If \(x = \frac{y}{2}\),evaluate\(\left(\frac{x^{3}}{y^{3}}+\frac{1}{2}\right) \div \left(\frac{1}{2} – \frac{x^{2}}{y^{2}}\right)\)
- A. 5/8
- B. 5/2
- C. 5/32
- D. 5/16
A car dealer bought a second-hand car for N250,000 and spent N70,000 refurbishing it. He then sold the car for N400,000. What is the percentage gain?
- A. 60%
- B. 32%
- C. 25%
- D. 20%
Given that \(p = 1 + \sqrt{2}\) and \(q = 1 – \sqrt{2}\), evaluate \(\frac{p^{2} – q^{2}}{2pq}\).
- A. 2(2+โ2)
- B. -2(2+โ2)
- C. 2โ2
- D. -2โ2
Evaluate 21.05347 – 1.6324 x 0.43 to 3 decimal places
- A. 20.980
- B. 20.351
- C. 20.981
- D. 20.352
The expression ax2 + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, c respectively?
- A. 1, 3, 1
- B. 1, 2, 1
- C. 2, 1, 1
- D. 1, 1, 3
A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
- A. y = \(\frac{3x^2}{2}\) + 2x
- B. y = (3x2)/2 + x
- C. y = 3x2 + (x/2)
- D. y = 3x2 +2x
In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
- A. 15
- B. 28
- C. 30
- D. 45
Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5
- A. 16
- B. 14
- C. 12
- D. 10
If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20}
E1 = {x : x is a multiple of 3}
E2 = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E2
- A. 3/4
- B. 3/10
- C. 1/4
- D. 1/20
Given that the various faces of a fair dice 1, 2, 3, 4, 5, 6 appeared 30, 43, 54, 40, 41, 32 times respectively in a single toss. Picture the figures as being represented in a simple table with number (X) against frequency (f).
If a pie chart is used to depict the data, the angle corresponding to 4 is?
- A. 10ยฐ
- B. 16ยฐ
- C. 40ยฐ
- D. 60ยฐ
In how many ways can the word MATHEMATICS be arranged?
- A. 11!/(9! 2!)
- B. 11!/(9! 2! 2!)
- C. 11!/(2! 2! 2!)
- D. 11!/(2! 2!)
If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.
- A. 0
- B. 2
- C. 3
- D. 4
X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.
- A. 0.30
- B. 0.50
- C. 0.57
- D. 1.80
If the volume of a hemisphere is increasing at a steady rate of 18ฯ m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?
- A. 2.50m/s
- B. 2.00 m/s
- C. 0.25 m/s
- D. 0.20 m/s
A bowl is designed by revolving completely the area enclosed by y = x2 – 1, y = 3 and x โฅ 0 around the y-axis. What is the volume of this bowl?
- A. 7ฯ cubic units
- B. 15ฯ/2 cubic units
- C. 8ฯ cubic units
- D. 17ฯ/2 cubic units
If y = 2xcos2x – sin2x, find dy/dx when x = ฯ/4
- A. ฯ
- B. -ฯ
- C. ฯ/2
- D. -ฯ/2
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
- A. ฯ
- B. ฯ/2
- C. -ฯ/2
- D. -ฯ
A predator moves in a circle of radius โ2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?
- A. (1,1) only
- B. (1,1) and (1,2)
- C. (0,0) and (1,1)
- D. (โ2,โ2) only
In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.
- A. 8
- B. 6
- C. 4
- D. 3