Free IGCSE Mathematics practice
IGCSE Mathematics questions with answers Free IGCSE Mathematics practice questions with full worked solutions and mark schemes, written by IGCSE tutors for Malaysian students in Year 7 to Year 11. Each question shows the answer, the method to get it right, the mark scheme and the common mistake to avoid.
8 worked examples below. Covers number, algebra, geometry, trigonometry and statistics.
Worked Mathematics questions Mathematics Year 7 Integers and ordering Easy 1 mark
1. Work out the value of -6 + 9.
-6 -3 0 3 6
Answer: 3
The method
Start at -6 and count up 9 places on the number line.
Worked solution
-6 + 9 means moving 9 to the right from -6, which lands on 3.
Common mistake
Students often give -3 by subtracting instead of adding.
Exam tip
Use a number line for directed numbers to avoid sign slips.
Mathematics Year 8 Percentages Easy 1 mark
2. Work out 25 percent of 80.
1 of 4 shaded
Answer: 20
The method
Per cent means out of 100. 25 percent is one quarter.
Worked solution
25% of 80 = 80 divided by 4 = 20.
Mark scheme
1 mark for 20.
Common mistake
Dividing by 25 instead of finding a quarter.
Exam tip
Learn that 25% is a quarter, 50% is a half, 10% divides by ten.
Mathematics Year 9 Straight line graphs Medium 2 marks
3. The graph shows a straight line. What is its gradient?
x y
The method
Gradient is the change in y divided by the change in x.
Worked solution
The line rises one unit for every one unit across, so the gradient is 1.
Mark scheme
1 mark for a method, 1 mark for 1.
Common mistake
Reading the intercept as the gradient.
Exam tip
Pick two clear points and divide the rise by the run.
Mathematics Year 10 Trigonometry Hard 2 marks
4. The diagram shows a right-angled triangle. The side opposite the angle is 6 cm and the adjacent is 8 cm. Work out the hypotenuse in cm.
Answer: 10
The method
With both shorter sides known, use Pythagoras to find the hypotenuse.
Worked solution
Hypotenuse = square root of (6^2 + 8^2) = square root of 100 = 10 cm.
Mark scheme
1 mark for 100, 1 mark for 10.
Common mistake
Using sine or cosine when you only need Pythagoras.
Exam tip
If you know two sides and want the third, Pythagoras is quickest.
Mathematics Year 11 Quadratics Hard 2 marks
5. The diagram shows the graph of a quadratic. How many real solutions does the equation have where the curve meets the x-axis?
The method
Solutions are where the curve crosses the x-axis.
Worked solution
The parabola crosses the x-axis at two points, so there are two real solutions.
Mark scheme
1 mark for linking crossings to solutions, 1 mark for 2.
Common mistake
Counting the turning point as a solution.
Exam tip
Real solutions are x-axis crossings, not the vertex.
Mathematics Year 9 Pythagoras Hard 3 marks
6. The diagram shows a right-angled triangle. Work out the length x in cm.
Answer: 10
The method
Pythagoras: the square on the longest side equals the sum of the squares on the other two.
Worked solution
x^2 = 6^2 + 8^2 = 36 + 64 = 100, so x = 10 cm.
Mark scheme
1 mark for squaring, 1 for adding to 100, 1 for 10.
Common mistake
Forgetting to square root at the end.
Exam tip
Label the hypotenuse first, it is always opposite the right angle.
Mathematics Year 11 Quadratics Hard 3 marks
7. Solve x^2 - 5x + 6 = 0. Give the larger solution.
Answer: 3
The method
Factorise into two brackets that multiply to give the equation.
Worked solution
x^2 - 5x + 6 = (x - 2)(x - 3) = 0, so x = 2 or x = 3. The larger is 3.
Mark scheme
1 mark for factors, 1 for both roots, 1 for 3.
Common mistake
Sign errors when finding the factor pair.
Exam tip
Find two numbers that multiply to 6 and add to -5.
Mathematics Year 11 Trigonometry Hard 2 marks
8. In a right-angled triangle the side opposite an angle is 6 cm and the hypotenuse is 10 cm. Work out the sine of the angle as a decimal.
Answer: 0.6
The method
Sine equals the opposite side divided by the hypotenuse.
Worked solution
sine = opposite / hypotenuse = 6 / 10 = 0.6.
Mark scheme
1 mark for the ratio, 1 mark for 0.6.
Common mistake
Dividing the wrong way round.
Exam tip
SOH: Sine is Opposite over Hypotenuse.
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Open the live dashboard demo More IGCSE practice questions IGCSE Mathematics questions: FAQs Are these IGCSE Mathematics questions free? Yes. Every question on this page is free to read, with the full answer, worked solution and mark scheme shown. For unlimited practice with instant marking, you can try the live Studywise dashboard, also free, with no sign up.
Do the questions follow the Cambridge IGCSE syllabus? Yes. The questions are written by IGCSE tutors and follow the Cambridge IGCSE Mathematics syllabus, covering number, algebra, geometry, trigonometry and statistics.
Which year levels are covered? The samples run from Year 7 to Year 11, so younger students can build foundations while Year 10 and 11 students focus on exam topics.
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