If 23_x + 101_x = 130_x, find the value of x

• A. 7
• B. 6
• C. 5
• D. 4

If y = (5 - x)\(^{-3}\), and \(\frac{dy}{dx}\)

• A. \(\frac{-15}{(5 - x)^4}\)
• B. \(\frac{-3}{(5 - x)^4}\)
• C. \(\frac{3}{(5 - x)^4}\)
• D. \(\frac{15}{(5 - x)^4}\)

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

The derivative of a function f with respect to x is given by \(f'(x) = 3x^{2} - \frac{4}{x^{5}}\). If \(f(1) = 4\), find f(x).

• A. \(f(x) = x^{3} - \frac{1}{x^{4}} + 2\)
• B. \(f(x) = x^{3} + \frac{1}{x^{4}} + 2\)
• C. \(f(x) = x^{3} - \frac{1}{x^{4}} - 2 \)
• D. \(f(x) = x^{3} + \frac{1}{x^{4}} - 2\)

Solve for the equation \(\sqrt{x}\) - \(\sqrt{(x - 2)}\) - 1 = 0

• A. \(\frac{3}{2}\)
• B. \(\frac{2}{3}\)
• C. \(\frac{4}{9}\)
• D. \(\frac{9}{4}\)

(a) A cottage is on a bearing of 200° and 110° from Dogbe's and Manu's farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to: (i) two significant figures, the distance between the two farms, (ii) the nearest degree, the bearing of Manu's farm from Dogbe's.

(b) A ladder 10 m long leaned against a vertical wall xm high. The distance between the wall and the foot of the ladder is 2 m longer than the height of the wall.

Calculate the value of x

The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.

• A. 25
• B. 15
• C. \(3\sqrt{7}\)
• D. \(\sqrt{10}\)

Find the 5th term of the sequence 2,5,10,17....?

• A. 22
• B. 24
• C. 36
• D. 26

In the diagram, PR is a diameter, ∠PRQ = (3x-8)° and ∠RPQ = (2y-7)°. Find x in terms of y

• A. \(x=\frac{75-2y}{3}\)
• B. \(x=\frac{105-3y}{2}\)
• C. \(x=\frac{105-2y}{3}\)
• D. \(x=\frac{75-3y}{2}\)

\(\begin{array}{c|c}

Values & 0 & 1 & 2 & 3 & 4 \\

\hline

Frequency & 1 & 2 & 2 & 1 & 9

\end{array}\)

Find the mode of the distribution above

• Find the mode of the distribution above A. 1
• B. 2
• C. 3
• D. 4