Pre-Calculus 12 Practice Exam 1
MULTIPLE-CHOICE (Calculator permitted )
1. Determine the smallest zero for y  4 sin 3  2 in
the interval 2    3
a. 0.38
b. 1.22
c. 6.66
d. 7.50
2. In high school, a shot put is thrown out of a circle
with a radius of 3.5 feet. A curved wooden
“stopboard” is placed in an arc around part of this
circle. The central angle is 65.5°. Determine the
length of the curved “stopboard.”
a.
b.
c.
d.
7. A restaurant offers a selection of 4 different
sandwiches, 3 different soups and 4 different
flavours of juice. In how many different ways can a
person select one item from each category?
a. 11
b. 18
c. 48
d. 54
8. Determine the 4th term in the expansion of
y

 4x  
2

8
a.
 7168 x 5 y 3
c. 16 x 4 y 4
b.
 128 x 5 y 3
d. 1120 x 4 y 4
9. A family of 6 (2 parents and 4 children) sit in a row
at a theatre. A parent must sit at either end with
the 4 children between them. In how many ways
can the family be seated?
3.5 ft
4.0 ft
4.5 ft
5.0 ft
a. 24
b. 48
c. 120
d. 720
10. From a standard deck of 52 cards, how many 5-card
hands can be formed containing at least 4 clubs?
3. On Oct. 2, 2010, the tide at New Westminster
reached a maximum height of 10.8 feet at
midnight. At 9 am the tide reached the next
minimum height of 5.8 feet. Assuming the
relationship is sinusoidal, what was the height of
the tide at 7 am?
a. 6.1 ft
4. Solve 7  2
a. -0.64
b. 6.4 ft
x 1
c. 8.7 ft
d. 9.9 ft
.
b. 1.36
15.5
b. 15.6
b. 27 885
c. 29 172 d. 34 320
11. A hockey team has played 10 games and has a
record of 5 wins, 3 losses and 2 ties. In how many
ways could this have happened if after the first 4
games the team’s record was 3 wins and a loss?
a. 90
b. 94
c. 360
d. 630
12. When the polynomial P(x ) is divided by x  3, the
c. 1.81
d. 3.81
5. The population in a particular community is
increasing at an annual rate of 6.5%. Assume this
trend will continue. In how many years will the
present population of 12 000 grow to 32 000?
a.
a. 20 592
c. 15.8
remainder is 2. Which point must be on the graph
corresponding to the function y  P(x ) ?
a.
 3,2 
b.  3,0 c.  3,2 
d. 3,2 
13. Determine the range of the rational function
graphed below.
d. 16.1
6. In a study which compared the pH of urine and
tears, the following data was collected.
On average, how
many times more
alkaline are tears
than urine?
a. 1.3
b. 1.5
c. 15.0
d. 31.6
a.
b.
c.
d.
all reals
( ,0],[8, )
( ,2], (2, )
( ,1), ( 1,0],[8, )
14. The graph y  f (x) is stretched horizontally by a
1
factor of . Determine the equation of the
4
transformed graph.
a.
b.
1
f ( x)
4
y  4 f ( x)
1
c. y  f ( x )
4
d. y  f (4 x )
y
20. A point with an x value of 2 lies on the circle with
equation x 2  y 2  5 . This point also lies on
the terminal arm of  in standard position.
Determine the value of sec  .
a.
MULTIPLE-CHOICE (Calculator NOT permitted)
5
2
b.
5
2
2
c.
2
5
d.
5
21. The graph of y  2 sin b x  c   1 is shown below.
Determine a value of c .
15. The students at a graduation dinner are separated
into groups to be seated at 10 different tables. The
order in which these 10 groups will approach the
buffet is to be determined randomly. In how many
ways can this order be determined?
a. 1010
b.
10 C10
c.
d. 10  10
10 P10
16. Consider the graph of y  3cos
 x  2
10
4.
a.

Which statement is false?
a.
b.
c.
d.
17. Solve cos x 
a.
 5
,
6 6
I
II
III
IV
b.
6
,
6
c.
 2
3
,
3
d.
 5
b.
5
 n, n  Z
6
2
 n, n  Z
3
a. cos x  0
b. cos x  1
5
 2n, n  Z
6
2
d.
 2n, n  Z
3
c.
a.
a.
2 3
b.
2 3

2
7
d.
4
c. sin x  0, cos x  1
d. cos x  0, cos x  1
 3
b.
,
4 4
 3
,
4 4
c.
3 7
,
4 4
d.
3 5
,
4 4
csc  sin 
sec  cos
b. cot 3 
cot 2 
c. tan 2 
d. tan 3 
25. Solve 2 3 x 1  8 2 x 1
19. Determine the exact value of tan 75
5 3
c.
4
3 3
d.
3

24. Simplify
a.
a.
c.
22. Determine all restrictions for the expression
tan x
cos x  1
,
3 3
18. Determine an expression for all angles coterminal
with a standard position angle measuring 120°.
Express your answer in radians.
a.
b. 2
23. Solve sin x   cos x ,    x  
3
, 0  x  2
2
 11
2
2
x
4
2
3
b. x  1 c. x   d. x  
3
3
4
26. Express log
a.
b.
x2
10 y 3
in terms of log x or log y
2 log x  1  3log y c. 2 log x  10  3log y
2 log x  1  3log y d. 2 log x  10  3log y
31. The graph of y  f (x) is shown below.
27. Evaluate log 3 27
a.
2
9
2
3
b.
c.
3
2
d.
9
2
Which graph represents
the graph of
y  f 2x  3  4 ?
28. Bart and Arnie presented separate solutions to the
statement “Write log 2 x  log 4 y as a single log”
a.
c.
b.
d.
Which statement is true?
a. Only Bart is correct c. They are both wrong
b. Only Arnie is correct d. They are both correct
29. Which statement must be true for
f ( x )  log 1 x when x 2  x1 ?
2
a.
b.
f ( x1 )  f ( x 2 )
f ( x 2 )  f ( x1 )
c. f ( x1 )  0, f ( x 2 )  0
d. f ( x 2 )  0, f ( x1 )  0
30. For which graph is the relation and its inverse both
functions?
a.
c.
32. Consider the following transformations on the
graph of y  f (x)
Which transformations will have
no effect on the zeros of the
original graph of y  f (x) ?
a. I and II only c. II and IV only
b. II and III only d. III and IV only
b.
d.
33. The graph of y  f (x) as shown below is
transformed to x  f ( y ) . Determine all invariant
points.
a.
b.
c.
d.
0,3
1,1
2,1
1,1 and 2,1
34. The point P 4,6 lies on the graph of y  f (x) .
Which point must lie on the graph
1 1

y   f  x  2 ?
2 2

a. 7,3 b. 4,3
c. 1,3
39. Given f ( x )  x  2 and g ( x )  x 2  3x  1 ,
determine the value of f g 3 .
a. 16
d.  2,3
c.
b.
d.
37. Which three expressions are factors of
y  9 x 3  36 x 2  4 x  16 ?
a.
b.
c.
d.
I, II, III only
I, II, IV only
I, III, IV only
II, III, IV only
a.
c.
b.
d.
41. As a furniture salesperson, Chacci gets a 3%
commission on all his weekly sales above $5000.
Which row in the table shows the composite
function that will determine his commission if
x represents his weekly sales?
a.
b.
38. When x 3  2kx 2  3k 2 x  15 is divided by x  2 , the
remainder is 1. Determine all values of k .
a. k  4
b. k 
d. 39
III only
IV only
I and IV only
II and III only
36. Which sketch best represents the graph of
y  ax3  bx2  cx  24 if a  0 ?
a.
c. 19
40. The graphs of y  f (x) and y  g (x ) are shown
below. Which graph represents y  f ( x )  g ( x ) ?
35. Which of the following functions are polynomial
functions?
a.
b.
c.
d.
b. 17
17
2
2
c. k   , 2 d. k  ,2
8
3
3
c.
d.
42. Consider the graphs of the functions f ( x )  x 2 and
g ( x )  f ( x ) . Which row describes the domain
and range of g (x ) ?
2. Prove algebraically.
(4 marks)
2
tan 2 1  tan  cos 
1

sin 2
1  tan
3. The graph of y  f (x) is shown below.
a.
b.
c.
d.
43. Given the graph of y  f (x) as shown, determine
the graph of y 
f (x )
Sketch the graph of y  2 f (  x)  3
4.
a.
c.
b.
d.
(4 marks)
Use the graphs of y  f (x ) and y  g (x ) shown to
sketch the graph of y  f ( x ) g ( x ) . Label enough
points to get an accurate representation of the
graph.
(4 marks)
WRITTEN-RESPONSE QUESTIONS
(Calculator NOT permitted)
44. Determine the range of the function
y  3x  9  2
1. Solve algebraically: log 15 3  x   log 15 1  x   1 .
Justify the validity of each solution
(4 marks)
2.
a. y  0
b. y  2
c. y  3
d. y  9
WRITTEN-RESPONSE QUESTIONS
(Calculator permitted)
1. Solve algebraically, over the set of real numbers,
giving exact values where possible. (4 marks)
3 sin 2   5 cos  1
Consider the graphs of f ( x ) 
g ( x) 
x2  x  6
x2  9
and
x
x 9
2
Use your knowledge of rational functions to outline
the similarities and differences between these two
graphs. You will be evaluated on the concepts
expressed, the organization and accuracy of your
work, and your use of language.
(4 marks)
Answers
1. d
2. b
3. b
4. c
5. b
6. d
7. c
8. a
9. b
10. c
11. c
12. c
13. b
14. d
15. c
16. b
17. b
18. d
19. a
20. a
21. d
22. d
MULTIPLE-CHOICE
23. a
24. b
25. a
26. a
27. c
28. d
29. a
30. a
31. d
32. c
33. b
34. b
35. c
36. a
37. c
38. c
39. c
40. a
41. d
42. d
43. a
44. b
3.
4.
WRITTEN-RESPONSE (Calculator permitted)
1.
WRITTEN-RESPONSE (No calculators)
1.
2.
2.