GCSE Maths Foundation 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 | 710 | 1 | B1 the right answer: 7/10 | Solved step by step · Learn it |
| 2 | 40% | 1 | B1 the right answer: 40% | Solved step by step · Learn it |
| 3 | 7 | 1 | B1 the right answer: 7 | Solved step by step · Learn it |
| 4 | 8 | 1 | B1 the right answer: 8 | Solved step by step · Learn it |
| 5(a) | 1104 | 2 | M1 Multiply A1 the right answer: 1104 | Solved step by step · Learn it |
| 5(b) | 84 | 2 | M1 Divide A1 the right answer: 84 | Solved step by step · Learn it |
| 6(a) | 3a + 8b | 2 | M1 Group like terms A1 the right answer: 3a + 8b | Solved step by step · Learn it |
| 6(b) | 4x + 24 | 1 | B1 the right answer: 4x + 24 | Solved step by step · Learn it |
| 6(c) | 5(x − 4) | 1 | B1 the right answer: 5(x − 4) | Solved step by step · Learn it |
| 7(a) | x = 28 | 1 | B1 the right answer: x = 28 | Solved step by step · Learn it |
| 7(b) | x = 7 | 2 | M1 Remove the − 5 A1 the right answer: x = 7 | Solved step by step · Learn it |
| 8 | 14 | 2 | M1 Put the numbers in A1 the right answer: 14 | Solved step by step · Learn it |
| 9 | an = 5n − 1 | 2 | M1 Find the difference A1 the right answer: a_n = 5n − 1 | Solved step by step · Learn it |
| 10 | x = 145 | 2 | M1 Use the angle fact A1 the right answer: x = 145 | Solved step by step · Learn it |
| 11(a) | A = 54 cm2 | 1 | B1 the right answer: A = 54 cm^2 | Solved step by step · Learn it |
| 11(b) | P = 30 cm | 1 | B1 the right answer: P = 30 cm | Solved step by step · Learn it |
| 12 | A = 40 cm2 | 2 | M1 Make a rectangle A1 the right answer: A = 40 cm^2 | Solved step by step · Learn it |
| 13 | V = 64 cm3 | 1 | B1 the right answer: V = 64 cm^3 | Solved step by step · Learn it |
| 14 | P(A or B) = 13 | 1 | B1 the right answer: P(A or B) = 1/3 | Solved step by step · Learn it |
| 15(a) | mean = 5 | 2 | M1 Add them all A1 the right answer: mean = 5 | Solved step by step · Learn it |
| 15(b) | mode = 5 | 1 | B1 the right answer: mode = 5 | Solved step by step · Learn it |
| 15(c) | range = 6 | 1 | B1 the right answer: range = 6 | Solved step by step · Learn it |
| 16(a) | 12 and 48 | 2 | M1 Count the parts A1 the right answer: 12 and 48 | Solved step by step · Learn it |
| 16(b) | 2 : 3 | 1 | B1 the right answer: 2 : 3 | Solved step by step · Learn it |
| 17 | 30% of 90 = 27 | 2 | M1 Find 10% A1 the right answer: 30% of 90 = 27 | Solved step by step · Learn it |
| 18(a) | 81 | 1 | B1 the right answer: 81 | Solved step by step · Learn it |
| 18(b) | 9 | 1 | B1 the right answer: 9 | Solved step by step · Learn it |
| 19 | 2648 ≈ 2600 | 1 | B1 the right answer: 2648 ≈ 2600 | Solved step by step · Learn it |
| 20 | LCM(6, 10) = 30 | 2 | M1 Count up A1 the right answer: LCM(6, 10) = 30 | Solved step by step · Learn it |
| 21(a) | 1112 | 2 | M1 Make the bottoms the same A1 the right answer: 11/12 | Solved step by step · Learn it |
| 21(b) | 310 | 2 | M1 Multiply tops and bottoms A1 the right answer: 3/10 | Solved step by step · Learn it |
| 21(c) | 32 | 2 | M1 Flip and multiply A1 the right answer: 3/2 | Solved step by step · Learn it |
| 22 | 2.15 | 1 | B1 the right answer: 2.15 | Solved step by step · Learn it |
| 23 | sale price: £60 | 2 | M1 Find the discount A1 the right answer: sale price: £60 | Solved step by step · Learn it |
| 24 | x = 120 | 2 | M1 Find what we know A1 the right answer: x = 120 | Solved step by step · Learn it |
| 25 | P' = (−3, 2) | 1 | B1 the right answer: P' = (−3, 2) | Solved step by step · Learn it |
| 26 | sum = 540° | 1 | B1 the right answer: sum = 540° | Solved step by step · Learn it |
| 27 | x ≤ 4 | 2 | M1 Remove the + 1 A1 the right answer: x ≤ 4 | Solved step by step · Learn it |
| 28 | 7.6 × 104 | 1 | B1 the right answer: 7.6 × 10^4 | Solved step by step · Learn it |
| 29 | (x, y) = (4, 2) | 3 | M1 Make the x parts opposite M1 Add the equations A1 the right answer: (x, y) = (4, 2) | Solved step by step · Learn it |
| 30 | triangle ABC: AB = 8 cm, BC = 6 cm, AC = 7 cm | 2 | M1 AB = 8 cm drawn and an arc of radius 6 cm from B or 7 cm from A A1 triangle complete with both arcs shown | Solved step by step · Learn it |
| 31 | c = 13 | 3 | M1 Name the sides M1 Squares on the sides A1 the right answer: c = 13 | Solved step by step · Learn it |
| 32 | 84 = 22 × 3 × 7 | 2 | M1 Make a factor tree A1 the right answer: 84 = 2^2 × 3 × 7 | Solved step by step · Learn it |
| 33 | 15% | 2 | M1 Find the change A1 the right answer: 15% | Solved step by step · Learn it |
| 34 | y8 | 1 | B1 the right answer: y^8 | Solved step by step · Learn it |
| 35 | 4 like neither | 3 | M1 Draw the Venn diagram M1 Fill the circles A1 the right answer: 4 like neither | Solved step by step · Learn it |
| 36 | x = 64 | 2 | M1 Use the angle fact A1 the right answer: x = 64 | Solved step by step · Learn it |
| 37 | x = 9 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 9 | Solved step by step · Learn it |
| 38 | A = 35 cm2 | 2 | M1 Half of a rectangle A1 the right answer: A = 35 cm^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 |
|---|---|
| 5 | 59 |
| 4 | 46 |
| 3 | 34 |
| 2 | 21 |
| 1 | 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.