Question 1
Solve for x: 3x + 5 = 20.
Show answer and explanation
Answer: x = 5
Subtract 5 from both sides to get 3x = 15, then divide both sides by 3.
Common misconception: Adding 5 instead of subtracting it from both sides.
Mathematics Practice Questions
12 questions. Work each one out before revealing the answer.
Question 2
What is 40% of 250?
- A. 75
- B. 100
- C. 110
- D. 125
Show answer and explanation
Answer: 100
40% is 0.4. Then 0.4 × 250 = 100. Alternatively, 10% is 25, so 40% is 4 × 25 = 100.
Common misconception: Dividing by 40 instead of multiplying by 0.4.
Question 3
What is the mean of 6, 8, 10 and 12?
- A. 8
- B. 9
- C. 10
- D. 36
Show answer and explanation
Answer: 9
The sum is 36 and there are four values, so the mean is 36 ÷ 4 = 9.
Common misconception: Forgetting to divide the sum by the number of values.
Question 4
Find the median of 3, 9, 5, 7 and 1.
Show answer and explanation
Answer: 5
Order the values: 1, 3, 5, 7, 9. The middle value is 5.
Common misconception: Taking the middle value without ordering the data first.
Question 5
A triangle has a base of 10 cm and a perpendicular height of 6 cm. What is its area?
Show answer and explanation
Answer: 30 cm²
Area = ½ × base × height = ½ × 10 × 6 = 30 cm².
Common misconception: Forgetting the half.
Question 6
A right-angled triangle has shorter sides of 9 cm and 12 cm. How long is the hypotenuse?
- A. 13 cm
- B. 15 cm
- C. 17 cm
- D. 21 cm
Show answer and explanation
Answer: 15 cm
c² = 9² + 12² = 81 + 144 = 225, so c = 15 cm.
Common misconception: Adding the sides (9 + 12) instead of squaring first.
Question 7
Solve x² − 7x + 12 = 0.
Show answer and explanation
Answer: x = 3 or x = 4
Two numbers that multiply to 12 and add to −7 are −3 and −4, so (x − 3)(x − 4) = 0. Check: 9 − 21 + 12 = 0 and 16 − 28 + 12 = 0.
Common misconception: Giving only one solution.
Question 8
A bag contains 4 red and 6 blue counters. One is picked at random. What is the probability it is red?
- A. 2/5
- B. 4/6
- C. 3/5
- D. 1/4
Show answer and explanation
Answer: 2/5
There are 10 counters and 4 are red, so the probability is 4/10 = 2/5.
Common misconception: Comparing red to blue (4/6) instead of red to total.
Question 9
A price rises from 50 to 65. What is the percentage increase?
- A. 15%
- B. 30%
- C. 23%
- D. 130%
Show answer and explanation
Answer: 30%
The increase is 15. Then 15 ÷ 50 × 100 = 30%.
Common misconception: Dividing by the new price instead of the original.
Question 10
Solve −3x < 12.
Show answer and explanation
Answer: x > −4
Divide both sides by −3 and reverse the inequality sign, giving x > −4. Check: x = 0 gives 0 < 12, which is true.
Common misconception: Forgetting to reverse the sign when dividing by a negative.
Question 11
A circle has radius 4 cm. Using π = 3.14, what is its area?
- A. 25.12 cm²
- B. 50.24 cm²
- C. 12.56 cm²
- D. 200.96 cm²
Show answer and explanation
Answer: 50.24 cm²
Area = πr² = 3.14 × 16 = 50.24 cm².
Common misconception: Using 2πr (circumference) or using the diameter as the radius.
Question 12
Write 3/8 as a decimal.
Show answer and explanation
Answer: 0.375
Divide the numerator by the denominator: 3 ÷ 8 = 0.375.
Common misconception: Dividing 8 by 3.
Study guides
- How to Revise AlgebraCornerstone guide
- Fractions, Decimals and Percentages ComparedSupporting explainer
- Solving Linear Equations Step by StepWorked example
- Solving Quadratic EquationsSupporting explainer