Test 1
MATH 1040
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
Student’s Printed Name: _______________________
CUID:___________________
Instructor: ______________________
Section # :_________
You are not permitted to use a calculator on any portion of this test. You are not allowed to use
any textbook, notes, cell phone, laptop, PDA, or any technology on either portion of this test. All
devices must be turned off while you are in the testing room.
During this test, any communication with any person (other than the instructor or his designated
proctor) in any form, including written, signed, verbal, or digital, is understood to be a violation
of academic integrity.
No part of this test may be removed from the testing room.
Read each question very carefully. In order to receive full credit for the free response portion of
the test, you must:
1.
Show legible and logical (relevant) justification which supports your final answer.
2.
Use complete and correct mathematical notation.
3.
Include proper units, if necessary.
4.
Give exact numerical values whenever possible.
You have 90 minutes to complete the entire test.
On my honor, I have neither given nor received inappropriate or unauthorized information
at any time before or during this test.
Student’s Signature: ________________________________________________
Do not write below this line.
Free
Response
Problem
Possible
Points
4
9
6
2
4
10
7
3
6
11
6
4
6
12
6
5
4
1
6
4
64
7
5
13
Free
Response
Multiple
Choice
8
5
Test Total
100
Free Response
Problem
Possible
Points
1
Points
Earned
Points
Earned
36
Page 1 of 12
Test 1
MATH 1040
Version A
Spring 2016
QP 1-14, 18, 19, 21-24
Multiple Choice. There are 15 multiple choice questions. Each question is worth 2 – 3
points and has one correct answer. The multiple choice problems will count as 36% of the
total grade. Use a number 2 pencil and bubble in the letter of your response on the
scantron sheet for problems 1 – 15. For your own record, also circle your choice on your
test since the scantron will not be returned to you. Only the responses recorded on your
scantron sheet will be graded. You are NOT permitted to use a calculator on any portion of
this test.
1.
(2 pts.)
Determine if the following table represents a function:
0
1
2
4
5
𝑥
1
2
2
0
6
𝑓(𝑥)
a) The table does not represent a function because the value 2 occurs in both the
input and the output.
b) The table does not represent a function because more than one input value has the
output value 2.
c) The table does not represent a function because 3 is not an input value.
d) The table does not represent a function because 6 is an output value, but not an
input value.
e) The table represents a function.
2.
(3 pts.)
⎧ x +1
x ≤0
⎪
The function f is defined as f (x) = ⎨ 3
0 < x < 2 . Find f(0), f(1), f(2).
⎪ 2
x ≥2
⎩2x −1
a) f(0) = 1, f(1) = 3, and f(2) = 7
b) f(0) = 3, f(1) = 3, and f(2) = 7
c) f(0) = 1, f(1) = 4, and f(2) = 3
d) f(0) = 1, f(1) = 3, and f(2) = 3
e) f(0) = 3, f(1) = 4, and f(2) = 3
Page 2 of 12
Test 1
MATH 1040
Version A
3.
(3 pts.)
Spring 2016
QP 1-14, 18, 19, 21-24
Factor x 6 − 16x 3 + 64 completely.
(
)
a) x 3 x 3 − 16 + 64
(
)
b) x 3 x 2 − 4 ( x + 4 ) + 64
(
)
(
c) x 3 + 8 ( x − 2 ) x 2 + 2x + 4
)
d) ( x 3 − 4 ) ( x + 4 )
2
e) ( x − 2 ) ( x 2 + 2x + 4 )
2
4.
2
Which of the following linear equations is NOT graphed in the figure below.
(3 pts.)
a) g(x) = 3x − 1
1
b) f (x) = − x − 1
2
c) h(x) = −2x + 1
1
1
d) p(x) = − x +
2
4
e) m(x) = x + 1
Page 3 of 12
Test 1
MATH 1040
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
5.
(2 pts.)
What is the domain of g(x) = 4 1− x 2 ?
a) [ −4, 4 ]
b)
( −∞,−4 ] ∪ [ 4,∞ )
c) ( −∞,−1] ∪ [1,∞ )
d) [ −1,1] e) ( −1,1)
6.
(2 pts.)
Which of the following is equal to
(3 pts.)
7π
radians
12
a) 15!
b)
c) 30!
d) −
e)
7.
π
radians?
12
13π
radians
12
11π
radians
12
⎛ 7π ⎞
⎛ 3π ⎞
⎛ 5π ⎞
Evaluate and simplify: cos⎜ ⎟ − sin⎜ − ⎟ + tan⎜ ⎟
⎝ 2 ⎠
⎝ 4⎠
⎝ 6⎠
−3 + 2
2
2
3
b)
−
2
3
3 2
c)
− 3
2
2
3
d) −1+
−
2
3
2
3
e) −
−
2
3
a)
Page 4 of 12
Test 1
MATH 1040
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
8.
(2 pts.)
Which of the following is a root to the polynomial?
x 3 − 7x − 6
a) x = 2
b) x = −3
c) x = 6
d) x = 3
e) x = 1
9.
At what point does the line y − 7 = 3(x − 1) have y-coordinate equal to 4?
(2 pts.)
a) (4,16)
b) (0, 4)
c) (3, 4)
d) (4,0)
e) (16, 4)
10.
(2 pts.)
If f (x) = x 2 + 3x − 1 , what is f (x + h) ?
a) ( x + h ) + 3( x + h ) − 1
b) x 2 + 3( x + h ) − 1
c) x 2 + 3x − 1+ h
d) ( x + h ) + 3( x + h ) − 1( x + h )
2
2
e) ( x + h ) + 3x − 1
2
11.
(3 pts.)
Suppose that f (x) = x 2 + 1 , g(x) = x − 4 , and h(x) = 3x − 7 . Compute
( h ! f ! g ) (x) .
a) ( h ! f ! g ) (x) = 3x − 16
b) ( h ! f ! g ) (x) = 3 x 2 − 3 − 7
c) ( h ! f ! g ) (x) = 3x − 22
d) ( h ! f ! g ) (x) = 9x 2 − 42x + 46
e) ( h ! f ! g ) (x) = 3x − 10
Page 5 of 12
MATH 1040
Test 1
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
12.
Which graph below represents an even function?
(2 pts.)
a)
b)
c)
d)
e)
Page 6 of 12
MATH 1040
Test 1
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
13.
(2 pts.)
If f (x) = 3 x , which is the graph of 2 f (x − 1) ?
a)
b)
c)
d)
e)
Page 7 of 12
Test 1
MATH 1040
Version A
14.
(3 pts.)
Spring 2016
QP 1-14, 18, 19, 21-24
⎛ ⎛ 3π ⎞ ⎞
Suppose f (x) = 3x 3 − 1 and g(x) = sin(x) . Evaluate f ⎜ 2g ⎜ ⎟ ⎟ .
⎝ ⎝ 2 ⎠⎠
⎛ ⎛ 3π ⎞ ⎞
a) f ⎜ 2g ⎜ ⎟ ⎟ = −1
⎝ ⎝ 2 ⎠⎠
⎛ ⎛ 3π ⎞ ⎞
b) f ⎜ 2g ⎜ ⎟ ⎟ = 23
⎝ ⎝ 2 ⎠⎠
⎛ ⎛ 3π ⎞ ⎞
c) f ⎜ 2g ⎜ ⎟ ⎟ = 6 2 − 1
⎝ ⎝ 2 ⎠⎠
⎛ ⎛ 3π ⎞ ⎞
d) f ⎜ 2g ⎜ ⎟ ⎟ = 2
⎝ ⎝ 2 ⎠⎠
⎛ ⎛ 3π ⎞ ⎞
e) f ⎜ 2g ⎜ ⎟ ⎟ = −25
⎝ ⎝ 2 ⎠⎠
15.
(2 pts.)
5x 2 +1
What is the domain of g(x) = 3
?
7 − 2x
a) ( −∞,∞ )
⎛
7⎞ ⎛ 7 ⎞
b) ⎜ −∞, ⎟ ∪ ⎜ ,∞ ⎟
⎝
2⎠ ⎝2 ⎠
⎛
7⎤
c) ⎜ −∞, ⎥
2 ⎦
⎝
⎛7 ⎞
d) ⎜ ,∞ ⎟ ⎝2 ⎠
⎛
7⎞
e) ⎜ −∞, ⎟
⎝
2⎠
The Free Response section follows.
PLEASE TURN OVER YOUR SCANTRON while you work on the Free Response questions. You
are welcome to return to the Multiple Choice section at any time.
Page 8 of 12
Test 1
MATH 1040
Spring 2016
QP 1-14, 18, 19, 21-24
Version A
Free Response. The Free Response questions will count as 64% of the total grade. Read
each question carefully. In order to receive full credit you must show legible and logical
(relevant) justification which supports your final answer. Give answers as exact answers.
You are NOT permitted to use a calculator on any portion of this test.
1. (4 pts.) Consider the function m(x) = sin
(
)
2x 2 − 8x + 8 . Decompose the function m into
three functions f , g , and h so that m(x) = f (g(h(x))) .
Your answer cannot include “trivial” functions like y = x or y = 1 .
cos(x)
even, odd, or neither? Circle one.
x2 Support your answer with valid mathematical reasoning including the algebraic definition(s) of
even and/or odd.
2. (4 pts.) Is the function g(x) =
3. (6 pts.) Graph f (x) = cos ( x − π ) − 1 on ⎡⎣ −2π ,2π ⎤⎦ .
Be sure to graph over the entire interval – not just show one period.
Page 9 of 12
Test 1
MATH 1040
Version A
Spring 2016
QP 1-14, 18, 19, 21-24
4. (6 pts.) Suppose that line L passes through the points (2,5) and (−4,6) , while the line P
passes through the points (7, 4) and (6,10) .
Are the lines L and P parallel, perpendicular, or neither? Circle one.
Justify your answer mathematically.
5. (4 pts.) After working on a computer repair for t hours, a repairwoman charges
C(t) = 40.50 + 10t dollars. Find the total cost of the repair if the repairwoman works for 3 hours
and 15 minutes.
6. (4 pts.) Write the equation of the circle centered at (2, 3) passing through the point ( 2,12 ) .
7. a. (4 pts.) Place the following quadratic equation into the form y = a ( x − h ) + k .
2
y = 2x 2 + 4x − 9
b. (1 pt.) What is the vertex of the quadratic equation y = 2x 2 + 4x − 9 ?
Page 10 of 12
MATH 1040
Test 1
Spring 2016
Version A
QP 1-14, 18, 19, 21-24
2
8. (5 pts.) Find the x -intercept(s) of the function g(x) = x − 3x + 1 .
State your answer(s) as point(s).
9. (6 pts.) Use the fact that x = 5 is a root of p ( x ) = x 3 − 3x 2 − 13x + 15 to help factor
p ( x ) = x 3 − 3x 2 − 13x + 15 completely. Show all of your work in a clear, logical manner.
10. (7 pts.) State the domain of the rational function g(x) =
2x 3 − 9x 2 − 5x
. Also find all the
2x 2 + x
real root(s) and the y-intercept.
If there are no roots or if there is no y-intercept say so.
Domain
use interval notation
Roots
list as x-value(s)
y-intercept
write as a point
Page 11 of 12
MATH 1040
Test 1
Spring 2016
Version A
QP 1-14, 18, 19, 21-24
3x 4
7
11. (6 pts.) Compute the following. Fully simplify your answer.
+ −
x +1 x x −1
⎧x
⎪
12. (6 pts.) Graph the function f (x) = ⎨−x
⎪x + 1
⎩
x ≤ −1
−1 < x <1
x ≥1
13. (1 pt.) Check to make sure your Scantron form meets the following criteria. If any of the
items are NOT satisfied when your Scantron is handed in and/or when your Scantron is
processed one point will be subtracted from your test total.
My scantron:
□ is bubbled with firm marks so that the form can be machine read;
□ is not damaged and has no stray marks (the form can be machine read);
□ has 15 bubbled in answers;
□ has MATH 1040 and my Section number written at the top;
□ has my Instructor’s name written at the top;
□ has Test No. 1 written at the top;
□ has Test Version A both written at the top and bubbled in below my CUID;
□ and shows my correct CUID both written and bubbled in (bubble in a 0 in place of the C).
Page 12 of 12