11 questions. Try each one, then open the answer to check yourself and read the explanation.
The curved surface area of a cylinder 7cm high is 140cm2. Find the radius of its base (π = 22/7)
Answer: A (3.18cm)
2πrh = 140 gives r = 140 ÷ (2 × 22/7 × 7) = 140 ÷ 44 ≈ 3.18 cm.
The locus of points equidistant from two points P and Q forms a
Answer: C (perpendicular line to PQ)
Points equally far from P and Q lie on the perpendicular bisector of PQ, a line perpendicular to PQ.
Find the sum to infinity of the series 1/4, 1/8, 1/16 ...
Answer: A (1/2)
a = 1/4 and r = 1/2, so S∞ = a/(1 − r) = (1/4)/(1/2) = 1/2.
A cylindrical tank has a capacity of 1540m3. What is the depth of the tank, assuming that the radius of its base is 7m?
Answer: A (10m)
πr²h = 1540: (22/7) × 49 × h = 154h = 1540, so h = 10 m.
Integrate with respect to t, (2t3 + 2t)/t
Answer: B (2t3/3 + 2t + k)
Simplify first: (2t³ + 2t)/t = 2t² + 2. Then ∫(2t² + 2)dt = 2t³/3 + 2t + k.
If the second term of a G.P is 8/9 and the 6th term is 4½. Find the common ratio
Answer: C (3/2)
ar⁵ ÷ ar = r⁴ = (9/2) ÷ (8/9) = 81/16, so r = 3/2.
From the diagram above, find the value of angle AD̂C
Answer: C (92°)
ABCD is a cyclic quadrilateral. The exterior angle PB̂C (92°) equals the interior opposite angle AD̂C, so AD̂C = 92°.
If line y = 5x + 3 is parallel to line y = kx + 5, estimate 2k + 1
Answer: C (11)
Parallel lines have equal gradients, so k = 5 and 2k + 1 = 11.
Calculate the perimeter of a sector of a circle of radius 12cm and angle 60°.
Answer: B ((24 + 4π)cm)
Arc = (60/360) × 2π × 12 = 4π; add the two radii (24 cm): perimeter = (24 + 4π) cm.
Given that 23x + 101x = 130x, find x
Answer: D (4)
(2x + 3) + (x² + 1) = x² + 3x, so 2x + 4 = 3x and x = 4.
Habib walked 16m up a slope and was 6m above the ground. If he walks 24m further up the slope, how far above the ground will he be?
Answer: C (15.0m)
Height grows in proportion to distance along the slope: h/40 = 6/16, so h = 15 m.