IGCSE Maths Extended Paper 2: 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 | x = 411 | 2 | M1 Call it x A1 the right answer: x = 4/11 | Solved step by step · Learn it |
| 2(a) | 4 112 | 3 | M1 Write as fractions M1 Make the bottoms the same A1 the right answer: 4 1/12 | Solved step by step · Learn it |
| 2(b) | 125 | 3 | M1 Write as fractions M1 Flip and multiply A1 the right answer: 12/5 | Solved step by step · Learn it |
| 3(a) | 8√2 | 2 | M1 Find a square number in each A1 the right answer: 8√2 | Solved step by step · Learn it |
| 3(b) | √5 − 1 | 3 | M1 Find the partner M1 Bottom: one square take away another A1 the right answer: √5 − 1 | Solved step by step · Learn it |
| 4(a) | 9 | 1 | B1 the right answer: 9 | Solved step by step · Learn it |
| 4(b) | 14 | 1 | B1 the right answer: 1/4 | Solved step by step · Learn it |
| 4(c) | 16x12 | 2 | M1 Power of a product A1 the right answer: 16x^12 | Solved step by step · Learn it |
| 5 | 2 × 107 | 2 | M1 Group the parts A1 the right answer: 2 × 10^7 | Solved step by step · Learn it |
| 6 | upper bound = 3.8 | 2 | M1 Bounds of each number A1 the right answer: upper bound = 3.8 | Solved step by step · Learn it |
| 7(a) | (x − 3)(x + 5) | 2 | M1 Find two numbers A1 the right answer: (x − 3)(x + 5) | Solved step by step · Learn it |
| 7(b) | x = 12 or x = −3 | 3 | M1 Find two numbers M1 Split the middle A1 the right answer: x = 1/2 or x = −3 | Solved step by step · Learn it |
| 8 | x − 3x | 3 | M1 Factor the top M1 Factor the bottom A1 the right answer: (x − 3)/(x) | Solved step by step · Learn it |
| 9 | 5x − 1(x + 1)(x − 2) | 3 | M1 Find the common bottom M1 Make the bottoms the same A1 the right answer: (5x − 1)/((x + 1)(x − 2)) | Solved step by step · Learn it |
| 10 | (x, y) = (2, 3) | 3 | M1 Add the equations M1 Find x A1 the right answer: (x, y) = (2, 3) | Solved step by step · Learn it |
| 11 | −2 ≤ x < 3 | 3 | M1 Remove the + 1 M1 Remove the 2 A1 the right answer: −2 ≤ x < 3 | Solved step by step · Learn it |
| 12(a) | f(g(2)) = 3 | 2 | M1 Work out the inside A1 the right answer: f(g(2)) = 3 | Solved step by step · Learn it |
| 12(b) | f −1(x) = x + 43 | 2 | M1 Write y for f(x) A1 the right answer: f ^−1(x) = (x + 4)/(3) | Solved step by step · Learn it |
| 13(a) | f′(x) = 6x2 − 10x + 4 | 2 | M1 The rule A1 the right answer: f′(x) = 6x^2 − 10x + 4 | Solved step by step · Learn it |
| 13(b) | min (3, −8) | 4 | M1 Find f′(x) M1 Solve f′(x) = 0 M1 Find f″(x) A1 the right answer: min (3, −8) | Solved step by step · Learn it |
| 14 | an = n2 + 2n | 3 | M1 First differences M1 Second differences A1 the right answer: a_n = n^2 + 2n | Solved step by step · Learn it |
| 15(a) | 2u − v = ⟨7, −8⟩ | 2 | M1 Multiply by 2 A1 the right answer: 2u − v = ⟨7, −8⟩ | Solved step by step · Learn it |
| 15(b) | AB = b − a | 1 | B1 the right answer: AB = b − a | Solved step by step · Learn it |
| 16(a) | x = 70 | 2 | M1 Use the circle rule A1 the right answer: x = 70 | Solved step by step · Learn it |
| 16(b) | x = 70 | 1 | B1 the right answer: x = 70 | Solved step by step · Learn it |
| 16(c) | angle ACB = 65° | 2 | M1 Use the rule A1 the right answer: angle ACB = 65° | Solved step by step · Learn it |
| 17 | y = 8 | 3 | M1 Write the rule M1 Find k A1 the right answer: y = 8 | Solved step by step · Learn it |
| 18 | P(all red) = 514 | 3 | M1 Order: yes or no M1 Count all the ways A1 the right answer: P(all red) = 5/14 | Solved step by step · Learn it |
| 20(a) | P' = (−4, 2) | 1 | B1 the right answer: P' = (−4, 2) | Solved step by step · Learn it |
| 20(b) | P' = (2, 3) | 1 | B1 the right answer: P' = (2, 3) | Solved step by step · Learn it |
| 22 | (x − 3)2 − 4 | 2 | M1 Complete the square A1 the right answer: (x − 3)^2 − 4 | Solved step by step · Learn it |
| 23 | the part shaded twice | 3 | M1 y = 2x − 1 drawn as a broken line M1 y = −x + 3 drawn as a solid line A1 the right region shaded (above the first line, below the second) | Solved step by step · Learn it |
| 25 | y = −12x + 4 | 3 | M1 Slope of the given line M1 Slope of the new line A1 the right answer: y = −1/2x + 4 | Solved step by step · Learn it |
| 26 | d = 10 | 2 | M1 Plot the points A1 the right answer: d = 10 | Solved step by step · Learn it |
| 27 | large volume = 160 | 2 | M1 Length scale factor A1 the right answer: large volume = 160 | Solved step by step · Learn it |
| 28 | x = −2 − p3 − q | 3 | M1 Get the x terms on one side M1 Take x out A1 the right answer: x = (−2 − p)/(3 − q) | Solved step by step · Learn it |
| 29 | x³ − 7x − 6 | 3 | M1 Multiply the first two M1 Times the third bracket A1 the right answer: x³ − 7x − 6 | Solved step by step · Learn it |
| 30 | heights 0.5, 0.6, 0.3 | 2 | M1 class widths 10, 20 and 30 used A1 frequency densities 0.5, 0.6 and 0.3 | Solved step by step · Learn it |
| 31 | distance = 120 m | 3 | M1 Read the graph M1 Distance = area A1 the right answer: distance = 120 m | Solved step by step · Learn it |
| 32 | points 3 cm from A | 2 | M1 compasses set to 3 cm with the point at A A1 a full circle, centre A, radius 3 cm | Solved step by step · Learn it |
| 34 | x = 4 | 3 | M1 Remove the fractions M1 Get x on one side A1 the right answer: x = 4 | Solved step by step · Learn it |
| 35 | x = 1 or x = −7 | 3 | M1 Complete the square M1 Write it as a square A1 the right answer: x = 1 or x = −7 | Solved step by step · Learn it |
| 37 | P(dog | girl) = 23 | 2 | M1 Make a table A1 the right answer: P(dog | girl) = 2/3 | Solved step by step · Learn it |
Estimated grade
Add up your marks out of 100. 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 |
|---|---|
| A* | 80 |
| A | 66 |
| B | 52 |
| C | 39 |
| D | 28 |
| E | 18 |
| 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.