(a) In a class of 45 students, 32 offered Physics(P), 28 offered Government(G) and 12 did not offer any of the two subjects. (i) Draw the Venn diagram to represent the information ; (ii) How many students offered both subjects? (iii) What is \(n(P \cup G)\)?

(b) If \(p = \frac{2u}{1 - u}\) and \(q = \frac{1 + u}{1 - u}\) ; express \(\frac{p + q}{p - q}\) in terms of u.

A boat travels due east at a speed 40ms^-1s across a river flow due south at 30ms^-1s. What is the resultant speed of the boat?

• A. 1.3ms^-1
• B. 10.0ms^-1
• C. 50.0ms^-1
• D. 70.0ms^-1

The trade document signed by a representative of the country to which is not discounted is also the?

• A. consular invoice
• B. certificate invoice
• C. consignment invoice
• D. proforma invoice

The coastline of West Africa in Liberia and Ghana especially near Monrovia and Sekondi respectively is an example of

• A. delta
• B. low cliff
• C. rias
• D. estuary

Which of the following subtances will not produce effervescence with dilute hydeochloric acid?

• A. Copper (ll) trioxocarbonate (IV)
• B. Potassium hydrogentrioxocarbonate (lV)
• C. Zinc granules
• D. Sodium chloride

The average density of sima is

• A. 2.0
• B. 2.9
• C. 3.0
• D. 3.7

The sa'y is performed

• A. As a kind execise for pilgrims
• B. in memory of search for water by Hajar
• C. to complete the work of Hajj
• D. So that one may distance oneself from satan

(a) Evaluate without using calculator, (\(\frac{1}{4} \times 9\frac{1}{7} + \frac{2}{5} (\frac{2}{2} + \frac{3}{4})) \div (\frac{2}{5} - \frac{1}{4})\)

(b) A hunter walked 250 m from point P to Q on a bearing 042\(^o\). Calculate, correct to the nearest meter the vertical distance he has moved.

In any chemical reaction, the total mass of the products is always equal to that of the reactants. This is statement of the law of

• A. definite proportion
• B. conservation of matter
• C. multiple proportions
• D. reciprocal proportions

A sample of RNA is sequenced and found to contain 22% adenine. Which of the following conclusions can also be drawn about the sample?

• A. The sample contains 22% thymine.
• B. The sample contains 28% thymine.
• C. The sample contains 22% uracil.
• D. The sample contains 28% uracil