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
A marine biologist in Jamaica is studying the growth of algae in Kingston Harbour. The algae population doubles every hour and is modelled by P = 50 × 2ᵗ, where t is time in hours. What is the initial population of algae?
- 100
- 0
- 2
- 50
Show answer & explanation
✓ Answer: D — 50
Award 1 mark for recognising that when t = 0, P = 50 × 2⁰ = 50 × 1 = 50. B is incorrect — the initial population is found at t = 0, giving 50. C is incorrect — 2 is the base of the exponential, not the initial value. A is incorrect — this would be the population after 1 hour.
Q2 · Difficulty 1/3
The vertical line test is used to determine whether a graph represents a function. What does the horizontal line test determine?
- Whether the function is many-to-one
- Whether the domain is restricted
- Whether the relation is one-to-many
- Whether the function is one-to-one
Show answer & explanation
✓ Answer: D — Whether the function is one-to-one
The horizontal line test checks if any horizontal line crosses the graph more than once. If it does not, the function is one-to-one. If it crosses more than once, the function is many-to-one.
Q3 · Difficulty 1/3
If y varies inversely as x, then:
- y = kx
- y = k + x
- y = kx²
- y = k/x
Show answer & explanation
✓ Answer: D — y = k/x
Inverse variation means y = k/x.
Q4 · Difficulty 2/3
y varies inversely as x. When x = 2, y = 10. Find k.
- 8
- 20
- 5
- 12
Show answer & explanation
✓ Answer: B — 20
y = k/x → 10 = k/2 → k = 20.
Q5 · Difficulty 2/3
A farmer in Guyana is designing a rectangular pen for chickens using 40 metres of fencing. One side of the pen is against an existing wall, so only three sides need fencing. If the width is x metres, the area A is given by A = x(40 - 2x). What width gives the maximum area?
- 5 m
- 10 m
- 15 m
- 20 m
Show answer & explanation
✓ Answer: B — 10 m
Award 1 mark for correct answer. Expanding: A = 40x - 2x². Using x = -b/(2a) = -40/(2×-2) = -40/(-4) = 10 m. A results from dividing total fencing by 4. C results from incorrect calculation. D results from dividing total fencing by 2.
Q6 · Difficulty 2/3
A graph shows the temperature (T °C) of rum during distillation in Trinidad plotted against time (t minutes). At t = 15 minutes, a tangent is drawn to the curve. The tangent passes through points (10, 65) and (20, 85). What is the gradient of the curve at t = 15 minutes?
- 1.5 °C per minute
- 2.0 °C per minute
- 3.0 °C per minute
- 4.0 °C per minute
Show answer & explanation
✓ Answer: B — 2.0 °C per minute
Award 1 mark for calculating gradient = (85 - 65)/(20 - 10) = 20/10 = 2.0 °C per minute. A is incorrect due to arithmetic error. C is incorrect, likely from calculating 20 - 10 = 10 but using 30 as rise. D is incorrect from calculation error.
Q7 · Difficulty 1/3
Which of the following inequalities is represented by the region ABOVE the line y = 2x + 3, where the boundary line is NOT included?
- y ≤ 2x + 3
- y ≥ 2x + 3
- y > 2x + 3
- y < 2x + 3
Show answer & explanation
✓ Answer: C — y > 2x + 3
A region above a line uses the 'greater than' inequality. Since the boundary is not included, the inequality is strict: y > 2x + 3. A solid line would indicate ≥ or ≤, while a dashed line indicates > or <.
Q8 · Difficulty 1/3
What is the equation of the axis of symmetry for the quadratic function y = x² - 6x + 11?
- x = 3
- x = 6
- x = -6
- x = -3
Show answer & explanation
✓ Answer: A — x = 3
Award 1 mark for correct answer. The axis of symmetry is x = -b/(2a) = -(-6)/(2×1) = 6/2 = 3. A results from using b directly with wrong sign. B results from incorrect sign application. D results from using b without dividing by 2a.
CXC CSEC Mathematics FAQ
What does the CXC CSEC Mathematics exam look like?
The CXC CSEC Mathematics exam is structured across 3 components. Paper 1 (Section A): 60 multiple-choice questions, 1 mark each. 75 minutes. Tests knowledge across the whole syllabus. Paper 2: Structured short-answer + 1 extended response question. Section A is compulsory; Section B has a choice. Approximately 2 hours 10 minutes. School-Based Assessment (SBA): Coursework component graded by the teacher, externally moderated. Worth ~20-30% of the final grade depending on subject. Total exam time: ~3.5 hours across Paper 1 and Paper 2 sittings.
Can I download a free CXC CSEC Mathematics past paper?
Real CXC past papers are published directly by CXC 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 CSEC Mathematics graded?
Grades: I (highest) to VI (lowest). A grade of III or above is typically required for further study. 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.