If \(25^{1 – x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
- A. x = -4
- B. x = 2
- C. x = -2
- D. x = 4
Express \((0.0439 \div 3.62)\) as a fraction.
- A. \(\frac{21}{100}\)
- B. \(\frac{21}{1000}\)
- C. \(\frac{12}{1000}\)
- D. \(\frac{12}{100}\)
If the volume of a frustrum is given as \(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\), find \(\frac{\mathrm d V}{\mathrm d R}\).
- A. \(\frac{\pi h}{3} (2R + r)\)
- B. \(2R + r + \frac{\pi h}{3}\)
- C. \(\frac{\pi h}{3} (2R^2 + r + 2r)\)
- D. \(\frac{2R^2}{3} \pi h\)
A man bought a car newly for ₦1,250,000. He had a crash with the car and later sold it at the rate of ₦1,085,000. What is the percentage gain or loss of the man?
- A. 43.7% loss
- B. 13.2% gain
- C. 13.2% loss
- D. 43.7% gain
Each of the interior angles of a regular polygon is 140°. Calculate the sum of all the interior angles of the polygon.
- A. 1080°
- B. 1260°
- C. 2160°
- D. 1800°
In the diagram above, O is the centre of the circle ABC, < ABO = 26° and < BOC = 130°. Calculate < AOC.
- A. 26°
- B. 13°
- C. 80°
- D. 102°
If \(P = (\frac{Q(R – T)}{15})^{\frac{1}{3}}\), make T the subject of the formula.
- A. \(T = \frac{15R - Q}{P^3}\)
- B. \(T = R - \frac{15P^3}{Q}\)
- C. \(T = \frac{R - 15P^3}{Q}\)
- D. \(T = \frac{R + P^3}{15Q}\)
Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
- A. 24°
- B. 56°
- C. 127°
- D. 156°
Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
- A. x = 3 or 7, y = 12 or 8
- B. x = 6 or 1, y = 11 or 5
- C. x = 2 or 5, y = 15 or 6
- D. x = 1 or 5, y = 10 or 7
Simplify \(\frac{0.0839 \times 6.381}{5.44}\) to 2 significant figures.
- A. 0.2809
- B. 2.51
- C. 3.5
- D. 0.098
If 2\(^{x + y}\) = 16 and 4\(^{x – y} = \frac{1}{32}\), find the values of x and y.
- A. x = \(\frac{3}{4}\), y = \(\frac{11}{4}\)
- B. x = \(\frac{3}{4}\), y = \(\frac{13}{4}\)
- C. x = \(\frac{2}{3}\), y = \(\frac{4}{5}\)
- D. x = \(\frac{2}{3}\), y = \(\frac{13}{4}\)
Evaluate \((\frac{6}{0.32} \div \frac{2}{0.084})^{-1}\) correct to 1 decimal place.
- A. 1.3
- B. 2.5
- C. 4.6
- D. 3.2
The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
- A. 15.5%
- B. 18.2%
- C. 14.8%
- D. 16.7%
The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
- A. 31°
- B. 30°
- C. 26°
- D. 48°
If S = (4t + 3)(t – 2), find ds/dt when t = 5 secs.
- A. 50 units per sec
- B. 35 units per sec
- C. 22 units per sec
- D. 13 units per sec
Find the value of \(\frac{(0.5436)^3}{0.017 \times 0.219}\) to 3 significant figures.
- A. 46.2
- B. 43.1
- C. 534
- D. 431
Simplify 81\(^{\frac{-3}{4}}\) x 25\(^{\frac{1}{2}}\) x 243\(^{\frac{2}{5}}\)
- A. \(\frac{2}{5}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{5}{2}\)
- D. \(\frac{5}{3}\)
The simple interest on ₦8550 for 3 years at x% per annum is ₦4890. Calculate the value of x to the nearest whole number.
- A. 19%
- B. 20%
- C. 25%
- D. 16.3%
Tade bought 200 mangoes at 4 for ₦2.50. 30 out of the mangoes got spoilt and the remaining were sold at 2 for ₦2.40. Find the percentage profit or loss.
- A. 43.6% loss
- B. 35% profit
- C. 63.2% profit
- D. 28% loss
If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.
- A. 12
- B. 8
- C. 9
- D. 16
Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)
- A. \(4\frac{1}{2}\)
- B. \(3\frac{1}{2}\)
- C. \(7\frac{1}{2}\)
- D. \(5\frac{1}{4}\)