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
In vector notation, the vector from point A to point B is written as:
- AB
- **AB**
- →AB
- with arrow from A to B above AB
Show answer & explanation
✓ Answer: D — with arrow from A to B above AB
Award 1 mark for recognising standard vector notation. A is incorrect — this represents a line segment without direction. B is incorrect — bold notation is used for single letter vectors like **a**. C is incorrect — the arrow should be above the letters, not before them.
Q2 · Difficulty 1/3
A translation moves every point on a shape by the vector (3, -2). Which of the following correctly describes this movement?
- 3 units left and 2 units up
- 3 units left and 2 units down
- 3 units right and 2 units down
- 3 units right and 2 units up
Show answer & explanation
✓ Answer: C — 3 units right and 2 units down
A translation vector (a, b) moves points a units in the positive x-direction and b units in the positive y-direction. Since a = 3 (positive), movement is 3 units right; since b = -2 (negative), movement is 2 units down. Option A confuses positive x with left. Option B incorrectly treats -2 as upward. Option D confuses both signs.
Q3 · Difficulty 1/3
Which matrix represents reflection in the y-axis?
- [[-1, 0], [0, -1]]
- [[1, 0], [0, -1]]
- [[-1, 0], [0, 1]]
- [[0, 1], [1, 0]]
Show answer & explanation
✓ Answer: C — [[-1, 0], [0, 1]]
Award 1 mark for correct identification. Reflection in y-axis maps (x, y) to (-x, y), giving the matrix shown. B is incorrect — this represents reflection in the x-axis. D is incorrect — this represents reflection in the line y = x. A is incorrect — this represents rotation 180° about the origin.
Q4 · Difficulty 2/3
A surveyor in Indonesia uses vectors to map terrain. She walks from point P to point Q along vector **p** = (5, 2), then from Q to R along vector **q** = (−3, 4). What is the resultant displacement vector from P to R?
- (8, 6)
- (2, 6)
- (−2, 2)
- (15, 8)
Show answer & explanation
✓ Answer: B — (2, 6)
Award 1 mark for correctly adding vectors: **p** + **q** = (5 + (−3), 2 + 4) = (2, 6). A is incorrect — this adds the absolute values (5 + 3, 2 + 4). C is incorrect — this subtracts both components incorrectly. D is incorrect — this multiplies the components.
Q5 · Difficulty 2/3
The transformation matrix M represents a reflection in the y-axis. Which matrix represents the inverse transformation M⁻¹?
- [[0, -1], [-1, 0]]
- [[-1, 0], [0, 1]]
- [[1, 0], [0, -1]]
- [[0, 1], [1, 0]]
Show answer & explanation
✓ Answer: B — [[-1, 0], [0, 1]]
Award 1 mark for recognising that a reflection is a self-inverse transformation, so M⁻¹ = M. The matrix for reflection in the y-axis is [[-1, 0], [0, 1]]. C is incorrect as this represents reflection in the x-axis. D is incorrect as this represents reflection in y = x. A is incorrect as this represents reflection in y = -x.
Q6 · Difficulty 2/3
In triangle OAB, OA = a and OB = b. Point M is the midpoint of AB. Which expression correctly gives the vector OM?
- OM = b − ½a
- OM = a + b
- OM = ½a + ½b
- OM = ½a − ½b
Show answer & explanation
✓ Answer: C — OM = ½a + ½b
OM = OA + AM = a + ½(b − a) = a + ½b − ½a = ½a + ½b. This equals ½(a + b). Option A omits the factor of ½. Option B incorrectly subtracts rather than adds the half-vectors. Option D uses an incorrect route and arithmetic.
Q7 · Difficulty 1/3
The point P(3, −2) is transformed by the matrix [[1, 0], [0, -1]]. What are the coordinates of the image P′?
- (−3, 2)
- (2, −3)
- (3, 2)
- (−3, −2)
Show answer & explanation
✓ Answer: C — (3, 2)
Award 1 mark for correct matrix multiplication. [[1, 0], [0, -1]][[3], [-2]] = [[3], [2]]. D is incorrect — this reflects in the y-axis. A is incorrect — this reflects in both axes. B is incorrect — this confuses x and y coordinates.
Q8 · Difficulty 1/3
Given that **p** = (−3, 4), what is 2**p**?
- (−3, 8)
- (−6, 8)
- (−1, 6)
- (−6, 4)
Show answer & explanation
✓ Answer: B — (−6, 8)
Award 1 mark for correct scalar multiplication: 2 × (−3, 4) = (2 × −3, 2 × 4) = (−6, 8). C is incorrect — this adds 2 to each component. D is incorrect — this only multiplies the x-component. A is incorrect — this only multiplies the y-component.
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.