IGCSE Maths Extended Paper 4: 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(a) | $11054.25 | 3 | M1 Find the start and the factor M1 Write the rule A1 the right answer: $11054.25 | Solved step by step · Learn it |
| 1(b) | x = 30000 | 3 | M1 Find what we know M1 Name the unknown A1 the right answer: x = 30000 | Solved step by step · Learn it |
| 1(c) | A ≈ $6146.28 | 3 | M1 Read the numbers M1 Find the rule A1 the right answer: A ≈ $6146.28 | Solved step by step · Learn it |
| 2 | upper bound = 93.75 cm² | 2 | M1 Bounds of each number A1 the right answer: upper bound = 93.75 cm² | Solved step by step · Learn it |
| 3(a) | c ≈ 8.1 | 3 | M1 Write the law of cosines M1 Put the numbers in A1 the right answer: c ≈ 8.1 | Solved step by step · Learn it |
| 3(b) | A ≈ 32.2 | 2 | M1 Find the height A1 the right answer: A ≈ 32.2 | Solved step by step · Learn it |
| 3(c) | b ≈ 11.4 | 3 | M1 Match sides and angles M1 Write the law of sines A1 the right answer: b ≈ 11.4 | Solved step by step · Learn it |
| 4 | 5.1 km north, 10.9 km east | 3 | M1 Draw the triangle M1 How far north A1 the right answer: 5.1 km north, 10.9 km east | Solved step by step · Learn it |
| 5(a) | D ≈ 11.2 | 2 | M1 Floor diagonal A1 the right answer: D ≈ 11.2 | Solved step by step · Learn it |
| 5(b) | θ ≈ 32.5° | 3 | M1 Find the right triangle M1 Base diagonal A1 the right answer: θ ≈ 32.5° | Solved step by step · Learn it |
| 6(a) | area = 9π ≈ 28.27 cm² | 2 | M1 What part of the circle A1 the right answer: area = 9π ≈ 28.27 cm² | Solved step by step · Learn it |
| 6(b) | V ≈ 301.44 cm3 | 3 | M1 Find the height M1 A third of the cylinder A1 the right answer: V ≈ 301.44 cm^3 | Solved step by step · Learn it |
| 6(c) | S ≈ 314 cm2 | 2 | M1 Use the rule A1 the right answer: S ≈ 314 cm^2 | Solved step by step · Learn it |
| 6(d) | V = 78π ≈ 244.92 cm³ | 3 | M1 Big cone M1 Small cone A1 the right answer: V = 78π ≈ 244.92 cm³ | Solved step by step · Learn it |
| 7 | large length = 10 | 2 | M1 Area factor A1 the right answer: large length = 10 | Solved step by step · Learn it |
| 8 | x ≈ 3.14 or x ≈ −0.64 | 4 | M1 Try factoring M1 Find a, b and c M1 Use the formula A1 the right answer: x ≈ 3.14 or x ≈ −0.64 | Solved step by step · Learn it |
| 9 | (−4, −3) and (3, 4) | 5 | M1 Put ② into ① M1 Open the brackets M1 Factor M1 One bracket is 0 A1 the right answer: (−4, −3) and (3, 4) | Solved step by step · Learn it |
| 10 | 2x + 4 ≠ 2x + 8 | 3 | M1 Find f(g(x)) M1 Find g(f(x)) A1 the right answer: 2x + 4 ≠ 2x + 8 | Solved step by step · Learn it |
| 11 | ≈ 13246 | 3 | M1 Find the start and the factor M1 Write the rule A1 the right answer: ≈ 13246 | Solved step by step · Learn it |
| 12 | mean ≈ 135 | 4 | M1 Find the midpoints M1 Multiply m × f M1 Add the columns A1 the right answer: mean ≈ 135 | Solved step by step · Learn it |
| 13 | median ≈ 22 | 3 | M1 Running total M1 Plot at the class ends A1 the right answer: median ≈ 22 | Solved step by step · Learn it |
| 14 | P(sum 7) = 16 | 3 | M1 List all outcomes M1 Count the ones we want A1 the right answer: P(sum 7) = 1/6 | Solved step by step · Learn it |
| 15 | x = 30°, 150° | 3 | M1 Remove the − 1 M1 Remove the 2 A1 the right answer: x = 30°, 150° | Solved step by step · Learn it |
| 16 | reflectionin the x-axis | 2 | M1 Draw both shapes A1 the right answer: reflectionin the x-axis | Solved step by step · Learn it |
| 17 | x = c − 3a − 2 | 3 | M1 Get the x terms on one side M1 Take x out A1 the right answer: x = (c − 3)/(a − 2) | Solved step by step · Learn it |
| 18 | x = 3 | 2 | M1 Write 81 as a power of 3 A1 the right answer: x = 3 | Solved step by step · Learn it |
| 19 | y = 50 | 3 | M1 Write the rule M1 Find k A1 the right answer: y = 50 | Solved step by step · Learn it |
| 20 | 2.8 × 109 | 2 | M1 Group the parts A1 the right answer: 2.8 × 10^9 | Solved step by step · Learn it |
| 21 | x ≈ 122.2 m | 3 | M1 Move the angle down M1 Name the sides A1 the right answer: x ≈ 122.2 m | Solved step by step · Learn it |
| 22(a) | b = 8 | 2 | M1 Use the chord rule A1 the right answer: b = 8 | Solved step by step · Learn it |
| 22(b) | x = 8 | 3 | M1 Use the rule M1 Put the numbers in A1 the right answer: x = 8 | Solved step by step · Learn it |
| 23 | 20 adult, 80 child | 4 | M1 Find what we know M1 Name the unknown M1 Write the equation A1 the right answer: 20 adult, 80 child | Solved step by step · Learn it |
| 24 | strong positive correlation | 3 | M1 all six points plotted M1 a ruled line of best fit with points on both sides B1 positive correlation | Solved step by step · Learn it |
| 25 | y = 6x − 9 | 3 | M1 Find the point M1 Find the slope A1 the right answer: y = 6x − 9 | Solved step by step · Learn it |
| 26 | angle = 60° | 3 | M1 Whole circle M1 What part of the circle A1 the right answer: angle = 60° | Solved step by step · Learn it |
Estimated grade
Add up your marks out of 100. This is our rough guide for one paper, not an official boundary: real boundaries change every year. Core papers lead to grades C to G, Extended papers to A* to E.
| Grade | Marks from |
|---|---|
| A* | 80 |
| A | 66 |
| B | 52 |
| C | 39 |
| D | 28 |
| E | 18 |
| U | 0 |
Steply practice papers are our own questions in the style of the Cambridge IGCSE Mathematics (0580) papers; they are not official and not endorsed by Cambridge University Press & Assessment. Official past papers: your school or the Cambridge website.