Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a – \frac{1}{4}b)\).
- A. \(\begin{pmatrix} \frac{17}{4} \\ 7 \end{pmatrix}\)
- B. \(\begin{pmatrix} \frac{17}{4} \\ 5 \end{pmatrix}\)
- C. \(\begin{pmatrix} \frac{17}{4} \\ 3 \end{pmatrix}\)
- D. \(\begin{pmatrix} \frac{17}{4} \\ 2 \end{pmatrix}\)
A fair die is tossed twice. What is its smple size?
- A. 6
- B. 12
- C. 36
- D. 48
In a class of 10 boys and 15 girls, the average score in a Biology test is 90. If the average score for the girls is x, find the average score for the boys in terms of x.
- A. \(200 - \frac{2x}{3}\)
- B. \(225 - \frac{3x}{2}\)
- C. \(250 - 2x\)
- D. \(250 - 3x\)
A curve is given by \(y = 5 – x – 2x^{2}\). Find the equation of its line of symmetry.
- A. \(x = \frac{-41}{8}\)
- B. \(x = \frac{-1}{4}\)
- C. \(x = \frac{1}{4}\)
- D. \(x = \frac{41}{8}\)
Differentiate \(\frac{5x^{3} + x^{2}}{x}, x\neq 0\) with respect to x.
- A. 10x+1
- B. 10x+2
- C. x(15x+1)
- D. x(15x+2)
The 3rd and 7th term of a Geometric Progression (GP) are 81 and 16. Find the 5th term.
- A. \(\frac{4}{729}\)
- B. \(\frac{81}{16}\)
- C. 27
- D. 36
There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys
- A. 1638
- B. 2730
- C. 6006
- D. 7520
Simplify \(\frac{\sqrt{128}}{\sqrt{32} – 2\sqrt{2}}\)
- A. \(2\sqrt{2}\)
- B. \(3\sqrt{2}\)
- C. 3
- D. 4
Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)
- A. \(\frac{7}{6}\)
- B. \(\frac{5}{6}\)
- C. \(\frac{-5}{6}\)
- D. \(\frac{-7}{6}\)
If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).
- A. \(\frac{2}{(1-x)^{2}}\)
- B. \(\frac{-2}{(1-x)^{2}}\)
- C. \(\frac{-1}{\sqrt{1-x}}\)
- D. \(\frac{1}{\sqrt{1-x}}\)
Given that \(f(x) = 5x^{2} – 4x + 3\), find the coordinates of the point where the gradient is 6.
- A. (4,1)
- B. (4,-2)
- C. (1,4)
- D. (1,-2)
A circle with centre (4,5) passes through the y-intercept of the line 5x – 2y + 6 = 0. Find its equation.
- A. \(x^{2} + y^{2} + 8x - 10y + 21 = 0\)
- B. \(x^{2} + y^{2} + 8x - 10y - 21 = 0\)
- C. \(x^{2} + y^{2} - 8x - 10y - 21 = 0\)
- D. \(x^{2} + y^{2} - 8x - 10y + 21 = 0\)
Given that \(\sin x = \frac{5}{13}\) and \(\sin y = \frac{8}{17}\), where x and y are acute, find \(\cos(x+y)\).
- A. \(\frac{130}{221}\)
- B. \(\frac{140}{221}\)
- C. \(\frac{140}{204}\)
- D. \(\frac{220}{23}\)
If \(B = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}\), find \(B^{-1}\).
- A. \(A = \begin{pmatrix} -3 & -5 \\ 1 & 2 \end{pmatrix}\)
- B. \(A = \begin{pmatrix} 3 & -5 \\ 1 & 2 \end{pmatrix}\)
- C. \(A = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)
- D. \(A = \begin{pmatrix} -3 & 5 \\ 1 & -2 \end{pmatrix}\)
\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} – 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)
- A. \(\frac{-9}{8}\)
- B. \(\frac{-7}{8}\)
- C. \(\frac{7}{8}\)
- D. \(\frac{9}{8}\)
\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} – 3x + 4 = 0\). Find \(\alpha + \beta\).
- A. -2
- B. -\(\frac{3}{2}\)
- C. \(\frac{3}{2}\)
- D. 2
A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.
- A. 2x-3y=2
- B. 2x-3y=-2
- C. 2x+3y=-4
- D. 2x+3y=4
Express cos150° in surd form.
- A. \(-\sqrt{3}\)
- B. \(-\frac{\sqrt{3}}{2}\)
- C. \(-\frac{1}{2}\)
- D. \(\frac{\sqrt{2}}{2}\)
If \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\), find the value of k.
- A. 1.2
- B. 3.6
- C. 0.8
- D. 0.5
How many ways can 6 students be seated around a circular table?
- A. 36
- B. 48
- C. 120
- D. 720
Find the 21st term of the Arithmetic Progression (A.P.): -4, -1.5, 1, 3.5,…
- A. 43.5
- B. 46
- C. 48.5
- D. 51