GCSE Maths Higher 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 | 252 = 22 × 32 × 7 | 2 | M1 Make a factor tree A1 the right answer: 252 = 2^2 × 3^2 × 7 | Solved step by step · Learn it |
| 2 | 1 512 | 3 | M1 Write as fractions M1 Make the bottoms the same A1 the right answer: 1 5/12 | Solved step by step · Learn it |
| 3 | 16 | 2 | M1 Take the root A1 the right answer: 16 | Solved step by step · Learn it |
| 5 | x = 311 | 3 | M1 Call it x M1 Move the point A1 the right answer: x = 3/11 | Solved step by step · Learn it |
| 6(a) | 3√3 | 2 | M1 Find a square number in each A1 the right answer: 3√3 | Solved step by step · Learn it |
| 6(b) | 3√3 − 3 | 3 | M1 Find the partner M1 Bottom: one square take away another A1 the right answer: 3√3 − 3 | Solved step by step · Learn it |
| 7 | 4.8 × 10−2 | 2 | M1 Group the parts A1 the right answer: 4.8 × 10^−2 | Solved step by step · Learn it |
| 8 | 3(x + 2)(x − 2) | 2 | M1 Common factor first A1 the right answer: 3(x + 2)(x − 2) | Solved step by step · Learn it |
| 9 | x = −23 or x = 4 | 3 | M1 Find two numbers M1 Split the middle A1 the right answer: x = −2/3 or x = 4 | Solved step by step · Learn it |
| 10 | (x + 4)2 − 13 | 3 | M1 Complete the square M1 Write the square A1 the right answer: (x + 4)^2 − 13 | Solved step by step · Learn it |
| 11 | −3 < x < 4 | 3 | M1 Find two numbers M1 Find the critical points A1 the right answer: −3 < x < 4 | Solved step by step · Learn it |
| 12 | (x, y) = (2, 3) | 4 | M1 Make the y parts opposite M1 Add the equations M1 Find x A1 the right answer: (x, y) = (2, 3) | Solved step by step · Learn it |
| 13 | x + 4x + 2 | 3 | M1 Factor the top M1 Factor the bottom A1 the right answer: (x + 4)/(x + 2) | Solved step by step · Learn it |
| 14 | x + 8(x − 1)(x + 2) | 3 | M1 Find the common bottom M1 Make the bottoms the same A1 the right answer: (x + 8)/((x − 1)(x + 2)) | Solved step by step · Learn it |
| 15(a) | f(g(2)) = 13 | 2 | M1 Work out the inside A1 the right answer: f(g(2)) = 13 | Solved step by step · Learn it |
| 15(b) | f −1(x) = x + 23 | 2 | M1 Write y for f(x) A1 the right answer: f ^−1(x) = (x + 2)/(3) | Solved step by step · Learn it |
| 16 | an = n2 + 5 | 3 | M1 First differences M1 Second differences A1 the right answer: a_n = n^2 + 5 | Solved step by step · Learn it |
| 17 | y = −12x + 3 | 3 | M1 Slope of the given line M1 Slope of the new line A1 the right answer: y = −1/2x + 3 | Solved step by step · Learn it |
| 18 | x2 + y2 = 49 | 2 | M1 Draw the circle A1 the right answer: x^2 + y^2 = 49 | Solved step by step · Learn it |
| 19 | turning point (3, 1) | 2 | M1 Read the changes A1 the right answer: turning point (3, 1) | Solved step by step · Learn it |
| 20 | x = 62 | 2 | M1 Use the circle rule A1 the right answer: x = 62 | Solved step by step · Learn it |
| 22 | b = 8 | 2 | M1 Use the tangent rule A1 the right answer: b = 8 | Solved step by step · Learn it |
| 24 | P(all red) = 16 | 3 | M1 Order: yes or no M1 Count all the ways A1 the right answer: P(all red) = 1/6 | Solved step by step · Learn it |
| 25 | P(yes | man) = 34 | 2 | M1 Make a table A1 the right answer: P(yes | man) = 3/4 | Solved step by step · Learn it |
| 26 | y = 4 | 3 | M1 Write the rule M1 Find k A1 the right answer: y = 4 | Solved step by step · Learn it |
| 27 | large area = 75 | 2 | M1 Length scale factor A1 the right answer: large area = 75 | Solved step by step · Learn it |
| 28 | x = −1 − a5 − b | 3 | M1 Get the x terms on one side M1 Take x out A1 the right answer: x = (−1 − a)/(5 − b) | Solved step by step · Learn it |
| 29 | x³ + 5x² + 2x − 8 | 3 | M1 Multiply the first two M1 Times the third bracket A1 the right answer: x³ + 5x² + 2x − 8 | Solved step by step · Learn it |
| 30 | x = 2 | 3 | M1 Remove the fractions M1 Get x on one side A1 the right answer: x = 2 | Solved step by step · Learn it |
| 32 | y = −x + 6 | 3 | M1 Find the midpoint M1 Slope of AB A1 the right answer: y = −x + 6 | Solved step by step · Learn it |
| 33 | 2(a + b + 1) | 2 | M1 two odd numbers written as 2n + 1 and 2m + 1 A1 their sum 2n + 2m + 2 = 2(n + m + 1), which is 2 × a whole number, so even | 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.