MHF 4U1 - CULMUNATING PART A: Fill in the blanks Place the simplified answer in the space provided. 1 mark each = 11 marks total 1. When f(x)= x3 +3x2 -6x+ 1 is divided by x-2, the remainder is 2. Evaluate: (a) log3 729 = 3. Convert the following into radians: 60 = 4. Determine all values for 0, 050S2nt, if cos 0 = 0.2588 0 = or 0 = 5. Determine the exact values of: (a) cos 6 = b) sin2250= 5. For the following graph, decide if: (a) the degree of the function is even or odd, and (b) if the leading coefficient is positive or negative. 'a) Degree: (b) Leading Coeff: Decide whether the following statements are true or false. 7. x-3 is a factor of f(x) iff(-3)=0 8. The function y point discontinuity at x = 1.MHF 4U1 Page 2 PART B: Full Solutions All steps must be shown. 42 total marks. 1. Solve for x: (a) 4x3 -12x2 -x+3=0 (c) log7(x+1) + log7(x-5) = 1 (e) 3sin x-8sinx-3=0, OS.xS2TIMIIF 4U1 Page 3 G) 2. Sketch the function x) = 2x(x + 3) 2(x 4) G) 3. Given: f (x): x2 + 2x 5 and g(x)= 3x1 determine ( f a g)(x) : 5. The displacement of an object, in metres, is given by t)=5t3 -41'2 + t 3, where tis time in seconds. (3) (a) Find the average rate of change of displacement with respect to time from r: ls to 1': 43. (3 (b) Determine the instantaneous rate of change of displacement with respect to time at t = 45. (Use an 11 value of 0.01 .)