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
Express 0.00347 in standard form.
- 34.7 × 10⁻⁴
- 0.347 × 10⁻²
- 3.47 × 10⁻³
- 3.47 × 10⁻²
Show answer & explanation
✓ Answer: C — 3.47 × 10⁻³
To write 0.00347 in standard form, move the decimal point 3 places to the right to get 3.47, giving 3.47 × 10⁻³. Option A uses the wrong power (10⁻² corresponds to moving only 2 places). Option B has A = 34.7 which is outside the required range 1 ≤ A < 10. Option D has A = 0.347 which is also outside the required range.
Q2 · Difficulty 1/3
A student calculates the variance of a sample of 10 values and obtains 36. What is the standard deviation of this sample?
- 1296
- 18
- 6
- 3.6
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✓ Answer: C — 6
Standard deviation = √variance = √36 = 6. Option B divides the variance by 10 (the sample size) instead of taking the square root. Option C halves the variance, confusing variance with standard deviation. Option D squares the variance instead of taking the square root.
Q3 · Difficulty 1/3
The midpoint of the line segment joining A(−3, 7) and B(5, −1) is:
- (−1, 4)
- (1, 3)
- (4, 4)
- (1, 4)
Show answer & explanation
✓ Answer: B — (1, 3)
Applying the midpoint formula: x = (−3 + 5)/2 = 2/2 = 1 and y = (7 + (−1))/2 = 6/2 = 3, giving midpoint (1, 3). Option B arises from finding the differences rather than sums. Option C miscalculates the x-average. Option D uses an incorrect y-calculation by not dividing by 2.
Q4 · Difficulty 1/3
What is the nth term of the arithmetic sequence 5, 8, 11, 14, …?
- 3n + 5
- 2n + 3
- 5n + 3
- 3n + 2
Show answer & explanation
✓ Answer: D — 3n + 2
The first term a = 5 and common difference d = 3. The nth term formula is a + (n−1)d = 5 + (n−1)×3 = 3n + 2. Option B gives 3(1)+5=8, not 5. Option C gives 5(1)+3=8, not 5. Option D gives 2(1)+3=5 but 2(2)+3=7, not 8.
Q5 · Difficulty 1/3
The product moment correlation coefficient (PMCC) for a data set is calculated as r = −0.92. Which interpretation is most appropriate?
- There is no linear relationship between the two variables
- There is a strong positive linear correlation between the two variables
- There is a strong negative linear correlation between the two variables
- There is a weak negative linear correlation between the two variables
Show answer & explanation
✓ Answer: C — There is a strong negative linear correlation between the two variables
A PMCC value of −0.92 is close to −1, indicating a strong negative linear correlation: as one variable increases, the other decreases in a nearly linear manner. Option A is incorrect because a negative r cannot indicate positive correlation. Option B is incorrect; r = 0 would indicate no linear relationship. Option D is incorrect; values of r close to −1 indicate strong, not weak, correlation.
Q6 · Difficulty 1/3
A geometric series has first term 8 and common ratio 1/2. What is the sum to infinity of this series?
- 8
- 4
- 12
- 16
Show answer & explanation
✓ Answer: D — 16
The sum to infinity formula is S∞ = a/(1 − r) = 8/(1 − 0.5) = 8/0.5 = 16. Option B arises from using S∞ = a/r. Option C is just the first term. Option D is the second term of the series.
Q7 · Difficulty 1/3
A line has equation y = 3x − 7. Which of the following is the equation of a line parallel to this line passing through (0, 4)?
- y = −(1/3)x + 4
- y = 3x + 4
- y = 7x + 4
- y = 3x − 4
Show answer & explanation
✓ Answer: B — y = 3x + 4
Parallel lines share the same gradient. The gradient of y = 3x − 7 is 3. A line through (0, 4) with gradient 3 has equation y = 3x + 4. Option A uses the perpendicular gradient instead. Option C has the correct gradient but the wrong y-intercept, using the original constant. Option D confuses the y-intercept value of the original line with the gradient.
Q8 · Difficulty 1/3
The vector AB = (6, -8). What is the magnitude of vector AB?
- √28 units
- 10 units
- 14 units
- 7 units
Show answer & explanation
✓ Answer: B — 10 units
The magnitude of a vector (a, b) is calculated using |AB| = √(a² + b²). Here, |AB| = √(6² + (-8)²) = √(36 + 64) = √100 = 10 units. Option A adds the components directly. Option C doubles the correct answer, a common scale error. Option D incorrectly computes √(4+24) by halving components.
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.