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8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Grade 12 Pre-Calculus
Mathematics (40S)
Standards Test
Student Booklet
(Part 2)
January 2007
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Manitoba Education, Citizenship and Youth Cataloguing in Publication Data
371.26097127 Grade 12 Pre-Calculus Mathematics (40S) Standards Tests.Student Booklet. (Part 2)
January 2007
ISBN-13: 978-0-7711-3617-4ISBN-10: 0-7711-3617-6
1. MathematicsExaminations, questions, etc.2. MathematicsExaminations. 3. Educational testsand measurementsManitoba. 4. MathematicsStudyand teaching (Secondary)Manitoba. 5. CalculusStudy andteaching (Secondary)Manitoba. 6. Mathematical ability-testing. 7.MathematicsStudy and teaching (Secondary). 8. CalculusStudyand teaching. (Secondary). I. Manitoba. Manitoba Education,Citizenship and Youth
Copyright 2007, the Crown in Right of Manitoba, as represented by the Minister of Education, Citizenship andYouth. Manitoba Education, Citizenship and Youth, Instruction, Curriculum and Assessment Branch, Winnipeg,Manitoba R3E 3J5
Permission is hereby given by the copyright owner to reproduce this document on a non-profit basis for educationalpurposes provided the source is mentioned.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 1
Multiple-Choice Questions
Instructions
There are 15 multiple-choice questions.
Each question is worth 1 mark.
Read each question carefully.
Examine all the choices before you decide on your answer.
You may use the spaces beside each question for rough work.
Record your answers on the sheet provided.
Provide only one answer per question.
There is no penalty for guessing.
Answer all questions.
Calculators (scientific or graphing) are not allowed for this part of the test.
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Page 2 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 3
Multiple-Choice Questions
10. The equation of an asymptote of the conic section whose equation is2 2
14 9
y x = is:
a)2
3y x=
b)3
2y x=
c)4
9y x=
d)9
4y x=
11. The sum of the infinite geometric series80
60 403
+ is:
a) 20
b) 36
c) 100
d) 180
12. A value of that satisfies the equation ( )sin 2sin 1 0 + = is:
a)5
6
b)7
6
c)2
d)3
2
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Page 4 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
13. The probability of Lisa winning a game is1
3. No game can end in a tie.
If she plays 2 games, what is the probability that she will lose them both?
a)1
3
b)2
3
c)4
9
d)8
9
14. The graph represented by the equation ( )3sin 4 5y = + has a maximum value of:
a) 2
b) 3
c) 5
d) 8
15. If ( )3log 5 and log 4 , then log 4 5a a aT R = = is:
a) 3RT
b) 3R T+
c) 3R T+
d) 3RT
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8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Page 6 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
19. An expression equivalent to3
1
2 i
i
x
=
is:
a) 14x
b) 2 32 4 8x x+ +
c) 2 32 2 2x x+ +
d) 66x
20. The value of5
sec3
is:
a)2
3
b)2
3
c) 2
d) 2
21. A party of 18 people is divided into 2 different groups consisting of 11 people and 7 people.
The number of different ways this can be done is:
a)18! 18!
7! 11!+
b)18!
11!7!
c) 18!18!7!11!
d) 11!7!2!
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 7
22. The coordinates of a point on the graph of ( )f x= are ( )2, 3 . Which of the following
points must be on the graph of ( )2f x= ?
a) ( )2, 6
b) ( )2, 6
c) ( )4, 3
d) ( )4, 3
23. An ellipse has a major axis of 20 and a minor axis of 12. A possible equation for this ellipse
is:
a)2 2
1400 144
x y+ =
b)2 2
120 12
x y+ =
c)2 2
1100 36
x y+ =
d)2 2
110 6
x y+ =
24. In the binomial expansion of( )12
2 3a b , the term containing 5b is the:
a) 4th term
b) 5th term
c) 6th term
d) 7th term
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Page 8 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 9
Short-Answer Questions
Instructions
There are 15 short-answer questions.
Each question is worth 1 mark.
Calculators are not allowed for this part of the test.
Write your final answer in the space provided.
Work need not be shown in order to obtain full marks for a correct answer. However, in thecase of an incorrect final answer, part marks may be given only if work is shown.
Solutions need not have rationalized denominators.
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Page 10 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 11
DO NO
USE
113
114
115
Short-Answer Questions
25. What is thex-coordinate of4
P
3
on the unit circle?
(1 mark)
26. A circle has a radius of 10 cm. An arc on this circle is intercepted by a central angle of 90 .Calculate the length of this arc, in centimetres.
(1 mark)
27. In how many ways can 10 people be seated at a round table?Leave your answer in factorial notation.
(1 mark)
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Page 12 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO NO
USE
116
117
118
28. State the measure of an angle, in radians, formed by the two hands of a clock at 7:00 p.m.(1 mark)
29. Expresscos
cotsin
i in terms of a single trigonometric function.
(1 mark)
30. State thex-intercept of ( ) 1f x x= .
(1 mark)
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 13
DO NO
USE
119
120
121
31. The probability that Stephan passes Spanish is 0.5 and the probability that he passes Mathis 0.4.
What is the probability that he passes Spanish or Math?(1 mark)
32. The parabola whose equation is ( ) ( )2
5 2x a y = + opens to the left.
State a possible numeric value fora.(1 mark)
33. State the domain of the function:
1cos x
=
(1 mark)
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Page 14 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO NO
USE
122
123
124
34. Find the exact value of sin 47 cos17 cos47 sin17 .
(1 mark)
35. If the period of ( )5cosy bx= is
4, find the value ofb .
(1 mark)
36. Simplify:
( )
( )
1 !
1 !
n
n
+
(1 mark)
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 15
DO NO
USE
125
126
37. Evaluate:
3
4
log 27
log 16
(1 mark)
38. Solve:
15 5x =
(1 mark)
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Page 16 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO NO
USE
12739. Complete the graph of ( )y f x= if it is an odd function.
(1 mark)
-4
-5
( )y f x=
y
x
4
5
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 17
Long-Answer Questions
Instructions
There are 10 long-answer questions worth a total of 35 marks.
Calculators are not allowed for this part of the test.
Write each solution in the space provided.
For full marks, your answers must show all pertinent diagrams, calculations, andexplanations.
Your solutions should be neat, clear, and well organized.
If any curve contains asymptotes, the asymptotes should be included in the graph.
Solutions need not have rationalized denominators.
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Page 18 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 19
DO NO
USE
128
129
Long-Answer Questions
40. Solve:
( ) ( )log 5 log 1 2x x+ = (4 marks)
41. The equation of a circle is given by
2 2
2 6 0x y x y k + + + =
.Find the value of k if the radius of the circle is 4.
(3 marks)
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Page 20 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO N
USE
130
131
42. a) State they-intercept of xe= .
(1 mark)
They-intercept is
b) Sketch a clearly labelled graph of 4xy e= .
(2 marks) y
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 21
DO NO
USE
132
133
43. a) Find the exact value of5
tan12
.
(3 marks)
b) Find the exact value of5
cot12
.
(1 mark)
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Page 22 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO N
USE
134
135
44. The equation of a conic section is given by 24 16 19x y y= + .
a) Write the equation in standard form.(2 marks)
b) Sketch a clearly labelled graph of the conic section.
(2 marks) y
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 23
DO NO
USE
136
45. The function ( )f x= is shown below:
(2 marks)
Sketch the graph of1
( )y
f x= .
y
1
1
y
1
1
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Page 24 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO NO
USE
137
46. The graph of a function ( )y f x= is shown below.
Sketch the graph of:
a)
(2 marks) 2y f
=
y
( )2, 2( )2, 2
( )3, 2
( )f x
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 25
DO NO
USE
138
139
Sketch the graph of:
b)
(2 marks)
47. Find the exact value of:
2 25 11sin sec tan csc3 6 4 6
(4 marks)
( )2 1y f x= +
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Page 26 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
DO NO
USE
14048. Prove the following identity:
3 2tan sec sin sin sec =
(3 marks)
Left-Hand Side Right-Hand Side
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 27
DO NO
USE
14149. A sinusoidal function has a maximum at ( )4, 6 .
The following maximum is at ( )16, 6 .
The range of this function is [ ]12, 6 .
Write an equation to represent this function.(4 marks)
y =
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Page 28 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
8/9/2019 Grade 12 Pre-Calculus | Part 2 | edu.gov.mb.ca
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 29
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
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Page 30 Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
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Student Booklet (Part 2)Pre-Calculus Mathematics (40S)January 2007 Page 31
NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.
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NO MARKS WILL BE AWARDED FOR WORK DONE ON
THIS PAGE.