25 questions. Try each one, then open the answer to check yourself and read the explanation.
The sum of the first n terms of an A.P is given by Sn = 3n2 + 2n. What is the fifth term of the progression?
Answer: C (29)
T₅ = S₅ − S₄ = (75 + 10) − (48 + 8) = 85 − 56 = 29.
If the radius of a circle is triples, by what factor does the area increase?
Answer: C (9)
Area is proportional to r²; tripling r multiplies the area by 3² = 9.
If sin x = 3/5 and x is in the second quadrant, what is cos x?
Answer: A (−4/5)
The adjacent side is √(5² − 3²) = 4, so |cos x| = 4/5; cosine is negative in the second quadrant, giving −4/5.
What is the equation of the line passing through the point (1, −2) and perpendicular to y = 2x + 3?
Answer: D (y = −½x − 3/2)
The perpendicular gradient is −1/2. y + 2 = −½(x − 1) gives y = −½x − 3/2.
What is the sum of the roots of the equation x2 + 5x − 6 = 0?
Answer: B (−5)
Sum of roots = −b/a = −5/1 = −5.
If a square has a perimeter of 24cm, what is its area?
Answer: A (36cm2)
Each side is 24 ÷ 4 = 6 cm, so the area is 6² = 36 cm².
If a cone has a height of 12cm and volume of 144πcm3, what is the radius of the cone?
Answer: D (6cm)
(1/3)πr² × 12 = 144π gives 4r² = 144, r² = 36, r = 6 cm.
What is the sum of the interior angles of a polygon with 12 sides
Answer: C (1800°)
Sum = (n − 2) × 180° = 10 × 180° = 1800°.
If f(x) = x3 − 2x2 + x − 1, evaluate f(2)?
Answer: A (1)
f(2) = 8 − 8 + 2 − 1 = 1.
What is the value of sin 60° + cos 30°
Answer: C (√3)
sin 60° = cos 30° = √3/2, so the sum is √3.
If f(x) = 2x2 − 3x + 4 and g(x) = x − 1, what is the value of f(g(2))?
Answer: D (3)
g(2) = 1, and f(1) = 2 − 3 + 4 = 3.
The sum of the first n terms of geometric progression is given by Sn = 15(2n − 1). What is the common ratio of the progression?
Answer: A (2)
This matches Sₙ = a(rⁿ − 1)/(r − 1) with r = 2 (and a = 15). Check: T₁ = 15, T₂ = S₂ − S₁ = 45 − 15 = 30.
The distance between the points (2, 3) and (−4, 1) is
Answer: C (2√10)
d = √((−4 − 2)² + (1 − 3)²) = √(36 + 4) = √40 = 2√10.
The equation of the circle with centre (2, −3) and radius 5 is
Answer: A ((x − 2)2 + (y + 3)2 = 25)
A circle with centre (a, b) and radius r is (x − a)² + (y − b)² = r², giving (x − 2)² + (y + 3)² = 25.
What is the remainder when 3x4 − 5x3 + 2x2 − x + 4 is divided by x − 2?
Answer: A (18)
f(2) = 48 − 40 + 8 − 2 + 4 = 18.
What is the value of sin2 θ + cos2 θ
Answer: A (1)
This is the Pythagorean identity: sin²θ + cos²θ = 1 for every θ.
The radius of a circle is increasing at a rate of 2cm/s. What is the rate of change of the area of the circle when the radius is 5cm?
Answer: B (20πcm2/s)
dA/dt = 2πr × dr/dt = 2π(5)(2) = 20π cm²/s.
What is the midpoint of the line segment with end points (3, 5) and (7, 9)?
Answer: A ((5, 7))
Midpoint = ((3 + 7)/2, (5 + 9)/2) = (5, 7).
log2(x + 3) − log2 x = 2, solve for x
Answer: D (1)
log₂((x + 3)/x) = 2, so (x + 3)/x = 4, x + 3 = 4x and x = 1.
Find the area of a triangle with sides of length 6, 8 and 10
Answer: B (24 square units)
6² + 8² = 10², so it is right-angled with legs 6 and 8: area = ½ × 6 × 8 = 24.
2x+1 = 16, find x
Answer: C (3)
16 = 2⁴, so x + 1 = 4 and x = 3.
If a cylinder has a radius of 4cm and a height of 10cm, what is its volume?
Answer: C (160πcm3)
V = πr²h = π × 16 × 10 = 160π cm³.
A circle has a radius of 5cm. What is the length of an arc subtending an angle of 60°?
Answer: D (5.24cm)
Arc length = (60/360) × 2π × 5 = 5π/3 ≈ 5.24 cm.
The ratio of boys to girls in a class is 5:3. If there are 40 students in the class, how many girls are there?
Answer: D (15)
Girls = 3/8 of 40 = 15.
The probability of rolling a prime number on a fair six-sided die is
Answer: A (1/2)
The primes on a die are 2, 3 and 5: 3 out of 6, so 1/2.