IGCSE Maths Core Paper 3: mark scheme
Every answer, how the marks are given, a link to its step-by-step solution and to the lesson that teaches it
M = a method mark (right working), A = an accuracy mark (the right answer, after the method), B = a mark on its own. A right answer gets all the marks of the part. A wrong answer: a mark for each right step of the working.
| Part | Answer | Marks | How the marks are given | Solution |
|---|---|---|---|---|
| 1(a) | 3.14159 ≈ 3.14 | 1 | B1 the right answer: 3.14159 ≈ 3.14 | Solved step by step · Learn it |
| 1(b) | 0.006284 ≈ 0.0063 | 1 | B1 the right answer: 0.006284 ≈ 0.0063 | Solved step by step · Learn it |
| 2 | 7 | 1 | B1 the right answer: 7 | Solved step by step · Learn it |
| 3 | 84 | 1 | B1 the right answer: 84 | Solved step by step · Learn it |
| 4 | x = 180 | 2 | M1 Find what we know A1 the right answer: x = 180 | Solved step by step · Learn it |
| 5 | A ≈ $2249.73 | 3 | M1 Read the numbers M1 Find the rule A1 the right answer: A ≈ $2249.73 | Solved step by step · Learn it |
| 6 | $350 = €322 | 2 | M1 Write the rate A1 the right answer: $350 = €322 | Solved step by step · Learn it |
| 7 | 24 | 2 | M1 Write the percent as a fraction A1 the right answer: 24 | Solved step by step · Learn it |
| 8 | density = 13 g/cm³ | 2 | M1 Write the rule A1 the right answer: density = 13 g/cm³ | Solved step by step · Learn it |
| 9 | 3.5 hours | 2 | M1 Find what we know A1 the right answer: 3.5 hours | Solved step by step · Learn it |
| 10(a) | A ≈ 132.67 cm2 | 2 | M1 Use the rule A1 the right answer: A ≈ 132.67 cm^2 | Solved step by step · Learn it |
| 10(b) | C ≈ 37.68 cm | 2 | M1 Use the rule A1 the right answer: C ≈ 37.68 cm | Solved step by step · Learn it |
| 11 | arc = 2π ≈ 6.28 cm | 2 | M1 What part of the circle A1 the right answer: arc = 2π ≈ 6.28 cm | Solved step by step · Learn it |
| 12 | V ≈ 502.4 cm3 | 2 | M1 Circle times height A1 the right answer: V ≈ 502.4 cm^3 | Solved step by step · Learn it |
| 13(a) | c ≈ 10.3 | 2 | M1 Name the sides A1 the right answer: c ≈ 10.3 | Solved step by step · Learn it |
| 13(b) | b = 12 | 2 | M1 Name the sides A1 the right answer: b = 12 | Solved step by step · Learn it |
| 14(a) | x ≈ 6.9 | 2 | M1 Name the sides A1 the right answer: x ≈ 6.9 | Solved step by step · Learn it |
| 14(b) | θ ≈ 35.0° | 2 | M1 Name the sides A1 the right answer: θ ≈ 35.0° | Solved step by step · Learn it |
| 15 | x ≈ 15.6 m | 2 | M1 Name the sides A1 the right answer: x ≈ 15.6 m | Solved step by step · Learn it |
| 16 | mean ≈ 17.5 | 3 | M1 Find the midpoints M1 Multiply m × f A1 the right answer: mean ≈ 17.5 | Solved step by step · Learn it |
| 17(a) | P(tails and even) = 14 | 2 | M1 Independent or not A1 the right answer: P(tails and even) = 1/4 | Solved step by step · Learn it |
| 17(b) | ≈ 150 | 1 | B1 the right answer: ≈ 150 | Solved step by step · Learn it |
| 18(a) | x = 5 | 3 | M1 Get x on one side M1 Remove the − 3 A1 the right answer: x = 5 | Solved step by step · Learn it |
| 18(b) | 17 | 2 | M1 Put the numbers in A1 the right answer: 17 | Solved step by step · Learn it |
| 19 | 4x(2x − 3) | 2 | M1 Take out the common factor A1 the right answer: 4x(2x − 3) | Solved step by step · Learn it |
| 20 | a30 = 121 | 2 | M1 Find the difference A1 the right answer: a_30 = 121 | Solved step by step · Learn it |
| 21(a) | y = 3x + 1 | 3 | M1 Find the slope M1 Find b A1 the right answer: y = 3x + 1 | Solved step by step · Learn it |
| 21(b) | M = (2, 5) | 2 | M1 Plot the points A1 the right answer: M = (2, 5) | Solved step by step · Learn it |
| 22 | (−1, −5), (0, −3), (1, −1) | 3 | M1 table of values right (−5, −3, −1, 1, 3) M1 the points plotted A1 a ruled straight line through them | Solved step by step · Learn it |
| 23 | 26 km | 2 | M1 Multiply both sides A1 the right answer: 26 km | Solved step by step · Learn it |
| 24(a) | P' = (2, 3) | 1 | B1 the right answer: P' = (2, 3) | Solved step by step · Learn it |
| 24(b) | P' = (6, 9) | 1 | B1 the right answer: P' = (6, 9) | Solved step by step · Learn it |
| 25 | 1.28 × 109 | 2 | M1 Group the parts A1 the right answer: 1.28 × 10^9 | Solved step by step · Learn it |
| 26 | 1 : 5 | 2 | M1 Same units A1 the right answer: 1 : 5 | Solved step by step · Learn it |
| 27 | 23.5 ≤ length < 24.5 | 2 | M1 Find the step A1 the right answer: 23.5 ≤ length < 24.5 | Solved step by step · Learn it |
| 28(a) | x = 115 | 2 | M1 Find the angle sum A1 the right answer: x = 115 | Solved step by step · Learn it |
| 28(b) | sides = 9 | 2 | M1 Find the exterior angle A1 the right answer: sides = 9 | Solved step by step · Learn it |
| 29 | x = 17.5 | 2 | M1 Match the sides A1 the right answer: x = 17.5 | Solved step by step · Learn it |
| 30 | P(both) = 15 | 2 | M1 Start in the middle A1 the right answer: P(both) = 1/5 | Solved step by step · Learn it |
| 31 | 15% | 2 | M1 Find the change A1 the right answer: 15% | Solved step by step · Learn it |
| 32 | 80, 120 and 160 | 2 | M1 Count the parts A1 the right answer: 80, 120 and 160 | Solved step by step · Learn it |
Estimated grade
Add up your marks out of 80. This is our rough guide for one paper, not an official boundary: real boundaries change every year. Core papers lead to grades C to G, Extended papers to A* to E.
| Grade | Marks from |
|---|---|
| C | 52 |
| D | 42 |
| E | 32 |
| F | 22 |
| G | 13 |
| U | 0 |
Steply practice papers are our own questions in the style of the Cambridge IGCSE Mathematics (0580) papers; they are not official and not endorsed by Cambridge University Press & Assessment. Official past papers: your school or the Cambridge website.