The probability of an event P happening is \(\frac{1}{5}\) and that of event Q is \(\frac{1}{4}\). If the events are independent, what is the probability that neither of them happens?

• A. \(\frac{4}{5}\)
• B. \(\frac{3}{4}\)
• C. \(\frac{3}{5}\)
• D. \(\frac{1}{20}\)

Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.

• A. t + 1
• B. 2t
• C. 2t + 1
• D. t

The marks scored by 35 students in a test are given in the table below.

Draw a histogram for the distribution.

If 25 bricklayers will spend 5 days to lay 25 000 blocks, how many days will 40 bricklayers take to lay 32 000 blocks?

• A. 3
• B. 4
• C. 5
• D. 8

The truth set of \(8 + 2x - x^2\) = 0 is {p, q}. Evaluate p + q.

• A. 4
• B. 2
• C. -6
• D. -2

Given that P and Q are non-empty subsets of the universal set, U. Find P \(\cap\) (Q U Q`).

• A. P
• B. P`
• C. Q
• D. Q`

Find the 7th term of the sequence: 2, 5, 10, 17, 6,...

• A. 37
• B. 48
• C. 50
• D. 63

In the figure above , TS//XY and XY = TY, ∠STZ = 34°, ∠TXY = 47°, find the angle marked n?

• A. 47°
• B. 52°
• C. 56°
• D. 99°

An exponential sequence (G.P.) is given by \(\frac{9}{2},\frac{3}{4},\frac{1}{8},\)....Find its sum to infinity.

• A. \(5\frac{2}{5}\)
• B. \(4\frac{1}{5}\)
• C. \(13\frac{1}{2}\)
• D. \(6\frac{3}{4}\)

(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.

(b) Solve the equations 2\(^x\)(4\(^{-7}\)) = 2 and 3\(^{-x}\)(9\(^{2y}\)) = 3 simultaneously.