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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

Calculate: -8 + 15 - 23 + 6

  1. -10
  2. -4
  3. 10
  4. 42
Show answer & explanation
✓ Answer: A — -10
Award 1 mark for correct calculation: -8 + 15 = 7, then 7 - 23 = -16, then -16 + 6 = -10. B is incorrect (likely adds -8 + 6 - 23 + 15 incorrectly). C is incorrect (sign error). D incorrectly adds absolute values without considering signs.
Q2 · 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.
Q3 · Difficulty 1/3

Two triangles are congruent. Which of the following conditions is sufficient to prove congruence?

  1. One pair of equal sides and one pair of equal angles
  2. Three pairs of equal angles (AAA)
  3. Two pairs of equal sides and one pair of equal angles (SSA)
  4. Two pairs of equal angles and one pair of equal corresponding sides (AAS)
Show answer & explanation
✓ Answer: D — Two pairs of equal angles and one pair of equal corresponding sides (AAS)
Award 1 mark for identifying AAS as a valid congruence condition. B is incorrect — AAA proves similarity, not congruence, as triangles could be different sizes. C is incorrect — SSA (or ASS) is not a valid congruence condition as it can produce two different triangles. A is incorrect — insufficient information to prove congruence.
Q4 · Difficulty 1/3

A data set has a mean of 50 and a standard deviation of 10. A value of 70 is included in the data set. What is the z-score of this value?

  1. z = 2.5
  2. z = 1.5
  3. z = 2.0
  4. z = 0.5
Show answer & explanation
✓ Answer: C — z = 2.0
The z-score is calculated using z = (x − μ) / σ = (70 − 50) / 10 = 20 / 10 = 2.0. Option A would result from using a difference of 15 instead of 20. Option C would result from dividing by 40 instead of 10. Option D would result from an arithmetic error giving a difference of 25.
Q5 · Difficulty 1/3

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

  1. 50°
  2. 60°
  3. 40°
  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 C (40°) results from subtracting only one angle from 90°. Option A (60°) is a common guess assuming an equilateral-like triangle. Option B (70°) results from an arithmetic error adding 47 + 83 incorrectly as 110 instead of 130.
Q6 · Difficulty 1/3

A bag contains 5 red balls and 3 blue balls. One ball is drawn at random. What is the probability that it is red?

  1. 3/5
  2. 3/8
  3. 5/8
  4. 5/3
Show answer & explanation
✓ Answer: C — 5/8
Probability = favourable outcomes / total outcomes = 5/8. Option C (3/8) is the probability of drawing blue, not red. Option D (5/3) is greater than 1 and cannot be a probability. Option B (3/5) incorrectly uses only the blue and red counts as a ratio rather than the full sample space.
Q7 · Difficulty 1/3

A solid cone has base radius 5 cm and perpendicular height 12 cm. Calculate the volume of the cone.

  1. 100 cm³
  2. 314 cm³
  3. 100π cm³
  4. 300 cm³
Show answer & explanation
✓ Answer: B — 314 cm³
Award 1 mark for correct application of V = ⅓πr²h = ⅓π(5)²(12) = 100π ≈ 314.16 cm³. C is incorrect — this gives 100π without evaluation. D is incorrect — this omits π from the calculation. A is incorrect — this uses the formula without the factor ⅓.
Q8 · Difficulty 1/3

In the diagram, PT is a tangent to the circle at T. O is the centre of the circle and angle OTP = 90°. If angle TOP = 54°, what is the size of angle TPO?

  1. 36°
  2. 54°
  3. 126°
  4. 27°
Show answer & explanation
✓ Answer: A — 36°
Award 1 mark for recognising that angles in a triangle sum to 180°. In triangle OTP: angle TPO = 180° − 90° − 54° = 36°. D is incorrect — this halves angle TOP incorrectly. B is incorrect — this confuses angle TPO with angle TOP. C is incorrect — this is 180° − 54°, ignoring the right angle.
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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.