GCSE Maths Higher 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 | 62.5% | 1 | B1 the right answer: 62.5% | Solved step by step · Learn it |
| 2 | £198 | 3 | M1 Down 10% of $200 M1 Up 10% of $180 A1 the right answer: £198 | Solved step by step · Learn it |
| 3 | m = 222.5 | 2 | M1 Write the rule A1 the right answer: m = 222.5 | Solved step by step · Learn it |
| 4 | x = 14 | 3 | M1 Open the brackets M1 Get x on one side A1 the right answer: x = 14 | Solved step by step · Learn it |
| 5 | 27a6b3 | 2 | M1 Power of a product A1 the right answer: 27a^6b^3 | Solved step by step · Learn it |
| 6 | (x + 4)(x2 + 3) | 2 | M1 Group in pairs A1 the right answer: (x + 4)(x^2 + 3) | Solved step by step · Learn it |
| 7 | a20 = −26 | 2 | M1 Find the difference A1 the right answer: a_20 = −26 | Solved step by step · Learn it |
| 8 | y = 3x + 1 | 3 | M1 Find the slope M1 Find b A1 the right answer: y = 3x + 1 | Solved step by step · Learn it |
| 9 | d = 10 | 2 | M1 Plot the points A1 the right answer: d = 10 | Solved step by step · Learn it |
| 10 | sides = 15 | 2 | M1 Walk around the shape A1 the right answer: sides = 15 | Solved step by step · Learn it |
| 11 | θ ≈ 32.5° | 3 | M1 Name the sides M1 Choose the ratio A1 the right answer: θ ≈ 32.5° | Solved step by step · Learn it |
| 12 | V = 416π/3 ≈ 435.41 | 4 | M1 Big cone M1 Small cone M1 Take away A1 the right answer: V = 416π/3 ≈ 435.41 | Solved step by step · Learn it |
| 13 | angle = 90° | 3 | M1 Whole circle M1 What part of the circle A1 the right answer: angle = 90° | Solved step by step · Learn it |
| 14 | min 3, Q1 6, median 12, Q3 16, max 21 | 3 | M1 median 12 M1 quartiles 6 and 16 A1 box plot from 3 to 21 with the box from 6 to 16 and the line at 12 | Solved step by step · Learn it |
| 15 | mean ≈ 7.6 | 4 | M1 Find the midpoints M1 Multiply m × f M1 Add the columns A1 the right answer: mean ≈ 7.6 | Solved step by step · Learn it |
| 16 | P(french only) = 716 | 3 | M1 Start in the middle M1 Fill the rest A1 the right answer: P(french only) = 7/16 | Solved step by step · Learn it |
| 17 | P(all blue) = 215 | 3 | M1 Order: yes or no M1 Count all the ways A1 the right answer: P(all blue) = 2/15 | Solved step by step · Learn it |
| 18 | x = 6 or x = −2 | 3 | M1 Complete the square M1 Write it as a square A1 the right answer: x = 6 or x = −2 | Solved step by step · Learn it |
| 19 | y = 4x − 4 | 3 | M1 Find the point M1 Find the slope A1 the right answer: y = 4x − 4 | Solved step by step · Learn it |
| 20 | ≈ 793 | 3 | M1 Find the start and the factor M1 Write the rule A1 the right answer: ≈ 793 | Solved step by step · Learn it |
| 21 | A ≈ 28.7 | 3 | M1 Find the height M1 Write the rule A1 the right answer: A ≈ 28.7 | Solved step by step · Learn it |
| 22 | C ≈ 73.4° | 3 | M1 Write the law of cosines M1 Put the numbers in A1 the right answer: C ≈ 73.4° | Solved step by step · Learn it |
| 23 | €290 = £250 | 2 | M1 Write the rate A1 the right answer: €290 = £250 | Solved step by step · Learn it |
| 24 | center (3, 0) and r = 4 | 3 | M1 Group x and y M1 Complete the square for x A1 the right answer: center (3, 0) and r = 4 | Solved step by step · Learn it |
| 25 | x = 4 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 4 | Solved step by step · Learn it |
| 26 | P' = (−1, 0) | 2 | M1 Draw the shape A1 the right answer: P' = (−1, 0) | Solved step by step · Learn it |
| 27 | 6.35 ≤ length < 6.45 | 2 | M1 Find the step A1 the right answer: 6.35 ≤ length < 6.45 | Solved step by step · Learn it |
| 28 | outliers: 2 and 45 | 2 | M1 Put them in order A1 the right answer: outliers: 2 and 45 | Solved step by step · Learn it |
| 29 | x = 3 | 3 | M1 Remove the fractions M1 Get x on one side A1 the right answer: x = 3 | Solved step by step · Learn it |
| 30 | A ≈ 7.74 | 3 | M1 The whole and the hole M1 Area of each part A1 the right answer: A ≈ 7.74 | 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. Foundation papers lead to grades 1 to 5, Higher papers to 3 to 9.
| Grade | Marks from |
|---|---|
| 9 | 62 |
| 8 | 53 |
| 7 | 43 |
| 6 | 33 |
| 5 | 23 |
| 4 | 14 |
| 3 | 9 |
| U | 0 |
Steply practice papers are our own questions in the style of GCSE Mathematics papers in England (layout and timing as AQA 8300); they are not official and not endorsed by AQA or any exam board. Official past papers: your exam board's website.