Evaluate: \(\int(2x + 1)^3 dx\)
- A. \(8(2x + 1)^2 + k\)
- B. \(6(2x + 1)^2 + k\)
- C. \(\frac{1}{8} (2x + 1)^4 + k\)
- D. \(\frac{1}{6} (2x + 1)^4 + k\)
In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
- A. 500
- B. 350
- C. 720
- D. 210
Adu’s scores in five subjects in an examination are 85, 84, 83, 86 and 87. Calculate the standard deviation.
- A. 2.0
- B. 1.4
- C. 1.8
- D. 1.6
An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)….Find its sum to infinity.
- A. \(5\frac{2}{5}\)
- B. \(4\frac{1}{5}\)
- C. \(13\frac{1}{2}\)
- D. \(6\frac{3}{4}\)
A uniform beam PQ of length 80 cm and weight 60 N rests on a support at X where | PX | = 30 cm. If the body is kept in equilibrium by a mass m kg which is placed at P , calculate the value of m
[Take g = 10 ms\(^{-2}\)]
- A. 2.0
- B. 3.0
- C. 2.5
- D. 4.0
If \(f : x β 2 tan x\) and \(g : x β β(x^2 + 8), find ( g o f )(45^o)\)
- A. 4
- B. 2β3
- C. 6
- D. 3β2
An exponential sequence (G.P.) is given by 8β2, 16β2, 32β2, … . Find the n\(^{th}\) term of the sequence
- A. \(8\sqrt2^n\)
- B. \(2^{(n+2)}\sqrt2\)
- C. \(\sqrt2^{(n+3)}\)
- D. \(8n\sqrt2\)
Solve 6 sin 2ΞΈ tan ΞΈ = 4, where 0ΒΊ < ΞΈ < 90ΒΊ
- A. 18.43ΒΊ
- B. 30.00ΒΊ
- C. 35.26ΒΊ
- D. 19.47ΒΊ
Given that r = (10 N , 200ΒΊ) and n = (16 N , 020ΒΊ), find (3r – 2n).
- A. (62 N , 240ΒΊ)
- B. (62 N , 200ΒΊ)
- C. (62 N , 280ΒΊ)
- D. (62 N , 020ΒΊ)
\(Simplify: \frac{log β27 – log β8}{log 3 – log 2}\)
- A. \(\frac{3}{2}\)
- B. -\(\frac{1}{4}\)
- C. -\(\frac{3}{2}\)
- D. \(\frac{1}{4}\)
The table shows the mark obtained by students in a test.
| Marks | 1 | 2 | 3 | 4 | 5 |
| Frequency | 2 | k | 1 | 1 | 2 |
If the mean mark is 3, find the value of k.
- A. 4
- B. 1
- C. 2
- D. 3
Express \(\frac{3}{3 – β6}\) in the form \(x + mβy\)
- A. 3 - 3 β6
- B. 3 + 3β6
- C. 3 + β6
- D. 3 - β6
\(Differentiate f (x) = \frac{1}{(1 – x^2)^5}\) with respect to \(x\).
- A. \(\frac{-5x}{(1-x^2)^6}\)
- B. \(\frac{-10x}{(1-x^2)^6}\)
- C. \(\frac{5x}{(1-x^2)^6}\)
- D. \(\frac{10x}{(1-x^2)^6}\)
Consider the statements:
x: The school bus arrived late
y: The student walked down to school
Which of the following can be represented by y β x?
- A. The school bus arrived early and Kate ran to school
- B. Mary walked to school because the school bus arrived late
- C. Either the school bus arrived late or Maryam walked to school
- D. Emmanuella did not go to school because the school bus arrived late
Given that P = {x : 2 β€ x β€ 8} and Q = {x : 4 < x β€ 12} are subsets of the universal set ΞΌ = {x : x β R}, find (P β Q\(^1\)).
- A. {x : 4 < x < 8}
- B. {x : 2 < x β€ 4}
- C. {x : 2 β€ x β€ 4}
- D. {x : 4 β€ x β€ 8}
Find the fifth term in the binomial expansion of \((q + x)^7\).
- A. \(21q^2x^5\)
- B. \(21q^4x^3\)
- C. \(35q^3x^4\)
- D. \(35q^5x^2\)
A particle began to move at \(27 ms^{-1}\) along a straight line with constant retardation of \(9 ms^{-2}\). Calculate the time it took the particle to come to a stop.
- A. 3 sec
- B. 2 sec
- C. 4 sec
- D. 1 sec
Given that M is the midpoint of T (2, 4) and Q (-8, 6), find the length of MQ .
- A. \(β26 units\)
- B. \(β28 units\)
- C. \(β24 units\)
- D. \(β30 units\)
Find the radius of the circle \(2x^2 + 2y^2 – 4x + 5y + 1 = 0\)
- A. \(\frac{\sqrt33}{4}\)
- B. \(\frac{\sqrt5}{6}\)
- C. \(\frac{5}{6}\)
- D. \(\frac{33}{4}\)
The table shows the operation * on the set {x, y, z, w}.
| * | X | Y | Z | W |
| X | Y | Z | X | W |
| Y | Z | W | Y | X |
| Z | X | Y | Z | W |
| W | W | X | W | Z |
Find the identity of the element.
- A. W
- B. Y
- C. Z
- D. X
If\((\frac{1}{9})^{2x-1} = (\frac{1}{81})^{2-3x}\)find the value of x
- A. \(-\frac{5}{8}\)
- B. \(-\frac{3}{4}\)
- C. \(\frac{3}{4}\)
- D. \(-\frac{5}{8}\)