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College Algebra

Practice Test

College AlgebraPractice Test
  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Key Terms
    9. Key Equations
    10. Key Concepts
    11. Review Exercises
    12. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  4. 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. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  5. 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. Key Terms
    6. Key Concepts
    7. Review Exercises
    8. Practice Test
  6. 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. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  7. 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. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  8. 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. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  9. 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. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  10. 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. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  11. 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
  12. Index

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

1.

5xy=12 x+4y=9 5xy=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 xy=0 1 2 x 1 3 y=4 3 2 xy=0

3.

1 2 x4y=4 2x+16y=2 1 2 x4y=4 2x+16y=2

4.

5xy=1 10x+2y=2 5xy=1 10x+2y=2

5.

4x6y2z= 1 10 x7y+5z= 1 4 3x+6y9z= 6 5 4x6y2z= 1 10 x7y+5z= 1 4 3x+6y9z= 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.

5x4y3z=0 2x+y+2z=0 x6y7z=0 5x4y3z=0 2x+y+2z=0 x6y7z=0

8.

y= x 2 +2x3 y=x1 y= x 2 +2x3 y=x1

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.

8x30 x 2 +10x+25 8x30 x 2 +10x+25

13.

13x+2 (3x+1) 2 13x+2 (3x+1) 2

14.

x 4 x 3 +2x1 x ( x 2 +1) 2 x 4 x 3 +2x1 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.

14x2y+13z=140 2x+3y6z=1 x5y+12z=11 14x2y+13z=140 2x+3y6z=1 x5y+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.

x6y=4 2x12y=0 x6y=4 2x12y=0

24.

2x+y+z=3 x2y+3z=6 xyz=6 2x+y+z=3 x2y+3z=6 xyz=6

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

25.

4x5y=50 x+2y=80 4x5y=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.

200x300y=2 400x+715y=4 200x300y=2 400x+715y=4

28.

0.1x+0.1y0.1z=1.2 0.1x0.2y+0.4z=1.2 0.5x0.3y+0.8z=5.9 0.1x+0.1y0.1z=1.2 0.1x0.2y+0.4z=1.2 0.5x0.3y+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?

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