IGCSE Maths Core Paper 1: 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 | 4827 ≈ 4800 | 1 | B1 the right answer: 4827 ≈ 4800 | Solved step by step · Learn it |
| 2 | 2320 | 2 | M1 Make the bottoms the same A1 the right answer: 23/20 | Solved step by step · Learn it |
| 3(a) | 38 | 1 | B1 the right answer: 3/8 | Solved step by step · Learn it |
| 3(b) | 35% | 1 | B1 the right answer: 35% | Solved step by step · Learn it |
| 4 | 9 | 2 | M1 Find 10% A1 the right answer: 9 | Solved step by step · Learn it |
| 5 | 32 and 40 | 2 | M1 Count the parts A1 the right answer: 32 and 40 | Solved step by step · Learn it |
| 6(a) | 3x + 4y | 2 | M1 Group like terms A1 the right answer: 3x + 4y | Solved step by step · Learn it |
| 6(b) | 6x − 15 | 1 | B1 the right answer: 6x − 15 | Solved step by step · Learn it |
| 6(c) | 3(2x + 5) | 1 | B1 the right answer: 3(2x + 5) | Solved step by step · Learn it |
| 7 | x = 6 | 2 | M1 Remove the + 7 A1 the right answer: x = 6 | Solved step by step · Learn it |
| 8 | x = 8 | 3 | M1 Open the brackets M1 Get x on one side A1 the right answer: x = 8 | Solved step by step · Learn it |
| 9 | 23 | 2 | M1 Put the numbers in A1 the right answer: 23 | Solved step by step · Learn it |
| 10 | an = 4n + 3 | 2 | M1 Find the difference A1 the right answer: a_n = 4n + 3 | Solved step by step · Learn it |
| 11(a) | x = 62 | 1 | B1 the right answer: x = 62 | Solved step by step · Learn it |
| 11(b) | x = 57 | 2 | M1 Use the angle fact A1 the right answer: x = 57 | Solved step by step · Learn it |
| 12(a) | sum = 720° | 1 | B1 the right answer: sum = 720° | Solved step by step · Learn it |
| 12(b) | one angle = 45° | 2 | M1 Walk around the shape A1 the right answer: one angle = 45° | Solved step by step · Learn it |
| 13 | A = 42 cm2 | 2 | M1 Half of a rectangle A1 the right answer: A = 42 cm^2 | Solved step by step · Learn it |
| 14 | A = 32 cm2 | 2 | M1 Two make a parallelogram A1 the right answer: A = 32 cm^2 | Solved step by step · Learn it |
| 15 | V = 60 cm3 | 2 | M1 Length × width × height A1 the right answer: V = 60 cm^3 | Solved step by step · Learn it |
| 16 | P(more than 4) = 13 | 1 | B1 the right answer: P(more than 4) = 1/3 | Solved step by step · Learn it |
| 17(a) | mean = 6 | 2 | M1 Add them all A1 the right answer: mean = 6 | Solved step by step · Learn it |
| 17(b) | median = 6.5 | 1 | B1 the right answer: median = 6.5 | Solved step by step · Learn it |
| 17(c) | range = 6 | 1 | B1 the right answer: range = 6 | Solved step by step · Learn it |
| 18 | 4.5 × 104 | 1 | B1 the right answer: 4.5 × 10^4 | Solved step by step · Learn it |
| 19 | m = 3 | 2 | M1 Plot the points A1 the right answer: m = 3 | Solved step by step · Learn it |
| 20 | P' = (3, −2) | 1 | B1 the right answer: P' = (3, −2) | Solved step by step · Learn it |
| 21 | A ∩ B = {6, 12} | 1 | B1 the right answer: A ∩ B = {6, 12} | Solved step by step · Learn it |
| 22 | x < 5 | 2 | M1 Remove the − 4 A1 the right answer: x < 5 | Solved step by step · Learn it |
| 23(a) | x7 | 1 | B1 the right answer: x^7 | Solved step by step · Learn it |
| 23(b) | x6 | 1 | B1 the right answer: x^6 | Solved step by step · Learn it |
| 24 | t = v − ua | 2 | M1 t on the left A1 the right answer: t = (v − u)/(a) | Solved step by step · Learn it |
| 25(a) | 360 = 23 × 32 × 5 | 2 | M1 Make a factor tree A1 the right answer: 360 = 2^3 × 3^2 × 5 | Solved step by step · Learn it |
| 25(b) | GCF(24, 36) = 12 | 2 | M1 List the factors A1 the right answer: GCF(24, 36) = 12 | Solved step by step · Learn it |
| 25(c) | LCM(6, 8) = 24 | 1 | B1 the right answer: LCM(6, 8) = 24 | Solved step by step · Learn it |
| 26 | c = 10 | 2 | M1 Name the sides A1 the right answer: c = 10 | Solved step by step · Learn it |
| 27 | (x, y) = (6, 4) | 3 | M1 Add the equations M1 Find x A1 the right answer: (x, y) = (6, 4) | Solved step by step · Learn it |
| 28 | x = 50 | 1 | B1 the right answer: x = 50 | Solved step by step · Learn it |
| 29 | $250 = €200 | 2 | M1 Write the rate A1 the right answer: $250 = €200 | Solved step by step · Learn it |
| 30 | 20% | 2 | M1 Find the change A1 the right answer: 20% | Solved step by step · Learn it |
| 31 | sale price: $60 | 2 | M1 Find the discount A1 the right answer: sale price: $60 | Solved step by step · Learn it |
| 32 | triangle ABC: AB = 7 cm, BC = 5 cm, AC = 6 cm | 2 | M1 AB = 7 cm drawn, arcs of radius 5 cm from B and 6 cm from A A1 triangle complete with the construction arcs shown | Solved step by step · Learn it |
| 33 | x2 + 8x + 15 | 2 | M1 Split the first bracket A1 the right answer: x^2 + 8x + 15 | Solved step by step · Learn it |
| 34 | 7 play neither | 2 | M1 Draw the Venn diagram A1 the right answer: 7 play neither | Solved step by step · Learn it |
| 35 | P' = (−3, −1) | 1 | B1 the right answer: P' = (−3, −1) | Solved step by step · Learn it |
| 36 | x = 7 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 7 | Solved step by step · Learn it |
| 37 | 5°C | 1 | B1 the right answer: 5°C | Solved step by step · Learn it |
| 38 | 0.12 | 1 | B1 the right answer: 0.12 | Solved step by step · Learn it |
| 39 | 3.476 ≈ 3.5 | 1 | B1 the right answer: 3.476 ≈ 3.5 | 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.