7 questions. Try each one, then open the answer to check yourself and read the explanation.
A man kept 6 black, 5 brown and 7 purple shirts in a drawer. What is the probability of him picking a purple shirt at random
Answer: B (7/18)
There are 18 shirts and 7 are purple, so the probability is 7/18.
A number of pencils were shared out among Peter, Paul and Audu in the ratio 2:3:5 respectively. If Peter got 5, how many were shared?
Answer: B (25)
Peter's share is 2/10 of the total. 2/10 × total = 5, so total = 25.
Evaluate the integral ∫12(x2 + 1/x)dx
Answer: B (7/3 + ln 2)
The integral is x³/3 + ln x. From 1 to 2: (8/3 + ln 2) − (1/3 + 0) = 7/3 + ln 2.
A man walks 30m from a point P on a bearing of 040° to a point Q. He then walks 30m on a bearing of 140° to a point R. The bearing of R from P is
Answer: A (90°)
At Q the angle PQR = 220° − 140° = 80°. PQ = QR, so the base angles are 50° each. Bearing of R from P = 40° + 50° = 090°.
A rectangular hexagon is constructed inside a circle of a diameter 12 cm. Calculate the area of the hexagon
Answer: C (54√3 cm2)
A regular hexagon in a circle of radius 6 cm splits into 6 equilateral triangles of side 6. Area = 6 × ½ × 6 × 6 × sin 60° = 54√3 cm².
If the three consecutive terms of a GP are n − 2, n and n + 3, find the common ratio
Answer: D (1½)
n/(n − 2) = (n + 3)/n gives n² = n² + n − 6, so n = 6. The terms are 4, 6, 9 and the ratio is 6/4 = 1½.
In a triangle ABC, if AB = 15cm and angle ABC = 45° while angle AĈB = 60°, find the length of line AC
Answer: D (5√6 cm)
Sine rule: AC/sin 45° = 15/sin 60°. AC = 15 × (√2/2) ÷ (√3/2) = 15√2/√3 = 5√6 cm.