Calculus Preparation & Placement Evaluation, 2009 Sample Evaluation

Calculus Preparation & Placement Evaluation, 2009 Sample Evaluation

Calculus Preparation & Placement Evaluation, 2009
Department of Mathematics
Wilfrid Laurier University
Sample Evaluation
Simplifying Expressions
1.
50
1
+9
5
25
2
( 1) =
A. 36
B. 46
3 4
2 +
4 5
2.
127
40
B.
p
D. 54
3
=
8
A. 12
3.
C. 14
C.
117
40
D.
25
8
3 is an example of a number from which set?
A. the natural numbers
B. the integers
C. the rational numbers
D. the irrational numbers
4 2 1
=
3+3 1
4.
A. undefined
5.
2 64x1=2 y 9
A.
6.
2=3
A.
7.
x
6
(x
3)
If x 6=
A.
B.
32x1=3 y 6
C.
1
8x1=3 y 6
D. 128x
C.
2 2x
x 1
D.
4 (x
1
1)
2 (x
1=2
3)
B.
3
1; 2, then
2
(x + 1) (x2 + 4)
9
32
D.
51
64
x (x
x 3
2
x
B.
3)
10
x
2x
1
=
2 x
C. p
x 3
x 6
D. p
x 3
x+1
=
2x 4
1
(x3
y
1=2
x
3
x+2
x4 16
1=6 25=3
=
B. 2x + 2
If x > 3, then
8.
C.
2 (x + 3)
x
2
A. q
15
16
=
256
3x1=2 y 6
If x 6= 1, then
B.
C.
2)
1
2
(x + 4) (x + 1)
D.
2 (x + 2)
(x + 1) (x2 + 4)
9.
If x 6= 3, then
A.
12
x2
x+4
x 1
10.
x x2
=
4x + 3
B.
4+x
1 x
C.
The remainder, when 9 + 3x + 4x3
A.
1
If h 6= 0, then x + h + 1
h
11.
A.
h
(x + 1) (x + h + 1)
12.
If x >
A. 3
C.
13.
9
, then
2
3
D.
(x + 3) (x + 4)
(x 3) (x 1)
2, is:
C.
61
D. 15
B.
1
(x + 1) (x + h + 1)
1
x+1 =
1
(x + 1) (x + h + 1)
C.
x
1
2x4 is divided by x
B. 9
2
4
x
1
D.
2
(x + 1)
2x
p
=
2x + 9
p
B.
2x 9
p
3 + 2x + 9
18
D.
p
3+
2x + 9
p
x 3 + 2x + 9
9 x
Which of the following statements are true?
I.
a
b
b
=
1+
a
b
A. All of them
14.
The expression x2
A. (x
2
3) + 2
II.
m
=0
0
III.
p
x2
B. I, III and IV
9=x
2
IV. (q + 2) = q 2 + 4
3
C. III and IV
D. I only
6x + 2, upon completing the square, is the same as:
2
B. (x
3)
2
C. (x + 3)
7
7
D. (x
5
15.
In the expansion of (2x + 1) , the coefficient of the x3 term is:
A. 80
B. 20
C. 40
2
D. 8
2
3)
1
Solving Equations and Inequalities
16.
The solution to 9 (x + 8) = 2x
A. x =
17.
38
3
x) is:
(4
38
3
B. x =
C. x =
The possible values of x for which (2x + 1) (x
A. x =
18.
1
;3
2
4) =
1
;4
2
B. x =
B. m
C. m
A. x =
20.
B. x =
2
p
x2 + 9 = 1
x + 5y
3, y =
D. x = 1;
3
2
D. m > 9
9
x are:
D. no solution
4; 4
=4
5x + 20y
A. x =
4; 3
C. x =
4
Solve the system of equations:
19
2
6x + m = 0 have no real solutions?
9
The possible values of x for which
19.
D. x =
7 are:
C. x =
For which value(s) of m would the equation x2
A. m = 9
19
2
= 13
7
5
B. x = 17, y =
C. inconsistent (no solution)
13
5
D. dependent (infinite solutions)
21.
A rectangle has a perimeter of 40 cm. If the length is 2 cm longer than twice the width, nd the area of
the rectangle?
A. 84 cm2
22.
B. 6 cm2
The set fx 2 R j x
A. ( 6; 2) [ (0; 1)
23.
The solution of x2
A.
24.
2
x
4
0 or
C. 14 cm2
6<x<
2g can be expressed in interval notation as:
B. [ 6; 2] [ [0; 1)
2x
B.
8
4
C. [ 6; 2] [ (0; 1)
2
,2
9
B. x =
D. ( 6; 2) [ [0; 1)
0 is the set of all x such that:
x
C. x
2
Find all possible solutions of the equation j5x
A. x =
D. 40 cm2
3
4
D. x
4 or x
D. x =
2
9
2j = 4x.
C. x = 2
2, 2
2 or x
2
25.
If jaj < jbj, then which of the following is true?
A. a < b
C.
B. a < b or
b < a < b or b < a <
D.
b
a<
b
a < b < a or a < b <
a
Functions and Graphing
26.
27.
If f (x) = x2 + 3x then f (h + 6) =
A. h2 + 3h + 42
B. h2 + 15h + 54
C. h2 + 3h + 6
D. h2 + 3h + 54
Which of the following represents a function?
A. f( 9; 4) ; ( 9; 8) ; ( 3; 3) ; (0; 5)g
B. f( 9; 5) ; ( 3; 5) ; (0; 5) ; (3; 5)g
C. f( 3; 9) ; ( 3; 3) ; ( 3; 0) ; ( 3; 6)g
28.
The domain of p
A. x 6=
29.
31.
is the set of all x such that:
x2
B.
C. 2 > x
2<x<2
D. x <
2 or x > 2
The function f (x) = x2 1 can be defined by:
(
(
x2 1 if x 0
x2 1 if x 1
A. f (x) =
B.
f
(x)
=
2
1 x if x < 0
1 x2 if x < 1
(
x2 1 if
1 x 1
1 x2 if x < 1 or x > 1
The function h (x) = x2 + 2x
A. f (x) = x2=3
g (x) = x2 + 2x
C. f (x) = x4=3
g (x) = (2x)
2=3
D. f (x) =
(
x2 1 if x
1 or x
1 x2 if
1<x<1
can be thought of as the composition f
2=3
1
g, where:
B. f (x) = x2 + 2x
g (x) = x2=3
D. f (x) = x2 + 2x
g (x) =
2
3
3
The inverse function of y = (x + 4) + 8 is:
A. y = (x
32.
4
2; 2
C. f (x) =
30.
1
D. f( 9; 4) ; (0; 5) ; (0; 5) ; (9; 4)g
1=3
4)
B. y = (x
1=3
4)
8
C. y = x1=3
12
D. y = (x
1=3
8)
Which of the following is not a polynomial?
A. f (x) = x2
4 + 6x
B. f (x) = x
2
C. f (x) =
+4
4
p
3
D. f (x) = x3
4
4
33.
If the graph of y = f (x) is obtained from the graph of y = x4 by shifting it one unit down and two
units to the right, then the formula for the function y = f (x) is:
A. f (x) = (x
34.
4
2)
1
4
B. f (x) = (x + 2)
1
C. f (x) = (x
The relationship between the graphs of y = f (x) and y =
4
1) + 2
4
D. f (x) = (x + 2) + 1
f (x) is:
A. a reflection in the x-axis
B. a reflection in the y-axis
C. a reflection in the line y = x
D. a reflection through the origin
35.
Graph the region represented by the solution of 6x
7y
A.
B.
C.
D.
42.
Geometry
36.
A.
37.
p
The distance between the points P (3; 7) and Q (6; 9) is:
p
5
B. 13
C. 13
p
175
An equation of the line with a slope of 3 and passing through the point (2; 1) is:
A. 3x
38.
D.
y
7=0
B. 3x
y
C. 3x
5=0
The vertex of the parabola given by y = 4x2
A. (1; 10)
8x
B. (1; 6)
y+5=0
y+3=0
2 is:
C. ( 1; 2)
5
D. 2x
D. ( 1; 10)
39.
Which of the following represent lines:
I. y = 3
II. xy = 3
A. IV only
40.
III. x2 + y 2 = 3
B. I and IV
IV. x + y = 3
C. I, II and IV
D. All of them
A circle centered at (0; 0) with radius 1 has equation:
A. x2 + y 2 = 0
B. x2
C. x2
D. x2 + y 2 = 1
y2 = 0
y2 = 1
Exponential and Logarithmic Functions
The expression log3
41.
A.
1
3
42.
1
27
evaluates to:
B.
3
C. 9
D.
Considering the domain x 2 ( 3; 0) [ (3; 1), the expression log
A.
log jx
3j log (x + 3)
3 log jxj
C. log (x + 3) + log jx
43.
B.
3j
The equation log5 (2x
A. x = 2
44.
45.
is equivalent to:
log 9
log jxj
2 log jxj log 9
3 log jxj
3) = 0 has solution:
B. x = 4
The equation 4x = 8x
A. x = 15
D.
3 log jxj
x2 9
x3
1
9
5
C. x =
3
2
D. no solution
has solution:
B. x = 10
The function f (x) = 2x+3
C. x =
D. x = 5
5
1 has an inverse function given by:
A. f
1
(x) = log2 (x + 3) + 1
B. f
1
(x) = log2 (x + 1)
C. f
1
(x) = log2 (x
D. f
1
(x) = 2x
3) + 1
6
3
+1
3
Trigonometry
46.
Convert 135 to radian measure:
A. 135 radians
47.
Evaluate cos
1
A.
2
48.
B. 135 radians
5
6
C.
3
radians
4
D.
3
radians
4
. The angle is in radians.
B.
1
2
C.
p
3
2
p
3
2
D.
Find the value of c in the given right triangle
if B = radians and a = 6 cm.
3
A. 12 cm
49.
B. 2 cm
p
C. 4 3 cm
p
D. 3 3 cm
C.
D.
Find the value of Angle C in the given triangle
p
if B = radians, b = 3 cm and c = 3 2 cm.
6
A.
4
50.
radians
B.
p
2
radians
2
3
radians
p
The function given by f ( ) = 3 sin (2 ) + 4 has period:
A. 2
B.
C. 4
7
D. 3
2 radians