"

72 Ch. 7 Practice Test – College Algebra 2e | OpenStax

  1. Review Exercises
  2. Practice Test
3

Functions
  1. Introduction to Functions
  2. 3.1 Functions and Function Notation
  3. 3.2 Domain and Range
  4. 3.3 Rates of Change and Behavior of Graphs
  5. 3.4 Composition of Functions
  6. 3.5 Transformation of Functions
  7. 3.6 Absolute Value Functions
  8. 3.7 Inverse Functions
  9. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  10. Exercises
    1. Review Exercises
    2. Practice Test
4

Linear Functions
  1. Introduction to Linear Functions
  2. 4.1 Linear Functions
  3. 4.2 Modeling with Linear Functions
  4. 4.3 Fitting Linear Models to Data
  5. Chapter Review
    1. Key Terms
    2. Key Concepts
  6. Exercises
    1. Review Exercises
    2. Practice Test
5

Polynomial and Rational Functions
  1. Introduction to Polynomial and Rational Functions
  2. 5.1 Quadratic Functions
  3. 5.2 Power Functions and Polynomial Functions
  4. 5.3 Graphs of Polynomial Functions
  5. 5.4 Dividing Polynomials
  6. 5.5 Zeros of Polynomial Functions
  7. 5.6 Rational Functions
  8. 5.7 Inverses and Radical Functions
  9. 5.8 Modeling Using Variation
  10. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  11. Exercises
    1. Review Exercises
    2. Practice Test
6

Exponential and Logarithmic Functions
  1. Introduction to Exponential and Logarithmic Functions
  2. 6.1 Exponential Functions
  3. 6.2 Graphs of Exponential Functions
  4. 6.3 Logarithmic Functions
  5. 6.4 Graphs of Logarithmic Functions
  6. 6.5 Logarithmic Properties
  7. 6.6 Exponential and Logarithmic Equations
  8. 6.7 Exponential and Logarithmic Models
  9. 6.8 Fitting Exponential Models to Data
  10. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  11. Exercises
    1. Review Exercises
    2. Practice Test
7

Systems of Equations and Inequalities
  1. Introduction to Systems of Equations and Inequalities
  2. 7.1 Systems of Linear Equations: Two Variables
  3. 7.2 Systems of Linear Equations: Three Variables
  4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
  5. 7.4 Partial Fractions
  6. 7.5 Matrices and Matrix Operations
  7. 7.6 Solving Systems with Gaussian Elimination
  8. 7.7 Solving Systems with Inverses
  9. 7.8 Solving Systems with Cramer’s Rule
  10. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  11. Exercises
    1. Review Exercises
    2. Practice Test
8

Analytic Geometry
  1. Introduction to Analytic Geometry
  2. 8.1 The Ellipse
  3. 8.2 The Hyperbola
  4. 8.3 The Parabola
  5. 8.4 Rotation of Axes
  6. 8.5 Conic Sections in Polar Coordinates
  7. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  8. Exercises
    1. Review Exercises
    2. Practice Test
9

Sequences, Probability, and Counting Theory
  1. Introduction to Sequences, Probability and Counting Theory
  2. 9.1 Sequences and Their Notations
  3. 9.2 Arithmetic Sequences
  4. 9.3 Geometric Sequences
  5. 9.4 Series and Their Notations
  6. 9.5 Counting Principles
  7. 9.6 Binomial Theorem
  8. 9.7 Probability
  9. Chapter Review
    1. Key Terms
    2. Key Equations
    3. Key Concepts
  10. Exercises
    1. Review Exercises
    2. Practice Test
Answer Key
  1. Chapter 1
  2. Chapter 2
  3. Chapter 3
  4. Chapter 4
  5. Chapter 5
  6. Chapter 6
  7. Chapter 7
  8. Chapter 8
  9. Chapter 9

Index

Practice Test

Is the following ordered pair a solution to the system of equations?

1.

−5x−y=12 x+4y=9

−5x−y=12 x+4y=9

with (−3,3) (−3,3)

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

2.

1 2 x− 1 3 y=4 3 2 x−y=0

1 2 x− 1 3 y=4 3 2 x−y=0

3.

− 1 2 x−4y=4 2x+16y=2

− 1 2 x−4y=4 2x+16y=2

4.

5x−y=1 −10x+2y=−2

5x−y=1 −10x+2y=−2

5.

4x−6y−2z= 1 10

x−7y+5z=− 1 4

3x+6y−9z= 6 5

4x−6y−2z= 1 10

x−7y+5z=− 1 4

3x+6y−9z= 6 5

6.

x+z=20 x+y+z=20 x+2y+z=10

x+z=20 x+y+z=20 x+2y+z=10

7.

5x−4y−3z=0 2x+y+2z=0 x−6y−7z=0

5x−4y−3z=0 2x+y+2z=0 x−6y−7z=0

8.

y= x 2 +2x−3 y=x−1

y= x 2 +2x−3 y=x−1

9.

y 2 + x 2 =25 y 2 −2 x 2 =1

y 2 + x 2 =25 y 2 −2 x 2 =1

For the following exercises, graph the following inequalities.

10.

y< x 2 +9 y< x 2 +9

11.

x 2 + y 2 >4 y< x 2 +1

x 2 + y 2 >4 y< x 2 +1

For the following exercises, write the partial fraction decomposition.

12.

−8x−30 x 2 +10x+25

−8x−30 x 2 +10x+25

13.

13x+2 (3x+1) 2

13x+2 (3x+1) 2

14.

x 4 − x 3 +2x−1 x ( x 2 +1) 2

x 4 − x 3 +2x−1 x ( x 2 +1) 2

For the following exercises, perform the given matrix operations.

15.

5[ 4 9 −2 3

]+ 1 2 [ −6 12 4 −8

] 5[ 4 9 −2 3

]+ 1 2 [ −6 12 4 −8

]

16.

[ 1 4 −7 −2 9 5 12 0 −4

][ 3 −4 1 3 5 10

] [ 1 4 −7 −2 9 5 12 0 −4

][ 3 −4 1 3 5 10

]

17.

[ 1 2

1 3

1 4

1 5

] −1

[ 1 2

1 3

1 4

1 5

] −1

18.

det| 0 0 400 4,000

| det| 0 0 400 4,000

|

19.

det| 1 2

− 1 2

0 − 1 2

0 1 2

0 1 2

0

| det| 1 2

− 1 2

0 − 1 2

0 1 2

0 1 2

0

|

20.

If det(A)=−6, det(A)=−6, what would be the determinant if you switched rows 1 and 3, multiplied the second row by 12, and took the inverse?

21.

Rewrite the system of linear equations as an augmented matrix.

14x−2y+13z=140 −2x+3y−6z=−1 x−5y+12z=11

14x−2y+13z=140 −2x+3y−6z=−1 x−5y+12z=11

22.

Rewrite the augmented matrix as a system of linear equations.

[ 1 0 3 −2 4 9 −6 1 2

| 12 −5 8

] [ 1 0 3 −2 4 9 −6 1 2

| 12 −5 8

]

For the following exercises, use Gaussian elimination to solve the systems of equations.

23.

x−6y=4 2x−12y=0

x−6y=4 2x−12y=0

24.

2x+y+z=−3 x−2y+3z=6 x−y−z=6

2x+y+z=−3 x−2y+3z=6 x−y−z=6

For the following exercises, use the inverse of a matrix to solve the systems of equations.

25.

4x−5y=−50 −x+2y=80

4x−5y=−50 −x+2y=80

26.

1 100 x− 3 100 y+ 1 20 z=−49 3 100 x− 7 100 y− 1 100 z=13 9 100 x− 9 100 y− 9 100 z=99

1 100 x− 3 100 y+ 1 20 z=−49 3 100 x− 7 100 y− 1 100 z=13 9 100 x− 9 100 y− 9 100 z=99

For the following exercises, use Cramer’s Rule to solve the systems of equations.

27.

200x−300y=2 400x+715y=4

200x−300y=2 400x+715y=4

28.

0.1x+0.1y−0.1z=−1.2 0.1x−0.2y+0.4z=−1.2 0.5x−0.3y+0.8z=−5.9

0.1x+0.1y−0.1z=−1.2 0.1x−0.2y+0.4z=−1.2 0.5x−0.3y+0.8z=−5.9

For the following exercises, solve using a system of linear equations.

29.

A factory producing cell phones has the following cost and revenue functions: C(x)= x 2 +75x+2,688 C(x)= x 2 +75x+2,688 and R(x)= x 2 +160x. R(x)= x 2 +160x. What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.

30.

A small fair charges $1.50 for students, $1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of $1,050. How many of each type of ticket was sold?

PreviousNext
Citation/Attribution

Want to cite, share, or modify this book? This book uses the

Creative Commons Attribution License
 and you must attribute OpenStax.

Attribution information

  • If you are redistributing all or part of this book in a print format,
    then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/college-algebra-2e/pages/1-introduction-to-prerequisites

  • If you are redistributing all or part of this book in a digital format,
    then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/college-algebra-2e/pages/1-introduction-to-prerequisites

Citation information

© Feb 2, 2022 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo
are not subject to the Creative Commons license and may not be reproduced without the prior and express written
consent of Rice University.

License

College Algebra 2e Copyright © by CA0522. All Rights Reserved.

Share This Book