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CXC CAPE · · Pure Mathematics

Free CXC CAPE Pure Mathematics
Practice Paper

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

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What the real CXC CAPE Pure Mathematics paper looks like

Paper 01 (Multiple Choice)
45 multiple-choice questions, 1 mark each. About 1 hour 30 minutes. Tests knowledge across all three Modules of the Unit.
Paper 02 (Essay / Structured)
Extended essay and structured questions, one per Module. Around 2 hours 30 minutes. Tests developed argument, application and use of examples.
Paper 03 (Internal Assessment)
School-Based Assessment for school candidates (Paper 03/1) or an alternative written paper for private candidates (Paper 03/2). Coursework/research component worth a significant share of the Unit grade.
Total written exam time: ~4 hours across Paper 01 and Paper 02, plus the Internal Assessment.
Grading: Unit grades: I (highest) to VII (lowest), with a Grade Point Average and per-Module profile. Grades I–V are the pass range for most purposes.

Mini practice paper: 8 questions

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

Q1 · Difficulty 1/3

What is the modulus of 3 + 0i?

  1. 3
  2. 0
  3. 9
  4. √3
Show answer & explanation
✓ Answer: A — 3
Award 1 mark. For a real number the modulus is simply its distance from zero along the real axis.
Q2 · Difficulty 1/3

Find 2(3 + i).

  1. 6 + i
  2. 3 + 2i
  3. 6 + 2i
  4. 5 + 3i
Show answer & explanation
✓ Answer: C — 6 + 2i
Award 1 mark. Both the real and the imaginary parts are multiplied by 2.
Q3 · Difficulty 1/3

What is the modulus of 0 + 4i?

  1. 0
  2. 4
  3. 16
  4. −4
Show answer & explanation
✓ Answer: B — 4
Award 1 mark. The modulus is a distance and is never negative, so it is 4 rather than −4.
Q4 · Difficulty 1/3

What is the imaginary part of 5 + 3i?

  1. 5
  2. 3i
  3. 3
  4. 8
Show answer & explanation
✓ Answer: C — 3
Award 1 mark. The imaginary part is the coefficient of i, quoted without the i itself.
Q5 · Difficulty 1/3

Evaluate √25.

  1. 12.5
  2. 625
  3. 10
  4. 5
Show answer & explanation
✓ Answer: D — 5
Award 1 mark. 5 × 5 = 25, so 5 is the positive square root.
Q6 · Difficulty 1/3

What is the complex conjugate of 4 − 5i?

  1. −4 + 5i
  2. 4 + 5i
  3. −4 − 5i
  4. 5 − 4i
Show answer & explanation
✓ Answer: B — 4 + 5i
Award 1 mark. The conjugate is formed by reversing the sign of the imaginary part only.
Q7 · Difficulty 1/3

Simplify (x²)³.

  1. x⁶
  2. x⁵
  3. x⁸
  4. x⁹
Show answer & explanation
✓ Answer: A — x⁶
Award 1 mark. Raising a power to a power multiplies the indices, and 2 × 3 = 6.
Q8 · Difficulty 1/3

What is a purely imaginary number?

  1. A number whose imaginary part is zero
  2. A number whose real part is zero but whose imaginary part is not
  3. Any number containing the symbol i
  4. A number that cannot be plotted on an Argand diagram
Show answer & explanation
✓ Answer: B — A number whose real part is zero but whose imaginary part is not
Award 1 mark. Such numbers lie on the vertical axis of an Argand diagram.
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CXC CAPE Pure Mathematics FAQ

What does the CXC CAPE Pure Mathematics exam look like?
The CXC CAPE Pure Mathematics exam is structured across 3 components. Paper 01 (Multiple Choice): 45 multiple-choice questions, 1 mark each. About 1 hour 30 minutes. Tests knowledge across all three Modules of the Unit. Paper 02 (Essay / Structured): Extended essay and structured questions, one per Module. Around 2 hours 30 minutes. Tests developed argument, application and use of examples. Paper 03 (Internal Assessment): School-Based Assessment for school candidates (Paper 03/1) or an alternative written paper for private candidates (Paper 03/2). Coursework/research component worth a significant share of the Unit grade. Total written exam time: ~4 hours across Paper 01 and Paper 02, plus the Internal Assessment.
Can I download a free CXC CAPE Pure Mathematics past paper?
Real CXC CAPE past papers are published directly by CXC CAPE 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 CXC CAPE Pure Mathematics graded?
Unit grades: I (highest) to VII (lowest), with a Grade Point Average and per-Module profile. Grades I–V are the pass range for most purposes. 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.