©Fry Texas A&M University
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Math 150 Precalculus
Spring 2015
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1
Neatly print first and last names: ________________________________________________
Lecture Time:
!
!
12:40 PM! !
!
1:50 PM !
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(Circle one.)
Exam 1
"On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work."
__________________________________________________________
Signature of student
My signature in this blank allows my instructor to place my exam in a stack near the front of the
room where I will pick it up on the day they are returned.
________________________________________________________________
Signature of student
1. Write all solutions in the space provided as full credit might not be given
without complete, correct accompanying work, even if the final answer is
correct.
2. Intervals should be stated in interval notation.
3. Intercepts are points so, when requested, state both coordinates.
4. Unnecessary absolute value signs should be removed.
5. You may not discuss the contents of the exam with anyone until the exam is
returned in class.
6. No calculators are allowed.
7. All cell phones must be turned off and placed in your backpack.
8. Continuing to write on the exam after time is called is considered cheating.
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
2
(1 point) NEATLY PRINT FIRST AND LAST NAMES: ________________________________
(1 point) LECTURE TIME:
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12:40 PM! !
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1:50 PM !
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PAGE 2 ______________________________________
PAGE 3 ______________________________________
PAGE 4 ______________________________________
PAGE 5 ______________________________________
PAGE 6 ______________________________________
PAGE 7 ______________________________________
PAGE 8 ______________________________________
PAGE 9 ______________________________________
PAGE 10 ______________________________________
TOTAL ______________________________________
(Circle one.)
©Fry Texas A&M University
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Math 150 Precalculus
Spring 2015
!
1. (7 points) Fill in the blanks:
a) ! __________ is the additive identity.
b) ! __________ is the multiplicative identity.
3
.
5
c)!
__________ is additive inverse of −
d)!
__________ is multiplicative inverse of −
e)!
__________ is the symbol used to represent the integers.
f)!
__________ is the symbol used to represent the rational numbers.
g)!
__________ is shorthand notation for the commonly used phrase “if and only if.”
3
.
5
2. (2 points) Below is a list a properties of real numbers.
A. Associative Property of Addition
B. Associative Property of Multiplication
C. Commutative Property of Addition
D. Commutative Property of Multiplication
E. Distributive Property of Multiplication over Addition
F. None of these
Below are two algebraic statements. Please indicate which of the properties is being used.
a)
( 48 + 39 ) + 12 = ( 39 + 48 ) + 12
_____________________________________________
b)
( 39 + 48 ) + 12 = 39 + ( 48 + 12 )
_____________________________________________
3
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
3. (5 points) A given circle has radius 7 meters. Determine the area of a sector of this circle
π
with central angle measuring
radians.
5
a)
7π 2
m
5
b)
14π 2
m
5
c)
49π 2
m
5
d)
49π 2
m
10
e) None of these
4. (5 points) Circle one:
a)
TRUE
FALSE
{(x, y) | x = π } is a function.
b)
TRUE
FALSE
{(x, y) | y = π } is a function.
c)
TRUE
FALSE
The set {(0, − 2), (0, − 1), (0, 0), (0, 1), (0, 2)}
represents a relation but not a function
d)
TRUE
FALSE
θ1 =
e)
TRUE
FALSE
11π
13π
and θ 2 =
are coterminal angles.
6
6
A function f (x) is increasing on an interval I iff
x1 < x2 →
f (x1 ) < f (x2 ) ∀ x1 , x2 ∈I
4
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
5. (5 points) If the line through (−1, 3) and (x2 , -5) is perpendicular to the line x + 2y = 2 ,
then determine the value of x2 .
x2 = __________
6. (5 points) (3, 0) is the midpoint of (6, -1) and (x2 , y2 ) . Determine x2 and y2
(x2 , y2 ) = ____________
5
©Fry Texas A&M University
!
Math 150 Precalculus
7. (5 points) Determine the solution of the system
Spring 2015
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6x + 20y = 4
15x + 12y = 10
(x, y) = ____________
8. (8 points) A pharmacist intends to create 150 milliliters of a 2% acid solution. The
pharmacist has access to a 1% acid solution and a 4% acid solution. How much of each
should be used?
The pharmacist should use !
!
!
!
!
!
__________ milliliters of the 1% acid solution and
__________ milliliters of the 4% acid solution
6
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
!
7
9. 4 points) Fill in the blanks:!
!
a) The graph of an even function has symmetry about the ______________
!
b) The graph of an odd function has symmetry about the _____________
!
c) A function is even iff f ( −x ) = ___________ for every x in the domain of f (x) .
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d) A function is odd iff f ( −x ) = ___________ for every x in the domain of f (x) .
10. ( 9 points) Above is the graph of f(x) on the interval (0, 5). Name the interval(s) where f(x)
is
a) increasing ___________________
b) decreasing ___________________
c) constant ___________________
d) Now assume that the function is even on the domain (-5, 5).
Sketch the graph of f(x) for -5 < x < 0.
©Fry Texas A&M University
!
Math 150 Precalculus
11. (11 points) f (x) = − x − 3 + 2
a) vertex ____________________
b) y -intercept _____________
c) x − intercept(s) __________
d) range _______________
e) graph f (x) = − x − 3 + 2
12. (11 points) g(x) =
(
)
4−x −2
a) domain ____________________________
b) anchor point ____________________
c) y -intercept _____________________
d) x − intercept ___________________
e) range ________________________
f) graph g(x) =
(
)
4−x −2
Spring 2015
!
8
©Fry Texas A&M University
!
Math 150 Precalculus
Spring 2015
13. (16 points) Fully simplify
a)
c)
6
4
x18 = _______________
b)
1
= _______________
5
d)
−4
5
⎛x ⎞
e) ⎜ −7 ⎟ = _______________
⎝x ⎠
g)
54 + 48 + 24 = _______________
f)
4
64 = _______________
1
= _______________
3+ 2
( 27 )
⎛ 2⎞
⎜⎝ − ⎟⎠
3
= _______________
!
9
©Fry Texas A&M University
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14. (4 points) Let f (x) = 3x + 1
a)
( f ! g )(1) =
( f ! g )( x ) =
!
b)
!
( f + g )( 5 ) = _____________________
and g(x) = 2x + 5 then
_________________!
16. (2 points) Let f (x) =
Spring 2015
and g(x) = x 2 + 5 then
_________________!
15. (4 points) Let f (x) = 6x + 35
a)
Math 150 Precalculus
!
⎛ f⎞
b) ⎜ ⎟ ( x ) = _____________________
⎝ g⎠
1
, then f (x + h) = _______________________
2x + 7
10