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IGCSE Mathematics 0580 Paper 1 (Core) Practice Paper | 56 marks, 1 hour, no calculator
IGCSE Mathematics 0580 Paper 1 (Core)
IGCSE Mathematics 0580 Paper 1 (Core) practice paper: 37 questions, 56 marks, 1 hour, no calculator allowed. Covers number, algebra, shape and space, and data. Full answer key with short worked steps, question and answer PDFs ready to download.
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Paper details Level: IGCSE (Core) ｜ Topics: number, algebra, shape and space, data ｜ Time: 1 hour ｜ Marks: 56 ｜ Questions: 37 ｜ No calculator
Section A — Number (16 marks)
Answer all questions. Calculators must not be used.
| # | Question | Answer and marking notes |
|---|---|---|
| 1 | Work out 47 + 68 − 29. | 47 + 68 = 115, 115 − 29 = 86 |
| 2 | Work out 6.4 × 5. | 6 × 5 = 30, 0.4 × 5 = 2, so 32 |
| 3 | Work out 3/4 + 5/8. Give your answer as a mixed number in its simplest form. | 6/8 + 5/8 = 11/8 = 1 3/8 (11 eighths = 1 whole and 3 eighths) |
| 4 | Write 0.35 as a fraction in its simplest form. | 35/100 = 7/20 |
| 5 | Find 15% of 240. | 10% = 24, 5% = 12, so 15% = 36 |
| 6 | A jacket costs $80. In a sale the price is reduced by 25%. Find the sale price. | 25% of $80 = $20, so $80 − $20 = $60 |
| 7 | Share $84 in the ratio 3 : 4. | 3 + 4 = 7 parts, $84 ÷ 7 = $12, so $36 and $48 |
| 8 | Work out the cube root of 216. | 6 × 6 × 6 = 216, so the answer is 6 |
| 9 | Write 4 786 correct to the nearest 100. | The tens digit is 8, so round up: 4800 |
| 10 | Work out 2³ + 3². | 2³ = 8 and 3² = 9, so 8 + 9 = 17 |
| 11 | Find the lowest common multiple (LCM) of 12 and 18. | Multiples of 18: 18, 36 …; 36 is also a multiple of 12, so LCM = 36 |
| 12 | Write 45 as a product of its prime factors. Give your answer in index form. | 45 = 3 × 3 × 5 = 3² × 5 |
| 13 | Write 3/8 as a decimal. | 3 ÷ 8 = 0.375 |
Section B — Algebra (15 marks)
Simplify and solve. Show your working.
| # | Question | Answer and marking notes |
|---|---|---|
| 14 | Simplify 5a + 3b − 2a + b. | 5a − 2a = 3a and 3b + b = 4b, so 3a + 4b |
| 15 | Expand 3(2x − 5). | 3 × 2x = 6x, 3 × (−5) = −15, so 6x − 15 |
| 16 | Solve 4x + 7 = 31. | 4x = 31 − 7 = 24, so x = 6 |
| 17 | Solve 3(x − 2) = 18. | x − 2 = 18 ÷ 3 = 6, so x = 8 |
| 18 | The first four terms of a sequence are 3, 7, 11, 15. (a) Write down the next term. (b) Find the nth term of the sequence. | (a) The difference is 4, so the next term is 19. (b) nth term = 4n − 1 |
| 19 | Work out the value of v when t = 5, given v = 3t² − 4. | v = 3 × 25 − 4 = 75 − 4 = 71 |
| 20 | Make x the subject of the formula y = 5x − 3. | 5x = y + 3, so x = (y + 3) ÷ 5 |
Section C — Shape and space (13 marks)
Diagrams are not drawn to scale.
| # | Question | Answer and marking notes |
|---|---|---|
| 21 | Two angles of a triangle are 48° and 65°. Work out the third angle. | 180° − 48° − 65° = 67° |
| 22 | Two angles lie on a straight line. One of them is 132°. Work out the other angle. | 180° − 132° = 48° |
| 23 | A rectangle measures 12 cm by 7 cm. Work out its area. | 12 × 7 = 84 cm² |
| 24 | A triangle has base 14 cm and height 9 cm. Work out its area. | (14 × 9) ÷ 2 = 63 cm² |
| 25 | A circle has radius 6 cm. Work out its circumference. Use π = 3.14. | 2 × 3.14 × 6 = 37.68 cm |
| 26 | A cuboid measures 8 cm by 5 cm by 4 cm. Work out its volume. | 8 × 5 × 4 = 160 cm³ |
| 27 | A right-angled triangle has two shorter sides of length 6 cm and 8 cm. Work out the length of the hypotenuse. | 6² + 8² = 36 + 64 = 100, and the square root of 100 is 10, so 10 cm |
| 28 | A regular pentagon is shown. (a) Work out the sum of its interior angles. (b) Work out the size of each exterior angle. | (a) (5 − 2) × 180° = 540° (b) 360° ÷ 5 = 72° |
| 29 | A map has a scale of 1 : 25 000. A straight road is 4 cm long on the map. Work out the real length of the road in kilometres. | 4 × 25 000 = 100 000 cm = 1 000 m = 1 km |
Section D — Data and probability (12 marks)
Give probabilities as fractions in their simplest form.
| # | Question | Answer and marking notes |
|---|---|---|
| 30 | The number of goals scored in five matches were 12, 15, 9, 18 and 6. Work out the mean. | (12 + 15 + 9 + 18 + 6) ÷ 5 = 60 ÷ 5 = 12 |
| 31 | Here are eight test scores: 3, 7, 7, 9, 11, 14. Write down (a) the mode, (b) the median, (c) the range. | (a) mode = 7 (b) (7 + 9) ÷ 2 = 8 (c) 14 − 3 = 11 |
| 32 | A fair dice is rolled once. Work out the probability of getting an even number. | Even numbers are 2, 4, 6, so P = 3/6 = 1/2 |
| 33 | A bag contains 4 red and 6 blue counters. One counter is taken at random. Work out the probability that it is blue. | 6 out of 10 counters are blue, so P = 6/10 = 3/5 |
| 34 | In a pie chart, one category is 25% of the total. Work out the angle of its sector. | 25% of 360° = 90° |
| 35 | In a class of 30 students there are 18 girls. 10 girls and 5 boys walk to school; the rest travel by bus. Copy and complete the two-way table. | Girls by bus = 18 − 10 = 8; boys = 30 − 18 = 12; boys by bus = 12 − 5 = 7; column totals 10 + 5 = 15 and 8 + 7 = 15 |
| 36 | The probability that it rains on a certain day is 0.35. Work out the probability that it does not rain. | 1 − 0.35 = 0.65 |
| 37 | A scatter graph of height against weight for 20 students shows points rising from left to right. Describe the correlation and what it means. | Positive correlation: taller students tend to weigh more |
A TutorZone practice paper; original questions and passages, not publisher material.
