Free Surds questions for IGCSE Mathematics (0580), Extended tier (Supplement content), part of Number. Each question has the answer and the marking points an examiner would look for.
Generate a full Surds worksheet →All Number questionsWrite the recurring decimal 0.2757575… (the digits 75 recur) as a fraction in its simplest form.
Show all your working.
| Part | Answer and marking points | Marks |
|---|---|---|
| 91330 e.g. 1000x = 275.7575… and 10x = 2.7575… M1 990x = 275 − 2 = 273 M1 91330 A1 | 3 |
Expand and simplify (3 + 2√7)2.
Hence, or otherwise, simplify √(37 + 12√7).
Rationalise the denominator and simplify −193 + 2√7.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 37 + 12√7 three or four correct terms M1 37 + 12√7 A1 | 2 |
| (b) | 3 + 2√7 3 + 2√7 B1 | 1 |
| (c) | 3 − 2√7 multiply by 3 − 2√73 − 2√7 M1 denominator −19 A1 3 − 2√7 A1 | 3 |
Without using a calculator, work out 116 ÷ 312.
Show all your working and give your answer as a mixed number in its simplest form.
| Part | Answer and marking points | Marks |
|---|---|---|
| 13 76 and 72 seen B1 76 × 27 M1 13 A1 | 3 |
Write 5 + √235 − √23 in the form a + b√23, where a and b are integers.
Show all your working.
| Part | Answer and marking points | Marks |
|---|---|---|
| 24 + 5√23 × 5 + √235 + √23 M1 numerator 48 + 10√23, denominator 2 A1 24 + 5√23 A1 | 3 |
Write the recurring decimal 0.6151515… (the digits 15 recur) as a fraction in its simplest form.
Show all your working.
| Part | Answer and marking points | Marks |
|---|---|---|
| 203330 e.g. 1000x = 615.1515… and 10x = 6.1515… M1 990x = 615 − 6 = 609 M1 203330 A1 | 3 |
Expand and simplify (5 + 3√2)2.
Hence, or otherwise, simplify √(43 + 30√2).
Rationalise the denominator and simplify 75 + 3√2.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 43 + 30√2 three or four correct terms M1 43 + 30√2 A1 | 2 |
| (b) | 5 + 3√2 5 + 3√2 B1 | 1 |
| (c) | 5 − 3√2 multiply by 5 − 3√25 − 3√2 M1 denominator 7 A1 5 − 3√2 A1 | 3 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in