Free AQA GCSE Mathematics (8300) Exam Questions and Answers
AQA GCSE Mathematics (8300) is AQA's GCSE Mathematics qualification, specification 8300, taken in England. It is sat at Foundation or Higher tier. The questions here come from AQA's published question papers from June 2017 to June 2025, plus its specimen papers, with answers and marking guidance taken from AQA's own mark schemes. Written-answer questions let you work out your answer and then reveal what the mark scheme accepts; diagrams, graphs and source material appear with the questions that use them.
If you searched for AQA GCSE Mathematics (8300) dumps, an ExamTopics discussion or a free PDF, this is the question bank for it: practice questions with verified answers and explanations, a timed practice test and updates whenever AQA changes the exam.
Last updated: October 14, 2026
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Question #1
Work out 1/4 + 0.5 Circle your answer.
Correct answer: C
Explanation
One independent mark for the answer 0.75 (1/4 + 0.5 = 0.25 + 0.5).
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Question #2
Which of these shapes has the most sides? Circle your answer.
Correct answer: B
Explanation
One independent mark for Octagon (8 sides).
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Question #3
Solve x – 3 = 0 Circle your answer.
Correct answer: D
Explanation
One independent mark for x = 3.
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Question #4
Work out 58 × 73
Type your answer, then reveal.
Correct answer: 4234
Explanation
Alternative method 3 (grid/lattice): method mark for at least three of the 2-digit numbers in the grid correct. Dependent method mark for a clear attempt to add each diagonal with at least one correct carrying figure. Accuracy mark for 4234. Diagonals must slope the correct way. If diagonal lines are not present it scores no method mark unless correct totals are seen around the grid. 50 × 70 + 8 × 3 (= 3524) scores no marks. In alternative method 1, a missing or mis-aligned place-holder 0 is allowed if the units digit 4 is seen in the answer. Carrying completed only once scores M1 M1dep A0.
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Question #5
500 people are asked if they drink coffee. 9/10 say Yes. 20% of the people who say Yes drink at least three cups each day. Complete the frequency tree.
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Correct answer: Drink coffee: Yes 450, No 50. At least three cups: Yes branch: 90 (at least three) and 360 (not).
Explanation
Independent mark for 450 in Drink coffee Yes. Follow through mark for 50 in Drink coffee No (500 – their 450). Follow through mark for 90 in At least three cups Yes (their 450 ÷ 5; must be truncated or rounded up to a whole number). Follow through mark for 360 in At least three cups No (their 450 – their 90; must be a positive integer). Unambiguous values elsewhere are accepted but diagram values take precedence. Do not accept probabilities (9/10, 1/10, 4/5, 1/5 or 0.9, 0.1, 0.8, 0.2). If relative frequencies are seen (e.g. 400/500, 100/500, 80/400, 320/400), the first mark is withheld.
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Question #6
500 people are asked if they drink coffee. 9/10 say Yes. 20% of the people who say Yes drink at least three cups each day. What fraction of the 500 people drink at least three cups of coffee each day? Give your answer in its simplest form.
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Correct answer: 9/50
Explanation
Method 1: first mark for their 90/500 (or partially simplified, or equivalent such as a decimal; follow through or correct). Second mark for their fraction fully simplified; 9/50 scores both marks. Method 2: method mark for 9/10 × 1/5 (or 0.9 × 0.2 or 0.18), accuracy mark for 9/50. 90/500 = 18/100 scores first mark only. 45/250 scores first mark only. Do not accept 18% for the first mark. Follow through is allowed from a different value in part (a), e.g. 80/500 = 4/25.
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Question #7
By rounding each number to the nearest 10, estimate the answer to (61 × 47)/102 You must show your working.
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Correct answer: 30
Explanation
Method mark for any two of 60, 50 and 100 (e.g. 60 × 50 / 100; 60 and 50 may be implied by 3000). Accuracy mark for 30. 30 with no working scores 0. Working out 28.1… from the original values and then rounding to 30 scores 0.
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Question #8
Nadia has £5 to buy pencils and rulers. She says, “I will buy 15 pencils. Then I will buy as many rulers as possible. With my change I will buy more pencils.” How many pencils and how many rulers does she buy?
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Correct answer: 17 pencils and 12 rulers
Explanation
Method 1 (pence): 15 × 8 = 120 (method mark). 500 – 120 = 380 (dependent method mark). 380 ÷ 30 = 12(…), or build up in 30s to at least 350 (dependent method mark; one error allowed in a build up). 12 × 30 = 360 (their 12 must be rounded down or chosen from a build up) (dependent method mark). Change 380 – 360 = 20, or 500 – (360 + 120), or 360 + 8 + 8 = 376, or 496 total; their change must be between 0 and 30 (dependent method mark). Accuracy mark for 17 pencils, 12 rulers. Method 2 uses pounds: 15 × 0.08 = 1.20; 5 – 1.20 = 3.80; 3.80 ÷ 0.30 = 12; 12 × 0.30 = 3.60; change 0.20 then buying 2 more pencils at 0.08 each. Do not allow mixed units unless recovered. If no change is considered after buying rulers, maximum is 4 method marks.
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Question #9
Work out 25.68 ÷ 12
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Correct answer: 2.14
Explanation
Full marks (2) for 2.14 or equivalent (e.g. 2 7/50). One mark for an answer of the form 2.1... other than 2.14, or for 0.214, 21.4, 214 or 2140. Alternative: divide by 2, 2 and 3 in any order (or 3 and 4, or 2 and 6) using a valid method for the method mark, then 2.14 for the accuracy mark. Remainders (2 remainder 1.68) score 0. Rounding up to 26 or 30 or truncating to 25 is not accepted.
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Question #10
Work out 3/8 × 11 Give your answer as a mixed number.
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Correct answer: 4 1/8
Explanation
One independent mark for 33/8 (or an equivalent fraction). One follow-through mark for their improper fraction correctly converted to a mixed number, which needn't be simplified. Answer only of 4 1/8 scores both marks. If their first answer is a proper fraction, the second mark can't be earned. 4.125 scores the first mark only. 33 ÷ 8 alone scores 0.
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