QUESTION ONE (30MARKS)
a. Solve for the variable x in each of the following equation. (i) 32x+ 3 = 27 (3marks) 92-x (ii) 2×2 – 7x – 15 = 0 (3marks) (iii) Log4 (x2 – 49) – log4 (x + 7) – 1 = 0 (2marks) b. Solve the following system of equationsType equation here.
7?? + ?? = 13 ?? – 4?? – 6 = 0
(3marks) c. Make x the subject of the formula y = ?? ??2 – 5 ?? (4marks) d. How long will it take Sh.50,000 to amount to Sh75,000 under simple interest at the rate of 10% p.a? (3marks) e. Kimathi invests some money which earns compound interest every year. His investment amounts to Sh.530 at the end of the first year and Sh.595.50 at the end of the 3rd year. Find the interest rate of the investment and the initial amount of the investment. (4marks)
f. From the table exchange rates given below, find the exchange rate between the Ush and the US$.
(2marks) g. Rationalize the denominator in the expression 3 + 5v2 (3marks)
5 – 2v3
h. Compute the matrix product AB given the matrices
A=
1 3 2 5 B =
6 – 4 8 7 (3marks)
QUESTION TWO (10MARKS)
a. Solve for the variable x in each of the following equations. (i) 22x – 12(2x) + 32 = 0 (4marks) (ii) 6×2 + 10x – 4 = 0 (3marks) b. Simplify the expression log256 – log16 log16 + log64 (3marks)
QUESTION THREE (10MARKS)
a. P is partly constant and partly varies as the square of Q. Given that P = 10 when Q = 2 and P = 228 when Q is 6, find the value of P when Q= 12. (5marks) b. Compute the value of AB given the matrices A and B below
?? =
1 2 6 4 – 5 3 ?? =
4 1 -1 3 2 5 (5marks)
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