IGCSE Maths Extended Paper 2: non-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, no calculator. 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.
- 3 parts need a drawing or words (a construction, a graph, a proof): do them on paper. At the end you mark them 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 Question 1
Write the recurring decimal 0.363636... as a fraction in its simplest form.[2 marks]
2(a) Question 2(a)
Work out 2 13 + 1 3/4. Give your answer as a mixed number.[3 marks]
2(b) Question 2(b)
Work out 2 23 ÷ 1 1/9. Give your answer as a fraction in its simplest form.[3 marks]
3(a) Question 3(a)
Simplify √50 + √18.[2 marks]
3(b) Question 3(b)
Rationalise the denominator of 4/(√5 + 1). Give your answer in its simplest form.[3 marks]
4(a) Question 4(a)
Find the value of 272/3.[1 mark]
4(b) Question 4(b)
Find the value of 16−12.[1 mark]
4(c) Question 4(c)
Simplify (2x³)⁴.[2 marks]
5 Question 5
Work out (6 × 10⁵) ÷ (3 × 10⁻²). Give your answer in standard form.[2 marks]
6 Question 6
x = 7.2 and y = 3.5, both correct to 1 decimal place. Find the upper bound of x − y.[2 marks]
7(a) Question 7(a)
Factorise x² + 2x − 15.[2 marks]
7(b) Question 7(b)
Solve 2x² + 5x − 3 = 0 by factorising.[3 marks]
8 Question 8
Simplify x² − 9x² + 3x.[3 marks]
9 Question 9
Write 2/(x + 1) + 3/(x − 2) as a single fraction in its simplest form.[3 marks]
10 Question 10
Solve the simultaneous equations 3x + 2y = 12 and 5x − 2y = 4.[3 marks]
11 Question 11
Solve the inequality −3 ≤ 2x + 1 < 7.[3 marks]
f(x) = 2x + 1 and g(x) = x² − 3.
12(a) Question 12(a)
Find f(g(2)).[2 marks]
12(b) Question 12(b)
h(x) = 3x − 4. Find the inverse function h⁻¹(x).[2 marks]
13(a) Question 13(a)
y = 2x³ − 5x² + 4x. Find dy/dx.[2 marks]
13(b) Question 13(b)
Find the coordinates of the turning point of y = x² − 6x + 1 and decide whether it is a maximum or a minimum.[4 marks]
14 Question 14
Find the nth term of the sequence 3, 8, 15, 24, 35, ...[3 marks]
15(a) Question 15(a)
u = (3, −2) and v = (−1, 4) as column vectors. Find 2u − v.[2 marks]
15(b) Question 15(b)
OA = a and OB = b. Write the vector AB in terms of a and b.[1 mark]
16(a) Question 16(a)
A, B and C are points on a circle, centre O. Angle ACB = 35°. Find angle AOB.[2 marks]
16(b) Question 16(b)
ABCD is a cyclic quadrilateral. Angle A = 110°. Find angle C.[1 mark]
16(c) Question 16(c)
The line TA is a tangent to a circle at A. B and C are on the circle. The angle between the tangent and AB is 65°. Find angle ACB.[2 marks]
17 Question 17
y is inversely proportional to x. y = 6 when x = 4. Find y when x = 3.[3 marks]
18 Question 18
A bag has 5 red and 3 blue counters. Two counters are taken at random without replacement. Find the probability that both are red.[3 marks]
20(a) Question 20(a)
The point (2, 4) is rotated 90° anticlockwise about the origin. Write down the coordinates of its image.[1 mark]
20(b) Question 20(b)
The point (3, 2) is reflected in the line y = x. Write down the coordinates of its image.[1 mark]
22 Question 22
Write x² − 6x + 5 in the form (x + a)² + b.[2 marks]
23 Question 23
Draw the lines y = 2x − 1 and y = −x + 3 on a grid. Shade the region where y > 2x − 1 and y ≤ −x + 3.[3 marks]
25 Question 25
Find the equation of the line through (2, 3) that is perpendicular to y = 2x + 1.[3 marks]
26 Question 26
Find the distance between the points (−1, 2) and (5, 10).[2 marks]
27 Question 27
Two solids are similar. Their lengths are 3 cm and 6 cm. The small solid has volume 20 cm³. Find the volume of the large solid.[2 marks]
28 Question 28
Make x the subject of 3x + p = qx − 2.[3 marks]
29 Question 29
Expand and simplify (x + 1)(x + 2)(x − 3).[3 marks]
30 Question 30
The masses, m kg, of some parcels are grouped: 0 < m ≤ 10: 5, 10 < m ≤ 30: 12, 30 < m ≤ 60: 9. Find the frequency density of each group, for a histogram.[2 marks]
31 Question 31
A car speeds up from rest to 12 ms in 4 seconds, keeps that speed for 6 seconds, then slows down to rest in 4 seconds. Find the total distance it travels.[3 marks]
32 Question 32
Using a ruler and compasses only, construct the locus of points 3 cm from a point A.[2 marks]
34 Question 34
Solve 12x + 1 = 4.[3 marks]
35 Question 35
Solve x² + 6x = 7 by completing the square.[3 marks]
37 Question 37
A survey: boys, 12 like cats and 8 like dogs; girls, 10 like cats and 20 like dogs. A girl is chosen at random. Find the probability she likes dogs.[2 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.