The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.

• A. 105
• B. 100
• C. 95
• D. 110

The bearing of Q from P is 122^o, what is the bearing of P from Q?

• A. 212^o
• B. 238^o
• C. 248^o
• D. 302^o

A man is four times as old as his son. The difference between their ages is 36 years Find the sum of their ages

• A. 45 years
• B. 48 years
• C. 60 years
• D. 74 years

A particle of mass 400g is moving under the action of two forces \(F_{1} = (35N, 210°), F_{2} = (35\sqrt{3} N, 300°)\) and a resistance of 40N. Find the magnitude of the

(a) resultant of \(F_{1}\) and \(F_{2}\).

(b) resultant force acting on the particle.

A binary operation ⊕ om real numbers is defined by x ⊕ y = xy + x + y for two real numbers x and y. Find the value of 3 ⊕ - 23.

• A. - 1/2
• B. 1/3
• C. -1
• D. 2

\(\begin{array}{c|c} \text{Class Interval} & Frequency & \text{Class boundaries} & Class Mid-point \\ \hline 1.5 - 1.9 & 2 & 1.45 - 1.95 & 1.7\\ 2.0 - 2.4 & 21 & 1.95 - 2.45 & 2.2\\ 2.5 - 2.9 & 4 & 2.45 - 2.95 & 2.7 \\ 3.0 - 2.9 & 15 & 2.95 - 3.45 & 3.2\\ 3.5 - 3.9 & 10 & 3.45 - 3.95 & 3.7\\ 4.0 - 4.4 & 5 & 3.95 - 4.45 & 4.2\\ 4.5 - 4.9 & 3 & 4.45 - 4.95 & 4.7\end{array}\)

The median of the distribution above is

• A. 4.0
• B. 3.4
• C. 3.2
• D. 3.0

By how much is the mean of 30, 56, 31, 55, 43 and 44 less than the median?

• A. 0.75
• B. 0.50
• C. 0.33
• D. 0.17

If 9^2x = \(\frac{1}{3}\)(27^x), find x

• A. 2
• B. 1
• C. -1
• D. -2

Convert 35 to a number in base two

• A. 1011_two
• B. 10011_two
• C. 100011_two
• D. 110010_two

Evaluate \(\frac{0.00000231}{0.007}\) and leave the answer in standard form

• A. 3.3 x 10^-4
• B. 3.3 x 10^-3
• C. 3.3 x 10^-5
• D. 3.3 x 10^-8