Pre-Calculus 12
Examination Booklet I
Multiple-Choice and Written-Response Questions
Calculator Permitted
RESOURCE EXAM B
DO NOT OPEN ANY EXAMINATION MATERIALS UNTIL INSTRUCTED TO DO SO.
Student Instructions
1. When answering questions in Booklet I:
• calculators are permitted for the first 45 minutes.
• you will be able to continue in Booklet I after 45 minutes, but without the use of a calculator.
2. When using a calculator:
• round final answers with decimals to at least two decimal places unless otherwise indicated in the question.
3. Once the calculator is put away, Booklet II will be handed out.
4. Diagrams are not necessarily drawn to scale.
5. You may use the provided Formula Page for reference.
Contents: 15 pages
14 multiple-choice and 4 Written-Response questions in Examination Booklet I
Examination: 2 hours
Additional Time Permitted: 60 minutes
© Province of British Columbia
MULTIPLE-CHOICE QUESTIONS
(Calculator permitted)
Value: 21 marks
INSTRUCTIONS: For each question, select the best answer.
You have a maximum of 45 minutes to work with your calculator. After
45 minutes you will be allowed to continue in Booklet I but without the use
of a calculator.
Note: some of the written-response questions in the Written-Response section
may require the use of a calculator and should be completed within the first
45 minutes.
1. Solve: cos 3x = sin x ,
0≤x≤
π
2
N—A5/5.3—E—MC—TRIG
*
A. 0.39
enter y = cos(3x + sin x)
B. 0.40 , 1.25
C. 0.79
enter y = cos(3x – sin x)
D. 0.79 , 1.18
enter y = cos3x + sin x
2. Determine the equation of a circle with centre ( 0 , 0 ) passing through the point P ( −2 , 5) .
N—A2/2.3—E—MC—TRIG
A. x 2 + y 2 = 3
take the sum of the coordinates
*
B.
x 2 + y2 = 9
take the sum of the coordinates and square this result
C.
x 2 + y 2 = 21
take the sum of the square of the coordinates and get the sign wrong for the square of –2
D.
x 2 + y 2 = 29
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 1
3. Determine the measure of the standard position angle θ if the point P ( −4 , 3) is on the terminal
arm of angle θ , where 0° ≤ θ < 360° .
P—A3/3.5—M—MC—TRIG
use of tan −1 ( 43 )
A. 37°
B.
53°
C. 127°
*
use of tan −1 ( 43 )
use of π − tan −1 ( 43 )
D. 143°
4. Express as a single logarithm: log a − log b − 3 log c
N—B8/8.3—M—MC—LOGS
*
A. log
a
bc3
B.
log
a
b3c3
C.
log
ac3
b
D. log
ac3
b3
5. Determine the x-intercept of the function y = 5 x − 3 .
N—B9/9.2—E—MC—LOGS
A. −2
y-intercept
*
B.
0.008
C.
D.
0.6
0.68
y-intercept of y = 5x −3
x-intercept of y = 5x − 3
6. An investment earns 2.25% per annum compounded daily. How many years would be required
for an investment to triple in value? Assume all years have 365 days.
P—B10/10.8—M—MC—LOGS
A.
*
Page 2
4.88
B. 5.41
C. 48.83
D. 49.37
(
3 = 1+
)
0.225 365t
365
3 = (1 + 0.225)t
3 = (1 + 0.0225)t
Pre-Calculus 12 – Resource Exam B Examination Booklet I
7. Determine the number of different arrangements of all the letters in the word TRIGONOMETRY.
N—C2/2.6—E—MC—COMB
*
A.
4 989 600
11!
2! 2! 2!
B.
59 875 200
12!
2! 2! 2!
C. 119 750 400
12!
2! 2!
D. 479 001 600
12!
8. An area code is the first 3 digits in a phone number and indicates the location of either the
province or the city. In Canada, the following area codes exist:
Q—C1/1.3—H—MC—COMB
Manitoba
204
Saskatchewan
306
Québec (Québec City)
418
Montreal
514
Newfoundland
709
Québec
450, 819
British Columbia
250, 604, 778
Alberta (south)
403
Ontario
519, 613, 705, 807
Yukon and NW Territories
867
Toronto (Ontario)
289, 647
Ontario (Toronto Metro)
416
New Brunswick
506
Alberta
780
Nova Scotia
902
Notice that there are 3 area codes for British Columbia: 250, 604 and 778. It will be necessary to
add another area code as the population increases. The new area code cannot be the same as an
existing code, it must begin with a 3 and end in an even number. Determine the number of
possible area codes to choose from.
*
A.
B.
C.
D.
40
44
49
50
1 × 10 × 4
1× 9 × 5 −1
1 × 10 × 5 − 1
1 × 10 × 5
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 3
9. In a standard deck of 52 cards, determine the number of 5-card hands that must contain at least
3 queens.
P—C4/4.3—M—MC—COMB
A. 4512
( 4 C3 ) ( 48 C2 )
*
B. 4560
C. 4704
D. 4752
( 4 C3 )
( 4 C3 )
( 4 C3 )
( 48 C2 )
( 49 C2 )
( 49 C2 )
+
( 4 C4 )
( 48 C1 )
+
( 4 C4 )
( 48 C1 )
10. A dance group has twelve people from which five need to be chosen to compete in a national
competition. Bob and Nancy are in the group of twelve and have recently obtained gold
at a regional competition. They are therefore required to be among the five selected for the
national competition. Given this requirement, how many different five-member teams are
possible?
P—C3/3.2—M—MC—COMB
*
A. 120
10 C3
B. 220
12 C3
C. 252
10 C5
D. 792
12 C5
11. Determine the 5th term in the expansion of ( 3x + 2y ) , where n ≥ 6 .
P—C4/4.6—M—MC—COMB
4
n −4
*
A. n C4 ( 3x ) ( 2y )
n
B.
C.
D.
Page 4
( 2y )5
n −4
4
n C4 ( 3x ) ( 2y )
n −5
5
n C5 ( 3x ) ( 2y )
n −5
n C5 ( 3x )
Pre-Calculus 12 – Resource Exam B Examination Booklet I
12. A sheet of metal 12 cm × 12 cm will be used to make an open-top box by removing a square of
length x in each corner and turning up the sides as shown in the diagram.
P—B12/12.7—M—MC—POLY
x
x
x
x
x
What is the volume of the box as a function of x ?
A. V = x 3
*
B.
V = x (12 − x )2
C.
V = 144 − 4x 2
D. V = x (12 − 2x )2
13. Determine all solutions for the equation
N—B13/13.6—M—MC—RADS
A. −0.61, 0.72
( x + 4 ) − 9x 2 = 0
*
B. −0.61
C.
0.72
D. 1.33
x + 4 = 3x .
x + 4 + 3x = 0
( x + 4 ) − 3x 2 = 0
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 5
14. Which equation represents the graph of f ( x ) after it has been horizontally stretched
1
by a factor of ?
2
N—B3/3.2—E—MC—TRANS
*
A.
y = f ( 2x )
B.
y = 2 f (x)
C.
y= f
D.
y=
( 12 x )
1
f (x)
2
This is the end of the Multiple-Choice section.
Answer the remaining questions directly in the Written-Response section.
Page 6
Pre-Calculus 12 – Resource Exam B Examination Booklet I
WRITTEN-RESPONSE QUESTIONS
(Calculator permitted)
Value: 16 marks
INSTRUCTIONS: Answer the following questions in the space provided.
Any questions with a
symbol should be attempted within the first
45 minutes while you have access to a calculator. After 45 minutes you will be
allowed to work on this section but without the use of a calculator.
Rough-work space has been incorporated into the space allowed for answering each
question. You may not need all the space provided to answer each question.
When using the calculator, you should provide a decimal answer that is accurate to
at least two decimal places (unless otherwise indicated). Such rounding should
occur only in the final step of the solution.
When asked to provide explanations, you are encouraged to use sketches, diagrams
or examples to support your work. You will be evaluated on the concepts expressed,
the organization and accuracy of your work, and your use of language.
Full marks will NOT be given for a final answer only.
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 7
1. A food sample contains 300 bacteria. The doubling time for bacteria left at room temperature
is 20 minutes. How many minutes will it take to reach an unsafe level of 100 000 bacteria?
Solve algebraically using logarithms. Answer must be written as a decimal accurate to at
least 2 decimal places.
P—B10/10.5—M—MC—LOGS
Page 8
(4 marks)
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 9
1
2
, where α is in quadrant I and cos β = where β is in quadrant IV,
5
3
determine the exact value of sin ( α − β ) .
P—A6/6.7—H—MN—TRIG
2. Given sin α =
Page 10
(4 marks)
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 11
3. Prove algebraically:
cos θ
= sec θ + sec θ csc θ − cot θ
1 − sin θ
(4 marks)
Q—A6/6.6—H—MC—TRIG
LEFT SIDE
Page 12
RIGHT SIDE
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 13
4. The graph of y = f ( x ) is sketched below. Determine the domain and range of y =
and explain how this was determined.
P—B13/13.4—M—WR—RADS
y
f (x)
(4 marks)
10
5
–10
–5
5
10
x
–5
–10
Page 14
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Pre-Calculus 12 – Resource Exam B Examination Booklet I
Page 15