IGCSE Maths Extended Paper 4: calculator
100 marks · 120 minutes · Extended tier · method marks for your working · estimated grade · step-by-step answers
How it works
- Like the real Cambridge IGCSE 0580 paper: 100 marks, 120 minutes, a calculator is allowed (one is on the screen). Answer all the questions. Solve it right here: no sign-up.
- Each part shows its marks, like [2 marks]. Type your answer and show your working, one line at a time: if the answer is wrong, right working still earns method marks, as in the exam. If an answer is not exact, give it to 3 significant figures (angles to 1 decimal place). For π use the π key or 3.142.
- 1 part needs a drawing or words (a construction, a graph, a proof): do it on paper. At the end you mark it yourself with the mark scheme.
- Use Back and Next, or the question list at the bottom. Mark for review the ones to look at again. The timer counts down (you can hide it).
- At the end: your marks out of 100, an estimated grade, your marks in each area, and every part marked, with your working line by line, the right answer and its step-by-step solution.
The grade is only an estimate: real grade boundaries change every year and use all the papers together. Core papers lead to grades C to G, Extended papers to A* to E. Your answers are kept in this browser, so you can close the page and come back.
1(a) Question 1(a)
A car costs $18 000. Its value goes down by 15% each year. Find its value after 3 years.[3 marks]
1(b) Question 1(b)
After a 12% pay rise, Sami earns $33 600 a year. Find his pay before the rise.[3 marks]
1(c) Question 1(c)
Lena invests $5000 at 3.5% per year compound interest. Find the amount after 6 years.[3 marks]
2 Question 2
A rectangle measures 12 cm by 7 cm, both correct to the nearest centimetre. Find the upper bound of its area.[2 marks]
In triangle ABC, BC = a, AC = b and AB = c.
3(a) Question 3(a)
a = 8 cm, b = 11 cm and angle C = 47°. Find c.[3 marks]
3(b) Question 3(b)
Find the area of the same triangle (a = 8 cm, b = 11 cm, angle C = 47°).[2 marks]
3(c) Question 3(c)
In another triangle, angle A = 52°, angle B = 71° and a = 9.5 cm. Find b.[3 marks]
4 Question 4
A ship sails 12 km on a bearing of 065°. How far north and how far east of its start is it?[3 marks]
A cuboid measures 5 cm by 8 cm by 6 cm.
5(a) Question 5(a)
Find the length of a diagonal from one corner to the opposite corner.[2 marks]
5(b) Question 5(b)
The cuboid is 5 cm by 8 cm on its base and 6 cm high. Find the angle between the diagonal and the base.[3 marks]
6(a) Question 6(a)
A sector has radius 9 cm and angle 40°. Find its area.[2 marks]
6(b) Question 6(b)
A cone has base radius 6 cm and slant height 10 cm. Find its volume.[3 marks]
6(c) Question 6(c)
A sphere has radius 5 cm. Find its surface area.[2 marks]
6(d) Question 6(d)
A frustum is made by cutting a small cone (radius 2 cm, height 4 cm) off a large cone (radius 5 cm, height 10 cm). Find the volume of the frustum.[3 marks]
7 Question 7
Two similar shapes have areas 9 cm² and 25 cm². A length on the small shape is 6 cm. Find the matching length on the large shape.[2 marks]
8 Question 8
Solve 2x² − 5x − 4 = 0. Give your answers correct to 2 decimal places.[4 marks]
9 Question 9
Solve the simultaneous equations x² + y² = 25 and y = x + 1.[5 marks]
10 Question 10
f(x) = x + 4 and g(x) = 2x. Find f(g(x)) and g(f(x)).[3 marks]
11 Question 11
A town has 12 000 people. The number grows by 2.5% each year. Find the number of people after 4 years.[3 marks]
12 Question 12
The heights, h cm, of 20 plants: 100 < h ≤ 120: 4, 120 < h ≤ 140: 9, 140 < h ≤ 160: 5, 160 < h ≤ 180: 2. Calculate an estimate of the mean height.[4 marks]
13 Question 13
Times, t minutes: 0 < t ≤ 10: 2, 10 < t ≤ 20: 6, 20 < t ≤ 30: 10, 30 < t ≤ 40: 2. Use a cumulative frequency table to find an estimate of the median.[3 marks]
14 Question 14
Two fair dice are rolled. Find the probability that the total is 7.[3 marks]
15 Question 15
Solve 2 sin x − 1 = 0 for 0° ≤ x ≤ 360°.[3 marks]
16 Question 16
Triangle P has corners A(2, 1) and B(4, 3). Its image has A'(2, −1) and B'(4, −3). Describe fully the single transformation.[2 marks]
17 Question 17
Make x the subject of ax + 3 = 2x + c.[3 marks]
18 Question 18
Solve 3x + 1 = 81.[2 marks]
19 Question 19
y is proportional to the square of x. y = 18 when x = 3. Find y when x = 5.[3 marks]
20 Question 20
Work out (4.2 × 10⁶) ÷ (1.5 × 10⁻³). Give your answer in standard form.[2 marks]
21 Question 21
From the top of a cliff 65 m high, the angle of depression of a boat is 28°. Find the distance from the foot of the cliff to the boat.[3 marks]
22(a) Question 22(a)
A circle has radius 10 cm. A chord is 12 cm long. Find the distance from the centre to the chord.[2 marks]
22(b) Question 22(b)
Two chords AB and CD meet at P inside a circle. AP = 4 cm, PB = 6 cm and CP = 3 cm. Find PD.[3 marks]
23 Question 23
Adult tickets cost $8 and child tickets cost $5. A cinema sold 4 times as many child tickets as adult tickets. It took $560. Form an equation and solve it to find how many of each ticket it sold.[4 marks]
24 Question 24
Plot the points (1, 2), (2, 4), (3, 5), (4, 4), (5, 7), (6, 8) on a scatter diagram, draw a line of best fit and describe the correlation.[3 marks]
25 Question 25
Find the equation of the tangent to the curve y = x² at the point where x = 3.[3 marks]
26 Question 26
A sector has radius 9 cm and arc length 3π cm. Find the angle of the sector.[3 marks]
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.