MATH 1100 – College Algebra Spring 2017 Exam 1
February 15, 2017
NAME:
STUDENT ID
INSTRUCTOR
SECTION (number or time)
INSTRUCTIONS
1. DO NOT OPEN THIS EXAM UNTIL YOU ARE TOLD TO DO SO.
2. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON.
3. This exam has 8 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout
questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions.
4. You will have 60 minutes to complete the exam. No notes or books are allowed. TI-30Xa and TI-30XIIS scientific calculators
are allowed. NO other calculators are allowed.
5. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam
to YOUR instructor.
USEFUL FORMULAS
•
y = mx + b
•
A3 − B 3 = (A − B)(A2 + AB + B 2 )
•
y − y0 = m(x − x0 )
•
d=
•
A2 − B 2 = (A + B)(A − B)
•
•
A3 + B 3 = (A + B)(A2 − AB + B 2 )
•
p
(x2 − x1 )2 + (y2 − y1 )2
x1 + x2 y1 + y2
,
2
2
−b ±
√
b2 − 4ac
2a
•
x=
•
I = P rt
•
A = P + P rt
•
a2 + b2 = c2
(x − h)2 + (y − k)2 = r2
Multiple Choice Section:
1. What is the slope of a line parallel to the line passing through the points (−1, 5) and (2, −4).
(a) m =
1
3
(b) m = −3
(c) m = −9
(d) m = 1
(e) m = −
2. Factor
1
3
6x2 + 17x + 5
completely.
One of the factors is:
(a) (6x + 5)
(b) (3x + 5)
(c) (2x + 1)
(d) (2x + 5)
(e) Cannot be factored
3. Solve and give your answer in interval notation: −4 ≤ 6 − 2x < 4
(a) (−5, 5]
(b) (−2, 5)
(c) (1, 2]
(d) (1, 5]
(e) (−2, 2]
4. Find the slope of the line with the given equation:
3x + 2y = 10
(a) m = 2
(b) m = −
3
2
(c) m = 3
(d) m =
3
2
(e) m = −
2
3
Page 2
5
5. Find the zeroes of y = 8 − x.
3
(a) x = −
24
5
(b) x =
40
3
(c) x =
24
5
(d) x = −
3
5
(e) x = 0
6. Perform the following operations and simplify:
4(8 − 6)2 − 4 · 3 + 2 · 8
32 + 190
(a) 2
(b)
5
7
(c)
6
5
(d) 4
(e)
7
9
7. Solve the following equation:
(a) x =
10
9
(b) x =
8
9
(c) x = −
3(x + 1) = 5 − 2(3x + 4)
2
3
(d) All real numbers
(e) No solution
8. Solve and write your answer in interval notation:
−∞, −
(a)
3x + 7 ≤ 2
5
∪ [1, ∞)
3
(b) (−∞, ∞)
(c)
5
− ,1
3
(d) (1, ∞)
(e) No solution
Page 3
or
2x + 3 ≥ 5
9. Find the equation of the line passing through the points
(2, −4) and
(0, 8).
(a) y = 6x + 8
(b) y = −2x + 8
(c) y = 2x + 8
(d) y = −6x
(e) y = −6x + 8
10. Write an equation for the line passing through the point (5, 5) with slope
m = 0.
(a) x = 5
(b) x = 10
(c) y = 10
(d) y = 5
(e) y = x
11. Perform the indicated operations and simplify:
(5x2 + 4xy − 3y 2 + 2) − (9x2 − 4xy + 2y 2 − 1)
(a) −4x2 − 5y 2 + 3
(b) −4x2 + 8xy − 5y 2 + 3
(c) −4x2 − y 2 + 1
(d) 14x2 + 8xy − 5y 2 + 3
(e) 14x2 − y 2 + 1
12. Truman the tiger makes an investment at 4% simple interest. At the end of 1 year, the total value of the investment
is $1560. How much was originally invested?
(a) $1500.00
(b) $1114.29
(c) $1622.40
(d) $1520.00
(e) Cannot be determined
Page 4
13. Simplify the following expression:
a
b
−
b
a
1 1
−
a b
(a) a + b
(b)
a+b
a 2 b2
(c)
a2 b − a3 − b3 + ab2
a 2 b2
(d)
−1
a+b
(e) −1(a + b)
14. Find the domain of the rational expression:
x−2
x2 − 2x − 24
(a) x 6= −4, 2, 6
(b) x 6= −6, −4
(c) x 6= 2, 6
(d) x 6= −6, −2, 4
(e) x 6= −4, 6
15. A graph of f (x) is given below. Calculate f (−2) + f (3) − f (5).
(a) −10
(b) 6
(c) −2
(d) −18
(e) −12
16. Write the slope-intercept equation for a line that passes through (−2, 6) and is perpendicular to the line y = 2x+9.
1
(a) y = − x + 5
2
(b) y =
1
x+7
2
(c) y = 2x + 10
(d) y = 2x + 2
1
(e) y = − x + 7
2
Page 5
17. Solve and give your answer in interval notation:
12 − 8y ≥ 10y − 6
(a) (−∞, 1]
(b) [−1, ∞)
(c) (−∞, −1]
(d) [1, ∞)
(e) (−∞, ∞)
18. Perform the indicated operations and simplify:
(a)
2
x+4
(b)
−4x − 10
(x + 4)(x − 4)
(c)
4x + 22
(x + 4)(x − 4)
(d)
−4x + 22
(x + 4)(x − 4)
x2
6
4
−
− 16 x + 4
(e) None of the above
Workout Section:
19. Given
g(x) = 3x2 − 2x + 1,
find the following:
(a) g(−2)=
(b) g(−a)=
(c) g(x + h)=
Page 6
20. Find the equation of the circle with a diameter whose endpoints are
(6, 14) and
(−4, −10).
(a) Find the center of the circle:
(b) Find the radius of the circle:
(c) Write the equation of the circle.
Multiple Choice Workout Total
Points:
90
10
100
Score:
Page 7
MATH 1100 – College Algebra Spring 2017 Exam 2
March 22, 2017
NAME:
STUDENT ID
INSTRUCTOR
SECTION (number or time)
INSTRUCTIONS
1. DO NOT OPEN THIS EXAM UNTIL YOU ARE TOLD TO DO SO.
2. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON.
3. This exam has 7 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout
questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions.
4. You will have 60 minutes to complete the exam. No notes or books are allowed. TI-30Xa and TI-30XIIS scientific calculators
are allowed. NO other calculators are allowed.
5. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam
to YOUR instructor.
USEFUL FORMULAS
•
y = mx + b
•
•
y − y0 = m(x − x0 )
•
•
A2 − B 2 = (A + B)(A − B)
•
•
A3 + B 3 = (A + B)(A2 − AB + B 2 )
•
A3 − B 3 = (A − B)(A2 + AB + B 2 )
d=
•
•
p
(x2 − x1 )2 + (y2 − y1 )2
x1 + x2 y1 + y2
,
2
2
(x − h)2 + (y − k)2 = r2
x=
−b ±
I = P rt
√
b2 − 4ac
2a
•
A = P + P rt
•
a2 + b2 = c2
•
f (x + h) − f (x)
h
• d = rt
• f (x) = a(x − h)2 + k
b
b
• − ,f −
2a
2a
Multiple Choice Section:
f (x) = −4(x + 3)(x + 3)(x + 3)(x − 4)
1. Find the zeros of the function
and state the multiplicity of each.
(a) x = −3 is a zero with mulitiplicity 3 and x = 4 is a zero with multiplicity 2.
(b) x = −3 is a zero with multiplicity 1 and x = 4 is a zero with multiplicity 1.
(c) x = 3 is a zero with multiplicity 3 and x = −4 is a zero with multiplicity 1.
(d) x = −3 is a zero with multiplicity 3 and x = 4 is a zero with multiplicity 1.
(e) x = 4 is a zero with multiplicity 1.
2. Given that
f (x) = 4x + 1
and
g(x) = x3 ,
find
(f ◦ g)(−2).
(a) −2
(b) 33
(c) 7
(d) −8
(e) −31
3. Find
h(−8) + h(−5) + h(2),
given the function


−2x − 14
h(x) = 1


x+5
(a) 10
(b) −4
(c) −22
(d) 4
(e) −10
4. Solve and write your answer in interval notation:
|10 − 5x| ≥ 20.
(a) (−∞, −2]
(b) (−∞, −2] ∪ [6, ∞)
(c) [−2, 6]
(d) (−∞, ∞)
(e) (−∞, −6] ∪ [2, ∞)
Page 2
for x < −5
for − 5 ≤ x < 1,
for x ≥ 1
5. Given that g(x) = x2 − 4
and h(x) = x − 5, find
(g − h)(a).
(a) a2 − a − 9
(b) a2 + a − 9
(c) x2 − x − 1 − a
(d) a2 − a + 1
(e) x2 − x + 1 − a
6. Use the Intermediate Value Theorem to determine if
f (x) = x3 + 4x2 − 8x − 22
has at least one zero
between x = −5 and x = −4.
(a) f (−5) and f (−4) have opposite signs, so the function f (x) does not have a real zero between −5 and −4.
(b) f (−5) and f (−4) have the same sign, so the function f (x) has a real zero between −5 and −4.
(c) f (−5) and f (−4) have opposite signs, so the function f (x) does have a real zero between −5 and −4.
(d) f (−5) and f (−4) have the same sign, so the function f (x) does not have a real zero between −5 and −4.
(e) None of the above
7. Find the maximum number of real zeros and the maximum number of turning points that the graph of the function
f (x) = x12 − 7x6 + 4x − 6
can have:
(a) Real zeros: 12; Turning points: 12
(b) Real zeros: 12; Turning points: 11
(c) Real zeros: 11; Turning points: 11
(d) Real zeros: 12; Turning points: 6
(e) Real zeros: 11; Turning points: 7
8. Describe how the function y = |x + 1| − 3
can be obtained from one of the basic graphs.
(a) Start with the graph of y = |x| and shift the graph left 3 units and up 1 unit.
(b) Start with the graph of y = |x| and shift the graph right 1 unit and down 3 units.
(c) Start with the graph of y = |x| and shift the graph left 1 unit and down 3 units.
(d) Start with the graph of y = |x| and shift the graph left 1 unit and up 3 units.
(e) Start with the graph of y = |x| and shift the graph right 3 units and down 1 unit.
Page 3
6
8
= .
x+2
x
9. Solve:
(a) x = −8
(b) x = 8
(c) x = 2
(d) x = 6
(e) x = 0
10. Determine the relative minima in the following function.
(a) (−1, 1)
(b) (1, 2)
(c) (2, 0)
(d) (−1, 0)
(e) (−2, 2)
14 − |x + 8| = 5.
11. Solve:
(a) x = −17, 1
(b) x = −17
(c) x = −1, 17
(d) x = 1
(e) x = −9, 9
12. Solve:
6x3 + x2 − 24x − 4 = 0.
1
(a) x = − , 4
6
(b) x = −2, 2
1
(c) x = − , 2
6
1
(d) x = −2, − , 4
6
1
(e) x = −2, − , 2
6
Page 4
13. Determine whether the graph of
6y = 3x2 + 4
is symmetric with respect to the x-axis, y-axis, or the origin.
(a) x-axis
(b) y-axis
(c) x-axis and y-axis
(d) Origin
(e) x-axis, y−axis, and origin
14. Choose the end behavior diagram that best describes the function
f (x) = x7 − 4x4 + x6 .
(a)
(d)
(c)
(b)
15. Solve:
√
x + 16 + 4 = x.
(a) x = 9
(b) x = 0, 9
(c) x = 0
(d) x = −9
(e) x = 7
16. Determine whether the function
f (x) = x4 − 2x2 + 7
is even, odd, or neither.
(a) Even
(b) Odd
(c) Neither
Page 5
17. Solve and write your answer in interval notation:
|6x + 1| < 5.
(a) (−6, 4)
2
− ,1
3
2
(c) −1,
3
(b)
(d) (−∞, ∞)
5
(e) (−1, )
6
18. Determine the interval(s) on which the function is increasing.
(a) (−3, −1)
(b) (−1, 2)
(c) (2, 5)
(d) (−3, −1) and (5, 7)
(e) (−1, 2) and (2, 5)
Workout Section:
19. Determine the following about the function
f (x) = x2 + 4x + 7.
(a) What is the vertex?
(b) Does f (x) have a maximum or minimum and what is its value?
(c) What is the axis of symmetry?
x=
Page 6
20. Consider the function f (x) = 3 − x2 .
(a) Find f (x + h) =
(b) Construct and simplify the difference quotient
f (x + h) − f (x)
h
for the function
Multiple Choice Workout Total
Points:
90
10
100
Score:
Page 7
f (x) = 3 − x2 .
MATH 1100 – College Algebra Spring 2017 Exam 3
April 19, 2017
NAME
STUDENT ID
INSTRUCTOR
SECTION (number or time)
· INSTRUCTIONS
1. DO NOT OPEN THIS EXAM UNTIL YOU ARE TOLD TO DO SO.
2. CAREFULLY MARK YOUR STUDENT ID ON YOUR SCANTRON.
3. This exam has 7 pages, including the cover sheet. There are 18 multiple-choice questions, each worth 5 points, and 2 workout
questions, worth a total of 10 points. No partial credit will be given on the multiple choice questions.
4. You will have 60 minutes to complete the exam. No notes or books are allowed. TI-30Xa and TI-30XIIS scientific calculators
are allowed. NO other calculators are allowed.
5. When you are finished, check your work carefully. Then, slide your scantron inside the exam packet before returning the exam
to YOUR instructor.
USEFUL FORMULAS
•
y = mx + b
•
y − y0 = m(x − x0 )
•
A2 − B 2 = (A + B)(A − B)
•
•
•
(x − h)2 + (y − k)2 = r2
−b ±
•
x=
•
I = P rt
√
b2 − 4ac
2a
3
3
2
•
A = P + P rt
•
a2 + b2 = c2
•
f (x + h) − f (x)
h
2
A − B = (A − B)(A + AB + B )
d=
p
(x2 − x1
)2
+ (y2 − y1
x1 + x2 y1 + y2
,
2
2
• f (x) = a(x − h)2 + k
•
−
b
,f
2a
)2
• d = rt
−
b
2a
• loga M N = loga M + loga N
• loga
A3 + B 3 = (A + B)(A2 − AB + B 2 )
•
•
M
N
= loga M − loga N
• loga M p = p loga M
• logb M =
loga M
loga b
• loga a = 1, loga 1 = 0
• loga ax = x, aloga x = x
Multiple Choice Section:
1. Given that
(a)
log2 x = 7
and
log2 y = 3,
find:
log2
x3
.
y5
7
3
(b) 21
(c) 6
(d) 36
(e)
7
5
2. Determine the vertical asymptote(s) of the function
g(x) =
x2
x3
.
+ 5x + 4
(a) x = 0, 1, 4
(b) x = 1, 4
(c) x = 0
(d) x = −4, −1, 0
(e) x = −4, −1
3. Solve the exponential equation:
2x
2
−2x
= 8.
(a) x = −1, 3
(b) x = −3, −1
(c) x = −7, −3
(d) x = −3
(e) x = −1
4. Solve and write your answer in interval notation:
3x
< 0.
(x + 8)(x − 6)
(a) (−∞, ∞)
(b) (−∞, −8) ∪ (6, ∞)
(c) (−8, 6)
(d) (−∞, −8) ∪ (0, 6)
(e) (−∞, 6)
Page 2
5. Convert the equation q k = 81
to a logarithmic equation.
(a) log81 k = q
(b) logk 81 = q
(c) logk q = 81
(d) log81 q = k
(e) logq 81 = k
6. Determine the y-intercept of the function g(x) =
1
.
x2 + 5
(a) (0, 0)
(b) (0, −5)
(c)
(d)
1
2
1
0,
5
0,
(e) g(x) does not have a y-intercept.
7. Determine the horizonal asymptote, if any, of the function
(a) y =
f (x) =
3x3 + 2
.
4x3 − 5
3
4
(b) y = 1
(c) y =
4
3
(d) y = −
2
5
(e) There is no horizontal asymptote.
8. Use the Horizontal Line Test to determine whether the function whose graph is shown is one-to-one.
(a) f (x) is one-to-one
(b) f (x) is not one-to-one
(c) Cannot be determined
Page 3
9. Solve and write your answer in interval notation:
x−5
≥ 1.
x−4
(a) (−∞, 4)
(b) (−∞, 4]
(c) (−∞, 0] ∪ (4, ∞)
(d) (4, ∞)
(e) (−∞, 4) ∪
10. Solve for x:
9
,∞
2
log5 (2x − 2) = 2.
(a) x = 15
(b) x = 6
(c) x = 17
(d) x = 5
(e) x =
27
2
11. Does the function
f (x) =
x3 − 3x2 + x − 5
x2 − 15
have a horizontal asymptote (HA)?
(a) Yes, f (x) has a HA because the degree of the numerator is larger than the degree of the denominator.
(b) No, f (x) does not have a HA because the degree of the numerator is larger than the degree of the denominator.
(c) Yes, f (x) has a HA because the degree of the numerator is smaller than the degree of the denominator.
(d) No, f (x) does not have a HA because the degree of the numerator is smaller than the degree of the denominator.
(e) Cannot be determined
12. Find f −1 (x) given that f (x) =
(a) f −1 (x) =
11
x−1
(b) f −1 (x) =
−7x + 4
x+1
(c) f −1 (x) =
x−7
x+4
(d) f −1 (x) =
7x + 4
x−1
x+4
.
x−7
(e) f (x) does not have an inverse.
Page 4
13. Express as a single logarithm:
5 log a + 6 log b
(a) log(a5 b6 )
(b) log(a5 + b6 )
(c) log(5a + 6b)
(d) log(30ab)
(e) 30 log(a + b)
14. Solve and write your answer in interval notation:
x2 + 5x − 12 ≥ x − 7.
(a) (−∞, −5] ∪ [1, ∞)
(b) [5, ∞)
(c) [−5, 1]
(d) (−∞, −5]
(e) (−∞, −1] ∪ [5, ∞)
15. Find the domain of f (x) =
−1
x2 + 3x − 28
and write your answer in interval notation.
(a) (−∞, −7) ∪ (4, ∞)
(b) (−∞, −4) ∪ (−4, 7) ∪ (7, ∞)
(c) (−∞, −7) ∪ (−7, 4) ∪ (4, ∞)
(d) (−∞, −1) ∪ (−1, ∞)
(e) (−∞, ∞)
16. Convert the equation
logm r = −z
to an exponential equation.
(a) mr = −z
(b) (−z)r = m
(c) (−z)m = r
(d) rm = −z
(e) m−z = r
Page 5
17. Express as a sum or difference of logarithms:
log
x3
y4 z7
(a) 3 log(x) − 4 log(y) + 7 log(z)
(b) 3 log(x) − 4 log(y) − 7 log(z)
(c) 3 log(x) + 4 log(y) + 7 log(z)
(d) log(3x) − log(4y) − log(7z)
(e) log(3x) − log(4y) + log(7z)
18. Find
log5
1
.
25
(a) 2
(b) 5
(c)
1
2
(d) −2
(e) −5
Workout Section:
19. Solve the polynomial inequality, determine the interval(s) for which the inequality is satisfied, and write your answer
in interval notation.
f (x) = x4 − 4x2 ≥ 0
Page 6
20. Consider the function f (x) =
x−5
.
x2 − 4
(a) Find the x-intercept(s) or write NONE if f (x) does not have an x-intercept.
(b) Find the y-intercept or write NONE if f (x) does not have a y-intercept.
(c) Find the vertical asymptote(s) or write NONE if f (x) does not have any vertical asymptote(s).
Note: Your answer should either be NONE or in the form x = b.
(d) Find the horizontal asymptote or write NONE if f (x) does not have a horizontal asymptote.
Note: Your answer should either be NONE or in the form y = a.
Points:
Score:
Multiple Choice:
90
Page 7
Workout
10
Total
100