Math Common Entrance 13+

Part 1 – Numbers & Word Problems (10 Questions)

1. Which of the following is a multiple of 18?

A) 62

B) 72

C) 81

D) 92

2. What is 0.004 × 1000?

A) 0.004

B) 0.4

C) 4

D) 40

3. Write 56/84 in simplest form.

A) 2/3

B) 3/4

C) 4/7

D) 5/7

4. The value of (3.2 × 10³) is:

A) 320

B) 3,200

C) 32,000

D) 320,000

5. What is √196?

A) 12

B) 13

C) 14

D) 15

6. A laptop is reduced by 15% from £480. What is the sale price?

A) £402

B) £408

C) £420

D) £450

7. A car travels 240 km in 3 hours. What is its average speed?

A) 60 km/h

B) 70 km/h

C) 75 km/h

D) 80 km/h

8. A tank contains 850 L of water. 35% is drained out. How much water remains?

A) 297.5 L

B) 425 L

C) 552.5 L

D) 650 L

9. The sum of three consecutive integers is 126. What is the middle number?

A) 41

B) 42

C) 43

D) 44

10. A shop sells pens at 5 for £4. How much for 12 pens?

A) £8.80

B) £9.60

C) £10.00

D) £10.40

Part 2 – Algebra (10 Questions)

11. Simplify: 5a – 3a + 7

A) 2a + 7

B) 8a

C) 5a + 4

D) 7 – 2a

12. Solve: 3x – 4 = 20

A) 6

B) 7

C) 8

D) 9

13. Expand: 3(2x + 5)

A) 6x + 5

B) 6x + 15

C) 6x + 25

D) 6x – 15

14. Factorise: x² – 16

A) (x – 16)(x + 1)

B) (x – 4)(x + 4)

C) (x – 8)(x + 2)

D) (x – 2)(x – 8)

15. Which of these represents a linear expression?

A) 3x² – 2

B) x³ + 1

C) 5 – 4x

D) 2x² + 5x

16. If f(x) = 2x² – 3x, find f(4).

A) 20

B) 22

C) 26

D) 28

17. Simplify: (2x)(3x²)

A) 5x²

B) 6x²

C) 6x³

D) 6x⁴

18. Solve: 7y + 2 = 37

A) 4

B) 5

C) 6

D) 7

19. Which inequality matches the sentence: “x is greater than 4”?

A) x < 4

B) x > 4

C) x ≤ 4

D) x ≥ 4

20. The nth term of a sequence is 4n – 1. What is the 8th term?

A) 32

B) 31

C) 29

D) 27

Part 3 – Graphs (5 Questions)

21. A straight line has equation y = 3x + 2. What is the gradient?

A) 2

B) 3

C) 5

D) 6

22. In the line y = –2x + 7, the y-intercept is:

A) –2

B) 7

C) –7

D) 2

23. A point lies on the line y = x + 4. Which point is on the line?

A) (1, 5)

B) (2, 3)

C) (3, 6)

D) (4, 3)

24. A distance-time graph shows a horizontal line. What does this mean?

A) Faster speed

B) Slower speed

C) Constant speed

D) No movement

25. If x = 3, find y when y = 1⁄2x – 1.

A) –1⁄2

B) 0

C) 1⁄2

D) 1

Part 4 – Ratio, Proportion & Rates of Change (5 Questions)

26. Simplify the ratio 15 : 45.

A) 1 : 3

B) 1 : 2

C) 2 : 3

D) 3 : 1

27. A map scale is 1 : 50 000. A distance on the map is 6 cm.

What is the real distance?

A) 600 m

B) 3 km

C) 6 km

D) 30 km

28. A recipe for 4 people uses 300 g of pasta. How much pasta for 10 people?

A) 600 g

B) 650 g

C) 700 g

D) 750 g

29. A car’s value decreases from £12,000 to £9,600.
What is the percentage decrease?

A) 10%

B) 15%

C) 20%

D) 25%

30. Speed is increased from 60 km/h to 75 km/h.
What is the percentage increase?

A) 15%

B) 20%

C) 22%

D) 25%

Part 5 – Geometry & Measures (5 Questions)

31. The sum of the interior angles of a pentagon is:

A) 360°

B) 450°

C) 540°

D) 720°

32. What is the area of a triangle with base 12 cm and height 8 cm?

A) 48 cm²

B) 60 cm²

C) 72 cm²

D) 96 cm²

33. A circle has radius 7 cm. What is its circumference? (Use π = 22/7)

A) 22 cm

B) 28 cm

C) 44 cm

D) 66 cm

34. Which 3D shape has 8 vertices?

A) Sphere

B) Cylinder

C) Cuboid

D) Cone

35. A cuboid has volume 120 cm³ and base area 24 cm². What is its height?

A) 3 cm

B) 4 cm

C) 5 cm

D) 6 cm

Part 6 – Probability & Statistics (5 Questions)

36. The mode of the data 4, 6, 7, 7, 7, 8, 9 is:

A) 6

B) 7

C) 8

D) 9

37. The probability of an event is 0.3. The probability it does NOT happen is:

A) 0.3

B) 0.5

C) 0.6

D) 0.7

38. The mean of 10, 20, 30, 40 is:

A) 20

B) 25

C) 30

D) 35

39. A box contains 5 red, 3 blue and 2 green balls.
What is the probability of drawing a green ball?

A) 1/5

B) 1/6

C) 1/10

D) 2/10

40. Which graph is most suitable for showing continuous data?

A) Pie chart

B) Line graph

C) Bar chart

D) Pictogram