Northeastern University

• MATH MHF4U

• Grade 12 Advanced Functions: MHF4U FINAL EXAM INSTRUCTOR: Ms. Vanderkamp TIME LIMIT: 3 hours DATE: PAGE 1 OF 10 STUDENT NAME: ________________________________________________________________________________________________________ Instructions: 1. Non-programmable scientific calculator, protractors, rulers and various writing utensils may be used. No electronic devices will be allowed, including graphing calculator. 2. Please answer multiple-choice questions by circling the correct answer directly on the exam paper. 3. Answer all other questions in the spaces provided. Please do not write on the backs of pages. If you require additional paper, let your proctor know. If you do use additional paper, please be sure to label the questions accordingly. 4. Please ensure that all 10 pages are included and returned. 5. Your proctor must return your exam to your instructor by uploading the exam via the link provided in the exam email. ________________________________________________________________________________________________________ Mark Breakdown Part A – Knowledge and Understanding 20 marks Part B – Thinking and Investigation 24 marks Part C – Communication 20 marks Part D – Application 20 marks Total: 84 marks Good Luck! Page 2 of 10 Part A – Multiple Choice [K/U – 20 marks] 1. An equation representing a function that extends from quadrant 1 to quadrant 3 is a. y = 2x 3 c. y = 5x 6 b. y = –6x 5 d. y = –4x 4 2. What is the degree and lead coefficient of ?(?) = −2? + 5? 2 − 6? 3 + 10? a. degree 1 with a lead coefficient of −1 c. degree 3 with a lead coefficient of −6 b. degree 3 with a lead coefficient of 6 d. degree 6 with a lead coefficient of −1 3. An equation for the graph shown to the right is: a. y = x 2 (x – 3) c. y = x 2 (x – 3)3 b. y = x(x – 3)3 d. y = −x 2 (x – 3)3 4. The graph of the function y = x 4 is transformed to the graph of the function y = –[2(x + 3)]4 + 1 by a. a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up b. a horizontal stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up c. a horizontal compression by a factor of , a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up d.a horizontal compression by a factor of , a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up 5. State the equation of f(x) if D {x R | x } and the y-intercept is (0, − ). a. f(x) b. f(x) c. f(x) d. f(x) 6. Use your calculator to determine the value of , to three decimal places. a. 0.652 b. 1.534 c. 0.012 d. 80.700 7. Which compound angle formula is the easiest to use to develop the expression ? a. addition formula for sine c. subtraction formula for sine b. addition formula for cosine d. subtraction formula for cosine 8. Which of the following expressions is NOT equivalent to ? a. c. b. d. 9. Which of these is a possible solution for in the interval ? a. c. b. d. Page 3 of 10 10. Which of the following functions has the longest period? a. c. b. d. 11. Which of the following statements is true? a. The domain of a transformed logarithmic function is always {x R}. b. Vertical and horizontal translations must be performed before horizontal and vertical stretches/compressions. c. A transformed logarithmic function always has a vertical asymptote. d. The vertical asymptote changes when a vertical translation is applied. 12. Another way of writing is