Pre-Calculus 12 Final Assignment Each question is worth 1 mark. You must Show all your work to obtain full marks. Marks will be deducted for no work shown. Polynomial and Rational Functions 1. Solve x3 + 9x2 + 233: + 15 = 0. 2. For the function y = 103:3 21x2 x + 6, nd the zeroes of the function and sketch the graph of the function. Clearly label your points. i 3. The polynomial function P(x) = il-x4 '73:3 + mx2 + M + 6 has (x 1) as one of its factors. When it is divided by (x + 1), the remainder is 30. Algebraically determine the values of m and n. 6. Write the equation for the graph shown in the form y = a sin b (x - c) + d and in the form y = a cos b(x - c) + d Sine graph: Cosine graph: 7. A spring modeling in a sinusoidal function rests 1.6 metres above the ground. If the mass on the spring is pulled 1.1 metres below its resting position and then released, it requires 0.5 seconds to move from the maximum position to its minimum position. Assuming friction and air resistance are neglected, write an equation in terms of cosine that describes this periodic function. 8. If the following graph is in the form y = a sin b(x - c) + d, then determine the equation of the graph. .25 (24.159. Sales of snowmobiles are seasonal. Suppose sales in Camrose, Alberta are approximated by S = 200 + 200 cos " (t + 2) , where t is time in months with t = 0 corresponding to January. For what month are sales equal to 0? Trigonometric Equations and Identities 10. Determine all solutions, in radian measure, for the equation: sin ( (x - ") ) = - 12 11. Prove the following identity for all permissible values of x. State the restrictions over all real numbers. sin x + sin x = tan x cos x + sin x cos x