GCSE Maths Higher 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 | 0.03846 ≈ 0.0385 | 1 | B1 the right answer: 0.03846 ≈ 0.0385 | Solved step by step · Learn it |
| 2 | A ≈ £5267.58 | 3 | M1 Read the numbers M1 Find the rule A1 the right answer: A ≈ £5267.58 | Solved step by step · Learn it |
| 3 | ≈ £13232.83 | 3 | M1 Find the start and the factor M1 Write the rule A1 the right answer: ≈ £13232.83 | Solved step by step · Learn it |
| 4 | x = 500 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 500 | Solved step by step · Learn it |
| 5 | upper bound ≈ 4.87 | 3 | M1 Bounds of each number M1 Choose the bounds A1 the right answer: upper bound ≈ 4.87 | Solved step by step · Learn it |
| 6(a) | c ≈ 7.4 | 3 | M1 Write the law of cosines M1 Put the numbers in A1 the right answer: c ≈ 7.4 | Solved step by step · Learn it |
| 6(b) | A ≈ 33.2 | 2 | M1 Find the height A1 the right answer: A ≈ 33.2 | Solved step by step · Learn it |
| 7 | b ≈ 16.8 | 3 | M1 Match sides and angles M1 Write the law of sines A1 the right answer: b ≈ 16.8 | Solved step by step · Learn it |
| 8 | D ≈ 12.1 | 3 | M1 Floor diagonal M1 Diagonal of the box A1 the right answer: D ≈ 12.1 | Solved step by step · Learn it |
| 9 | V ≈ 314 cm3 | 3 | M1 Find the height M1 A third of the cylinder A1 the right answer: V ≈ 314 cm^3 | Solved step by step · Learn it |
| 10 | S ≈ 150.72 cm2 | 2 | M1 Count the parts A1 the right answer: S ≈ 150.72 cm^2 | Solved step by step · Learn it |
| 11 | area = 60π ≈ 188.50 cm² | 2 | M1 What part of the circle A1 the right answer: area = 60π ≈ 188.50 cm² | Solved step by step · Learn it |
| 12 | x ≈ 0.39 or x ≈ −1.72 | 4 | M1 Try factoring M1 Find a, b and c M1 Use the formula A1 the right answer: x ≈ 0.39 or x ≈ −1.72 | Solved step by step · Learn it |
| 13 | (−1, −3) and (1, 3) | 5 | M1 Put ② into ① M1 Open the brackets M1 Get x² alone M1 Square root of both sides A1 the right answer: (−1, −3) and (1, 3) | Solved step by step · Learn it |
| 14 | heights 0.8, 0.6, 0.5 | 3 | M1 class widths 10, 10 and 20 used M1 two densities right A1 0.8, 0.6 and 0.5 | Solved step by step · Learn it |
| 15 | median ≈ 24.7 | 3 | M1 Running total M1 Plot at the class ends A1 the right answer: median ≈ 24.7 | Solved step by step · Learn it |
| 16 | large volume = 250 | 2 | M1 Length scale factor A1 the right answer: large volume = 250 | Solved step by step · Learn it |
| 17 | θ ≈ 45.0° | 3 | M1 Find the right triangle M1 Base diagonal A1 the right answer: θ ≈ 45.0° | Solved step by step · Learn it |
| 18 | x = 60°, 300° | 3 | M1 Remove the − 1 M1 Remove the 2 A1 the right answer: x = 60°, 300° | Solved step by step · Learn it |
| 19 | x = 7 | 2 | M1 Write 64 as a power of 2 A1 the right answer: x = 7 | Solved step by step · Learn it |
| 20 | y = 125 | 3 | M1 Write the rule M1 Find k A1 the right answer: y = 125 | Solved step by step · Learn it |
| 21 | distance = 80 m | 3 | M1 Read the graph M1 Distance = area A1 the right answer: distance = 80 m | Solved step by step · Learn it |
| 22 | P(2 heads) = 38 | 3 | M1 Binomial: yes or no M1 Write the rule A1 the right answer: P(2 heads) = 3/8 | Solved step by step · Learn it |
| 23 | 3 × 1011 | 2 | M1 Group the parts A1 the right answer: 3 × 10^11 | Solved step by step · Learn it |
| 24 | 8.7 km north, 5.0 km east | 3 | M1 Draw the triangle M1 How far north A1 the right answer: 8.7 km north, 5.0 km east | Solved step by step · Learn it |
| 25 | x ≈ 17.1 m | 3 | M1 Name the sides M1 Choose the ratio A1 the right answer: x ≈ 17.1 m | Solved step by step · Learn it |
| 26 | 5 | 2 | M1 Find the two points A1 the right answer: 5 | Solved step by step · Learn it |
| 27 | upper bound = 5.6 | 2 | M1 Bounds of each number A1 the right answer: upper bound = 5.6 | Solved step by step · Learn it |
| 28 | S ≈ 452.16 m2 | 3 | M1 Find the slant height M1 Count the parts A1 the right answer: S ≈ 452.16 m^2 | 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.