36, so total area is \(6\times36=216\).

Question 44

Cambridge Lower Secondary 9

In a \right triangle, \(\sin\theta=\frac{3}{5}\). Which is possible?

Explanation
Sine is opposite divided by hypotenuse.

Question 45

Cambridge Lower Secondary 9

Find the lower bound of 4.8 kg rounded to 1 decimal place.

Explanation
To 1 decimal place, the lower bound is halfway below: 4.75.

Question 46

Cambridge IGCSE 10

A cylinder is not needed here: estimate \(\frac{0.049 \times 602}{1.98}\) using 1 significant figure.

Explanation
Round to 0.05, 600 and 2. Then \(0.05 \times 600 \div 2 = 30 \div 2 = 15\).

Question 47

Cambridge IGCSE 10

The upper bound of a length rounded to the nearest centimetre is 18.5 cm. What value was it rounded to?

Explanation
A measurement rounded to 18 cm to the nearest centimetre has bounds \(17.5 \leq x < 18.5\). The upper bound is 18.5 cm.

Question 48

Cambridge IGCSE 10

The lower bound of a rounded mass is 7.35 kg and the upper bound is 7.45 kg. To what nearest amount was the mass rounded?

Explanation
The interval width is 0.10 kg, so the value was rounded to the nearest 0.1 kg.

Question 49

Cambridge IGCSE 10

Simplify \(\frac{(2^3)^4 \times 2^{-5}}{2^2}\).

Explanation
(2³)⁴=2¹². Then \(2^{12} \times 2^{-5} \div 2^2 = 2^{12-5-2}=2^5\).

Question 50

Cambridge IGCSE 10

Find the lowest common multiple (LCM) of 18 and 24.

Explanation
18=2 × 3² and 24=2³ × 3. Use the highest powers: 2³ × 3²=72.

Question 51

Cambridge IGCSE 11

Expand (x-4)(x+7).

Explanation
Multiply out: x²+7x-4x-28=x²+3x-28.

Question 52

Cambridge IGCSE 11

Make x the subject of \(y=\frac{3x-2}{5}\).

Explanation
Multiply by 5: 5y=3x-2. Add 2 and divide by 3.

Question 53

Cambridge IGCSE 11

In a \right triangle, \(\sin\theta=\frac{3}{5}\). Which is possible?

Explanation
Sine is opposite divided by hypotenuse.

Question 54

Cambridge IGCSE 11

Find \(\cos\theta\) if adjacent = 8 and hypotenuse = 10.

Explanation
Cosine is adjacent divided by hypotenuse: 8/10=0.8.

Question 55

Cambridge IGCSE 11

Which graph represents direct proportion?

Explanation
Direct proportion has form y=kx.

Question 56

Cambridge AS Level

Solve 2^x=32.

Explanation
Since 32=2⁵, x=5.

Question 57

Cambridge AS Level

Find f(3) if f(x)=2x²-x+1.

Explanation
f(3)=2(9)-3+1=16.

Question 58

Cambridge AS Level

What is the range of y=(x-1)²+4?

Explanation
A square is never negative, so minimum value is 4.

Question 59

Cambridge AS Level

Find \(\int \frac1x\,dx\).

Explanation
The integral of 1/x is \(\ln|x|+C\).

Question 60

Cambridge AS Level

Find the coefficient of x² in (1+3x)⁴.

Explanation
Term is \(\binom42(3x)^2=6\times9x^2=54x^2\).

Question 61

Cambridge A Level

If \(z=2e^{i\pi/3}\), what is z³?

Explanation
By De Moivre, \(z^3=8e^{i\pi}=-8\).

Question 62

Cambridge A Level

Differentiate ln x.

Explanation
The derivative of ln x is 1/x.

Question 63

Cambridge A Level

Solve x²-5x+6<0.

Explanation
The roots are 2 and 3, and the quadratic is negative between the roots.

Question 64

Cambridge A Level

Find the coefficient of x³ in (2+x)⁶.

Explanation
Term is \(\binom63 2^3x^3=20\times8x^3=160x^3\).

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