Reference no: EM132614371

Question 1. (a) If 3^x x 9^2y = 27 and 2^x x 4^-y = 1/8, calculate the values of x and y.

(b) Use logarithm to Solve 3^x = 5^x-2.

(c) Simplify the expression √243 - √12 + 2 √75 .

(d) Simplify, without using tables or calculators, the value of 1/(3 - √2)+ 1/(3 + √2)

Question 2. (a) (i) Five children are to be seated on a bench, find how many ways the children can be seated.

(ii) Find the number of selections in which a party of four members can be chosen from nine people.

(b) Express 5x² - 2x -19/( x + 3)( x -1)² in partial fractions.

(c) Prove by induction that 1+ 5 + 9 + .... + (4n - 3) = n(2n -1)

Question 3. (a) An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference.

(b) Find the sum of the geometric series

8 - 4 + 2 -1+

Where there are 5 terms in the series.

(c) Expand the binomial expression (4x + 2)³

Question 4. (a) Evaluate the limit:

lim_x→2 (x² + 4x -12)/(x - 2x)

(b) If y = (x⁴ - 3x² +1)³ find y '

(c) Find the derivative of (1- x³ )e^2x

(d) Find the minimum value of the function f (x) = x² - x - 6.

Question 5. (a) Find the derivative, with respect to x , of the function y² + x³ - y³ + 6 = 3y

(b) Find ∫e^4xdx.

(c) Find ∫1/√(4-x²) dx.

(d) Find ∫x sin xdx