Grade 12 Pre-Calculus Mathematics Achievement Test. Booklet 2

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1 Grade 2 Pre-Calculus Mathematics Achievement Test Booklet 2 June 207

2 Manitoba Education and Training Cataloguing in Publication Data Grade 2 pre-calculus mathematics achievement test. Booklet 2. June 207 This resource is available in print and electronic formats. ISBN: (print) ISBN: (pdf). Mathematics Eaminations, questions, etc. 2. Educational tests and measurements Manitoba. 3. Mathematics Stud and teaching (Secondar) Manitoba. 4. Precalculus Stud and teaching (Secondar) Manitoba. 5. Mathematical abilit Testing. I. Manitoba. Manitoba Education and Training Manitoba Education and Training Winnipeg, Manitoba, Canada Permission is hereb 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. Order online at This resource will also be available on the Manitoba Education and Training website at Websites are subject to change without notice. Disponible en français. While the department is committed to making its publications as accessible as possible, some parts of this document are not full accessible at this time. Available in alternate formats upon request.

3 Instructions Selected Response Questions There are 0 questions worth a total of marks. Calculators are not allowed for this part of the test. You ma use the spaces beside each question for rough work. Provide onl one answer per question. There is no penalt for guessing. Record our answers on the sheet provided. Constructed Response Questions There are 22 questions worth a total of 46 marks. Calculators are not allowed for this part of the test. For full marks, our answer must show all pertinent diagrams, calculations, and eplanations. 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 8 mark If P ( 3, 5) is a point on the graph of f ( ) = f ( ) + 7. a) ( 2,2 ) b) ( 4, 2) c) ( 2, 2) d) ( 4,2 ) =, identif the corresponding point on the graph of Question 9 mark Identif how the graph of = is transformed to the graph of = 3. 3 a) reflected over the -ais b) reflected over the -ais c) reflected over both the -ais and the -ais d) reflected over the line = Question 20 mark Identif the equation log a b = c in eponential form. a) b) c) c b c a b a = a = b = c d) a c = b Pre-Calculus Mathematics: Booklet 2 (June 207)

6 Question 2 mark Identif the graph of = tan. a) b) π 2 π 2 c) d) π 2 π 2 2 Pre-Calculus Mathematics: Booklet 2 (June 207)

7 Question 22 mark Identif which of the following graphs represents a logarithmic function. a) b) c) d) Pre-Calculus Mathematics: Booklet 2 (June 207) 3

8 Question 23 mark If the volume of a bo is represented b V ( ) ( ) ( ) ( ) a) 4 b) c) d) 4 = , identif a possible value of. Question 24 mark π Identif a coterminal angle for θ =. 3 a) b) c) π 3 4π 3 7π 3 d) π 3 Question 25 mark Identif the value of n in the equation C = C n 3 n 6. a) 3 b) 6 c) 9 d) 8 4 Pre-Calculus Mathematics: Booklet 2 (June 207)

9 Question 26 mark Identif the equation of the function, f ( ), for the following graph. f ( ) a) f ( ) b) f ( ) c) f ( ) d) f ( ) = = = = ( + 3) 3 2 ( + 2) Pre-Calculus Mathematics: Booklet 2 (June 207) 5

10 Question 27 2 marks 8 Match the following radical functions with their graphs. Place the appropriate letter in this column. ( ) = 2 ( + 3) f ( ) = 2 ( + 3) g ( ) = 3 ( 2) h ( ) = 3( 2) k A) B) C) D) 6 Pre-Calculus Mathematics: Booklet 2 (June 207)

11 Question 28 3 marks 9 Epress ( ) 3 2 p = + as a product of factors. p( ) = Pre-Calculus Mathematics: Booklet 2 (June 207) 7

12 Question 29 a) 3 marks b) mark 20 2 Given the graph of f ( ) = ( + ) ( ) 3, f ( ) a) sketch the graph of ( ). ( ) g = f f ( ) The graph of f ( ) has alread been drawn for our reference. No marks will be awarded for the graph of f ( ). b) describe how to sketch the graph of h( ) = f ( ). 8 Pre-Calculus Mathematics: Booklet 2 (June 207)

13 Question 30 mark 22 Describe how the value of m in the equation ( ) graph of = log. 3 log m, m 3 =, affects the asmptote on the Question 3 2 marks 23 Solve algebraicall = 5 Pre-Calculus Mathematics: Booklet 2 (June 207) 9

14 Question 32 4 marks 24 Solve cos 2θ = 0, where θ. 0 Pre-Calculus Mathematics: Booklet 2 (June 207)

15 Question 33 mark 25 Describe a difference between the graphs of f ( ) ( ) = 2( + ) ( + 3) f ( ) = 2( + ) ( + 3) 2 2 g = and = g( ). Pre-Calculus Mathematics: Booklet 2 (June 207)

16 Question 34 2 marks 26 Given the graph of = f ( ), sketch the graph of f ( ). f ( ) f ( ) The graph of f ( ) has alread been drawn for our reference. No marks will be awarded for the graph of f ( ). 2 Pre-Calculus Mathematics: Booklet 2 (June 207)

17 Question 35 mark 27 Describe the relationship between the zeros of the function f ( ) ( ) ( ) 2 equation ( ) ( ) = 0, and the -intercepts of the graph of = f ( ). = 2 + 3, the roots of the Question 36 3 marks 28 Sketch a graph of at least one period of the function ( ) π f = cos Pre-Calculus Mathematics: Booklet 2 (June 207) 3

18 Question 37 mark 29 4π Verif that θ = is a solution of the equation cos 0. θ = 4 Pre-Calculus Mathematics: Booklet 2 (June 207)

19 Question 38 mark 30 Describe how to determine the equation of the horizontal asmptote of a rational function when the degree of the polnomial in the numerator and the degree of the polnomial in the denominator are equal. Question 39 2 marks 3 Evaluate. 5π cot 6 7π sin 3 Pre-Calculus Mathematics: Booklet 2 (June 207) 5

20 Question 40 4 marks 32 Sketch the graph of the function f ( ) = ( ) 2 and determine the range. Range: 6 Pre-Calculus Mathematics: Booklet 2 (June 207)

21 Question 4 a) mark b) mark Given f ( ) = 2 and g( ) a) determine g( f ( )). 2 = +, g( f ( )) = b) eplain wh the domain of g( f ( )) is restricted. Pre-Calculus Mathematics: Booklet 2 (June 207) 7

22 Question 42 3 marks 35 Solve algebraicall. 2 log 3 + log 4 = 2, where a > 0 a a Question 43 2 marks 36 Solve sec + 2 = 0 θ over the interval [ π ] 0, 2. 8 Pre-Calculus Mathematics: Booklet 2 (June 207)

23 Question 44 mark 37 Determine the -intercept of the graph of f ( ) = e. Question 45 mark 38 Given the 5 th row of Pascal s triangle, determine the values of the net row Pre-Calculus Mathematics: Booklet 2 (June 207) 9

24 Question 46 2 marks 39 Evaluate. log 80 log Question 47 mark 40 State the amplitude of f ( ) ( ) = 2sin π. 20 Pre-Calculus Mathematics: Booklet 2 (June 207)

25 Question 48 3 marks 4 Determine the eact value of cos5. Pre-Calculus Mathematics: Booklet 2 (June 207) 2

26 Question 49 a) mark b) mark Given f ( ) = , g( ) 3, a) determine h( ). = + and h( ) = f ( ) g( ), h( ) = b) sketch the graph of = h( ). 22 Pre-Calculus Mathematics: Booklet 2 (June 207)

27 No marks will be awarded for work done on this page. Pre-Calculus Mathematics: Booklet 2 (June 207) 23

28 24 Pre-Calculus Mathematics: Booklet 2 (June 207)

29 Pre-Calculus Mathematics: Booklet 2 (June 207) 25

30 26 Pre-Calculus Mathematics: Booklet 2 (June 207)

Grade 12 Pre-Calculus Mathematics Achievement Test. Booklet 2

Grade 12 Pre-Calculus Mathematics Achievement Test Booklet 2 June 2015 Manitoba Education and Advanced Learning Cataloguing in Publication Data Grade 12 pre-calculus mathematics achievement test. Booklet