ADVANCED FUNCTIONS (MHF 4U) FINAL EXAMINATION

Transcription

1 Canadian International Matriculation Programme Sunway College (KL) Sdn. Bhd. ADVANCED FUNCTIONS (MHF 4U) FINAL EXAMINATION Date/Day : 4 November 014, Monday Time : 8.30 am am Length : hours Lecturers : Ms. Dzura Mr. Grandy Mr.Nithyananthan Mr. Pagé Ms. Pecarski Mr. Welch (Please circle your teacher s name) Student Name: Section/Period: Please read the following instructions carefully before you begin the examination: 1. This exam paper has 15 printed pages including this cover page and the formula sheet.. The examination is worth 30 percent of your overall mark for this course. 3. The examination consists of THREE parts as follows: Parts Content Number of Questions Marks A MULTIPLE CHOICE 16 3 B SHORT ANSWERS 9 34 C PROBLEM SOLVING 5 (choose only 4) 4 OVERALL COMMUNICATION 10 TOTAL Please enter your multiple choice answers on the sheet provided on page Solutions for Parts B and C must be written in the space provided. 6. Answer 4 questions only for Part C. 7. Scientific or Graphing Calculators and paper dictionary are permitted. NO SHARING is allowed. 8. All answers must be written legibly in black/blue pen or pencil. For office use only: K/U T/I COM APPL TOTAL /35 /0 /10 /35 /100 MHF 4U FINAL EXAMINATION November 4,, 014

2 Multiple Choice [3 marks] Identify the choice that best completes the statement or answers the question. 1. Which expression below is equivalent to the following? A. ab log a log b log C. log( a b 1) B. log(10 b) a D. log 3.5ab. Which one of the following relations is a function? A. x 3 4log y C. y x 1 B. x y 0 D. x sin y 3. Determine the zeros in the function x 4 8x. A. {-, 0, } C. {0, 8} B. {0} D. {0, } 4. Which expression is NOT equivalent tocos x? A. cos( x) C. 1 sec x B. 1 sin (x) D. cos (x) 1 5. Which of the following statements about a polynomial function is true? A. A polynomial function of degree n has at least n turning points. B. A polynomial function of degree n has at most (n-1) distinct zeros. C. A polynomial function of odd degree has opposite end behaviors. D. A polynomial function of even degree always has at least one zero. MHF 4U FINAL EXAMINATION November 4, 014 Page

3 Multiple Choice [3 marks] cont d: Identify the choice that best completes the statement or answers the question. 6. What is the average rate of change of the function initial value and its only zero? A. 6 C B. 3 D. - ( x 3) between its 7. Which radian measures is equivalent to a central angle of 40 o? A. B C. 3 7 D What is the domain of the function log 3( ( x 4)) 5? A. x 4 C. x 4 B. x 4 D. x 4 9. Which of the following rational functions has an oblique asymptote? A. B. x 8 x 8 C. x( x ) x 1 D. x x 8x 4 x 16x x Which of the following is a characteristic of the function ( x 1)( x )? A. R : y y B. f (x) has two zeros. C. f (x) is odd. D. f (x) is decreasing over its entire domain. MHF 4U FINAL EXAMINATION November 4, 014 Page 3

4 Multiple Choice [3 marks] cont d: Identify the choice that best completes the statement or answers the question. 11. Solve the inequality x x 6. A. (, 3, ) C.,3 B. (, 3, ) D. 3, 1. Using end behaviours, turning points, and initial value, determine the polynomial equation that represents the graph shown below. 3 A. ( x )( x 1)( x 3) C. ( x ) ( x 1) ( x 3) B. ( x )( x 1)( x 3) D. ( x ) ( x 1)( x 3) 13. If x 1 and ( x) x 4 3x g, what is f 1 g? A. C. - B. 0 D. 6 MHF 4U FINAL EXAMINATION November 4, 014 Page 4

5 Multiple Choice [3 marks] cont d: Identify the choice that best completes the statement or answers the question. 14. Consider the expression: log c 4c log 40 log c c 4 Which of the following expressions is equivalent to the expression above? A. log 4c C. Log 40 c B. log 4 D. log c For which value of x is the instantaneous rate of change in the graph negative? y x A. -1 C. 3 B. D Which is the best list of possible zeros of the function x x 4x 8? A. ±1/4, ±1/, ±1, ±, ±4, ±8 C. 1,, -4, -8 B. ±1, ±, ±4, ±8 D. -, MHF 4U FINAL EXAMINATION November 4, 014 Page 5

6 MULTIPLE CHOICE ANSWER SHEET NAME : PERIOD: Answer all multiple choice questions on this sheet: MHF 4U FINAL EXAMINATION November 4, 014 Page 6

7 Part B- Short Answers [34 marks] 3 1. Given the function x 1 16 ; state the parent function and describe the transformations that were applied to the parent function. [K/U : 3 marks] Parent Function: Transformations:. Determine an equation for the sinusoidal function represented by the graph below. [APPL : 4 marks] 3. Solve for x and round your answers to the nearest hundredth. [APPL : 3 marks] x x MHF 4U FINAL EXAMINATION November 4, 014 Page 7

8 Short Answers [34 marks] cont d: 4. The height of a square-based box is 4 cm more than the side length of its square base. If the volume of the box is 5 cm 3, what are its dimensions? [APPL : 4 marks] 5. Solve the equation : cos x 3sin x 3 0 for x 0,. [T/I : 4 marks] 6. Find the inverse of x 1 [T/I : 4 marks] x 3 MHF 4U FINAL EXAMINATION November 4, 014 Page 8

9 Short Answers [34 marks] cont d: 7. Solve 5 x 4 3 x 1 for x. Express your answers to two decimal places. [T/I : 4 marks] 8. Given log b = P and log b 7= Q find the expression that represents the value of [T/I : 4 marks] log b 98b 9. Determine the value of a so that the average rate of change of the function over the interval is equal to 7. [T/I : 4 marks] MHF 4U FINAL EXAMINATION November 4, 014 Page 9

10 Problem Solving [4 marks] Answer 4 questions only. 1. The diagram shows the graph of a quadratic function. Find the equation of its reciprocal. Find the equation of any asymptote(s) for the reciprocal function. Graph the reciprocal of f(x) [APPL : 6 marks] MHF 4U FINAL EXAMINATION November 4, 014 Page 10

11 Problem Solving [4 marks] cont d: Answer 4 questions only.. The following data represents the population in Grandy town. Years since 000 (x) Population (y) a) Using your knowledge of Advanced Functions, predict which type of function would be represented by this situation. b) Write out the equation of the most suitable regression model from part a) correct to decimal places. c) Suppose the population growth keeps following this model, when will the population reach ? [APPL : 6 marks] MHF 4U FINAL EXAMINATION November 4, 014 Page 11

12 Problem Solving [4 marks] cont d: Answer 4 questions only. 3. Ali and Zoe are debating about the simplication of the following trigonometric expression: cos x cos xcot Ali says that it cannot be reduced to a single trigonometric term and Zoe says it is possible. x Who is right? Prove it [APPL : 6 marks] MHF 4U FINAL EXAMINATION November 4, 014 Page 1

13 Problem Solving [4 marks] cont d: Answer 4 questions only. 4. If the graph of the function y = x 3 is compressed vertically by a factor of, and translated units to the left and 4 unit downward: i) determine the equation for the graph of the transformed function ii) draw the graph of the transformed function, and iii) determine the following: a. Domain b. Range c. End-behavior d. Intercepts (correct to decimal places) e. Negative interval. [APPL : 6 marks] MHF 4U FINAL EXAMINATION November 4, 014 Page 13

14 Problem Solving [4 marks] cont d: Answer 4 questions only. 5. Describe how you could walk in front of a motion sensor to produce the distance versus time graph shown below. [APPL : 6 marks] 10 d t During which interval of time is the speed the lowest? ***** END OF QUESTIONS ***** MHF 4U FINAL EXAMINATION November 4, 014 Page 14

15 Compound Angle (Addition and Subtraction) Formulae: Addition Formula for Cosine cos(a + b) = cos a cos b - sin a sin b Addition Formula for Sine Subtraction Formula for Cosine cos(a b) = cos a cos b + sin a sin b Subtraction Formula for Sine sin(a + b) = sin a cos b + cos a sin b sin(a - b) = sin a cos b - cos a sin b Addition Formula for Tangent tan a tan b tan( a b) 1 tan a tan b Subtraction Formula for Tangent tan a tan b tan( a b) 1 tan a tan b Double Angle Formulae: sin (x) = sin x cos x cos (x) = cos x - sin x cos (x) = cos x 1 tan x tan(x) cos (x) = 1 sin x 1 tan x Pythagorean Identity: sin x + cos x = 1 sin x = 1 cos x cos x = 1 sin x Quotient Identities: sin x tan x cos x cos x cot x sin x Reciprocal Identities: 1 sec x cos x 1 cot x tan x csc x 1 sin x MHF 4U FINAL EXAMINATION November 4, 014 Page 15