GCSE maths Foundation questions, with worked answers

Where the Foundation marks are

Ofqual sets how much each area is worth: number 25%, ratio, proportion and rates of change 25%, algebra 20%, geometry 15%, and probability and statistics 15%. Spend your practice time in roughly the same proportions. For exam dates, the formula sheet and grade boundaries, see the GCSE Maths guide.

Number

Question 1: work out 3/5 of 45. Answer: divide by the bottom, multiply by the top: 45 ÷ 5 = 9, then 9 × 3 = 27.

Question 2: a jacket costs £80. In a sale it is reduced by 15%. What is the sale price? Answer: 10% of £80 is £8 and 5% is £4, so 15% is £12. The sale price is £80 − £12 = £68. On a calculator paper, 80 × 0.85 = 68 does it in one step.

Ratio and proportion

Question 3: share £64 in the ratio 3 : 5. Answer: there are 3 + 5 = 8 parts, so one part is £64 ÷ 8 = £8. The shares are 3 × £8 = £24 and 5 × £8 = £40. Check: £24 + £40 = £64.

Question 4: a pack of 6 rolls costs £1.80 and a pack of 10 costs £2.80. Which is better value? Answer: find the price of one roll: £1.80 ÷ 6 = 30p, and £2.80 ÷ 10 = 28p. The pack of 10 is better value. Always say which, with your working.

Algebra

Question 5: solve 5x − 7 = 18. Answer: add 7 to both sides: 5x = 25. Divide by 5: x = 5. Check: 5 × 5 − 7 = 18.

Expanding brackets comes up on every Foundation paper. Try one from our Algebra course and press Mark.

Geometry

Question 6: find the angle x in this triangle.

Answer: x = 180° − 62° − 47° = 71°. If the question asks for a reason, write "angles in a triangle add up to 180°".

Question 7: a trapezium has parallel sides of 6 cm and 10 cm, 4 cm apart. Find its area. Answer: the formula is on the sheet: ½(a + b)h = ½ × (6 + 10) × 4 = 32 cm². Remember the units are squared for area.

Probability and statistics

Question 8: find the mean of 4, 7, 9, 6 and 9. Answer: add them to get 35, then divide by how many there are: 35 ÷ 5 = 7. The mode is 9 and the median, from 4, 6, 7, 9, 9, is 7. Check more in the Mean, Median and Mode Calculator.

Mistakes these questions are built to catch

• Finding the discount but not the sale price. Read what the question asks for.
• Dividing by 3 or 5 in a ratio instead of the total number of parts.
• Comparing best buys without a unit price. Work out the cost of one item each time.
• Forgetting to put numbers in order before finding the median.
• Missing units, especially cm² for area.

A new Foundation paper every day

For more GCSE maths Foundation questions, sit today's GCSE Maths Foundation paper. If your mocks are coming up, the GCSE Maths mocks guide shows how to sit and grade a full paper at home.

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