Solve for x in the equation x\(^3\) – 5x\(^2\) – x + 5 = 0
- A. 1, - 1, or 5
- B. 1, 1, or -5
- C. -1, 1, or -5
- D. 1, 1, or 5
If \(y = x^2 – \frac{1}{x}\). find dy/dx
- A. 2x - (1/x2)
- B. 2x + x2
- C. 2x - x2
- D. 2x + (1/x2)
A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?
- A. 2ฯ
- B. 5ฯ
- C. ฯ
- D. 4ฯ
Evaluate \(\int \sin 3x \mathrm d x\)
- A. (2/3) cos 3x + c
- B. (1/3) cos 3x + c
- C. (-1/3) cos 3x + c
- D. (-2/3) cos 3x + c
The slope of the tangent to the curve y = 3x\(^2\) – 2x + 5 at the point (1, 6) is
- A. 4
- B. 1
- C. 6
- D. 5
Find the derivative of \(y = \sin^{2} (5x)\) with respect to x.
- A. 10 sin 5x cos 5x
- B. 5 sin5x cos 5x
- C. 2 sin 5x cos 5x
- D. 15 sin 5x cos 5x
If dy/dx = 2x – 3 and y = 3 when x = 0, find y in terms of x.
- A. 2x2 - 3x
- B. x2 - 3x
- C. x2 - 3x - 3
- D. x2 - 3x + 3
A trader bought goats for N4000 each. He sold them for N180,000 at a loss of 25%. How many goats did he buy?
- A. 60
- B. 50
- C. 45
- D. 36
Evaluate: \(\frac{0.21 \times 0.072 \times 0.00054}{0.006 \times 1.68 \times 0.063}\)
- A. 0.01286
- B. 0.01285
- C. 0.1286
- D. 0.1285
Simplify \((\sqrt{0.7} + \sqrt{70})^{2}\)
- A. 84.7
- B. 70.7
- C. 217.7
- D. 168.7
In a school, 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 mathematics. How many offer Biology but not Mathematics?
- A. 95
- B. 80
- C. 125
- D. 110
Without using tables, evaluate \((343)^{\frac{1}{3}} \times (0.14)^{-1} \times (25)^{-\frac{1}{2}}\)
- A. 10
- B. 12
- C. 8
- D. 7
Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?
- A. 2/3
- B. 1/2
- C. 1/3
- D. 1/4
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. The mean score is
- A. 7.0
- B. 8.7
- C. 9.5
- D. 11.0
Given the scores: 4, 7, 8, 11, 13, 8 with corresponding frequencies: 3, 5, 2, 7, 2, 1 respectively. Find the square of the mode.
- A. 49
- B. 121
- C. 25
- D. 64
Find the dimensions of a rectangle of greatest area which has a fixed perimeter p.
- A. square of sides p
- B. square of sides 2p
- C. square of sides (p/2)
- D. square of sides (p/4)
If y = x sinx, find dy/dx when x = ฯ/2.
- A. -ฯ/2
- B. -1
- C. 1
- D. ฯ/2
Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.
- A. 12ฯ
- B. 4ฯ
- C. 24ฯ
- D. 8ฯ
Find the area bounded by the curves y = 4 – x2 and y = 2x + 1
- A. 20(1/3) sq. units
- B. 20(2/3) sq. units
- C. 10(2/3) sq. units
- D. 10(1/3) sq. units