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Free IGCSE Additional Mathematics practice

IGCSE Additional Mathematics questions with answers

Free IGCSE Additional 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.

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8 worked examples below. Covers functions, indices, surds, differentiation and integration.

Worked Additional Mathematics questions

Additional MathematicsYear 7SequencesEasy1 mark
1. A sequence starts 3, 6, 9, 12. What is the next term?
36912?
Answer: 15
The method
Find the constant difference and add it on.
Worked solution
The terms go up by 3 each time, so after 12 comes 15.
Mark scheme
1 mark for 15.
Common mistake
Multiplying instead of adding the difference.
Exam tip
Check the gap between terms is the same before continuing.
Additional MathematicsYear 8Linear functionsMedium2 marks
2. The graph shows a straight line through the origin with gradient 1. Which equation matches it?
xy
  • Ay = xcorrect
  • By = x + 2
  • Cy = 2x
  • Dy = -x
The method
A line through the origin has the form y equals gradient times x.
Worked solution
Gradient 1 and no intercept gives y = x.
Mark scheme
1 mark for y = x.
Common mistake
Adding a constant when the line passes through the origin.
Exam tip
Through the origin means the constant term is zero.
Additional MathematicsYear 9Straight lineMedium2 marks
3. A line has gradient 3 and passes through (0, 2). What is the y value when x = 4?
xy
Answer: 14
The method
Use y = mx + c with the gradient and intercept given.
Worked solution
y = 3x + 2, so at x = 4, y = 12 + 2 = 14.
Mark scheme
1 mark for the equation, 1 mark for 14.
Common mistake
Forgetting to add the intercept.
Exam tip
Write the equation first, then substitute the x value.
Additional MathematicsYear 10Quadratic functionsHard2 marks
4. The diagram shows the curve y = x^2. What are the coordinates of its lowest point?
xy
  • A(0, 0)correct
  • B(1, 1)
  • C(0, 2)
  • D(2, 0)
The method
The lowest point of y = x^2 is its turning point.
Worked solution
The curve has its minimum at the origin, so the point is (0, 0).
Mark scheme
1 mark for identifying the turning point, 1 mark for (0, 0).
Common mistake
Reading an x-axis crossing rather than the minimum.
Exam tip
For y = x^2 the vertex sits at the origin.
Additional MathematicsYear 11DifferentiationHard3 marks
5. Differentiate y = x^3 and give the gradient function dy/dx at x = 2.
xy
Answer: 12
The method
Bring the power down and reduce it by one, then substitute.
Worked solution
dy/dx = 3x^2, so at x = 2 it is 3(4) = 12.
Mark scheme
1 mark for 3x^2, 1 for substitution, 1 for 12.
Common mistake
Forgetting to substitute after differentiating.
Exam tip
Differentiate first to get the gradient function, then put in the x value.
Additional MathematicsYear 8SequencesHard2 marks
6. The nth term of a sequence is 4n - 1. Work out the 10th term.
Answer: 39
The method
Substitute the term number into the rule.
Worked solution
4(10) - 1 = 40 - 1 = 39.
Mark scheme
1 mark for 40, 1 mark for 39.
Common mistake
Using n = 9 for the 10th term.
Exam tip
The 10th term means n = 10. Substitute carefully.
Additional MathematicsYear 9FunctionsHard2 marks
7. A function is f(x) = 2x^2 - 3. Work out f(3).
xy
Answer: 15
The method
Substitute the input and follow the order of operations.
Worked solution
f(3) = 2(3^2) - 3 = 2(9) - 3 = 18 - 3 = 15.
Mark scheme
1 mark for 18, 1 mark for 15.
Common mistake
Squaring after multiplying by 2.
Exam tip
Square first, then multiply, then subtract.
Additional MathematicsYear 9SurdsHard1 mark
8. Explain why the square root of 9 is rational but the square root of 2 is not.
Answer: 9 is a perfect square
The method
Think about which roots give exact whole numbers.
Worked solution
The square root of 9 is 3, a whole number, while the square root of 2 cannot be written as an exact fraction.
Mark scheme
1 mark for noting 9 is a perfect square or root 2 is non-terminating.
Common mistake
Assuming all square roots are irrational.
Exam tip
Perfect squares have whole-number roots and are rational.

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IGCSE Additional Mathematics questions: FAQs

Are these IGCSE Additional 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 Additional Mathematics syllabus, covering functions, indices, surds, differentiation and integration.

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.

How do I practise more Additional Mathematics questions?

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