A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4 cm deep. Calculate its volume.
- A. 304ฯ/3 cm3
- B. 144ฯ cm3
- C. 128ฯ cm3
- D. 72ฯ cm3
Find the equation of the set of points which are equidistant from the parallel lines x = 1 and x = 7
- A. y = 3
- B. x = 3
- C. x = 4
- D. y = 4
If tan ฮธ = 4/3, calculate sin\(^2\) ฮธ – cos\(^2\) ฮธ.
- A. 16/25
- B. 24/25
- C. 7/25
- D. 9/25
A chord of a circle subtends an angle of 120ยฐ degrees at the centre of a circle of diameter 4โ3 cm. Calculate the area of the major sector.
- A. 4ฯ cm2
- B. 32 ฯ cm2
- C. 16 ฯ cm2
- D. 8 ฯ cm2
If x varies directly as โn and x = 9 when n = 9, find x when n = (17/9)
- A. 4
- B. 27
- C. โ3
- D. โ17
The sum to infinity of the series: 1 + (1/3) + (1/9) + (1/27) + … is
- A. 11/3
- B. 10/3
- C. 5/2
- D. 3/2
The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2 * (3 * 4).
- A. 59
- B. 19
- C. 67
- D. 38
If -2 is the solution of the equation 2x + 1 – 3c = 2c + 3x – 7, find the value of c.
- A. 4
- B. 3
- C. 2
- D. 1
The inverse function f(x) = 3x + 4 is
- A. (x-4)/3
- B. (x-5)/5
- C. (x+3)/4
- D. (x+4)/3
Make r subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
- A. \(\frac{a^{2}}{(x-a)}\)
- B. \(\frac{a^{2}}{(x+a)}\)
- C. \(\frac{a}{x-a}\)
- D. \(\frac{a}{x+a}\)
If the 9th term of an A.P is five times the 5th term, find the relationship between a and d.
- A. 2a + 2 = 0
- B. 3a + 5d = 0
- C. a + 3d = 0
- D. a + 2d = 0
Find the maximum value of y in the equation y = 1 – 2x – 3x\(^2\)
- A. 5/4
- B. 5/3
- C. 3/4
- D. 4/3
Find the range of values of x for which \(\frac{(x+2)}{4}-\frac{2x-3}{3}<4\)
- A. x > -6
- B. x > -3
- C. x < 8
- D. x < 4
The time taken to do a piece of work is inversely proportional to the number of men employed. if it takes 45 men to do a piece of work in 5 days, how long will it take 25 men?
- A. 15 days
- B. 12 days
- C. 5 days
- D. 9 days
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