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College Algebra Final review

Total questions: 96

Worksheet time: 18hrs 8mins

Name
Class
Date
1.
Factor:
x2 + 7x - 30
a)
(x + 10)(x - 7)
b)
(x - 10)(x + 3)
c)
(x + 10)(x + 3)
d)
(x + 10)(x - 3)
2.
Factor
x2 + 9x - 36
a)
(x + 12)(x - 3)
b)
(x + 9)(x - 4)
c)
(x - 12)(x + 3)
d)
(x - 9)(x - 4)
3.
Factor
n2 + 5n - 6
a)
(n - 2)(n - 3)
b)
(n - 1)(n + 6)
c)
(n + 1)(n - 6)
d)
(n + 2)(n - 3)
4.
Factor
a2 - a - 12
a)
(a - 4)(a + 3)
b)
(a + 6)(a - 4)
c)
(a - 6)(a + 4)
d)
(a + 4)(a - 3)
5.

Factor completely:

3x2 + 18x +15

a)

3(x2 + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

6.
Factor
3a2 + 4a + 1
a)
(7a-10)(a-8)
b)
Not factorable
c)
(3a+1)(a+1)
d)
(3a-1)(a-1)
7.
Factor:
 2m² + 3m - 9
a)
2(m + 3)(m - 3)
b)
(2m - 3)²
c)
(m + 3)(2m - 3)
d)
(2m + 3)(m - 3)
8.
a)
A
b)
B
c)
C
d)
D
9.
a)
A
b)
B
c)
C
d)
D
10.
a)
A
b)
B
c)
C
d)
D
11.
a)
A
b)
B
c)
C
d)
D
12.
a)
A
b)
B
c)
C
d)
D
13.
Which set of sides would make a right triangle?
a)
(4,5,6)
b)
(8,10,12)
c)
(5,12,13)
d)
(5,10,12)
14.
a = 2.1, b = 7.2, c = 7.5
Is this a right triangle?
a)
yes 
b)
no
15.
Do the segment lengths 9, 12, and 15 form a right triangle?
a)
Yes
b)
No
16.
If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?
a)
9
b)
40
c)
41
17.
Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.
a)
3 hours
b)
4 hours
c)
1 hour
d)
2 hours
18.
Bob has $150 in his savings account and saves $40 per month.  Which equation represents the amount Bob has in his account after x months?
a)
y = 150 + 40
b)
y = 40x + 150
c)
y = 150x + 40
19.
A holiday meal costs $12.50 a person plus a delivery fee of $30.  Which equation represents the amount a holiday meal costs, including delivery, for x people?
a)
y = 30 + 12.5x 
b)
y = 12.5 + 30
c)
y = 12.5 + 30x
20.
Easy Car Rental charges $8.50 an hour plus a rental fee of $25.50. Which equation represents the total charges for x hours?
a)
y = 8.5 + 25.5
b)
y = 25.5 + 8.5x
c)
y = 8.5 + 25.5x
21.
Jerry has $20 and makes $7 per hour. Which equation represents the total amount of money Jerry has after working x hours?
a)
y = 7x + 20
b)
y = 7 + 20x
c)
y = 20 + 7
22.
The drama club sold tickets to a play for $5 each.  They also made $55 in soda and popcorn sales.  If the drama club made a total of $290, how many tickets were sold?
a)
47
b)
58
c)
69
d)
113
23.
Andrea earns a flat fee of $20 per day plus an additional x dollars for each sale she makes.  Andrea made 10 sales last Saturday and earned a total of $80.  How much does Andrea earn for each sale she makes?
a)
$6
b)
$8
c)
$10
d)
$12
24.
Billy's car needed repairs. The mechanic charged him $140 for the parts and an additional $48 an hour for labor. How many hours of labor did the mechanic work on the car if her total bill was $260?
a)
3 hours
b)
12 hours
c)
2.5 hours
d)
5 hours
25.

What are the intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

26.
a)

Symmetric with respect to the x-axis

b)

Symmetric with respect to the y-axis

c)

Symmetric with respect to the origin

d)

The function does not have any of these symmetries

27.

Which statement correctly describes the symmetry of an EVEN function?

a)

An EVEN function is symmetric with respect to the x-axis.

b)

An EVEN function is symmetric with respect to the y-axis.

c)

An EVEN function is symmetric with respect to the origin.

d)

An EVEN function is symmetric with respect to the line y = x.

28.

Which function graphed is an EVEN function?

a)
b)
c)
29.
a)

The function f(x) is an EVEN function.

b)

The function f(x) is an ODD function.

c)

The function f(x) is neither EVEN nor ODD function.

30.
The function shown in the graph is:
a)
even
b)
odd
c)
neither even nor odd
d)
both even and odd
31.
Is the graph an even, odd, or neither function
                        f(x) = x4 + x2 
a)
Even
b)
Odd
c)
Neither
32.
Is the graph an even, odd, or neither function 
f(x)=x3-x2
a)
even
b)
odd
c)
neither
33.
Which one of the following functions is even?
a)
f(x) = x⁴ + x³
b)
g(x) = x⁴ + x²
c)
h(x) = x⁵ + x³
d)
k(x) = x³ + x
34.
Which one of the following functions is odd?
a)
f(x) = 3x⁴ - 4x³
b)
g(x) = 5x⁴ + 3x²
c)
h(x) = 6x⁵ - x³
d)
k(x) = x⁶ + 8x²
35.
(5-2i) + (-7+8i)
a)
-2+6i
b)
12+6i
c)
-35-16i2
d)
-35 -16i
36.
What does i2 = ?
a)
-1
b)
√-1
c)
1
d)
-√1
37.
Simplify.
(5-i)(5+i)
a)
26
b)
24
c)
25+i2
d)
25-i2
38.
a)

A

b)

B

c)

C

d)

D

39.

What is the simplified form of (8 -3i)2?

a)

73

b)

16 - 6i

c)

55 + 48i

d)

55 - 48i

40.
Multiply
3i(-2 + 4i)
a)
-6+12i
b)
-12-6i
c)
-2+7i
d)
12+6i
41.
Determine the slope and y-intercept from the following equation:   y = 3/2x + 3
a)
slope: 5   y-intercept:  (0,3) 
b)
slope: 3/2   y-intercept:  (0,3) 
c)
slope:  4  y-intercept:  (0,3/2)
d)
slope: 1/5   y-intercept:  (0,5) 
42.
What is the slope in the equation y=2x + 3?
a)
2
b)
3
c)
5
d)
Cannot be Determined 
43.
What is the y-intercept in the equation y= -2x + 5
a)
-2
b)
3
c)
5
d)
Cannot be Determined
44.
What is the y-intercept of the line y = 4x - 10?
a)
4
b)
-4
c)
10
d)
-10
45.
What is the slope of the line y= -4x + 10?
a)
10
b)
4
c)
-4
d)
-10
46.

Which of the following are written in standard/ general form?

a)

y=3x-5

b)

3x+16=5y

c)

2/3 x + 9/13 y = 21

d)

5x+7y=-12

47.

Write in standard or general form.

2x - 8 = -3y + 2

a)

2x + 3y = 10

b)

2x - 3y = 10

c)

2x + 3y = -6

d)

2x - 3y = -6

48.
What would the graph of the equation x = -4 look like? 
a)
Horizontal line
b)
Vertical line
c)
Slanted line
d)
No way to tell
49.
The graph of x = 4 would be parallel to what?
a)
The x-axis
b)
The y-axis
c)
Both axes
d)
Neither axis
50.
Vertical or horizontal?
x = 4
a)
vertical 
b)
horizontal
c)
neither
51.
Vertical or horizontal?
Slope of 0
a)
vertical
b)
horizontal
c)
neither
52.
Vertical or horizontal?
Undefined slope
a)
vertical
b)
horizontal
c)
neither
53.
Which is the graph of y= -x + 2?
a)
A
b)
B
c)
C
d)
D
54.
Which equation is being represented by this line?
a)
y = -1x + 2
b)
y = 1/2x + 2
c)
y = 3x -4
d)
y = -3x +2
55.
Consider the equation:
y=-x+4
Identify the slope and y-intercept.
a)
m=4, b=-x
b)
m=-x, b=4
c)
m=1, b=4
d)
m=-1, b=4
56.
What type of slope does the graph have?
a)
Positive
b)
Negative
c)
Zero Slope
d)
Undefined
57.
Which equation represents the following graph?
a)
y = 3x + 2
b)
y = -2x + 3
c)
y = 2x + 3
d)
y = -3x + 2
58.

Graph x = 2

a)

A

b)

B

c)

C

d)

D

59.
Graph y = -3
a)
A
b)
B
c)
C
d)
D
60.
Which equation matches the graph? (Click me to see the image)
a)
y = 2x
b)
y = 1/4 x + 2
c)
y = 1x + 4
d)
y = -2x
61.
Graph y=-1/2x
a)
A
b)
B
c)
C
d)
D
62.
a)

$1250

b)

$12500

c)

$20000

d)

$50000

63.
a)

$100,000

b)

$150,000

c)

$175,000

d)

$200,000

64.
Does
y = -4x2
have a maximum or minimum value?

a)
maximum
b)
minimum
65.

What is the minimum value of the quadratic function

f(x) = x² - 2x + 7

a)

6

b)

7

66.
When a basketball is shot, it forms an arc (also known as a parabola). When the basketball reaches it's highest point, what is that point called?
a)
Minimum value
b)
Basketball
c)
Maximum Value
d)
A parabola
67.

Does the function have a minimum/maximum/both/neither? y = 3x2 + 2x + 4

a)

minimum

b)

maximum

c)

both

d)

neither

68.

A toy rocket is launched into the air at an initial speed of 97 feet per second from an initial height of 10ft. Its path is modeled by the equation: s(t)= -16t2+97t+10. What is the maximum height that the rocket will reach, and when will it reach this height?

a)

max height: 303 ft, when: 1.57 sec

b)

max height: 157 ft, when: 3.03 sec

c)

max height: 162 ft, when: 3.48 sec

d)

max height: 155 ft, when: 2.7 sec

69.

A toy rocket is launched into the air at an initial speed of 97 feet per second from an initial height of 10ft. Its path is modeled by the equation: s(t)= -16t2+97t+10. When will the rocket hit the ground?

a)

0.101 seconds

b)

3.03 seconds

c)

6.16 seconds

d)

6.52 seconds

70.

An object is launched into the air with an initial velocity of 123 ft/sec from an initial height of 5 ft. Its path is modeled by the equation: s(t)= -16t2+123t+5. When will it reach its maximum height, and when will it hit the ground?

a)

reach max at after 3.84 seconds, hit ground after 7.73 seconds

b)

reach max at after 3.84 seconds, hit ground after 0 seconds

c)

reach max at after 241 seconds, hit ground after 7.73 seconds

d)

reach max at after 3.84 seconds, hit ground after 5 seconds

71.

The number of people infected by a virus can be modeled by h(t) = 5.7 + 19ln(t). Where "t" is time in days. How many people will be infected after 17 days?

a)

80822 people

b)

2 people

c)

9 people

d)

60 people

72.

What is the range of this function: x2 - 2x - 3?

a)

-4 ≤ y ≤ 5

b)

-1 ≤ x ≤ 3

c)

All Real Numbers

d)

y ≥ -4

73.
What is the domain of this graph?
a)
All real numbers
b)
-∞ ≤ y ≤ ∞
c)
y ≥ -9
d)
-5 ≤ x ≤ 1
74.

What is the range of the function: -x2 + 6x - 12?

a)

R:{y is less than or equal to 3}

b)

R:{y is greater than or equal to 3}

c)

R:{all real numbers}

d)

R:{y is between and including -6 and 3}

75.
What is the range of the function?
*Hint: Range is all of the y-values included in the function. 
a)
y≤3
b)
y≥3
c)
All real numbers
d)
-6≤y≤3
76.
a)

y = 0

b)

y = 1/2

c)

y = 2

d)

None

77.
Find the horizontal asymptote.
a)
y = -2
b)
none
c)
y = 0
d)
y = 1/2
78.
What is the Horizontal Asymptote?
a)
None
b)
y= 0
c)
y= 1
d)
y= 5/4
79.

Find the horizontal asymptote of y = (5x3)/ (x+6).

a)

There is no horizontal asymptote

b)

y = 0

c)

y = 5

d)

What's horizontal?

80.
            Is (x-2) a factor of             f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is a factor. There is a remainder.
b)
No, (x-2) is  not a factor. The remainder is zero.
c)
Yes, (x-2) is a factor. The remainder is zero.
d)
No, (x-2) is  not a factor. There is a remainder. 
81.

Is (x-4) a factor of (x3 +x2 -16x-16)?

a)

Yes, because the remainder is 1

b)

No, because the remainder is 1

c)

Yes, because the remainder is 0

d)

No, because the remainder is 0

82.

Is (x-8) a factor of (x2-16x+64)?

a)

Yes

b)

No

83.
Simplify the following logarithmic function:
log228 =
a)
8
b)
2
c)
1
d)
16
84.
Simplify the following:
6log636
a)
6
b)
36
c)
1
d)
2
85.
Condense:
 log4- logx- log5+log3
a)
log(20/3x)
b)
log(12x/5)
c)
log(12/5x)
d)
log(5x/12)
86.

Simplify the following:

9log981

a)

2

b)

81

c)

3

d)

27

87.
f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)
a)
16
b)
4
c)
-4
d)
None of these.
88.
Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))
a)
19
b)
23
c)
-10
d)
None of these.
89.
f(x) = 3x + 10
g(x) = x - 2
Find g(f(-10))
a)
-42
b)
-26
c)
-18
d)
None of these.
90.
Largest number of individuals of a population that the environment can support...  
a)
carrying capacity
b)
population crash
c)
lag phase
d)
mutualism
91.
What is the formula for continuously compounded interest?
a)
A = Pert
b)
A = Pet
92.

Riley invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Riley earn in 15 years?

a)

$1,584.62

b)

$2,651.39

c)

$2,706.86

d)

$1,825.10

93.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

94.

Principal: $5000

Interest Rate: 3.75%

Time: 25 years

Compounded Monthly

State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

95.
If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?
a)
$1,225,54
b)
$2,225.54
c)
$22,255.40
d)
$225.54
96.
P = 26,000 | Rate = 2.4% | 4 years | Compounded Continuously | Amount owed???
a)
$2,496
b)
$28,496
c)
$3,406,924
d)
$28,619.74

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