Math120R: Precalculus Test 1 Review, Fall 2016
Sections 1.3-1.5, 1.10-1.11, 2.1-2.7
Note: This study aid is intended to help you review for test 1. Do not expect this
review to be identical to the actual test 1 given
...
Math120R: Precalculus Test 1 Review, Fall 2016
Sections 1.3-1.5, 1.10-1.11, 2.1-2.7
Note: This study aid is intended to help you review for test 1. Do not expect this
review to be identical to the actual test 1 given in your class.
Multiple Choice Practice
1. Which ONE of the following represents the complete factorization of
32x 14 82x 13
(A) 2x 16x 5
(B) 52x 1
(C) 2x 136x 5
(D) 52x 13
(E) 2x 136x 11
2. Simplify the expression n1
n
p p
completely. The simplified form is:
(A) p (B)
1 p
(C) 1 (D) p2n1 (E) pn(n1)3. Solve for x : 0
3 1
2
x
x x
(A) x 0, x 3, or x 1 only.
(B) x 1 only
(C) x 3 or x 1 only.
(D) x 3 or x 0 only.
(E) x 0 only.
4. Solve for y : 4y2 y
(A) y 3 4 only.
(B) y 0 only.
(C) y 0 or y 3 4 only.
(D)
1 4
y only.
(E) y 3 4 or y 3 4 only.5. Solve for x : x 25x 1 3
(A)
2 5
x or x 5 only.
(B)
10
9 61
x or
10
9 61
x only.
(C)
2
9 101
x or
2
9 101
x only.
(D)
10
9 101
x or
10
9 101
x only.
(E)
2
9 61
x or
2
9 61
x only.
6. Simplify the expression
xy
x y x y
2
2 2
completely. The simplified form is:
(A) 0 (B) 2xy (C) x y
(D) x y (E) 27. Solve for w :
w
L 4 3
(A) 2
2
3
16
L
w
(B) 2
48 2
L
w
(C) 248 2
L
w
(D)
48
2 2
L
w
(E) 2
2
16
3
L
w
8. Solve for b : 4a2b 5ab 7
(A)
5 7
4 2
a
a
b (B) 2
4
7 5
a
a
b (C)
a
a
b
5
4 2 7
(D)
7
(4 5)
a a
b (E)
4 5
7
a a
b9. If
f (t) 3t2 2, find f (k 2).
(A) 3k 2 12k 12 (B) 3k 2 8 (C) 3k 2 4k 2
(D) 3k 2 4 (E) None of these
10. If
3 3
1 3
4 1
( ) 2
x if x
x if x
x if x
f x , find f (2)
(A) 6 (B) 4 (C) 2 (D) 1 (E) None of these
11. Express the area of a rectangle as a function of its width if the width is 25% of its
length. Let L and W represent length and width respectively.
(A) A (.25W)(W) (B) A (.75W)(W) (C) A (4W )(W )
(D) A 4LW (E) None of these
12. The linear function f whose graph passes through the ordered pair (a,0) and is parallel
to the line x 2y 7 is:
(A) f x x a
1 2
(B)
2 2
1 a
f x x (C) f x x a
1 2
(D)
2 2
1 a
f x x (E) None of these13. Find the domain of the function f (t) 81 t2 .
(A) ,9 (9,)
(B) (,9][9,)
(C) (9,9)
(D) [9,9]
(E) all real numbers
14. The stopping distance, D , of a car after the brakes have been applied varies directly as the
square of the speed s . A certain car traveling 40 miles per hour can stop in 152 feet. What
is the stopping distance for the same car traveling 65 miles per hour? Round your answer to
the nearest whole foot.
(A) 93 feet (B) 247 feet (C) 342 feet
(D) 401 feet (E) 518 feet
15. Let f (x) x 4 . Simplify [ f (x)]2 f (x2) .
(A) 8x 12
(B) 8x 20
(C) 12
(D) 0
(E) None of these16. Find the value of k so that the slope of the line connecting the points (k ,4) and k ,9
is 3.
(A)
2
15
k (B)
6 5
k (C)
5 6
k
(D)
5 6
k (E)
2
15
k
17. Let
9 if 1
8 if 5 1
3 5 if 5
( ) 2
x x
x x
x x
f x
Find the y intercept of f (x) .
(A) 0,13
(B) 0,8
(C) 0,3
(D) 0,5
(E) 0, 918. Let
9 if 1
8 if 5 1
3 5 if 5
( ) 2
x x
x x
x x
f x
Find the x intercept(s) of f (x) .
(A) x 8 and x 8 only
(B) x 8 only
(C)
5 3
x only
(D)
5 3
x , x 9, x 8 and x 8 only
(E) There are no x -intercepts.
19. Consider f t represented in the table below. Use the information given in the table to find
the average rate of change of f (t) from t 4 to t 10 .
t f(t)
2 -6
4 -3
8 0
10 13
20 16
(A) 0 (B)
3 8
(C)
8 3
(D) 5 (E) None of these20. An equation of a graph obtained from vertically shrinking the graph of y x
then shifting the graph up twenty units is:
(A) 20
5 3
y x (B) 20
7 2
y x (C) 20
3 4
y x
(D) y 2 x 20 (E) None of these
21. If f (x) is a function with domain 8,12, find the domain of 3
1 2
f x .
(A) 5,6 (B) 7,12 (C) 5,15
(D) 11,9 (E) 13,12
22. You can get the graph of y g(2x) by transforming the graph of y g(x) in the
following way:
(A) Shrink horizontally and reflect across the x -axis.
(B) Shrink horizontally and reflect across the y -axis.
(C) Stretch vertically and reflect across the x -axis.
(D) Stretch vertically and reflect across the y -axis.
(E) None of these
23. If (4,7) is a point on the graph of y h(t) , which of the following must be a point on
the graph of y h(t) 2 ?
(A) (4,9) (B) (4,5) (C) (4,5) (D) (4,9) (E) None of these24. Given the functions f (w) 5 2w and g(w) w2 4, find h(w) ( f g)(w).
(A) h(w) 2w 9 (B) h(w) 2w2 1
(C) h(w) ( 5 2w)(w2 4) (D) h(w) 2w 1
(E) h(w) 2w2 13
25. Find Q1(t) if
4 1
( )
C t
Q t . (C is a nonzero real number)
(A) Q t C t C
4
1( ) (B)
t C
Q1(t) 4 1 (C) , 0
4
1( ) t
t
C t
t
(D) 1( ) 4 , t 0
t
C t
Q t (E) None of these
26. Suppose g(4) 30 means the volume of water in a container is 30 ounces when the depth
of the water is 4 inches. What is the meaning of g1(50) 10 ?
(A) The volume of the water is 10 ounces when the depth of the water is 50 inches.
(B) The depth of the water is 10 inches when the volume of the water is 50 ounces.
(C) The depth of the water is 0.2 inches when the volume of the water is 50 ounces.
(D) The volume of the water is 5 ounces when the depth of the water is 10 inches.
(E) None of these27. If f (x) is a one-to-one function, and f (8) 11, then which of the following CANNOT
be true?
(A) f (11) 8 (B) f 1(11) 8 (C) f 1(5) 3
(D) f 1(11) 5 (E) f (8) 11
28. Using the tables of the functions f and g below, find f g15
x f(x) x g(x)
0 5 0 2
2 8 4 5
4 11 5 8
6 14 6 11
8 17 7 14
(A) 17 (B) 14 (C) 11
(D) 8 (E) 229. Given the graph of the function y h(t) , which ONE of the following is the graph of
y h1(t)?
y h(t)
(A) (B)
(C) (D)Short Response Practice
1. The relationship between the tuition in dollars, T, and the number of credits, c, at a
particular college is given by
100 120 0 6
( )
800 120( 6) 6 18
c c
T c
c c
a. What is the tuition for 7 credits?
b. If the tuition was $1880, how many credits were taken?
c. What is the domain of this function?
d. What are the practical interpretations of the y - intercept and the slope?
2. Let f (t) t2 7t 5. Find and simplify
h
f (t h) f (t)
.
3. Let f (x) 5x2 9 . Find and simplify
h
f x h f x h
2
( ) ( )
.-2
-1
4 3 2 1 0
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
4. Use the graph at the right to answer the
questions below.
a. Find f (0) .
b. On what intervals is f x ( ) increasing?
c. Find x so that f x ( ) 2 .
d. Find the zeros of f x ( ) .
e. Approximate any value(s) of x such that f x x .
f. Find f ( f (9)) .
g. Find the average rate of change of f from x 2 to x 7.
h. Does f 1 exist? Why or why not?5. Let G(v) be a linear function representing the grade point average of a high school student
who plays video games for v minutes a day. When a student plays video games for 85
minutes a day, the student’s grade point average is 2.89. When a student plays video games
for 155 minutes a day, the student’s grade point average is 2.05.
a. Determine the formula for the linear function G(v).
b. Gi
f x . Determine the vertical intercept of f 1.
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