A 24N force acts on a body such that it changes its velocity from 5m/s to 9m/s in 2 secs.If the body is travelling in a straight line, calculate the distance covered in the period.
- A. 22m
- B. 18m
- C. 14m
- D. 10m
If \(2\sin^{2} \theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find the value of \(\theta\).
- A. 90°
- B. 60°
- C. 45°
- D. 30°
Simplify: \(^{n}C_{r} ÷ ^{n}C_{r-1}\)
- A. \(\frac{n(n-r)}{r}\)
- B. \(\frac{n}{r(n-r)}\)
- C. \(\frac{1}{r(n-r)}\)
- D. \(\frac{n+1-r}{r}\)
In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean.
- A. 24
- B. 23
- C. 21
- D. 19
Four fair coins are tossed once. Calculate the probability of having equal heads and tails.
- A. \(\frac{1}{4}\)
- B. \(\frac{3}{8}\)
- C. \(\frac{1}{2}\)
- D. \(\frac{15}{16}\)
Given that \(y = 4 – 9x\) and \(\Delta x = 0.1\), calculate \(\Delta y\).
- A. 9.0
- B. 0.9
- C. -0.3
- D. -0.9
A particle starts from rest and moves in a straight line such that its acceleration after t secs is given by \(a = (3t – 2) ms^{-2}\). Find the distance covered after 3 secs.
- A. \(10m\)
- B. \(9m\)
- C. \(\frac{13}{3} m\)
- D. \(\frac{9}{2} m\)
A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t – 2) ms^{-2}\). Find the other time when the velocity would be zero.
- A. \(\frac{1}{3} seconds\)
- B. \(\frac{3}{4} seconds\)
- C. \(\frac{4}{3} seconds\)
- D. \(2 seconds\)
Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.
- A. \((5\frac{2}{5}, \frac{2}{5})\)
- B. \((\frac{2}{5}, 5\frac{2}{5})\)
- C. \((\frac{-2}{5}, 5\frac{2}{5})\)
- D. \((\frac{2}{5}, 4\frac{1}{5})\)
Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)
- A. \(x^{2} + 10x + c\)
- B. \(x + \frac{5}{3}x^{3} + x^{4} + c\)
- C. \(x - 5x^{2} - 2x^{3} + c\)
- D. \(x - \frac{5}{x} - \frac{1}{2x^{2}} + c\)
If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.
- A. \(x = 3, -2\)
- B. \(x = 4, \frac{-2}{3}\)
- C. \(x = -4, \frac{3}{2}\)
- D. \(x = 4, \frac{-3}{2}\)
Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.
- A. \(\frac{28}{45}\)
- B. \(\frac{4}{9}\)
- C. \(\frac{8}{45}\)
- D. \(\frac{1}{9}\)
A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with constant velocity. \([g = 9.8ms^{-2}]\)
- A. 750N
- B. 745N
- C. 735N
- D. 98N
| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| Number of candidates | 6 | 4 | 8 | 10 | 9 |
3 |
The table above shows the distribution of marks scored by students in a test. Find the interquartile range of the distribution.
- A. 4
- B. 3
- C. 2
- D. 1
| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| Number of candidates | 6 | 4 | 8 | 10 | 9 | 3 |
The table above shows the distribution of marks scored by students in a test. How many candidates scored above the median score?
- A. 3
- B. 12
- C. 22
- D. 30
Given that \(r = 2i – j\), \(s = 3i + 5j\) and \(t = 6i – 2j\), find the magnitude of \(2r + s – t\).
- A. \(\sqrt{15}\)
- B. 4
- C. \(\sqrt{24}\)
- D. \(\sqrt{26}\)
Given the statements:
p : the subject is difficult
q : I will do my best
Which of the following is equivalent to ‘Although the subject is difficult, I will do my best’?
- A. \(p \vee q\)
- B. \(\sim p \vee q\)
- C. \(p \wedge (\sim q)\)
- D. \( p \wedge q\)
Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.
- A. k = 5, r = -1
- B. k = 5, r = 2
- C. k = 2, r = -5
- D. k = -1, r = 5
If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x – 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).
- A. \(\frac{5}{4}\)
- B. \(\frac{3}{4}\)
- C. \(\frac{1}{4}\)
- D. \(\frac{-3}{4}\)
The gradient of a curve at the point (-2, 0) is \(3x^{2} – 4x\). Find the equation of the curve.
- A. \(y = 6x - 4\)
- B. \(y = 6x^{2} - 4x + 12\)
- C. \(y = x^{3} - 2x^{2}\)
- D. \(y = x^{3} - 2x^{2} + 16\)
If \(x = i – 3j\) and \(y = 6i + j\), calculate the angle between x and y.
- A. 60°
- B. 75°
- C. 81°
- D. 85°