11+ Mathematics Problem Solving 1 — Questions and Answers
Question 1: A shop sells apples at 35p each. How much change would you get from £5 if you bought 12 apples?
- £0.60
- £0.80 (Correct answer)
- £0.70
- £0.90
Correct answer: £0.80
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, ?
- 35
- 46
- 47 (Correct answer)
- 45
Correct answer: 47
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?
- 54 cm²
- 72 cm² (Correct answer)
- 36 cm²
- 108 cm²
Correct answer: 72 cm²
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?
- 40
- 53.33 (Correct answer)
- 45
- 80
Correct answer: 53.33
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?
- 1 hour 25 minutes
- 1 hour 35 minutes (Correct answer)
- 1 hour 45 minutes
- 2 hours 25 minutes
Correct answer: 1 hour 35 minutes
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.
Question 6: A bag contains 3 red balls, 5 blue balls, and 2 green balls. What is the probability of picking a blue ball?
- 1/2 (Correct answer)
- 3/10
- 1/5
- 2/5
Correct answer: 1/2
Total balls = 3 + 5 + 2 = 10. Blue balls = 5. Probability = 5/10 = 1/2.
11+ Mathematics Problem Solving 1
A shop sells apples at 35p each.
How much change would you get from £5 if you bought 12 apples?