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
Which method is most commonly used to solve a pair of simultaneous equations where one is linear and one is quadratic?
- A) Elimination by adding the two equations
- B) Substitution of the linear equation into the quadratic
- C) Graphing only, without algebraic working
- D) Multiplying both equations by the same constant
Show answer & explanation
✓ Answer: B — B) Substitution of the linear equation into the quadratic
When one equation is linear and one is quadratic, substitution is the standard method. The linear equation is rearranged for one variable and substituted into the quadratic, producing a quadratic equation in one unknown. Elimination by adding is used for two linear equations, not this type.
Q2 · Difficulty 1/3
What is the formula for the volume of a cylinder with radius r and height h?
- V = πr²h
- V = 2πrh
- V = πrh²
- V = πr²h²
Show answer & explanation
✓ Answer: A — V = πr²h
The volume of a cylinder is found by multiplying the area of the circular cross-section (πr²) by the height h. Common errors include confusing this with the curved surface area formula 2πrh.
Q3 · Difficulty 1/3
y is inversely proportional to x. When x = 5, y = 8. Which equation correctly represents this relationship?
- A) y = 8x/5
- B) y = 5x/8
- C) y = 40/x
- D) y = x/40
Show answer & explanation
✓ Answer: C — C) y = 40/x
Inverse proportion gives y = k/x where k = xy = 5 × 8 = 40. Therefore y = 40/x. Option A and B confuse direct and inverse proportion, and option D inverts the relationship incorrectly.
Q4 · Difficulty 2/3
A car travels a fixed distance. The time taken (t) is inversely proportional to the speed (v). It takes 3 hours at 60 mph. How long will it take at 90 mph?
- A) 1 hour
- B) 1.5 hours
- C) 2 hours
- D) 4.5 hours
Show answer & explanation
✓ Answer: C — C) 2 hours
k = tv = 3 × 60 = 180. At 90 mph: t = 180/90 = 2 hours. Option D incorrectly adds the ratio, and option A confuses the relationship by tripling instead of applying inverse proportion correctly.
Q5 · Difficulty 2/3
A triangular prism has a right-angled triangular cross-section with base 6 cm and height 4 cm. The length of the prism is 10 cm. What is the volume of the prism?
- 120 cm³
- 240 cm³
- 60 cm³
- 480 cm³
Show answer & explanation
✓ Answer: A — 120 cm³
The area of the triangular cross-section is (1/2) × 6 × 4 = 12 cm². Multiplying by the length gives 12 × 10 = 120 cm³. A common error is forgetting the factor of 1/2 in the triangle area formula, giving 240 cm³.
Q6 · Difficulty 2/3
A box has 5 chocolates: 3 dark and 2 milk. Two are chosen at random without replacement. What is the probability that the second chocolate is dark, given that the first was also dark?
- A) 3/5
- B) 2/4
- C) 3/4
- D) 2/5
Show answer & explanation
✓ Answer: B — B) 2/4
After one dark chocolate is removed, 4 chocolates remain of which 2 are dark. So P(dark second | dark first) = 2/4 = 1/2. Option A incorrectly uses the original proportion, and C and D are errors in counting remaining chocolates.
Q7 · Difficulty 3/3
The pressure P of a gas is inversely proportional to its volume V (at constant temperature). A gas has pressure 120 kPa at volume 5 m³. A second gas sample has pressure 80 kPa. What volume does the second sample occupy?
- A) 3.33 m³
- B) 6 m³
- C) 7.5 m³
- D) 53.3 m³
Show answer & explanation
✓ Answer: C — C) 7.5 m³
k = PV = 120 × 5 = 600. For the second sample: V = 600/80 = 7.5 m³. Option B incorrectly uses a linear ratio (80/120 × something), and option A divides the pressures without using the constant k.
Q8 · Difficulty 3/3
A bag contains 4 green and 6 yellow balls. Two balls are drawn without replacement. Using a tree diagram, what is P(one green and one yellow) in either order?
- A) 8/15
- B) 4/15
- C) 24/100
- D) 12/25
Show answer & explanation
✓ Answer: A — A) 8/15
P(GY) = 4/10 × 6/9 = 24/90 and P(YG) = 6/10 × 4/9 = 24/90. Adding gives 48/90 = 8/15. Option C uses replacement (4/10 × 6/10 + 6/10 × 4/10 = 48/100), a common error when students do not adjust denominators.
AQA GCSE Mathematics FAQ
What does the AQA GCSE Mathematics exam look like?
The AQA GCSE Mathematics exam is structured across 3 components. Paper 1: Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 1-4 of the specification. Paper 2: Approximately 1 hour 30 minutes, ~70-100 marks. Covers Topics 5-8 of the specification. Paper 3: Where applicable — e.g. Combined Science, Languages. Includes synoptic and applied questions. Total exam time: ~3 hours across two or three papers.
Can I download a free AQA GCSE Mathematics past paper?
Real AQA past papers are published directly by AQA 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 AQA GCSE Mathematics graded?
Grades: 9 (highest) to 1 (lowest), with U (ungraded). A grade of 4 is a standard pass; 5 is a strong pass. 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.