If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

• A. p varies directly as r³
• B. p varies inversely as r⁶
• C. p varies inversely as⁶√P
• D. p varies directly as r⁶

Find p, q for which \(\begin{pmatrix} 2p & 8 \\ 3 & -5q \end{pmatrix}\)\(\begin{pmatrix} 1 \\ 2\end{pmatrix}\) = \(\begin{pmatrix}24 \\ -17\end{pmatrix}\)

• A. -4
• B. 45
• C. 4,2
• D. 2

A binary operation * on the set of rational numbers is defined as \(x \ast y = \frac{x^2 - y^2}{2xy}\). Find \(-5 \ast 3\)

• A. \(\frac{-8}{15}\)
• B. \(\frac{8}{15}\)
• C. \(\frac{17}{15}\)
• D. \(\frac{-17}{15}\)

If \(T = 2\pi \sqrt{\frac{l}{g}}\), make g the subject of the formula

• A. (4π l²) / T
• B. (4π²l) / T²
• C. (4π²l²) / T²
• D. (2π√l) / T

The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). find the equation of the curve.

• A. y = x² + 7x + 9
• B. y = x² + 7x - 18
• C. y = x² + 7x + 18
• D. y = x² + 14x + 11

Find the value of k if the expression kx³ + x² - 5x - 2 leaves a remainder 2 when it is divided by 2x + 1

• A. 10
• B. 8
• C. -10
• D. -8

If the mean of five consecutive integers is 30, find the largest of the numbers

• A. 28
• B. 30
• C. 32
• D. 34

The cost of renovating a 6 m square room is N540. What is the cost of renovating a 9 m square room?

• A. N1215
• B. N720
• C. N1620
• D. N810

In triangle XYZ, ∠XYZ = 15°, ∠XZY = 45° and lXYl = 7 cm. Find lYZl.

• A. 14√2 cm
• B. 7(√6/2) cm
• C. 7√2 cm
• D. 7 cm

If x = \(\begin{pmatrix} 1 & 0 & 1 \\ 2 & -1 & 0 \\ -1 & 0 & 1\end{pmatrix}\) and y = \(\begin{pmatrix} -1 & 1 & 2 \\ 0 & -1 & -1 \\ 2 & -1 & 1\end{pmatrix}\)

find 2x - y

• A. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -3 & -1 \\ -4 & 1 & 1\end{pmatrix}\)
• B. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -1 & 1 \\ -4 & 1 & 1\end{pmatrix}\)
• C. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & -3 & 1 \\ -4 & 1 & 1\end{pmatrix}\)
• D. \(\begin{pmatrix} 3 & -1 & 0 \\ 4 & 1 & 1 \\ -4 & -1 & 1\end{pmatrix}\)