GCSE Maths Foundation 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 | 1, 2, 4, 7, 14, 28 | 1 | B1 the right answer: 1, 2, 4, 7, 14, 28 | Solved step by step · Learn it |
| 2 | −3 | 1 | B1 the right answer: −3 | Solved step by step · Learn it |
| 3 | 9.75 | 1 | B1 the right answer: 9.75 | Solved step by step · Learn it |
| 4(a) | x2 + 7x + 12 | 2 | M1 Split the first bracket A1 the right answer: x^2 + 7x + 12 | Solved step by step · Learn it |
| 4(b) | x = −2 or x = −3 | 3 | M1 Factor M1 One bracket is 0 A1 the right answer: x = −2 or x = −3 | Solved step by step · Learn it |
| 5 | x > 4 | 2 | M1 Get x on one side A1 the right answer: x > 4 | Solved step by step · Learn it |
| 6 | a40 = 275 | 2 | M1 Find the difference A1 the right answer: a_40 = 275 | Solved step by step · Learn it |
| 7 | m = 2 | 2 | M1 Plot the points A1 the right answer: m = 2 | Solved step by step · Learn it |
| 8 | y = −3x + 7 | 2 | M1 Remove the 3x A1 the right answer: y = −3x + 7 | Solved step by step · Learn it |
| 9 | M = (4, 1) | 2 | M1 Plot the points A1 the right answer: M = (4, 1) | Solved step by step · Learn it |
| 10 | x = 120 | 2 | M1 Find the angle sum A1 the right answer: x = 120 | Solved step by step · Learn it |
| 11 | A = 84 | 3 | M1 The whole and the hole M1 Area of each part A1 the right answer: A = 84 | Solved step by step · Learn it |
| 12 | V = 54 cm3 | 2 | M1 Length × width × height A1 the right answer: V = 54 cm^3 | Solved step by step · Learn it |
| 13 | θ ≈ 33.7° | 3 | M1 Name the sides M1 Choose the ratio A1 the right answer: θ ≈ 33.7° | Solved step by step · Learn it |
| 14 | b = 15 | 3 | M1 Name the sides M1 Squares on the sides A1 the right answer: b = 15 | Solved step by step · Learn it |
| 15(a) | median = 2 | 1 | B1 the right answer: median = 2 | Solved step by step · Learn it |
| 15(b) | mean = 2.5 | 2 | M1 Add them all A1 the right answer: mean = 2.5 | Solved step by step · Learn it |
| 16 | P(heads and 6) = 112 | 2 | M1 Independent or not A1 the right answer: P(heads and 6) = 1/12 | Solved step by step · Learn it |
| 17 | x = 55 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 55 | Solved step by step · Learn it |
| 18 | y = 56 | 3 | M1 Write the rule M1 Find k A1 the right answer: y = 56 | Solved step by step · Learn it |
| 19 | x = 18 | 2 | M1 Find what we know A1 the right answer: x = 18 | Solved step by step · Learn it |
| 20 | 40,000 cm² | 2 | M1 Change the length A1 the right answer: 40,000 cm² | Solved step by step · Learn it |
| 21 | 307000 | 1 | B1 the right answer: 307000 | Solved step by step · Learn it |
| 22 | 15 | 2 | M1 Find the prime factors A1 the right answer: 15 | Solved step by step · Learn it |
| 23 | 3 : 8 | 2 | M1 Same units A1 the right answer: 3 : 8 | Solved step by step · Learn it |
| 24 | bearing 180° | 1 | B1 the right answer: bearing 180° | Solved step by step · Learn it |
| 25 | P' = (2, −5) | 1 | B1 the right answer: P' = (2, −5) | Solved step by step · Learn it |
| 26 | 17 | 2 | M1 Put the numbers in A1 the right answer: 17 | Solved step by step · Learn it |
| 27 | 40°, 80°, 60° | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: 40°, 80°, 60° | Solved step by step · Learn it |
| 28 | V ≈ 904.32 | 2 | M1 Use the rule A1 the right answer: V ≈ 904.32 | Solved step by step · Learn it |
| 29 | V ≈ 150.72 cm3 | 2 | M1 A third of the cylinder A1 the right answer: V ≈ 150.72 cm^3 | Solved step by step · Learn it |
| 30 | strong negative correlation | 2 | M1 all six points plotted B1 negative correlation | Solved step by step · Learn it |
| 31 | £48 | 3 | M1 Up 20% of $50 M1 Down 20% of $60 A1 the right answer: £48 | Solved step by step · Learn it |
| 32 | arc = 4π ≈ 12.57 cm | 3 | M1 What part of the circle M1 Whole circle A1 the right answer: arc = 4π ≈ 12.57 cm | Solved step by step · Learn it |
| 33 | P(exactly 1 head) = 12 | 2 | M1 List all outcomes A1 the right answer: P(exactly 1 head) = 1/2 | Solved step by step · Learn it |
| 34 | x = 64 | 2 | M1 Use the isosceles fact A1 the right answer: x = 64 | Solved step by step · Learn it |
| 35 | 3.5 km = 3500 m | 1 | B1 the right answer: 3.5 km = 3500 m | Solved step by step · Learn it |
| 36 | (x, y) = (80, 70) | 5 | M1 Make the y parts opposite M1 Add the equations M1 Find x M1 Find y A1 the right answer: (x, y) = (80, 70) | 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.