Mathematics
Explore 17 authentic past paper questions categorized by topic.
If 15 men can do a piece of work in 20 days, how many days will 10 men take to do the same work?
Explanation: Inverse proportion: (15 men * 20 days) / 10 men = 30 days.
A train 150 meters long is moving at a speed of 90 km/h. How long will it take to cross a pole?
Explanation: First convert speed to m/s: 90 * (5/18) = 25 m/s. Time = Distance/Speed = 150/25 = 6 seconds.
What is the sum of adjacent angles formed on a straight line?
Explanation: Adjacent angles formed on a straight line are called linear pairs, and their sum is always 180°. This is the property of supplementary angles on a straight line.
What is the circumference of a circle with a radius of 8 cm?
Explanation: Circumference = 2πr = 2 × 3.14159 × 8 ≈ 50.27 cm. Using π ≈ 3.14 gives approximately 50.24 cm, rounded to 50.27 cm in exact calculation.
A cube has a volume of 64 cm³ and is painted on all sides. What is its total surface area?
Explanation: Volume = a³ = 64 → a = 4 cm. Surface Area = 6a² = 6 × (4)² = 6 × 16 = 96 cm². The total painted surface area of the cube is 96 cm².
What is the result of 21 ÷ 3?
Explanation: 21 ÷ 3 = 7. This is a basic division operation: 3 multiplied by 7 equals 21, confirming the answer.
A worker makes a basket in 2/3 of an hour. How many baskets does he make in 7.5 hours?
Explanation: Number of baskets = 7.5 ÷ (2/3) = 7.5 × 3/2 = 22.5/2 = 45/4 = 11.25 baskets. The answer expressed as a fraction is 45/4.
What is the sum of the absolute values of the coordinates of the point (-6, 8)?
Explanation: The sum of the absolute values of the coordinates of (-6, 8) is |-6| + |8| = 6 + 8 = 14. This gives the "taxicab" or Manhattan distance from the origin.
If 12 : 68 :: 30 : x, find the value of x.
Explanation: The ratio 68/12 = 17/3. Applying the same ratio: x = 30 × (17/3) = 170. Therefore, 12 : 68 :: 30 : 170.
A and B together can complete a work in 10 days. A alone can complete the same work in 12 days. In how many days can B alone complete that work?
Explanation: B's daily work = (A+B)'s daily work − A's daily work = 1/10 − 1/12 = 6/60 − 5/60 = 1/60. Therefore, B alone can complete the work in 60 days.
Simplify: (3x + 3y + x² − y²) ÷ (x + y) = ?
Explanation: (3x + 3y + x² − y²) ÷ (x + y) = [3(x + y) + (x + y)(x − y)] ÷ (x + y) = 3 + (x − y) = 3 + x − y.
If F(x) = x² − 1, what is the value of F(F(−1))?
Explanation: F(−1) = (−1)² − 1 = 1 − 1 = 0. Then F(F(−1)) = F(0) = (0)² − 1 = −1. Therefore, F(F(−1)) = −1.
If A and B are mutually exclusive events, which of the following is true?
Explanation: For mutually exclusive events, A and B cannot occur simultaneously. Therefore, their intersection A ∩ B is an empty set (∅), meaning P(A ∩ B) = 0.
In a creative writing competition, 45% of participants are boys. If 135 boys take part, what is the total number of participants?
Explanation: If 45% = 135 boys, then total = 135 ÷ 0.45 = 300. Therefore, the total number of students who participated in the competition is 300.
A rope is 75 cm long. When stretched, it reaches 90 cm. What is the percentage increase in length?
Explanation: Percentage increase = [(90 − 75) / 75] × 100 = [15 / 75] × 100 = 20%. The rope increased in length by 20%.
In radioactive decay, if the decay constant Lambda (λ) relates to half-life T½, which formula is correct?
Explanation: The decay constant λ is related to half-life T½ by the formula λ = ln(2) / T½, where ln(2) ≈ 0.693. This means a shorter half-life corresponds to a larger decay constant and faster decay.
What is the value of 10! ÷ 7!?
Explanation: 10! / 7! = (10 × 9 × 8 × 7!) / 7! = 10 × 9 × 8 = 720. Only the three extra factorial terms need to be multiplied.