Algebra I Semester 2 Review
Below is a list of every Khan Academy module that has been assigned this semester followed by
each of the Chapter Tests we have taken. Khan Academy should be reviewed this week along with
the material from each of the Chapter Tests. Answer keys for each test can be found immediately
following the test items. The Semester Exam will be made up of questions from these tests with
different values substituted.
Chapter 6: Linear Inequalities
Khan Academy Support:
• Inequalities on a Number Line
• One Step Inequalities
• Linear Inequalities
• Compound Inequalities
• Absolute Value
• Comparing Absolute Values
• Absolute Value Equations
• Graphing Inequalities
• Graphing Inequalities 2
Chapter 7: Solving Systems of Equations
and Inequalities
Khan Academy Support:
• Graphing Systems of Equations
• Solutions to Systems of Equations
• Systems of Equations with Substitution
• Systems of Equations with Elimination 0.5
• Systems of Equations with Elimination
• Systems of Equations
• Systems of Equations Word Problems
• Graphing Systems of Inequalities
Chapter 8: Exponential Functions
We did some EMaths stuff for this Chapter and
Spring Break cut us off before a test in this
Chapter, so it was dropped.
Khan Academy Support:
• Exponents 1
• Exponents 2
• Exponent Rules
• Simplifying Expressions with Exponents
• Exponents 3
• Exponents 4
Chapter 9: Polynomials
Khan Academy Support:
• Adding and Subtracting Polynomials
• Multiplying Expressions 0.5
• Multiplying Expressions 1
• Multiplying Polynomials
• Factoring Polynomials 1
• Factoring Polynomials 2
• Factoring Difference of Squares 1
• Factoring Difference of Squares 2
• Solving Quadratics by Factoring
• Solving Quadratics by Factoring 2
• Factoring Polynomials with Two Variables
• Factoring Difference of Squares 3
• Factoring Polynomials by Grouping
Chapter 10: Quadratic Equations
Khan Academy Support:
• Solving Quadratics by Factoring
• Solving Quadratics by Factoring 2
• Solving Quadratics by Taking the Square
Root
• Completing the Square 1
• Recognizing Conic Sections
• Parabola Intuition 1
• Parabola Intuition 2
• Graphing Parabolas 0.5
• Simplifying Radicals (review)
• Quadratic Equation
• Vertex of a Parabola
• Graphing Parabolas 1
• Graphing Parabolas 2
Name: _____________________ Class: ________________ Date: __________ID: A
Chapter 6 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is the graph of the inequality in the coordinate plane?
1.
(1 point)
x≥2
a.
c.
b.
d.
What are the solutions of the inequality?
2.
(1 point)
−3 (−2x − 3 ) ≥ 6x + 5
f. x ≥ 4
g. x ≤ −8
h. all real numbers
j. no solution
1
Name: ________________________
ID: A
What is the graph of the inequality?
3.
4.
(1 point)
(1 point)
x ≤ −6
f.
d < –1
a.
g.
b.
h.
c.
j.
d.
What inequality represents the graph?
5.
(1 point)
a.
b.
c.
d.
x<8
x > –8
x ≤ −8
x < –8
What are the solutions of the inequality? Graph the solutions.
6.
(1 point)
x − 3 ≤ −4
f.
x≤7
g.
x≤
h.
x ≤ −1
j.
x ≤ −7
−4
3
2
Name: ________________________
ID: A
What are the solutions of the inequality? Graph the solutions.
7.
8.
(1 point)
x + 8 ≤ − 10
a.
x≤ −
x ≤ 18
c.
x ≤ −2
d.
−6x > −6
5
4
b.
(1 point)
f.
x≤1
g.
x>0
h.
x≥0
j.
x≥1
x ≤ − 18
Write and solve an inequality for each of the problems below.
9.
10.
(1 point)
Suppose you had d dollars in your bank
account. You spent $17 but have at least
$36 left. How much money did you have
initially? Write and solve an inequality
that represents this situation.
a. d − 17 > 36 ; d > 53
b. d + 17 ≤ 36 ; d ≤ 70
c. d + 17 ≥ 36 ; d ≥ 70
d. d − 17 ≥ 36 ; d ≥ 53
(1 point)
The width of a rectangle is 33
centimeters. The perimeter is at least
776 centimeters. Write and solve an
inequality to find the possible lengths of
the rectangle.
f.
g.
h.
j.
33 + ™ ≥ 776 ; ™ ≥ 743
2(33) + 2™ ≥ 776 ; ™ ≥ 355
2(33) + 2™ ≤ 776 ; ™ ≤ 355
33 + ™ ≤ 776 ; ™ ≤ 743
What are the solutions of the inequality?
11.
12.
(1 point)
10
a.
b.
c.
d.
(1 point)
11m − 7 ≤ 23m + 17
5
f. m ≥ −
17
5
g. m ≥
6
h. m ≥ –2
12
j. m ≥
17
+ 12w ≥ 7(w + 10)
w ≥ 16
w ≥ − 12
w ≥ 14
w ≥ 12
3
Name: ________________________
ID: A
What compound inequality represents the phrase? Graph the solutions.
13.
(1 point)
all real numbers g that are less than –7 or greater than 19
a. g < –7 or g ≥ 19
b.
g < 19 or g > –7
c.
–7 < g < 19
d.
g < –7 or g > 19
What are the solutions of the compound inequality? Graph the solutions.
14.
15.
(1 point)
g.
h.
j.
(1 point)
2x − 1
+ 3 ≤ −4
3
–13 < 2x – 3 < 3
f. –5 < x < 3
or
a.
x ≤ − 10 or x ≥ 2
b.
x ≤ − 2 or x ≥ 2
c.
x ≤ − 4 or x ≥
d.
x ≥ − 10 or x ≥ 2
−8 < x < 0
–18 < x < –2
–12 < x < 4
4
9
8
8x − 2
−1≥ 6
2
Name: ________________________
16.
ID: A
(1 point)
A student scored 83 and 88 on her first two quizzes. Write and solve a compound
inequality to find the possible values for a third quiz score that would give her an average
between 85 and 90, inclusive.
f.
g.
h.
j.
85 + 88
3
83 + 88
85 ≤
3
83 + 88
90 ≤
3
83 + 88
85 ≤
2
83 ≤
+ n
+ n
+ n
≤ 90; 76 ≤ n ≤ 97
≤ 90; 84 ≤ n ≤ 99
≤ 85; 99 ≤ n ≤ 84
+ n ≤ 90; − 0.5 ≤ n ≤ 4.5
What are the solutions of the inequality? Graph the solution.
17.
(1 point)
|d − 4| ≥ 3
18.
a.
d ≤ 1 or d ≥ 7
b.
d ≤ 1 or d ≥ 7
c.
d≥7
d.
d≤1
(1 point)
The ideal width of a safety belt strap for a certain automobile is 4 cm. The actual width can
vary by at most 0.3 cm. Write an absolute value inequality for the range of acceptable
widths and solve the inequality.
f. | w − 0.3 | ≤ 4 ; −3.7 ≤ w ≤ 4.3
g. | w − 4 | ≤ 0.3 ; 3.7 ≤ w ≤ 4.3
h. | w + 4 | ≤ 0.3 ; −4.3 ≤ w ≤ −3.7
j. | w + 0.3 | ≤ 4 ; −4.3 ≤ w ≤ 3.7
5
Name: ________________________
ID: A
Graph the inequality.
19.
(1 point)
y < 3x − 2
a.
c.
b.
d.
6
Name: ________________________
20.
ID: A
(1 point)
6x + 2y ≥ 20
f.
h.
g.
j.
What are the solutions of the equation?
21.
(1 point)
|2x − 5| = 13
a. x = 4
b. x = −9 or x = 9
c. x = −4 or x = 9
d. No solution
7
Name: ________________________
ID: A
Graph each equation.
22.
(1 point)
y =| x + 2 |
f.
h.
g.
j.
8
Name: ________________________
23.
ID: A
(1 point)
You have $50 to spend on music and movie downloads. Each album download costs $9 and
each movie download costs $10. Write and graph a linear inequality that represents this
situation. Let x represent the number of albums and y the number of movies.
a. 9x + 10y ≥ 50
c. 10x + 9y ≥ 50
b.
10x + 9y ≤ 50
d.
9x + 10y ≤ 50
Which ordered pair is a solution of the inequality?
24.
(1 point)
y+3 < x
f. (4, 14)
g. (–1, –13)
h. (–1, –4)
j. (–2, 9)
9
Name: ________________________
ID: A
Short Answer
Graph the inequality.
25.
(3 points)
4x − 3y > 12
Graph each equation.
26.
(3 points)
1
y = | 2 x − 2|
10
ID: A
Chapter 6 Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
H
A
F
D
H
D
F
D
G
D
H
D
F
A
G
B
G
C
J
C
H
D
G
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
STA: A1.2.1| A1.2.3
STA:
STA:
STA:
STA:
STA:
STA:
STA:
A1.2.1|
A1.2.1|
A1.2.3
A1.2.1|
A1.2.1|
A1.2.1|
A1.2.1|
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
STA: L1.2.2| A1.2.4
STA: L1.2.2| A1.2.4
STA: L1.2.2| A1.2.4
STA: A2.1.2| A2.2.2| A2.3.3
1
ID: A
SHORT ANSWER
25. ANS:
PTS: 3
26. ANS:
PTS: 3
STA: A2.1.2| A2.2.2| A2.3.3
2
Name: _____________________ Class: ________________ Date: __________ID: A
Chapter 7 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1.
2.
(1 point)
A company ships two different products,
one in smaller packages that weighs 12
pounds and the other in a 20-pound
package. A shipment of nine packages
weighs a total of 124 pounds. What is
the total weight of the smaller packages?
a.
b.
c.
d.
e.
48
60
84
72
37
(1 point)
Sally has 42 coins, all dimes and nickels,
that have a total value of $3.00. How
many nickels does she have?
f.
g.
h.
j.
k.
lb
lb
lb
lb
lb
18
22
20
26
24
What is the solution of the system? Use substitution.
3.
4.
(1 point)
a.
b.
c.
d.
(1 point)
1
3y = – x + 2
2
y = –x + 9
y = 5x + 10
y = 4x
(10, 40)
(–10, –40)
(40, 10)
(1.1, 4.4)
f.
g.
h.
j.
1
(10, –1)
(3, 6)
(–1, 8)
(20, –4)
Name: ________________________
ID: A
What is the solution of the system? Use a graph.
5.
(1 point)
y = 3x + 3
y=x–1
a.
c.
b.
d.
2
Name: ________________________
6.
ID: A
(1 point)
2x + 5y = −4
4x + 2y = 8
f.
h.
g.
j.
What is the solution of the system? Use elimination.
7.
8.
(1 point)
(1 point)
2x – 2y = –8
x + 2y = –1
5x + 8y = –29
7x – 2y = –67
a.
b.
c.
d.
f.
(1, 5)
(–3, 1)
(–14, 1)
(0, 4)
3
g.
(–7, 9)
ÊÁ
ˆ
ÁÁ −10, 21 ˜˜˜
ÁÁ
˜
8 ˜˜¯
ÁË
h.
j.
(–1, –3)
(–9, 2)
Name: ________________________
9.
ID: A
(1 point)
6x – 6y = 42
10x – 4y = 52
a.
b.
c.
d.
(4, –3)
(–3, 4)
(10, 6)
(7, 0)
Solve each problem below using the method you determine to be appropriate.
10.
12.
(2 points)
Tom has a collection of 21 CDs and Nita
has a collection of 14 CDs. Tom is adding
3 CDs a month to his collection while
Nita is adding 4 CDs a month to her
collection. Find the number of months
after which they will have the same
number of CDs.
f.
g.
h.
j.
11.
The length of a rectangle is 3
centimeters more than 3 times the
width. If the perimeter of the rectangle is
46 centimeters, find the dimensions of
the rectangle.
f.
g.
h.
j.
1 month
7 months
2 months
42 months
13.
length
length
length
length
=
=
=
=
5 cm; width = 18
13 cm; width = 5
18 cm; width = 5
13 cm; width = 8
cm
cm
cm
cm
(2 points)
A corner store sells two kinds of baked
goods: cakes and pies. A cake costs $10
and a pie costs $14. In one day, the
store sold 8 baked goods for a total of
$92. How many cakes did they sell?
(2 points)
Kendra owns a restaurant. She charges
$3.00 for 2 eggs and one piece of toast,
and $1.80 for one egg and one piece of
toast. How much does Kendra charge for
an egg? A piece of toast?
a.
b.
c.
d.
(2 points)
a.
b.
c.
d.
$1.20 per egg; $.60 for toast
$.60 per egg; $.60 for toast
$.60 per egg; $1.20 for toast
$1.20 per egg; $1.20 for toast
4
5
2
3
8
cakes
cakes
cakes
cakes
Name: ________________________
14.
ID: A
(2 points)
The school cafeteria sells two kinds of
wraps: vegetarian and chicken. The
vegetarian wrap costs $1.00 and the
chicken wrap costs $1.10. Today they
made $104.80 from the 100 wraps sold.
How many of the wraps sold were
vegetarian?
f.
g.
h.
j.
43
36
52
48
wraps
wraps
wraps
wraps
Short Answer
15.
(4 points)
A chemist has HCl in 5% and 15% solutions in the stock room. He needs 200 mL of a 7%
HCl solution for a lab experiment? How much of each solution will he need to mix to obtain
200 mL of a 7% acid solution?
(a) Write a system of equations to represent this problem.
(b) How much of each solution is required?
16.
(4 points)
Sharon has some one-dollar bills and some five-dollar bills. She has 14 bills. The value of
the bills is $30. Write and solve a system of equations using elimination to find how many
of each kind of bill she has.
5
ID: A
Chapter 7 Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
K
B
F
A
G
B
J
A
G
A
H
A
H
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
A1.2.3
SHORT ANSWER
15. ANS:
(a)
x + y = 200
0.05x + 0.15y = 14
(b) 40 mL of the 15% and 160 mL of the 5%
STA: A1.2.3
16. ANS:
4 five-dollar bills, 10 one-dollar bills
STA: A1.2.3
1
Name: ________________________ Class: ___________ Date: _________ ID: A
Quiz 3/22
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is the simplified form of each expression?
1) (1 point)
4
(8g )
a.
3
8g
12
7
b.
512g
b.
625t
12
16c
b.
64
c.
8g
d.
512g
c.
20t
12
8c
d.
625t
2c
9c
8
k
c.
−6k
10
2c
d.
9k
3c
b.
12
c.
1
64
d.
–64
b.
5
16
c.
15
d.
125
b.
–1.4
c.
1
d.
–1
12
2) (1 point)
ÊÁ 4 ˆ˜ 4
ÁÁ 5t ˜˜
ÁÁ
˜
ÁÁ 3 ˜˜˜
ÁË 2c ˜¯
a.
10t
16
c
12
16
16
16
3) (1 point)
ÊÁ 4 ˆ˜ −2
ÁÁ k ˜˜
ÁÁ
˜˜
ÁÁÁ 3c 5 ˜˜˜
Ë
¯
a.
8
3k c
10
10
8
8
4) (1 point)
(−4)
a.
−3
−
1
64
5) (1 point)
8
5 ⋅5
a.
5
2
10
10
6) (1 point)
(−1.4 )
a.
0
0
1
10
Name: ________________________
ID: A
7) (1 point)
3
j ⋅ 5j
a.
4
5j
7
b.
5j
b.
t
12
c.
6j
c.
t
7
d.
6j
d.
1
9
t
12
8) (1 point)
15
t
6
t
a.
t
21
9) (1 point)
ÊÁ 7 8 ˆ˜ 0 3 −2
ÁÁ x y ˜˜ x y
Ë
¯
−1
x y
a.
x
2
4
90
9
=?
b.
x
4
y
4
c.
x
6
d.
3
x y
x
e.
5
y
10) (1 point)
y
−8
y
10
a.
y
2
18
b.
y
b.
7g
b.
9x y
c.
1
18
y
d.
1
2
y
c.
−
7
g
d.
g
c.
9x y
d.
3x y
11) (1 point)
1
−7
g
a.
−g
7
7
12) (1 point)
3
2
(3xy ) (xy)
a.
3
2x y
12
6
8
9
8
2
12
8
12
ID: A
Quiz 3/22
Answer Section
MULTIPLE CHOICE
1) ANS:
2) ANS:
3) ANS:
4) ANS:
5) ANS:
6) ANS:
7) ANS:
8) ANS:
9) ANS:
10) ANS:
11) ANS:
12) ANS:
D
B
B
A
A
C
A
C
B
C
D
C
STA:
STA:
STA:
STA:
STA:
STA:
STA:
STA:
L1.1.4|
L1.1.4|
L1.1.4|
L1.1.4|
L1.1.4|
L1.1.4|
L1.1.4|
L1.1.4|
L2.1.2|
L2.1.2|
L2.1.2|
L2.1.2|
L2.1.2|
L2.1.2|
L2.1.2|
L2.1.2|
A1.1.2
A1.1.2
A1.1.2
A1.1.2
A1.1.2
A1.1.2
A1.1.2
A1.1.2
STA: L1.1.4| L2.1.2| A1.1.2
STA: L1.1.4| L2.1.2| A1.1.2
STA: L1.1.4| L2.1.2| A1.1.2
1
Name: ________________________ Class: _____________ Date: __________ID: B
Quiz 3/30
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is each number written in standard notation?
____
1. (1 point)
−3
1.13 × 10
a. 0.0113
b. 0.000113
c. 0.00113
d. –33.9
What is each number written in scientific notation?
____
2. (1 point)
856,000,000
a.
0.856 × 10
9
b.
c.
85.6 × 100
8.56 × 10
8
8.56 × 10
7
d.
____
3. (1 point)
0.000407
−5
b.
c.
40.7 × 100
−3
0.407 × 10
4.07 × 10
d.
4.07 × 10
a.
−4
Is the number written in scientific notation? If not, explain.
____
4. (1 point)
−6
6.8 × 1000
a. No; it is not written as a number times a power of 10.
b. No; the first factor is not a number between 1 and 10.
c. Yes; the number is written in scientific notation.
____
5. (1 point)
−1 0
5.8 × 10
a. No; it is not written as a number times a power of 10.
b. No; the first factor is not a number between 1 and 10.
c. Yes; the number is written in scientific notation.
1
Name: ________________________
ID: B
Find the simplified form of the expression. Give your answer in scientific
notation.
____
6. (1 point)
ÊÁ
6ˆ
3ˆ
˜ ÊÁ
˜
ÁÁ 3 × 10 ˜˜ ÁÁ 8 × 10 ˜˜
Ë
¯Ë
¯
c.
d.
1.1 × 10
b.
____
19
1.1 × 10
19
2.4 × 10
10
2.4 × 10
a.
10
7. (1 point)
Astronomers measure large distances in light-years. One light-year is the distance that
light can travel in one year, or approximately 5.88 × 10
12
miles. Suppose a star is
1
3.4 × 10 light-years from Earth. In scientific notation, approximately how many miles
is it?
14
a. 2.0 × 10 miles
12
b. 3.4 × 10 miles
c.
d.
____
13
5.88 × 10 miles
12
5.88 × 10 miles
8. (1 point)
Suppose a population of 80 crickets doubles in size every month. The function
x
f(x) = 80 ⋅ 2 gives the population after x months. How many crickets will there be after
2 years?
a. 320 crickets
b. 320 crickets
c. 1,342,177,280 crickets
d. 3,840 crickets
2
ID: B
Quiz 3/30
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
D
D
A
C
C
A
C
STA:
STA:
STA:
STA:
STA:
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L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
L1.1.4| L2.1.2| A1.1.2
A3.4.1| A2.1.7| A2.3.1| A2.3.3| A3.2.1
1
Name: ________________________ Class: _____________ Date: __________ID: A
Chapter 9 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the sum.
1.
(1 point)
(8u3 + 2u2 + 7) + (3u3 – 7u + 8)
a.
b.
c.
d.
5u3 – 7u2 + 2u – 15
5u3 + 2u2 – 7u + 15
15 – 7u + 2u2 + 11 u3
11u3 + 2u2 – 7u + 15
Simplify the difference.
2.
3.
(1 point)
(–7x –
f.
g.
h.
j.
5x4
+ 5) –
(–7x4
(1 point)
(2w2 – 4w – 8) – (5w2 + 3w – 2)
– 5 – 9x)
2x4 + 2x + 8
–14x4 + 10x + 10
–14x4 – 10x + 10
2x4 + 2x + 10
a.
b.
c.
d.
–3w2 – w – 10
7w2 + 7w + 6
7w2 – w – 10
–3w2 – 7w – 6
Simplify the product using the Distributive Property.
4.
5.
(1 point)
2n(n2 + 3n + 4)
f.
g.
h.
j.
(1 point)
(2n2 + 5n + 4)(2n – 4)
2n3 + 3n + 4
2n3 + 6n2 + 8n
2n3 + 6n + 8
n2 + 5n + 4
a.
b.
c.
d.
1
4n3
4n3
4n3
4n3
– 2n2 + 28n – 16
+ 18n2 – 28n – 16
+ 2n2 – 12n – 16
+ 12n2 – 2n – 16
Name: ________________________
ID: A
Simplify the product using FOIL.
6.
8.
(1 point)
(5h − 3)(3h + 7)
(3x – 7)(3x – 5)
f.
g.
h.
j.
7.
9x2
9x2
9x2
9x2
(1 point)
– 36x + 35
– 36x – 35
+ 6x + 35
+ 36x + 35
2
h.
15h + 26h − 21
2
15h − 44h + 21
2
15h + 44h + 21
j.
15h − 26h − 21
f.
g.
2
(1 point)
(4x − 4)(3x − 4)
a.
b.
c.
d.
2
12x + 4x − 16
2
12x + 28x + 16
2
12x − 28x + 16
2
12x − 4x − 16
What is the factored form of the following expressions?
9.
d2
a.
b.
c.
d.
10.
12.
(1 point)
+ 12d + 32
(d
(d
(d
(d
2
d − 16d + 64
– 8)(d – 4)
+ 8)(d – 4)
+ 8)(d + 4)
– 8)(d + 4)
(1 point)
d2 – 14d + 40
f.
g.
h.
j.
11.
(d
(d
(d
(d
13.
(d − 8)
(d − 64)(d − 1)
h.
j.
(d + 8)
(d − 8)(d + 8)
2
(1 point)
2
d2 + 4d – 21
(d
(d
(d
(d
2
f.
g.
d − 26d + 169
+ 4)(d – 10)
– 4)(d + 10)
+ 4)(d + 10)
– 4)(d – 10)
(1 point)
a.
b.
c.
d.
(1 point)
– 3)(d – 7)
+ 3)(d + 7)
– 3)(d + 7)
+ 3)(d – 7)
2
2
a.
b.
(d + 13)
(d − 13)(d + 13)
c.
d.
(d − 13)
(d − 169)(d − 1)
2
Name: ________________________
14.
15.
17.
(1 point)
(1 point)
6x2
+ 13x + 6
x2 – 10xy + 24y2
f.
g.
h.
j.
(2x
(2x
(2x
(2x
a.
b.
c.
d.
– 3)(3x – 2)
– 3)(3x + 2)
+ 3)(3x + 2)
+ 3)(3x – 2)
18.
(1 point)
12g2
a.
b.
c.
d.
16.
ID: A
– 2)(4g – 3)
+ 2)(4g + 3)
– 2)(4g + 3)
+ 2)(4g – 3)
x2 + 3xy – 4y2
(x
(x
(x
(x
(1 point)
f.
g.
h.
j.
(1 point)
f.
g.
h.
j.
– 6y)(x – 4y)
+ 2y)(x – 12y)
+ 6y)(x + 4y)
– 2y)(x + 12y)
The area of a rectangular barnyard is
given by the trinomial 2x2 + 10x – 72.
What are the possible dimensions of the
barnyard? Use factoring.
+g–6
(3g
(3g
(3g
(3g
(x
(x
(x
(x
x – and 2x – 8
x + 9 and 2x – 8
– x + 9 and –2x + 8
x – 9 and 2x + 8
– 4y)(x – y)
– 4y)(x + y)
+ 4y)(x + y)
+ 4y)(x – y)
What is a simpler form of each product?
19.
20.
(1 point)
(2x –
a.
b.
c.
d.
6)2
4x2
4x2
4x2
4x2
(1 point)
The area of a rectangular garden is given
by the trinomial x2 + 2x – 63. What are
the possible dimensions of the rectangle?
Use factoring.
– 8x + 36
+ 36
– 24x + 36
– 12x + 36
f.
g.
h.
j.
3
x
x
x
x
+ 7 and x – 9
– 7 and x – 9
+ 7 and x + 9
– 7 and x + 9
Name: ________________________
21.
ID: A
(1 point)
A square painting is surrounded by a frame. The outside edges of the frame are x inches
in length and there is a 3-inch border between the painting and the frame. What is the
total area of the border?
a.
b.
c.
d.
–6x + 9
–12x – 36
12x – 36
x2 + 12x + 36
What is the factored form of the expression?
22.
23.
24.
(1 point)
(1 point)
9b2
– 100
32x − 50
f.
g.
h.
j.
(3b + 10)(3b – 10)
(3b + 10)(3b + 10)
(3b – 10)(3b – 10)
(10b + 3)(10b – 3)
f.
2 (4x + 5) (4x − 5)
g.
2 (4x + 5 )
h.
j.
2 (4x − 5 )
2 (5x + 4) (5x − 4)
2
(1 point)
s2 – 49
a.
b.
c.
d.
(s
(s
(s
(s
– 7)(s + 9)
– 7)(s + 7)
+ 7)(s + 7)
– 7)(s – 7)
4
2
2
Name: ________________________
ID: A
What are the solutions of the equation?
25.
(1 point)
(x − 9)(x + 7) = 0
a.
b.
c.
d.
26.
–9, −7
–1,1
9, 7
9,−7
(1 point)
2
z − 6z − 27 = 0
f.
g.
h.
j.
27.
3, –9
–3, –9
–3, 9
3, 9
(1 point)
2
3z + 3z − 6 = 0
a.
b.
c.
d.
1, 2
3, –2
1 , –2
3, 2
5
ID: A
Chapter 9 Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
ANS:
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ANS:
ANS:
ANS:
D
J
D
G
C
F
C
F
C
J
C
F
C
H
C
J
A
G
C
J
C
F
B
F
D
H
C
STA: A1.1.3
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A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
A1.1.3
STA: A1.1.3
STA:
STA:
STA:
STA:
STA:
STA:
A1.1.3
A1.1.3
A1.1.3
A3.3.5
A3.3.5
A3.3.5
1
Name: ________________________ Class: _____________ Date: __________ID: A
Chapter 10 Test
Matching
Match each graph with the the name of the correct conic section.
a. Parabola
c. Ellipse
b. Circle
d. Hyperbola
1.
(1 point)
3.
(1 point)
2.
(1 point)
4.
(1 point)
1
Name: ________________________
ID: A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Order the group of quadratic
functions from widest to narrowest
graph.
5.
(1 point)
2
2
y = 5x , y = x , y = 2x
2
2
2
2
2
2
2
a.
y = x , y = 2x , y = 5x
b.
y = x , y = 5x , y = 2x
c.
y = 5x , y = 2x , y = x
d.
y = 2x , y = x , y = 5x
2
2
2
2
2
2
What are the coordinates of the vertex of the graph? Is it a maximum or
minimum?
6.
(1 point)
a.
b.
(1, 2); maximum
(2, 1); maximum
c.
d.
(2, 1); minimum
(1, 2); minimum
2
Name: ________________________
7.
(1 point)
a.
b.
8.
ID: A
(–3, 2); maximum
(2, –3); maximum
c.
d.
(–3, 2); minimum
(2, –3); minimum
(1 point)
How is the graph of y = 3x2 + 3 different from the graph of y = 3x2?
a. It is shifted 3 unit(s) up.
c. It is shifted 3 unit(s) left.
b. It is shifted 3 unit(s) down.
d. It is shifted 3 unit(s) right.
3
Name: ________________________
ID: A
Graph the function. Identify the vertex and axis of symmetry.
9.
(1 point)
2
f(x) = x + 4x + 1
a.
c.
axis of symmetry: x = 2
vertex: (2, –3)
b.
axis of symmetry: x = −2
vertex: (–2, –3)
d.
axis of symmetry: x = −2
vertex: (–2, 3)
axis of symmetry: x = 2
vertex: (2, 3)
4
Name: ________________________
10.
ID: A
(1 point)
2
What are the solutions of the equation x − 9 = 0 ? Use a graph of the related function.
a.
c.
There are two solutions: –3 and
3.
b.
There are two solutions: –3 and
3.
d.
There are two solutions: ±
3.
There are no real number
solutions.
5
Name: ________________________
ID: A
Solve the equation using square roots.
11.
12.
(1 point)
2
(1 point)
2
x − 81 = 0
a. − 9 , 9
b. –81, 81
c. –9, 9
d. no real number solutions
3x − 147 = 0
a. –49, 49
b. − 7 , 7
c. –7, 7
d. no real number solutions
Solve the equation using the Zero-Product Property.
13.
(1 point)
(x − 9)(x + 7) = 0
a. 9, 7
b. –9, −7
c.
d.
–1,1
9,−7
What are the solutions of the equation?
14.
16.
(1 point)
2
2
z − 6z − 27 = 0
a. 3, 9
b. 3, –9
c. –3, 9
d. –3, –9
15.
x + 3x = 18
a. 3, –6
b. –3, 6
c. 4.42, –4.42
d. 18.75, –21.75
17.
(1 point)
3z
a.
b.
c.
d.
2
(1 point)
(1 point)
What is the value of c such that
+ 3z − 6 = 0
1 , –2
1, 2
3, –2
3, 2
2
x − 8x + c is a perfect-square trinomial?
a. 32
b. −4
c. 16
d. 64
6
Name: ________________________
18.
ID: A
(1 point)
What is the value of c such that
2
x + 20x + c is a perfect-square trinomial?
a. 10
b. 400
c. 100
d. 200
Solve the equation by completing the square. Round to the nearest hundredth if
necessary.
19.
20.
(1 point)
2
(1 point)
2
x − 6x = −8
a. 2, 4
b. –2, –4
c. –2, 4
d. 2, –4
x + 8x + 15 = 0
a. –5, –3
b. 5, 3
c. 5, –3
d. –5, 3
Use the quadratic formula to solve the equation. If necessary, round to the
nearest hundredth.
21.
22.
(1 point)
2
(1 point)
2
x + 3 = −4x
a. 1, 3
b. –1, –3
c. 1, –3
d. 1, –3
x − 8 = 2x
a. 2, 4
b. 2, 4
c. –2, 4
d. 2, –4
7
Name: ________________________
23.
ID: A
25.
(1 point)
What is the equation of the parabola that
Solve the equation. Check your solution.
2
2
moves the parent graph y = x to the
right 1 unit?
x + 17x + 72 = 0
a. –8, –9
b. –5, –6
c. –6, –7
d. –4, –5
2
a.
y = x −1
b.
y = (x + 1)
2
c.
y = (x − 1)
2
d.
y = x +1
(1 point)
2
26.
(1 point)
2
24.
Solve x − 2x − 8 = 0 by completing the
square.
a. 0, 6
b. 1, 5
c. –1, 7
d. –2, 4
(1 point)
What is the equation of the parabola that
2
moves the parent graph y = x to the left
9 units?
2
a.
y = x +9
b.
y = (x + 9)
2
c.
y = (x − 9)
2
d.
y = x −9
27.
2
(1 point)
Use the Quadratic Formula to solve the
2
equation. 4x + 5x − 6 = 0
4
a. − , 2
3
4
b. − , –2
3
c. 2, –2
3
d. –2,
4
8
Name: ________________________
ID: A
Short Answer
Complete problems 28 and 29 on the lines provided on your bubble sheet. Use the first column
of lines for number 28 and the second column of lines for number 29. Remember to show any
required work for your solution on the lines on your bubble sheet.
28.
(4 points)
For the quadratic function below, describe how the graph changes from the parent graph of
2
y = x . Then name the vertex of the graph.
2
y = ( x − 2) + 5
29.
(4 points)
Use the Quadratic Formula to solve the equation. Show all of your work, and write your
answer in simplest radical form.
2
2x − 7x − 6 = 0
9
ID: A
Chapter 10 Test
Answer Section
MATCHING
1.
2.
3.
4.
ANS:
ANS:
ANS:
ANS:
B
D
A
C
MULTIPLE CHOICE
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
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ANS:
ANS:
ANS:
A
A
D
A
C
C
C
C
D
C
A
A
C
C
A
A
B
C
C
B
A
D
D
STA:
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A3.3.1|
A3.3.1|
A3.3.1|
A3.3.1|
A3.5.1|
A3.3.4
A3.3.4
A3.3.4
A3.3.5
A3.3.5
A3.3.5
A3.3.5
A3.3.3
A3.3.3
A3.3.3
A3.3.3
STA:
STA:
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MI
MI
MI
MI
MI
A3.3.2
A3.3.2
A3.3.2
A3.3.2
A2.1.7| A2.3.1| A2.3.3| A3.3.1
II.2.3 | MI II.2.1
II.2.3 | MI II.2.1
V.2.3 | MI V.2
V.2.3 | MI V.2
V.2.3 | MI V.2
1
ID: A
SHORT ANSWER
28. ANS:
shifts right 2 units, up 5 units; ÁÊË 2, 5 ˜ˆ¯
2
Given a quadratic equation written in the form y = ( x + b) + c, if c is greater than 0 the
parent graph shifts upward and if c is less than 0 the parent graph shifts downward. A
positive b value shifts the parent graph to the left and a negative b value shifts the graph
to the right.
The x-coordinate of the vertex is the value that will result in zero inside the parentheses.
The y-coordinate of the vertex is c.
STA: MI II.2.3 | MI II.2.1
29. ANS:
7±
97
4
2
Solve the equation ax + bx + c = 0 using the Quadratic Formula, x =
STA: MI V.2.3 | MI V.2
2
−b ±
2
b − 4ac
, a ≠ 0.
2a