Find the sum of the exponential series \(96 + 24 + 6 +...\)

• A. 144
• B. 128
• C. 72
• D. 64

Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3}\)

• A. \(\frac{2x^2 - 3x - 4}{(x-2)(x+3)}\)
• B. \(\frac{2x^2 + 3x - 4}{(x-2)(x+3)}\)
• C. \(\frac{2}{(x-2)(x+3)}\)
• D. \(\frac{ 3x + 4}{(x-2)(x+3)}\)

If -2 is the solution of the equation 2x + 1 - 3c = 2c + 3x - 7, find the value of c.

• A. 4
• B. 3
• C. 2
• D. 1

P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =8/5

• A. 12⁸/₅
• B. 15
• C. 10
• D. 28⁸/₅

Find the remainder when 3x³ + 5x² - 11x + 4 is divided by x + 3

• A. -4
• B. 4
• C. 1
• D. -1

If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?

• A. x = -5
• B. x = 10
• C. x + 10 = 0
• D. bc = 750

Find the gradient to the normal of the curve \(y = x^{3} - x^{2}\) at the point where x = 2.

• A. \(\frac{-1}{8}\)
• B. \(\frac{1}{8}\)
• C. \(\frac{-1}{24}\)
• D. \(1\)

(a) The universal set U is the set of integers, P, Q and R are subsets of U defined as follows:

\(P = x : x \leq 2 \) ; \(Q = x : -7 < x < 15\) ; \(R = x : -2 \leq x < 19\).

Find (i) \(P \cap Q\) ; (ii) \(P \cap (Q \cup R')\), where R' is the complement of R with respect to U.

(b) The following data shows the marks of 40 students in a History examination.

41 52 37 56 63 48 65 46 54 32 51 66 74 23 35 61 58 44 49 53 45 57 56 38 59 28 50 49 67 56 36 45 79 68 43 56 26 47 55 71.

(i) Form a grouped frequency table with the class intervals 20 - 29, 30 - 39, 40 - 49 etc; (ii) Find the mean of the distribution.

1, 3, 5 ,7 , 9, ?

• (a) 8
• (b) 11
• (c) 12
• (d) 13

Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)

• A. \(\frac{x+7}{x^2 - 1}\)
• B. \(\frac{x-7}{x^2 + 1}\)
• C. \(\frac{x-7}{x^2 - 1}\)
• D. \(\frac{x-11}{x^2 - 1}\)