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CIE · IGCSE · Mathematics

Free CIE IGCSE Mathematics
Practice Paper

8 mixed-difficulty practice questions in the style of real CIE IGCSE papers — answers, mark-scheme-style explanations, and the official exam structure all on one page.

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What the real CIE IGCSE Mathematics paper looks like

Paper 1 (Multiple Choice)
40 multiple-choice questions, 1 mark each. 45 minutes. Tests breadth of knowledge.
Paper 2 (Core) / Paper 4 (Extended)
Structured written paper. 1 hour 30 minutes (Core) or 1 hour 45 minutes (Extended). Tests depth of understanding and application.
Paper 6 (Alternative to Practical)
Written paper assessing practical skills for candidates without lab access. 1 hour. Worth ~20% of the total.
Total exam time: ~3 hours, depending on tier (Core vs Extended).
Grading: Grades: A* (highest) to G (lowest), with U (ungraded). Most universities require C or above.

Mini practice paper: 8 questions

Mixed-difficulty questions from across the Mathematics syllabus. Tap "Show answer" after each to check yourself.

Q1 · Difficulty 1/3

Which of the following is the correct definition of a rational number?

  1. A number whose square root is always an integer
  2. A number that has a finite decimal expansion only
  3. A number that is always a positive integer or zero
  4. A number that can be written as p/q where p and q are integers and q ≠ 0
Show answer & explanation
✓ Answer: D — A number that can be written as p/q where p and q are integers and q ≠ 0
A rational number is defined as any number expressible in the form p/q where p and q are integers and q ≠ 0. Option B is wrong because rational numbers can also be recurring decimals, not just finite ones. Option C incorrectly restricts rationals to non-negative integers. Option D describes perfect squares, not rational numbers.
Q2 · Difficulty 1/3

In the diagram, O is the centre of the circle. Points A, B and C lie on the circumference. Angle AOB = 124°. What is the size of angle ACB?

  1. 56°
  2. 62°
  3. 124°
  4. 236°
Show answer & explanation
✓ Answer: B — 62°
Award 1 mark for correct application of the angle at centre theorem: the angle at the centre is twice the angle at the circumference standing on the same arc. Angle ACB = 124° ÷ 2 = 62°. A is incorrect — this would be 180° − 124° which is not relevant here. C is incorrect — this confuses the angle at the centre with the angle at the circumference. D is incorrect — this is the reflex angle at the centre, not the angle at the circumference.
Q3 · Difficulty 1/3

Which of the following correctly states the condition for two triangles to be congruent by the SAS (Side-Angle-Side) rule?

  1. All three sides are proportional between both triangles
  2. Two sides and any angle are equal in both triangles
  3. Two sides and the included angle are equal in both triangles
  4. Two angles and the included side are equal in both triangles
Show answer & explanation
✓ Answer: C — Two sides and the included angle are equal in both triangles
SAS congruence requires two sides AND the angle between them (the included angle) to be equal. Option A is incorrect because the angle must specifically be the included one. Option C describes the ASA rule, not SAS. Option D describes similarity (SSS~), not congruence.
Q4 · Difficulty 1/3

A triangle has interior angles of 47° and 83°. What is the size of the third interior angle?

  1. 50°
  2. 40°
  3. 60°
  4. 70°
Show answer & explanation
✓ Answer: A — 50°
The sum of interior angles in any triangle is 180°. So the third angle = 180° − 47° − 83° = 50°. Option A (40°) results from subtracting incorrectly. Option C (60°) is a common guess assuming an equilateral triangle. Option D (70°) arises from adding the two given angles incorrectly.
Q5 · Difficulty 1/3

An engineer is designing a circular gear mechanism. Points P, Q and R lie on the circumference of a circle with centre O. PR is a diameter of the circle. What is the size of angle PQR?

  1. 45°
  2. 90°
  3. 180°
  4. Cannot be determined
Show answer & explanation
✓ Answer: B — 90°
Award 1 mark for applying the theorem that the angle in a semicircle is a right angle. Since PR is a diameter, angle PQR = 90°. A is incorrect — this is half of the correct answer, a common misconception. C is incorrect — this confuses the angle with a straight line. D is incorrect — the angle can always be determined as 90° when the angle is subtended by a diameter.
Q6 · Difficulty 1/3

A circular garden feature is designed with a decorative stone path forming a chord AB. The perpendicular from the centre O of the circle to the chord AB meets AB at point M. Which statement about this construction is correct?

  1. AM = MB
  2. Angle OMA = 45°
  3. OM = MA
  4. Angle AMO = angle BMO = 60°
Show answer & explanation
✓ Answer: A — AM = MB
Award 1 mark for recognising that the perpendicular from the centre of a circle to a chord bisects the chord. B is incorrect — angle OMA = 90° as OM is perpendicular to AB. C is incorrect — there is no theorem stating these lengths are equal. D is incorrect — angle AMO = angle BMO = 90°, not 60°.
Q7 · Difficulty 1/3

What is the sum of the interior angles of a triangle?

  1. 90°
  2. 180°
  3. 270°
  4. 360°
Show answer & explanation
✓ Answer: B — 180°
Award 1 mark for correctly stating the angle sum of a triangle. A is incorrect — 90° is a right angle, not the sum of angles in a triangle. C is incorrect — 270° is the sum of three right angles. D is incorrect — 360° is the sum of angles in a quadrilateral, not a triangle.
Q8 · Difficulty 1/3

What is the sum of the interior angles of a hexagon?

  1. 540°
  2. 720°
  3. 900°
  4. 1080°
Show answer & explanation
✓ Answer: B — 720°
Award 1 mark for correct answer. Using the formula (n-2) × 180° where n = 6: (6-2) × 180° = 4 × 180° = 720°. A is incorrect — this is the sum for a pentagon (n=5). C is incorrect — this is the sum for a heptagon (n=7). D is incorrect — this is the sum for an octagon (n=8).
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CIE IGCSE Mathematics FAQ

What does the CIE IGCSE Mathematics exam look like?
The CIE IGCSE Mathematics exam is structured across 3 components. Paper 1 (Multiple Choice): 40 multiple-choice questions, 1 mark each. 45 minutes. Tests breadth of knowledge. Paper 2 (Core) / Paper 4 (Extended): Structured written paper. 1 hour 30 minutes (Core) or 1 hour 45 minutes (Extended). Tests depth of understanding and application. Paper 6 (Alternative to Practical): Written paper assessing practical skills for candidates without lab access. 1 hour. Worth ~20% of the total. Total exam time: ~3 hours, depending on tier (Core vs Extended).
Can I download a free CIE IGCSE Mathematics past paper?
Real CIE past papers are published directly by CIE on their official website. Kramizo doesn't redistribute copyrighted past papers, but we do generate free AI-written practice papers in the exact same style — same command words, same difficulty tier, same mark conventions. Use this practice paper as warm-up, then time yourself on official past papers before exam day.
How is CIE IGCSE Mathematics graded?
Grades: A* (highest) to G (lowest), with U (ungraded). Most universities require C or above. Kramizo's practice questions are tagged with difficulty 1-3 mapping roughly to the lower, middle, and top grade boundaries you'll encounter in the real exam.