Find the variance of 1, 2, 0, -3, 5, -2, 4.
- A. \(\frac{52}{7}\)
- B. \(\frac{40}{7}\)
- C. \(\frac{32}{7}\)
- D. \(\frac{27}{7}\)
In how many ways can 9 people be seated on a bench if only 3 places are available?
- A. 1200
- B. 504
- C. 320
- D. 204
A particle accelerates at 12\(ms^{-2}\) and travels a distance of 250m in 6 seconds. Find the initial velocity of the particle.
- A. 5.7\(ms^{-1}\)
- B. 6.0\(ms^{-1}\)
- C. 60.0\(ms^{-1}\)
- D. 77.5\(ms^{-1}\)
For what values of m is \(9y^{2} + my + 4\) a perfect square?
- A. \(\pm {2}\)
- B. \(\pm {3}\)
- C. \(\pm {6}\)
- D. \(+12\)
The first term of a linear sequence is 9 and the common difference is 7. If the nth term is 380, find the value of n.
- A. 45
- B. 54
- C. 56
- D. 65
Find the equation of a circle with centre (2, -3) and radius 2 units.
- A. \(x^{2} + y^{2} - 4x + 6y + 9 = 0\)
- B. \(x^{2} + y^{2} + 4x - 6y - 9 = 0\)
- C. \(x^{2} + y^{2} + 4x + 6y - 9 = 0\)
- D. \(x^{2} + y^{2} + 4x - 6y + 9 = 0\)
The deviations from the mean of a set of numbers are \((k+3)^{2}, (k+7), -2, \text{k and (} k+2)^{2}\), where k is a constant. Find the value of k.
- A. 3
- B. 2
- C. -2
- D. -3
Forces 90N and 120N act in the directions 120° and 240° respectively. Find the resultant of these forces.
- A. \(-45(2i + \sqrt{2}j)\)
- B. \(60(\sqrt{3}i + 7j)\)
- C. \(30(7i + \sqrt{3}j)\)
- D. \(-15(7i + \sqrt{3}j)\)
If a fair coin is tossed four times, what is the probability of obtaining at least one head?
- A. \(\frac{1}{2}\)
- B. \(\frac{1}{4}\)
- C. \(\frac{13}{16}\)
- D. \(\frac{15}{16}\)
Find the coefficient of \(x^3\) in the binomial expansion of \((3x + 4)^4\) in ascending powers of x.
- A. 432
- B. 194
- C. 144
- D. 108
Find the angle between \((5i + 3j)\) and \((3i – 5j)\).
- A. 180°
- B. 90°
- C. 45°
- D. 0°
Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.
- A. \(4\sqrt{2}\)
- B. \(6\sqrt{2}\)
- C. \(2\sqrt{10}\)
- D. \(4\sqrt{10}\)
Integrate \((x – \frac{1}{x})^{2}\) with respect to x.
- A. \(\frac{1}{3}(x - \frac{1}{x})^{3} + c\)
- B. \(\frac{x^{3}}{3} - x\sqrt{\frac{1}{x^{3}}} + c\)
- C. \(\frac{x^{3}}{3} - 2x + \frac{1}{x^{3}} + c\)
- D. \(\frac{x^3}{3} - 2x - \frac{1}{x} + c\)
If \(Px^{2} + (P+1)x + P = 0\) has equal roots, find the values of P.
- A. \(\text{-1 and }\frac{-1}{3}\)
- B. \(\text{1 and }\frac{-1}{3}\)
- C. \(\text{-1 and }\frac{1}{3}\)
- D. \(\text{1 and }\frac{1}{3}\)
| Age in years | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 |
| Frequency | 6 | 8 | 14 | 10 | 12 |
Find the mean of the distribution.
- A. 23.4
- B. 23.6
- C. 24.3
- D. 24.6
| Age in years | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 |
| Frequency | 6 | 8 | 14 | 10 | 12 |
In which group is the upper quartile?
- A. 15 - 19
- B. 20 - 24
- C. 25 - 29
- D. 30 - 34
| Age in years | 10 – 14 | 15 – 19 | 20 – 24 | 25 – 29 | 30 – 34 |
| Frequency | 6 | 8 | 14 | 10 | 12 |
What is the class mark of the median class?
- A. 17
- B. 22
- C. 27
- D. 32
The radius of a sphere is increasing at a rate \(3cm s^{-1}\). Find the rate of increase in the surface area, when the radius is 2cm.
- A. \(8\pi cm^{2}s^{-1}\)
- B. \(16\pi cm^{2}s^{-1}\)
- C. \(24\pi cm^{2}s^{-1}\)
- D. \(48\pi cm^{2}s^{-1}\)
A function is defined by \(h : x \to 2 – \frac{1}{2x – 3}, x \neq \frac{3}{2}\). Find \(h^{-1}(\frac{1}{2})\).
- A. \(6\)
- B. \(\frac{11}{6}\)
- C. \(\frac{11}{4}\)
- D. \(\frac{5}{3}\)
A function is defined by \(h : x \to 2 – \frac{1}{2x – 3}, x \neq \frac{3}{2}\). Find \(h^-1\), the inverse of h.
- A. \(\frac{3x - 4}{2x - 7}, x \neq \frac{7}{2}\)
- B. \(\frac{3x - 7}{2x - 4}, x \neq 2\)
- C. \(\frac{2x - 7}{4x - 3}, x \neq \frac{3}{4}\)
- D. \(\frac{4x - 7}{2x - 4}, x \neq 2\)
If \(T = \begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatrix}\), find \(T^{-1}\), the inverse of T.
- A. \(\begin{pmatrix} -8 & -5 \\ 3 & 2 \end{pmatrix}\)
- B. \(\begin{pmatrix} -8 & -5 \\ 3 & -2 \end{pmatrix}\)
- C. \(\begin{pmatrix} -8 & -5 \\ -3 & 2 \end{pmatrix}\)
- D. \(\begin{pmatrix} -8 & -5 \\ -3 & -2 \end{pmatrix}\)