Download Algebra 2 - Chapter 8 Review

Name: ________________________ Class: ___________________ Date: __________
ID: A
Algebra 2 - Chapter 8 Review
Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If
it is a direct or inverse variation, write a function to model it.
____
1.
a.
b.
c.
x
–9
–7
–2
–1
y
36
28
8
4
324
x
direct variation; y  4x
neither
inverse variation; y 
____
2. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse
variation.
2
80
a. y 
c. y 
x
x
18
b. y 
d. y = 0.8x
x
____
3. Suppose that x and y vary inversely and that y 
variation and find y when x = 4.
1 1
a. y 
;
3x 24
8 16
b. y 
;
3x 3
c.
d.
8
when x = 8. Write a function that models the inverse
3
8
;
3x
64
y 
;
3x
y 
8
3
16
3
____
4. Suppose that y varies jointly with w and x and inversely with z and y = 175 when w = 5, x = 20 and z = 4. Write
the equation that models the relationship. Then find y when w = 2, x = 24 and z = 6.
4wx
7z 7
a. y 
; 32
c. y 
;
z
wx 8
4z
7wx
b. y 
;2
d. y 
; 56
wx
z
____
5. The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of
the speed. The ship uses 34 barrels of oil in traveling 60 miles at 20 mi/h. How many barrels of oil are used
when the ship travels 32 miles at 23 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.
a. 3.0 barrels
c. 18.1 barrels
b. 45.0 barrels
d. 24.0 barrels
1
Name: ________________________
ID: A
Graph the function.
____
6. y 
4
x
a.
c.
b.
d.
2
Name: ________________________
ID: A
Sketch the asymptotes and graph the function.
____
____
7. y 
5
1
x1
a.
c.
b.
d.
8. Write an equation for the translation of y 
a.
b.
4
7
x6
4
y 
6
x7
y 
4
that has the asymptotes x = 7 and y = 6.
x
4
c. y 
6
x7
4
d. y 
7
x6
3
Name: ________________________
____
9. This graph of a function is a translation of y 
a.
b.
4
4
x3
4
y
4
x3
y
ID: A
4
. What is an equation for the function?
x
c.
d.
4
3
x4
4
y
3
x4
y
Find any points of discontinuity for the rational function.
____ 10. y 
a.
b.
(x  3)(x  5)(x  7)
(x  1)(x  4)
x = 1, x = 4
x = –1, x = –4
c.
d.
x = 3, x = –5, x = 7
x = –3, x = 5, x = –7
____ 11. What are the points of discontinuity? Are they all removable?
y 
a.
b.
(x  7)(x  3)
x 2  10x  21
x = 1, x = –8, x = –2; yes
x = 7, x = 3; yes
c.
d.
x = –7, x = –3; no
x = –1, x = 8, x = 2; no
____ 12. Describe the vertical asymptote(s) and hole(s) for the graph of y 
a.
b.
c.
d.
asymptotes: x = –4, –2 and hole: x = 1
asymptote: x = 1 and no holes
asymptote: x = 1 and holes: x = –4, –2
asymptotes: x = –4, –2 and no holes
4
x1
.
x 2  6x  8
Name: ________________________
ID: A
2x 3  3x  2
.
2x 3  6x  2
c. no horizontal asymptote
d. y = 0
____ 13. Find the horizontal asymptote of the graph of y 
a.
b.
y=1
y = 1
What is the graph of the rational function?
____ 14. y 
2x  4
x1
a.
c.
b.
d.
Simplify the rational expression. State any restrictions on the variable.
____ 15.
t 2  4t  32
t8
a. t  4; t  8
b. t  4; t  8
c.
d.
5
t  4; t  8
t  4; t  8
Name: ________________________
____ 16.
n 4  10n 2  24
n 4  9n 2  18
n2  4
a.
;n  
n2  3
b.
6, n  
ID: A
3
n2  4
; n  6, n  3
n2  3
c.
d.
n2  4
; n  6, n  3
n2  3
(n 2  4)
n2  3
;n  
6, n  
What is the product in simplest form? State any restrictions on the variable.
____ 17.
____ 18.
3g 5
10h 2

h5
10g 2
a.
3g 3 h 3
, g  0, h  0
100
c.
b.
100
, g  0, h  0
3g 3 h 3
d.
3g 7
, g  0, h  0
100h 7
3 7 7
g h , g  0, h  0
100
y2
y2  y  6

y3
y 2  1y
a.
y 2  2y
, y  3,  1
y1
c.
y2
, y  3, 0,  1
y1
b.
y 2  2y
, y  3, 0,  1
y1
d.
y2
, y  3,  1
y1
What is the quotient in simplified form? State any restrictions on the variable.
____ 19.
a2
a1

a  5 a 2  8a  15
(a  2)(a  3)
, a  5,  1, 3
a.
a1
(a  2)(a  1)
, a  5, 3,  1
b.
(a  5) 2 (a  3)
c.
d.
(a  2)(a  3)
, a  3,  1
a1
(a  2)(a  1)
, a  5, 3
(a  5) 2 (a  3)
____ 20. Find the least common multiple of x 2  7x  6 and x 2  3x  4 .
a. (x  6)(x  1)(x  4)
c. (x  6)(x  4)(x  1)
b. (x  1)(x  4)(x  6)
d. (x  6)(x  1)(x  4)
6
3
Name: ________________________
ID: A
Simplify the sum.
____ 21.
____ 22.
4
5

m  9 m2  81
9
a.
(m  9)(m  9)
4m  31
b.
(m  9)(m  9)
c.
d 2  d  30
d 2  14d  48
 2
2
d  3d  40
d  2d  48
2
2d  15d  18
a.
2d 2  d  88
d 2  14d  16
b.
(d  8)(d  8)
c.
2d 2  14d  16
(d  8)(d  8)
d.
2d 2  15d  18
(d  8)(d  8)
c.
n  13
d.
n 2  10n  15
n 2  13n  42
d.
9
m  m  72
4m  41
(m  9)(m  9)
2
Simplify the difference.
____ 23.
n 2  10n  24
9

n 2  13n  42 n  7
n  13
a.
n7
b.
____ 24.
n4
n7
z 2  11z  30 z 2  2z  24
 2
z 2  z  20
z  9z  18
a.
z  34
(z  4)(z  3)
c.
2z 2  2
(z  4)(z  3)
b.
17z  2
(z  4)(z  3)
d.
2z 2  8z  34
2z 2  34
c.
4x
3x  10x  3
d.
not here
Simplify the complex fraction.
4
x3
____ 25.
1
3
x
12x  4
a.
x 2  3x
4x
b.
3x  9
7
2
Name: ________________________
ID: A
y1
2
____ 26.
y y6
y6
y3
(y  1)(y  6)
a.
2
(y  3) (y  2)
y1
(y  6)(y  2)
b.
c.
(y  1)(y  6)
(y  3)(y  2)
d.
(y  1)(y  2)
(y  6)(y  2)
c.

c.
c.
Solve the equation. Check the solution.
____ 27.
____ 28.
____ 29.
4
1

x1
x5
19
a. 
4
b.
1
3
a
2
1


a

6
a
6
a  36
a. –9
b. –6
19
3
d.
2
–9 and –6
d.
6
1  73
2
d.
3 or –4
2
6
1

 1
x

3
x 9
2
a.
4
b.
2
____ 30. 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, Kaitlin can paint a certain room in 3 hours. Brianna
can paint the same room in 7 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.
3 7
3 7
a.

 1; 10 hours
c.

 1; 5 hours
x
x
x
x
x
x
x
x
b.

 1; 5 hours
d.

 1; 2.1 hours
7 3
3 7
8
ID: A
Algebra 2 - Chapter 8 Review
Answer Section
1. ANS: B
PTS: 1
DIF: L2
REF: 8-1 Inverse Variation
OBJ: 8-1.1 To recognize and use inverse variation NAT:
CC A.CED.2| CC A.CED.4
TOP: 8-1 Problem 1 Identifying Direct and Inverse Variations
KEY: inverse variation
2. ANS: C
PTS: 1
DIF: L2
REF: 8-1 Inverse Variation
OBJ: 8-1.1 To recognize and use inverse variation NAT:
CC A.CED.2| CC A.CED.4
TOP: 8-1 Problem 2 Determining an Inverse Variation
KEY: inverse variation
3. ANS: D
PTS: 1
DIF: L3
REF: 8-1 Inverse Variation
OBJ: 8-1.1 To recognize and use inverse variation NAT:
CC A.CED.2| CC A.CED.4
TOP: 8-1 Problem 2 Determining an Inverse Variation
KEY: inverse variation
4. ANS: D
PTS: 1
DIF: L4
REF: 8-1 Inverse Variation
OBJ: 8-1.2 To use joint and other variations
NAT: CC A.CED.2| CC A.CED.4
TOP: 8-1 Problem 4 Using Combined Variation
KEY: inverse variation | combined variation | joint variation
5. ANS: D
PTS: 1
DIF: L4
REF: 8-1 Inverse Variation
OBJ: 8-1.2 To use joint and other variations
NAT: CC A.CED.2| CC A.CED.4
TOP: 8-1 Problem 5 Applying Combined Variation
KEY: combined variation | joint variation
6. ANS: C
PTS: 1
DIF: L2
REF: 8-2 The Reciprocal Function Family
OBJ: 8-2.1 To graph reciprocal functions
NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
TOP: 8-2 Problem 1 Graphing an Inverse Variation Function
KEY: reciprocal function
7. ANS: C
PTS: 1
DIF: L3
REF: 8-2 The Reciprocal Function Family
OBJ: 8-2.2 To graph translations of reciprocal functions
NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
TOP: 8-2 Problem 3 Graphing a Translation
KEY: reciprocal function
8. ANS: C
PTS: 1
DIF: L2
REF: 8-2 The Reciprocal Function Family
OBJ: 8-2.2 To graph translations of reciprocal functions
NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function
9. ANS: D
PTS: 1
DIF: L3
REF: 8-2 The Reciprocal Function Family
OBJ: 8-2.2 To graph translations of reciprocal functions
NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c
TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function
10. ANS: B
PTS: 1
DIF: L2
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 1 Finding Points of Discontinuity
KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of
discontinuity
1
ID: A
11. ANS: B
PTS: 1
DIF: L2
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 1 Finding Points of Discontinuity
KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of
discontinuity
12. ANS: D
PTS: 1
DIF: L2
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 2 Finding Vertical Asymptotes
KEY: rational function
13. ANS: B
PTS: 1
DIF: L3
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.1 To identify properties of rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 3 Finding Horizontal Asymptotes
KEY: rational function
14. ANS: B
PTS: 1
DIF: L2
REF: 8-3 Rational Functions and Their Graphs
OBJ: 8-3.2 To graph rational functions
NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h
TOP: 8-3 Problem 4 Graphing Rational Functions
KEY: rational function
15. ANS: B
PTS: 1
DIF: L2
REF: 8-4 Rational Expressions
OBJ: 8-4.1 To simplify rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 1 Simplifying a Rational Expression
KEY: rational expression | simplest form
16. ANS: A
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.1 To simplify rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 1 Simplifying a Rational Expression
KEY: rational expression | simplest form
17. ANS: A
PTS: 1
DIF: L2
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 2 Multiplying Rational Expressions
KEY: rational expression | simplest form
18. ANS: B
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 2 Multiplying Rational Expressions
KEY: rational expression | simplest form
19. ANS: A
PTS: 1
DIF: L3
REF: 8-4 Rational Expressions
OBJ: 8-4.2 To multiply and divide rational expressions
NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e
TOP: 8-4 Problem 3 Dividing Rational Expressions
KEY: rational expression | simplest form
20. ANS: A
PTS: 1
DIF: L2
REF: 8-5 Adding and Subtracting Rational Expressions
OBJ: 8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
TOP: 8-5 Problem 1 Finding the Least Common Multiple
2
ID: A
21. ANS:
REF:
OBJ:
TOP:
22. ANS:
REF:
OBJ:
TOP:
23. ANS:
REF:
OBJ:
TOP:
24. ANS:
REF:
OBJ:
TOP:
25. ANS:
REF:
OBJ:
TOP:
26. ANS:
REF:
OBJ:
TOP:
27. ANS:
OBJ:
NAT:
TOP:
28. ANS:
OBJ:
NAT:
TOP:
29. ANS:
OBJ:
NAT:
TOP:
30. ANS:
OBJ:
NAT:
TOP:
B
PTS: 1
DIF: L2
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 2 Adding Rational Expressions
C
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 2 Adding Rational Expressions
A
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 3 Subtracting Rational Expressions
B
PTS: 1
DIF: L4
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 3 Subtracting Rational Expressions
C
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 4 Simplifying a Complex Fraction
KEY: complex fraction
B
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
NAT: CC A.APR.7| N.5.e| A.3.c| A.3.e
8-5 Problem 4 Simplifying a Complex Fraction
KEY: complex fraction
C
PTS: 1
DIF: L2
REF: 8-6 Solving Rational Equations
8-6.1 To solve rational equations
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 1 Solving a Rational Equation
KEY: rational equation
A
PTS: 1
DIF: L4
REF: 8-6 Solving Rational Equations
8-6.1 To solve rational equations
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 1 Solving a Rational Equation
KEY: rational equation
A
PTS: 1
DIF: L3
REF: 8-6 Solving Rational Equations
8-6.1 To solve rational equations
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 1 Solving a Rational Equation
KEY: rational equation
D
PTS: 1
DIF: L3
REF: 8-6 Solving Rational Equations
8-6.2 To use rational equations to solve problems
CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11
8-6 Problem 2 Using Rational Equations
KEY: rational equation
3