ABC is a triangle, right-angled at C. P is the mid-point of AC, < PBC = 37° and |BC| = 5 cm. Calculate :

(a) |AC|, correct to 3 significant figures ;

(b) < PBA.

A committee consists of 6 boys and 4 girls. In how many ways can a sub-committee consisting of 3 boys and 2 girls be formed if one particular boy and one particular girl must be on the sub-committee?

• A. 120
• B. 80
• C. 56
• D. 30

If the polynomial \(f(x) = 3x^{3} - 2x^{2} + 7x + 5\) is divided by (x - 1), find the remainder.

• A. -17
• B. -7
• C. 5
• D. 13

The sum of the interior angles of a pentagon is 6x + 6y. Find y in the terms of x

• A. y = 90 - x
• B. y = 150 - x
• C. y = 60 - x
• D. y = 120 -x

Given that cos x^o = \(\frac{1}{r}\), express tan x in terms of r

• A. \(\frac{1}{\sqrt{r}}\)
• B. \(\sqrt{r}\)
• C. \(\sqrt{r^2 + 1}\)
• D. \(\sqrt{r^2 - 1}\)

If y = x cos x, find dy/dx

• A. sin x - x cos x
• B. sin x + x cos x
• C. cos x + x sin x
• D. cos x - x sin x

The area and a diagonal of a rhombus are 60 cm² and 12 cm respectively. Calculate the length of the other diagonal.

• A. 5cm
• B. 6cm
• C. 10cm
• D. 12cm

(a) Copy and complete the following table of values for \(y = 3\sin 2\theta - \cos \theta\).

(b) Using a scale of 2cm to 30° on the \(\theta\) axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 3 \sin 2\theta - \cos \theta\) for \(0° \leq \theta \leq 180°\).

(c) Use your graph to find the : (i) solution of the equation \(3 \sin 2\theta - \cos \theta = 0\), correct to the nearest degree; (ii) maximum value of y, correct to one decimal place.

Find the domain of \(f(x) = \frac{x}{3 - x}, x \in R\), the set of real numbers.

• A. \({x : x \in R, x \neq 3}\)
• B. \({x : x \in R, x \neq 1}\)
• C. \({x : x \in R, x \neq 0}\)
• D. \({x : x \in R, x\neq -3}\)

How many students scored at least 25%

• A. 16
• B. 19
• C. 3
• D. 8