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IGCSE Mathematics 0580 Paper 2 (Extended) Practice Paper | 70 marks, 1 hour 30 minutes, calculator allowed
IGCSE Mathematics 0580 Paper 2 (Extended)
IGCSE Mathematics 0580 Paper 2 (Extended) practice paper: 20 questions, 70 marks, 1 hour 30 minutes, calculator allowed. Covers number and algebra, shape and space, and data and probability, with a full answer key and worked steps; question and answer PDFs download instantly. All questions original.
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Paper details Level: IGCSE (Extended) ｜ Topics: number, algebra, shape and space, data ｜ Time: 1 hour 30 minutes ｜ Marks: 70 ｜ Questions: 20 ｜ Calculator allowed
Section A — Number and algebra (28 marks)
Answer all questions. Show your working.
| # | Question | Answer and marking notes |
|---|---|---|
| 1 | Expand and simplify 5(2x − 3) − 2(x − 4). | 10x − 15 − 2x + 8 = 8x − 7 |
| 2 | Solve 3x + 7 = 4x − 5. | 3x + 7 = 4x − 5 gives x = 12; check 3 × 12 + 7 = 43 = 4 × 12 − 5 |
| 3 | In a sale a jacket is reduced by 15 per cent and now costs $680. Work out the original price. | 680 ÷ 0.85 = $800 |
| 4 | Expand and simplify (x + 6)(x − 4). | x² + 2x − 24 |
| 5 | Factorise completely 6x² + 15x. | 3x(2x + 5) |
| 6 | y is directly proportional to x². When x = 7, y = 98. Find y when x = 11. | k = 98 ÷ 49 = 2, so y = 2 × 121 = 242 |
| 7 | Work out (4.2 × 10⁵) × (3.5 × 10⁻³), giving your answer in standard form. | 14.7 × 10² = 1.47 × 10³ |
| 8 | $4,500 is invested at 3.2 per cent per year compound interest. Find the value after 3 years, to the nearest cent. | 4500 × 1.032³ = $4,945.97 |
| 9 | Simplify (x² − 9) ÷ (x² + x − 12). | (x − 3)(x + 3) ÷ (x − 3)(x + 4) = (x + 3)/(x + 4) for x ≠ 3 |
Section B — Shape and space (23 marks)
Give units with your answers unless told otherwise.
| # | Question | Answer and marking notes |
|---|---|---|
| 10 | A right-angled triangle has legs 9 cm and 12 cm. Work out the length of the hypotenuse and the area of the triangle. | hypotenuse = √(81 + 144) = 15 cm; area = ½ × 9 × 12 = 54 cm² |
| 11 | A sector of a circle of radius 7 cm has angle 120°. Using π = 3.142, work out the arc length. | 120/360 × 2 × 3.142 × 7 = 14.66 cm |
| 12 | A cone has base radius 6 cm and height 10 cm. Using π = 3.142, work out its volume. | ⅓ × 3.142 × 36 × 10 = 377.04 cm³ |
| 13 | Two triangles are similar. The area of the smaller is 50 cm² and the ratio of corresponding lengths is 5 : 7. Find the area of the larger triangle. | 50 × 49 ÷ 25 = 98 cm² |
| 14 | A ladder 6.5 m long leans against a vertical wall with its foot 2.5 m from the wall. Work out the height reached and the angle the ladder makes with the ground. | height = √(42.25 − 6.25) = 6.0 m; angle = cos⁻¹(2.5 ÷ 6.5) = 67.4° |
| 15 | Work out the interior angle of a regular 12-sided polygon. | (12 − 2) × 180 ÷ 12 = 150° |
Section C — Data and probability (19 marks)
Probabilities may be given as fractions or decimals.
| # | Question | Answer and marking notes |
|---|---|---|
| 16 | Five test scores are 12, 15, 9, 18 and 21. Work out the mean score. | total 75 ÷ 5 = 15 |
| 17 | The ages of 10 club members are 3, 5, 7, 8, 8, 10, 12, 14, 15 and 18. Work out the median age. | median = (8 + 10) ÷ 2 = 9 |
| 18 | A bag holds 5 red, 3 blue and 2 green counters. One counter is taken at random. (a) Work out the probability that it is not red. (b) Two counters are then taken without replacement; work out the probability that both are red. | (a) 5 of the 10 counters are not red, so 1/2. (b) 5/10 × 4/9 = 2/9 ≈ 0.222 |
| 19 | A scatter graph of 20 students plots height against shoe size, with the points rising from left to right. Describe the correlation and say what it means. | Positive correlation: taller students tend to have larger shoe sizes |
| 20 | The probability that a component is faulty is 0.04. In a batch of 500 components, work out the expected number of faulty components. | 500 × 0.04 = 20 |
A TutorZone practice paper; original questions and passages, not publisher material.
