(a) The fourth term of an A.P is 37 and 6th term is 12 more than the fourth term . Find the first and seventh terms.

(b) If \(P = {1, 2, 3, 4}\) and \(Q = {3, 5, 6}\), find (i) \(P \cap Q\) ; (ii) \(P \cup Q\) ; (iii) \((P \cap Q) \cup Q\) ; (iv) \((P \cap Q) \cup P\).

In the diagram, \(\overline{PU}\)/\(\overline{SR}\), \(\overline{PS}\)/\(\overline{TR}\), \(\overline{QS}\)/\(\overline{UR}\), \(\overline{UR}\) = 15cm, \(\overline{SR}\) = 8 cm, \(\overline{PS}\) = 10 cm and area of?SUR = 24 cm\(^2\). Calculate the area of PTRS.

• A. 40 cm\(^2\)
• B. 48 cm\(^2\)
• C. 80 cm\(^2\)
• D. 120 cm\(^2\)

If 55\(_x\) + 52\(_x\) = 77\(_{10}\) find X

• A. 5
• B. 6
• C. 7
• D. 10

Evaluate \(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x\).

• A. \(-16\)
• B. \(\frac{-16}{3}\)
• C. \(\frac{16}{3}\)
• D. \(16\)

The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium

• A. 21cm²
• B. 4Ocm²
• C. 8Ocm²
• D. 150cm²

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?

• A. 180°
• B. 36°
• C. 60°
• D. 108°

Factorize 3a² - 11a + 6

• A. (3a - 2)(a - 3)
• B. (2a -2)(a - 3)
• C. (3a - 2)(a + 3)
• D. (3a + 2)(a - 3)

Evaluate \(\int^{2} _{3}(x^2 - 2x)dx\)

• A. 4
• B. 2
• C. 4/3
• D. 1/3

Simplify \( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] \)

• A. \( \frac{2}{(x + 1)^2} \)
• B. \( \frac{2}{(x + 1)(x + 2} \)
• C. \( \frac{2}{(x + 1)(x + 2} \)
• D. \( \frac{2}{(x + 1)(x + 3} \)

Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)

• A. y = \(\frac{2}{3} x - 3\)
• B. y = \(\frac{2}{3} x - 2\)
• C. y = \(\frac{2}{3} x\)
• D. y = \(\frac{-2}{3} x\)