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Question 1 a Simplify 272 x 322+x 81*4 x 82 b Solve the following equations: i. 25*-1=124 ii. log2 (x+3) = 3-10g2(x+1) iii. log, (3x-2) =2 Question 2 a. What is the 20" term of the sequence 4, 9, 14, 19, 2? b. The forth term of AP is 20 and the 8th term is 60. Find the 15th term. C. The eight term of an AP is 35 and the sum of the first 20 terms is 900. Find the value of the term and common difference. d. Given that the second term of GP is - and the forth term is-. Find the first term and the eight term of the GP if r > 0 Question 3 a. Using Cramer's rule, solve the system of linear equations. i. x+2y-52 =7 ii. 3x+4y+z=4 iii. 5x-6y-3z =5 b A company manufactures bicycles for $1,200 each and the overhead cost of producing a bicycle is$5,120. If each bicycle is sold for $3,450, determine the: i. cost function ii. revenue function iii. profit function iv. least number of bicycles needed to be manufactured to break even Question 4 a. i. Expand and simplify (5x-2)* . ii. Hence, what are the constant term and the coefficient of x? b. Evaluate |n' +1 mo ( n + 1 ) C. Solve 514 =222 d. Find the equation of the line perpendicular to the line 7y-3x+28 =0 and passes through the point (-2, -3). e. Find the sum to infinity of 5+4+ 16. 64 5 25 +... - Question 5 a. When the polynomial f(x) =5x + ax -31x+b is divided by (x+3) it leaves a remainder -84 but when divided by (x + 1) it leaves a remainder of 16. Determine the values of a and b and hence solve the polynomial f(x) . b. By using the substitutionu = 3", solve the equation 328-1 -23(3") +14 =0. C. 1. What is the coefficient of x' in the expansion of (1-2x)' ? ii. Expand, writing your answer in ascending powers of x, (1--x)