11+ Mathematics Problem Solving

Question 1

A shop sells apples at 35p each. How much change would you get from £5 if you bought 12 apples?

Accepted Answer

£0.80

Answer

12 apples × 35p = £4.20. Change from £5: £5.00 - £4.20 = £0.80.

Question 2

What is the next number in the sequence: 2, 5, 11, 23, ?

Accepted Answer

47

Answer

Each number is doubled and then 1 is added: 2×2+1=5, 5×2+1=11, 11×2+1=23, 23×2+1=47.

Question 3

A rectangle has a perimeter of 36 cm. If the length is twice the width, what is the area?

Accepted Answer

72 cm²

Answer

Let width = w. Length = 2w. Perimeter = 2(w + 2w) = 6w = 36, so w = 6 cm. Length = 12 cm. Area = 6 × 12 = 72 cm².

Question 4

If 3/4 of a number is 60, what is 2/3 of the same number?

Accepted Answer

53.33

Answer

3/4 of the number = 60, so the number = 60 × 4/3 = 80. Then 2/3 of 80 = 160/3 ≈ 53.33.

Question 5

A train departs at 09:45 and arrives at 11:20. How long is the journey?

Accepted Answer

1 hour 35 minutes

Answer

From 09:45 to 11:20: 09:45 to 10:45 = 1 hour, 10:45 to 11:20 = 35 minutes. Total = 1 hour 35 minutes.

11+ Practice Test