IGCSE Maths Core Paper 3: calculator
80 marks · 90 minutes · Core tier · method marks for your working · estimated grade · step-by-step answers
How it works
- Like the real Cambridge IGCSE 0580 paper: 80 marks, 90 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 80, 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)
Write 3.14159 correct to 3 significant figures.[1 mark]
1(b) Question 1(b)
Write 0.006284 correct to 2 significant figures.[1 mark]
2 Question 2
Work out (5.6 + 2.8) ÷ 1.2.[1 mark]
3 Question 3
Work out 35% of 240.[1 mark]
4 Question 4
Priya invests $1500 at 3% per year simple interest. Work out the interest she earns in 4 years.[2 marks]
5 Question 5
Omar invests $2000 at 4% per year compound interest. Work out the amount in his account after 3 years.[3 marks]
6 Question 6
$1 = €0.92. Change $350 into euros.[2 marks]
7 Question 7
75% of a number is 18. Find the number.[2 marks]
8 Question 8
A metal block has mass 156 g and volume 12 cm³. Work out its density.[2 marks]
9 Question 9
A cyclist rides at 18 km/h. How many hours does it take to ride 63 km?[2 marks]
10(a) Question 10(a)
A circle has radius 6.5 cm. Work out its area.[2 marks]
10(b) Question 10(b)
A circle has diameter 12 cm. Work out its circumference.[2 marks]
11 Question 11
A sector has radius 8 cm and angle 45°. Work out the arc length.[2 marks]
12 Question 12
A cylinder has radius 4 cm and height 10 cm. Work out its volume.[2 marks]
13(a) Question 13(a)
A right-angled triangle has shorter sides 5 cm and 9 cm. Work out the length of the hypotenuse.[2 marks]
13(b) Question 13(b)
A right-angled triangle has hypotenuse 13 cm and one shorter side 5 cm. Work out the length of the other side.[2 marks]
14(a) Question 14(a)
In a right-angled triangle the hypotenuse is 12 cm and one angle is 35°. Work out the side opposite the 35° angle.[2 marks]
14(b) Question 14(b)
In a right-angled triangle the side opposite angle x is 7 cm and the side next to it (adjacent) is 10 cm. Work out x.[2 marks]
15 Question 15
From a point 25 m from the foot of a tree, the angle of elevation of the top of the tree is 32°. Work out the height of the tree.[2 marks]
16 Question 16
The table shows the times, t minutes, of 20 runs: 0 < t ≤ 10: 4, 10 < t ≤ 20: 9, 20 < t ≤ 30: 5, 30 < t ≤ 40: 2. Calculate an estimate of the mean time.[3 marks]
17(a) Question 17(a)
A fair coin is thrown and a fair dice is rolled. Find the probability of a tail and an even number.[2 marks]
17(b) Question 17(b)
In a school, 3 out of every 10 students cycle to school. Estimate how many of 500 students cycle to school.[1 mark]
18(a) Question 18(a)
Solve 7x − 3 = 2x + 22.[3 marks]
18(b) Question 18(b)
v = u + at. Find v when u = 5, a = 3 and t = 4.[2 marks]
19 Question 19
Factorise completely 8x² − 12x.[2 marks]
20 Question 20
The sequence 5, 9, 13, 17, ... continues in the same way. Find the 30th term.[2 marks]
21(a) Question 21(a)
Find the equation of the straight line through (0, 1) and (2, 7). Give it in the form y = mx + c.[3 marks]
21(b) Question 21(b)
Find the midpoint of the line joining (−2, 3) and (6, 7).[2 marks]
22 Question 22
Complete a table of values for y = 2x − 3 for x = −1, 0, 1, 2, 3 and draw the graph.[3 marks]
23 Question 23
A map has a scale of 1 cm to 4 km. Two towns are 6.5 cm apart on the map. Work out the real distance.[2 marks]
24(a) Question 24(a)
The point (5, −1) is translated 3 units left and 4 units up. Write down the coordinates of its image.[1 mark]
24(b) Question 24(b)
The point (2, 3) is enlarged with scale factor 3, centre the origin. Write down the coordinates of its image.[1 mark]
25 Question 25
Work out (3.2 × 10⁵) × (4 × 10³). Give your answer in standard form.[2 marks]
26 Question 26
Write the ratio 40 cm : 2 m in its simplest form.[2 marks]
27 Question 27
A length is 24 cm, correct to the nearest centimetre. Write down the lower bound and the upper bound of the length.[2 marks]
28(a) Question 28(a)
Four angles of a pentagon are 100°, 120°, 95° and 110°. Find the fifth angle, x.[2 marks]
28(b) Question 28(b)
Each interior angle of a regular polygon is 140°. How many sides does it have?[2 marks]
29 Question 29
Two triangles are similar. The small one has sides 4 cm, 6 cm and 7 cm. The large one has sides 10 cm, 15 cm and x cm. Find x.[2 marks]
30 Question 30
In a group of 40 students, 22 play football, 15 play tennis and 8 play both. A student is picked at random. Find the probability that they play both.[2 marks]
31 Question 31
A car was worth $8000. It is now worth $6800. Find the percentage decrease.[2 marks]
32 Question 32
Share $360 in the ratio 2 : 3 : 4.[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.