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CIE · IGCSE · Additional Mathematics

Free CIE IGCSE Additional 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 Additional 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 Additional Mathematics syllabus. Tap "Show answer" after each to check yourself.

Q1 · Difficulty 1/3

cos 0° equals:

  1. 0
  2. 0.5
  3. −1
  4. 1
Show answer & explanation
✓ Answer: D — 1
cos 0° = 1.
Q2 · Difficulty 1/3

A function is a rule that gives each input exactly one:

  1. axis
  2. gradient
  3. output
  4. graph
Show answer & explanation
✓ Answer: C — output
A function maps each input to exactly one output.
Q3 · Difficulty 1/3

The value of sin 30° is:

  1. 0.87
  2. 0.5
  3. 1
  4. 0
Show answer & explanation
✓ Answer: B — 0.5
sin 30° = 0.5.
Q4 · Difficulty 2/3

Solve: 2x + y = 7 and y = 1. Find x.

  1. 4
  2. 2
  3. 7
  4. 3
Show answer & explanation
✓ Answer: D — 3
2x + 1 = 7 → 2x = 6 → x = 3.
Q5 · Difficulty 2/3

|x| represents the ____ of x.

  1. reciprocal
  2. negative
  3. absolute value (magnitude)
  4. square
Show answer & explanation
✓ Answer: C — absolute value (magnitude)
|x| is the absolute value.
Q6 · Difficulty 2/3

An object at rest (not moving) has a velocity of:

  1. 1
  2. maximum
  3. undefined
  4. 0
Show answer & explanation
✓ Answer: D — 0
At rest, velocity = 0.
Q7 · Difficulty 1/3

Which of the following is the correct identity for sin²θ + cos²θ?

  1. 0
  2. 1
  3. 2
  4. tan²θ
Show answer & explanation
✓ Answer: B — 1
Award 1 mark for recognising the Pythagorean identity sin²θ + cos²θ = 1. A is incorrect — the sum of squares equals 1, not 0. C is incorrect — 2 would only result if sin²θ = cos²θ = 1, which is impossible simultaneously. D confuses this identity with the tan²θ + 1 = sec²θ identity.
Q8 · Difficulty 1/3

The function f(x) = 2x + 3 is defined for all real numbers. What is the inverse function f⁻¹(x)?

  1. f⁻¹(x) = x/2 - 3
  2. f⁻¹(x) = (x - 3)/2
  3. f⁻¹(x) = (x + 3)/2
  4. f⁻¹(x) = 2x - 3
Show answer & explanation
✓ Answer: B — f⁻¹(x) = (x - 3)/2
Award 1 mark for correct inverse. Let y = 2x + 3, then x = (y - 3)/2, so f⁻¹(x) = (x - 3)/2. C is incorrect — this adds 3 instead of subtracting. D is incorrect — this reverses operations in wrong order. A is incorrect — this subtracts 3 after dividing instead of before.
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CIE IGCSE Additional Mathematics FAQ

What does the CIE IGCSE Additional Mathematics exam look like?
The CIE IGCSE Additional 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 Additional 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 Additional 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.