Grade 12 Pre-Calculus Mathematics Achievement Test. Booklet 2

Transcription

1 Grade 2 Pre-Calculus Mathematics Achievement Test Booklet 2 January 206

2 Manitoba Education and Advanced Learning Cataloguing in Publication Data Grade 2 pre-calculus mathematics achievement test. Booklet 2. January 206 Issued in print and electronic formats. ISBN: (print) ISBN: (pdf). Mathematics Examinations, questions, etc. 2. Educational tests and measurements Manitoba. 3. Mathematics Study and teaching (Secondary) Manitoba. 4. Precalculus Study and teaching (Secondary) Manitoba. 5. Mathematical ability Testing. I. Manitoba. Manitoba Education and Advanced Learning Manitoba Education and Advanced Learning School Programs Division Winnipeg, Manitoba, Canada Permission is hereby given to reproduce this resource for non-profit educational purposes provided the source is cited. After the administration of this test, print copies of this resource will be available for purchase from the Manitoba Learning Resource Centre (formerly the Manitoba Text Book Bureau). Order online at < This resource will also be available on the Manitoba Education and Advanced Learning website at < Websites are subject to change without notice. Disponible en français. Available in alternate formats upon request.

3 Instructions Selected Response Questions There are 8 questions worth a total of 8 marks. Calculators are not allowed for this part of the test. You may use the spaces beside each question for rough work. Provide only one answer per question. There is no penalty for guessing. Record your answers on the sheet provided. Constructed Response Questions There are 24 questions worth a total of 55 marks. Calculators are not allowed for this part of the test. For full marks, your answer must show all pertinent diagrams, calculations, and explanations. Your solutions should be neat, clear, and well organized. Write each solution in the space provided. i

4 No marks will be awarded for work done on this page. ii

5 Question 4 mark Identify the maximum number of x-intercepts for a polynomial function of degree 3. a) b) 2 c) 3 d) 4 Question 5 mark The graph of y = f ( x) contains the point ( a, b ). The graph of ( ) graph of f ( x ) and contains the point ( 3, a b ). Identify the function that represents g( x ). a) g( x) = f ( 3x) b) g( x) = 3 f ( x) x g x = f 3 c) ( ) 3 d) g( x) = f ( x) g x is a transformation of the Question 6 mark The angle 2.95 radians, in standard position, terminates in quadrant: a) I b) II c) III d) IV Pre-Calculus Mathematics: Booklet 2 (January 206)

6 Question 7 mark Evaluate: a) 2 2sin π π cos 8 8 b) 2 2 c) d) 2 Question 8 mark 2 3 Identify which of the following represents the 5th term in the expansion of ( 4x 2y ) a) C ( x 2 3 ) ( y ) b) C ( x 2 3 ) ( y ) c) C ( x 2 3 ) ( y ) d) C ( x 2 3 ) ( y ) Pre-Calculus Mathematics: Booklet 2 (January 206)

7 Question 9 mark Identify which of the following graphs of polynomial functions has a zero with a multiplicity of 3. y y a) b) x x c) y d) y x x Pre-Calculus Mathematics: Booklet 2 (January 206) 3

8 Question 20 mark A non-permissible value of x for the function f ( x) = cos x + is: a) b) 0 c) π d) 3π 2 Question 2 Identify which of the following statements is true for the rational function f ( x) = mark ( x )( x ) ( x )( x+ 3) 4 2. a) The equation of the horizontal asymptote is y = 4. b) The equation of the vertical asymptote is x =. c) The y-intercept is 0. d) There is a point of discontinuity (hole) when x = 2. 4 Pre-Calculus Mathematics: Booklet 2 (January 206)

9 Question 22 3 marks 5 Determine the equation of the polynomial function, px, ( ) represented by the graph. y px ( ) 2 2 x px ( ) = Pre-Calculus Mathematics: Booklet 2 (January 206) 5

10 Question 23 mark 6 Evaluate: log Pre-Calculus Mathematics: Booklet 2 (January 206)

11 Question 24 2 marks 7 Evaluate: π π cos csc 3 6 Pre-Calculus Mathematics: Booklet 2 (January 206) 7

12 Question 25 mark 8 Estimate the value of Justify your answer. log Pre-Calculus Mathematics: Booklet 2 (January 206)

13 Question 26 2 marks 9 If θ terminates in quadrant III and 6 cosθ =, determine the exact value of tanθ. 7 Pre-Calculus Mathematics: Booklet 2 (January 206) 9

14 Question 27 mark 20 Given 2 f( x) = x + x 4 and gx ( ) = x+ 5, Taz was asked to find f( gx ( )). Taz s solution: ( ) f (g (x))= x x -4 2 = x _x - 4 =2 x +, x -5 Describe the error in Taz s solution. 0 Pre-Calculus Mathematics: Booklet 2 (January 206)

15 Question 28 3 marks 2 Sketch the graph of the function f ( x) 3log ( x ) = +. 2 y x Pre-Calculus Mathematics: Booklet 2 (January 206)

16 Question 29 mark 22 Write an equation of a rational function that would not have any vertical asymptotes. 2 Pre-Calculus Mathematics: Booklet 2 (January 206)

17 Question 30 2 marks 23 Determine the exact value of tan 75. Pre-Calculus Mathematics: Booklet 2 (January 206) 3

18 Question 3 4 marks 24 Sketch the graph of the following function: f ( x) = ( x+ 3)( x 3) x( x 3) y x 4 Pre-Calculus Mathematics: Booklet 2 (January 206)

19 Question 32 2 marks 25 In the binomial expansion of 9 2 2x 3, determine which term contains 3 x x. Pre-Calculus Mathematics: Booklet 2 (January 206) 5

20 Question 33 4 marks 26 José and Dana get on a Ferris wheel, which is metre off the ground. The diameter of the Ferris wheel is 6 metres. Their ride lasts for 4 minutes, in which time the Ferris wheel makes one revolution. Determine the values of A, B, C, and D, if the sinusoidal function that models the situation is ht ( ) = Acos[ Bt ( C)] + D, where h is the height at which José and Dana are located on the Ferris wheel, from the ground, in metres, and t is the time, in minutes. A = 6m B = m C = D = 6 Pre-Calculus Mathematics: Booklet 2 (January 206)

21 Question 34 3 marks 27 Solve algebraically: P n 3 ( n ) = 4! Pre-Calculus Mathematics: Booklet 2 (January 206) 7

22 Question 35 2 marks 28 Given f ( x) = 2 x, determine the equation of the inverse, f ( x). 8 Pre-Calculus Mathematics: Booklet 2 (January 206)

23 Question 36 3 marks 29 Solve: 4 log 2 log 8 = log a Pre-Calculus Mathematics: Booklet 2 (January 206) 9

24 Question 37 3 marks 30 Sketch the graph of at least one period of the function y ( x) = 3cos π. y x 20 Pre-Calculus Mathematics: Booklet 2 (January 206)

25 Question 38 3 marks 3 Using the laws of logarithms, fully expand the expression: 3 x log a y z Pre-Calculus Mathematics: Booklet 2 (January 206) 2

26 Question 39 4 marks 32 Sketch the graph of f ( x) = 3 x 2 +. y x 22 Pre-Calculus Mathematics: Booklet 2 (January 206)

27 Question 40 a) Determine the domain of the graph of the function 2 f( x) = x 4. a) mark b) mark b) Explain why the domain of 2 = x is restricted. f( x) 4 Pre-Calculus Mathematics: Booklet 2 (January 206) 23

28 Question 4 a) mark b) mark Given the point ( 2, 8) on the graph of f ( ) transformations of f ( x ). x, determine the new points after the following a) f( x) b) f ( x) Pre-Calculus Mathematics: Booklet 2 (January 206)

29 Question 42 mark 37 Explain why there is no solution for the equation cscθ =. 2 Pre-Calculus Mathematics: Booklet 2 (January 206) 25

30 Question 43 3 marks 38 Given the graph of y = f ( x), y x sketch the graph of y f ( x) = 2 +. y x The graph of f ( x ) has already been drawn for your reference. No marks will be awarded for the graph of f ( x ). 26 Pre-Calculus Mathematics: Booklet 2 (January 206)

31 Question 44 mark 39 x Given f( x ) = 2 +, state the equation of the horizontal asymptote. Pre-Calculus Mathematics: Booklet 2 (January 206) 27

32 Question 45 2 marks 40 Given the following graphs of f ( x) = x 3 and g( x) x f ( x ) g( x ) y = +, y x x sketch the graph of h( x) = ( f g)( x). y x 28 Pre-Calculus Mathematics: Booklet 2 (January 206)

33 No marks will be awarded for work done on this page. Pre-Calculus Mathematics: Booklet 2 (January 206) 29

34 No marks will be awarded for work done on this page. 30 Pre-Calculus Mathematics: Booklet 2 (January 206)