Honors Algebra 2-Final Exam Review Sheet
____
a.
b.
1.
Solve the equation. Check for extraneous solutions.
x = 2 or x =
x=
____
2.
1
b.
x < 1
x = 2 or x =
14
27
Solve the inequality. Graph the solution.
7
7
<x<1
24
24
3.
c. x = 2
d.
14
27
a.
____
14
13
7
7
or x > 1
24
24
c.
1
d.
x < 1
7
1
<x<1
12
12
7
1
or x > 1
12
12
Write an inequality for the graph.
y
6
3
–6
–3
O
–3
–6
a. y  |x – 3| + 3
b. y  |x – 3| + 3
____
4.
Solve the system
c. (4, –1)
d. (1, –4)
a. (–4, 1)
b. (–1, 4)
____
5.
c. y  |x + 3| + 3
d. y  |x – 3| – 3
Solve the system
a. infinitely many solutions
b. no solutions
c. (7, –5)
d. (–7, 5)
3
6
x
Honors Algebra 2-Final Exam Review Sheet
____
6.
Solve the system
a. infinitely many solutions
b. no solutions
c. (2, 8)
d. (–2, –8)
____ 7.
The length of a rectangle is 9.9 cm more than 4 times the width. If the perimeter of the rectangle is 60.8
cm, what are its dimensions?
a. length = 26.3 cm; width = 14 cm
b. length = 4.1 cm; width = 26.3 cm
____
8.
c. length = 26.3 cm; width = 4.1 cm
d. length = 6.5 cm; width = 14 cm
Given the system of constraints, name all vertices. Then find the maximum value of the given objective.
Objective function:
a.
,
,
value of 28
b.
,
,
value of 0
____
9.
a. (–9, 7, –3)
b. (9, 7, –3)
,
; maximum
,
; maximum
c.
,
,
value of 8
d.
,
,
value of –3
,
; maximum
,
; maximum
Solve the system
c. (9, 7, 3)
d. (9, –7, –3)
____ 10.
A candy store makes a 14-lb mixture of gummy worms, candy corn, and sourballs. The cost of gummy
worms is $1.00 per pound, candy corn cost $1.00 per pound, and sourballs cost $2.00 per pound. The mixture calls for
three times as many gummy worms as candy corn. The total cost of the mixture is $16.00. How much of each ingredient
did the store use?
a. 10 lb gummy worms, 3 lb candy corn, 1 lb c. 10 lb gummy worms, 1 lb candy corn, 3 lb
sourballs
sourballs
b. 9 lb gummy worms, 3 lb candy corn, 2 lb d. 3 lb gummy worms, 9 lb candy corn, 2 lb
sourballs
sourballs
Honors Algebra 2-Final Exam Review Sheet
____
11.
Use the vertex form to write the equation of the parabola.
y
8
6
4
2
–8 –6 –4 –2 O
–2
2
4
6
8
x
–4
–6
–8
a.
b.
c.
d.
____ 12.
Suppose a parabola has vertex (–4, 1) and also passes through the point (–3, 2). Write the equation of the
parabola in vertex form.
a.
c.
b.
d.
____
13.
What are the vertex and the axis of symmetry of the equation?
a. vertex: ( –7, 92)
axis of symmetry:
b. vertex: ( 7, 92)
axis of symmetry:
____
14.
c. vertex: ( –7, –92)
axis of symmetry:
d. vertex: ( 7, 92)
axis of symmetry:
What is the vertex form of the equation?
a.
b.
𝑦 = −2(𝑥 − 1)2 − 7
c.
d.
_ 15. A historian took a count of the number of people in a Gold Rush town for six years in the 1870’s.
Year
1870
1871
1872
1873
1874
1875
1876
Population
460
480
488
484
468
440
400
Find a quadratic function that models the data as a function of x, the number of years since 1870. Use the model to
estimate the number of people in the town in 1878.
a.
b.
c.
d.
; 74 people
; 284 people
; 348 people
; 130 people
Honors Algebra 2-Final Exam Review Sheet
____
16.
What is the expression in factored form?
a.
b.
c.
d.
____
a.
b.
17.
____ 18.
a. –8, 2
b.
–8, 
9
2
What is the expression in factored form?
c.
d.
What are the solutions of the quadratic equation?
c.
9 1
 ,
2 4
d.
1
8, 
4
=0
____ 19.
The function
models the height y in feet of your pet frog's jump t seconds
after it jumps. How far did the frog jump? How high did it go?
a. The frog jumped about 24.09 ft far and
about 6.38 ft. high.
b. The frog jumped about 48.18 ft. far and
about 24.09 ft. high.
c. The frog jumped about 48.18 ft. far and
about 6.38 ft. high.
d. The frog jumped about 6.38 ft. far and
about 48.18 ft. high.
____ 20.
a.
1

2
b.
1
Solve the quadratic equation by completing the square.
c.
1
____ 21.
a. 9
Use the Quadratic Formula to solve the equation.
c. 10
d.
10
b.
9
d.
9
5
____
22.
23.
9
5
What is the number of real solutions?
a. one solution
b. cannot be determined
____
a.
b.
1
2
c. no real solutions
d. two solutions
Simplify the number using the imaginary unit i.
c.
d.
Honors Algebra 2-Final Exam Review Sheet
____
24.
Simplify the expression.
a.
c.
b.
d.
____
25.
What are the solutions?
a.
b.
____
c.
d.
26.
Use graphing to find the solutions to the system of equations.
(–2, –4)
(5, 3)
d. (2, –4)
(–5, 3)
a.
(2, 4)
(–5, –3)
b. (–2, 4)
(5, –3)
____
27.
c.
Consider the leading term of each polynomial function. What is the end behavior of the graph?
a. The leading term is
down.
b. The leading term is
c. The leading term is
down.
d. The leading term is
up.
____
a.
b.
28.
. Since n is odd and a is negative, the end behavior is up and
. Since n is odd and a is negative, the end behavior is up and up.
. Since n is odd and a is negative, the end behavior is down and
. Since n is odd and a is negative, the end behavior is down and
What is a quartic polynomial function in standard form with zeros 1, –1, –3, and 2?
c.
d.
____ 29.
What is the relative maximum and minimum of the function?
a. The relative maximum is at (–0.56, 2.05) and the
relative minimum is at (0.89, –1.02).
b. The relative maximum is at (–0.56, 1.02) and the
relative minimum is at (0.89, –2.05).
c. The relative maximum is at (–0.89, 1.02) and the
relative minimum is at (0.56, –2.05).
d. The relative maximum is at (–0.89, 2.05) and the
relative minimum is at (0.56, –1.02).
Honors Algebra 2-Final Exam Review Sheet
____ 30.
a.
5
 ,
3
b. 5
,
3
What are the real or imaginary solutions of each polynomial equation?
c.
5 5
 ,
3 3
____ 31.
a. 5, –5
b. 5, –4
What are the real or imaginary solutions of each polynomial equation?
c. 5, –5, 4, –4
d. no solution
____ 32.
a. x + 4
b. x + 3
Determine which binomial is not a factor of
c. x – 5
d. 4x + 3
____ 33.
width is (
the depth.)
d. no solution
The polynomial
expresses the volume, in cubic inches, of a shipping box, and the
) in. If the width of the box is 17 in., what are the other two dimensions? (Hint: The height is greater than
a. height: 20 in.
depth: 5 in.
b. height: 18 in.
depth: 5 in.
____
a.
34.
b.
.
c. height: 20 in.
depth: 7 in.
d. height: 18 in.
depth: 7 in.
Find the roots of the polynomial equation.
c.
d.
____
a.
b.
35.
Find a third-degree polynomial equation with rational coefficients that has roots –3 and 4 + i.
c.
d.
____
a.
b.
36.
Find a quadratic equation with roots –1 + 4i and –1 – 4i.
c.
d.
____ 37.
What does Descartes' Rule of Signs tell you about the real roots of the polynomial?
a. There are either 2 or 0 positive roots and one negative root.
b. There are either 2 or 0 positive roots and there are either 2 or 0 negative roots.
c. There is one positive root and either 2 or 0 negative roots.
d. There is one positive root and one negative root.
____
38.
a. 1, –5,
b. 5, –5, i,
Find all the zeros of the equation.
c. 1, 5, i
d. 1, 5, –5, i,
Honors Algebra 2-Final Exam Review Sheet
____
a.
b.
c.
d.
39.
Use Pascal’s Triangle to expand the binomial.
____
161)
a.
b.
40.
What polynomial has a graph that passes through the given points? (–3, 133), (–1, 1), (0, 1), (3, 49), (4,
____
41.
c.
d.
What is the equation of
with the given transformations? vertical compression by a factor of
horizontal shift 5 units to the left, reflection across the x-axis
a.
c.
b.
d.
____ 42.
a. 11
What is the solution of the equation?
b. 49
c. 45
d. 53
____ 43.
a. –5, 11
What is the solution of the equation?
b. 5
c. 11
d. –11
____ 44.
a. –2
What is the solution of the equation?
b. –8 and –2
c. 8 and –2
d. –8
____
Let
45.
a.
____
a.
b.
and
b.
46.
. Find
.
c.
What is the inverse of the given relation?
c.
d.
d.
.
,
Honors Algebra 2-Final Exam Review Sheet
____
a.
47.
Graph
–8
8
4
4
–4
4
48.
49.
–4
–4
–4
–8
–8
d.
8
4
4
–4
4
8
4
8
x
4
8
x
y
8
–8
x
–4
–4
–4
–8
–8
Graph
c.
y
–12
–8
x
You can model the population of a certain city between the years 1965 and 2000 by the radical function
. Using this model, in what year was the population of that city 275,000?
c. 1986
d. 1995
a. 1991
b. 1992
____
a.
8
y
–8
y
8
b.
____
c.
y
–8
y
12
12
8
8
4
4
–4
4
8
12 x
–12
–8
–4
4
–4
–4
–8
–8
–12
–12
8
12 x
Honors Algebra 2-Final Exam Review Sheet
b.
d.
y
–12
–8
y
12
12
8
8
4
4
–4
4
8
–12
12 x
–8
–4
4
–4
–4
–8
–8
–12
–12
8
12 x
____ 50.
Suppose you invest $1500 at an annual interest rate of 3.4% compounded continuously. How much will
you have in the account after 30 years?
a. $46,556.31
b. $4,159.79
c. $4,158.97
d. $63,222.64
____
a.
b.
51.
Write the equation in logarithmic form.
c.
d.
____
52.
Evaluate the logarithm.
a. –2
____
a.
b. –1
53.
–12
c. 2
d. 3
Graph the logarithmic equation.
y
c.
–8
y
12
12
8
8
4
4
–4
4
8
12 x
–12
–8
–4
4
–4
–4
–8
–8
–12
–12
8
12 x
Honors Algebra 2-Final Exam Review Sheet
b.
–12
____
a.
d.
y
54.
–8
12
8
8
4
4
–4
4
8
–12
12 x
–4
4
–4
–8
–8
–12
–12
8
Write the expression as a single logarithm.
c.
d.
55.
Expand the logarithmic expression.
a.
c.
b.
d.
____
a. 2
–8
–4
b.
____
y
12
56.
What is the value of log8 2?
c.
b. 3
1
2
d.
____ 57.
a. –1.8847
Solve the exponential equation.
b. –0.1069
c. 0.3375
d. 1.0378
____ 58.
a. 0.0090
Solve the logarithmic equation.
b. 0.3103
c. 3.2222
d. 111
____
a. 6
Solve
59.
____ 60.
a. 0.165
.
b. 6e
c.
Use natural logarithms to solve the equation.
b. 0.506
c. 0.280
d. ln 6
d. –1.595
12 x
Honors Algebra 2-Final Exam Review Sheet
____
61.
Simplify the rational expression. State any restrictions on the variable.
a.
c.
7, z
2
b.
d.
7, z
____
62.
2
What is the quotient in simplified form? State any restrictions on the variable.
a.
c.
b.
d.
____
63.
Simplify the sum.
a.
c.
b.
d.
____
a.
64.
b.
21
25
____
65.
a.
39
50

66.
9
4
c.
50
39
d.
25
21
Solve the equation. Check the solution.
b. 2
____
a.
Simplify the complex fraction.
d. 3 or –4
c.
Solve the equation. Check the solution.
b.
25
3
c.

13
16
d.

25
12
Honors Algebra 2-Final Exam Review Sheet
____ 67.
A group of college students are volunteering for Help the Homeless during their spring break. They are
putting the finishing touches on a house they built. Working alone, Jorge can paint a certain room in 10 hours. Maria can
paint the same room in 8 hours. Write an equation that can be used to find how long it will take them working together to
paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest
hundredth.
a.
c.
; 9 hours
; 9 hours
b.
____
68.
a. 56
____
d.
; 4.44 hours
What is the
term in the sequence using the given formula?
b. -156
69.
c. 167
d. 156
What is an equation of a parabola with the given vertex and focus?
a.
c.
b.
d.
____
a.
70.
Write an equation for the translation of
c.
b.
vertex:
by 2 units right and 7 units down.
d.
____ 71.
a. foci
What are the foci of the ellipse?
c. foci
b. foci
____
a.
; 18 hours
d. foci
72.
Graph the conic section.
c.
y
–8
y
8
8
4
4
–4
4
8
x
–8
–4
4
–4
–4
–8
–8
8
x
; focus:
Honors Algebra 2-Final Exam Review Sheet
b.
–8
____
73.
a. 502º
____
a.
d.
y
74.
8
8
4
4
–4
4
8
–4
4
–4
–8
–8
8
Which of the following angles is not coterminal with the other three?
b. 142º
c. 38º
d. –218º
Find the exact values of cos 330º and sin 330º.
c.
d.
____
a.
75.
____
76.
a. 4.71º
77.
a.
____
–8
x
–4
b.
____
y
Find the radian measure of an angle of –310º.
b.
c.
Find the degree measure of an angle of
º
b.
Find the exact values of
b.
78.
a. 1
79.
____
80.
a. 1.73
radians.
d. 270º
º
and
c.
.
d.
What is the value of the expression? tan
b. -
____
a. 0
c.
d.
c.
d.
Find the exact value. csc 135º
b. undefined
c.
d.
3
Evaluate
b. –0.58
3
to the nearest hundredth. The angle is given in radians.
c. 0
d. 0.58
x
Honors Algebra 2-Final Exam Review Sheet
Answer Key
1.
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D
C
A
D
B
A
C
A
B
B
D
A
D
C
B
D
D
B
C
D
A
A
D
A
A
B
A
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D
A
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A
A
A
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A
A
Honors Algebra 2-Final Exam Review Sheet
50.
51.
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56.
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B
C
A
A
B
B
D
C
A
A
C
A
A
C
C
A
D
B
D
C
B
C
A
C
B
B
D
C
D
D
D