The base diameter of a cone is 14cm, and its volume is 462 cm³. Find its height. [Taken \(\pi = \frac{22}{7}\)]

• A. 3.5cm
• B. 5cm
• C. 7cm
• D. 9cm

\(\begin{array}{c|c} x & 1 & 2 & 3 & 4 & 5 \\ \hline f & y + 2 & y - 2 & 2y - 3 & y + 4 & 3y - 4\end{array}\)

This table shows the frequency distribution of a data if the mean is \(\frac{43}{14}\) find y

• A. 1
• B. 2
• C. 3
• D. 4

A binary operation ⊕ defined on the set of real number is such that x⊕y = xy/6 for all x, y ∈ R. Find the inverse of 20 under this operation when the identity element is 6

• A. 1/12
• B. 10/3
• C. 1/20
• D. 9/5

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

• A. \(\frac{1}{25}\)
• B. \(\frac{1}{4}\)
• C. 4
• D. 25

Find the x and z intercepts of the graph of 3x - z ≤ 9

• A. (3, -9)
• B. (-3, 9)
• C. (-3, -9)
• D. (-3, 0)

Using ruler and a pair of compasses only,

(a) construct, (i) triangle XYZ with |XY| = 8cm, < YXZ = 60° and < XYZ = 30° ; (ii) the perpendicular ZT to meet XY in T ; (iii) the locus \(l_{1}\) of points equidistant from ZY and XY.

(b) If \(l_{1}\) and ZT intersect at S, measure |ST|.

If x₁₀ = 1214₅ find x

• A. 124
• B. 121
• C. 184
• D. 180

The universal set \(\varepsilon\) is the set of all integers and the subset P, Q, R of \(\varepsilon\) are given by:

\(P = {x : x < 0} ; Q = {... , -5, -3, -1, 1, 3, 5} ; R = {x : -2 \leq x < 7}\)

(a) Find \(Q \cap R\).

(b) Find \(R'\) where R' is the complement of R with respect to \(\varepsilon\).

(c) Find \(P' \cup R'\)

(d) List the members of \((P \cap Q)'\).

The distribution above shows the number of days a group of 260 students were absents from school in a particular term. How many students were absent for at least four days in the term

• A. 210
• B. 40
• C. 120
• D. 160

The gradient of the line passing through the points P(4, 5) and Q(x, 9) is \(\frac{1}{2}\). Find the value of x.

• A. -4
• B. 0
• C. 4
• D. 12