1. Write √72 in the form a√2.
- A6√2
- B36√2
- C3√2
- D12√2
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Answer: A. 72 = 36 × 2, so √72 = √36 × √2 = 6√2. The 36 must be square-rooted when it comes out of the root.
GCSE Maths (AQA) chapter 1: Number MCQs with answers
By Team Megalecture · Updated 4 Nov 2026
46 exam-style questions on Number, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.
46 questions · 5 topics · 10 per test
What chapter 1 covers
- N1–N5 Structure and calculation 9 questions
- N6–N7, N9 Powers, roots, indices and standard form 11 questions
- N8 Surds and exact calculation 9 questions
- N10–N12 Fractions, decimals and percentages 8 questions
- N13–N16 Measures, estimation and bounds 9 questions
Ten Number questions with answers
Try each one, then open the answer. These ten stay the same; the test draws new ones every time.
2. Rationalise the denominator of 4/(3 − √5), simplifying fully.
- A(12 + 4√5)/14
- B3 − √5
- C3 + √5
- D12 + 4√5
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Answer: C. Multiply top and bottom by 3 + √5: the denominator becomes 9 − 5 = 4, so 4(3 + √5)/4 = 3 + √5. Using 9 + 5 in the denominator is the common slip.
3. Ali and Bina share some money. Ali gets 2/7 of the money and Bina gets the rest. What is the ratio of Ali's share to Bina's share?
- A2 : 7
- B5 : 2
- C7 : 5
- D2 : 5
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Answer: D. Bina gets 5/7, so Ali : Bina = 2/7 : 5/7 = 2 : 5. 2 : 7 compares Ali with the total.
4. Write 360 as a product of its prime factors.
- A23 × 32 × 5
- B22 × 32 × 10
- C23 × 45
- D22 × 33 × 5
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Answer: A. 360 = 8 × 45 = 23 × 32 × 5. 10 and 45 are not prime, and 22 × 33 × 5 = 540.
5. Which statement is true?
- A2/3 < 0.67
- B−5 > −3
- C0.6 ≠ 3/5
- D(−0.5)2 < 0
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Answer: A. 2/3 = 0.666…, which is less than 0.67. −5 is below −3, 0.6 equals 3/5, and a square is never negative.
6. Expand and simplify (3 + √5)(3 − √5).
- A14
- B9 − √5
- C9 − 5√5
- D4
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Answer: D. This is a difference of two squares: 32 − (√5)2 = 9 − 5 = 4. The middle terms +3√5 and −3√5 cancel.
7. A bus on route A leaves the station every 12 minutes and a bus on route B every 18 minutes. Both leave together at 9:00 am. When do they next leave together?
- A9:06 am
- B12:36 pm
- C9:30 am
- D9:36 am
Show answer
Answer: D. Next time together is the LCM of 12 and 18, which is 36 minutes, so 9:36 am. 6 is the HCF, and 12 × 18 = 216 is a common multiple but not the lowest.
8. Write 0.444… (0.4 recurring) as a fraction.
- A4/9
- B4/10
- C4/99
- D9/4
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Answer: A. Let x = 0.444…; then 10x = 4.444…, so 9x = 4 and x = 4/9. 4/10 is only 0.4, which stops.
9. Work out (4 × 105) × (6 × 10−2). Give your answer in standard form.
- A2.4 × 104
- B24 × 103
- C2.4 × 103
- D2.4 × 10−10
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Answer: A. 4 × 6 = 24 and 105 × 10−2 = 103, so 24 × 103 = 2.4 × 104. 24 × 103 is the right value but not standard form, because 24 is not between 1 and 10.
10. Work out the value of 163/4.
- A12
- B8
- C64
- D6
Show answer
Answer: B. Take the fourth root first: 4√16 = 2, then cube: 23 = 8. 12 comes from multiplying 16 by 3/4.
Read the notes for this chapter
Ways to practise this chapter
- Chapter test. Ten questions from Number, drawn fresh each time, about ten minutes.
- Practice mode. The right answer and the explanation after every question, with no clock. Exam mode keeps the marks until the end and runs a timer.
- Hints. One tap for a nudge, a second to remove two wrong options.
- My mistakes. Every question you get wrong is kept, and leaves the list once you get it right.
- Formula sheet. All GCSE Maths (AQA) rules on one page.
Number: questions students ask
How many Number MCQs are there?
46, each with the answer and a short explanation, across 5 topics: N1–N5 Structure and calculation, N6–N7, N9 Powers, roots, indices and standard form, N8 Surds and exact calculation, N10–N12 Fractions, decimals and percentages, N13–N16 Measures, estimation and bounds. Every chapter test draws ten of them, so you can take it many times.
Is the GCSE Maths (AQA) chapter 1 test free?
Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.
How is the chapter test marked?
The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.