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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

Give the degree and leading coefficient of the following polynomial function.

1.

f(x)= x 3 ( 36 x 2 2 x 2 ) f(x)= x 3 ( 36 x 2 2 x 2 )

Determine the end behavior of the polynomial function.

2.

f(x)=8 x 3 3 x 2 +2x4 f(x)=8 x 3 3 x 2 +2x4

3.

f(x)=2 x 2 (43x5 x 2 ) f(x)=2 x 2 (43x5 x 2 )

Write the quadratic function in standard form. Determine the vertex and axes intercepts and graph the function.

4.

f(x)= x 2 +2x8 f(x)= x 2 +2x8

Given information about the graph of a quadratic function, find its equation.

5.

Vertex (2,0) (2,0) and point on graph (4,12). (4,12).

Solve the following application problem.

6.

A rectangular field is to be enclosed by fencing. In addition to the enclosing fence, another fence is to divide the field into two parts, running parallel to two sides. If 1,200 feet of fencing is available, find the maximum area that can be enclosed.

Find all zeros of the following polynomial functions, noting multiplicities.

7.

f(x)= (x3) 3 (3x1) (x1) 2 f(x)= (x3) 3 (3x1) (x1) 2

8.

f(x)=2 x 6 12 x 5 +18 x 4 f(x)=2 x 6 12 x 5 +18 x 4

Based on the graph, determine the zeros of the function and multiplicities.

9.
Graph of an odd-degree polynomial with two turning points.

Use long division to find the quotient.

10.

2 x 3 +3x4 x+2 2 x 3 +3x4 x+2

Use synthetic division to find the quotient. If the divisor is a factor, write the factored form.

11.

x 4 +3 x 2 4 x2 x 4 +3 x 2 4 x2

12.

2 x 3 +5 x 2 7x12 x+3 2 x 3 +5 x 2 7x12 x+3

Use the Rational Zero Theorem to help you find the zeros of the polynomial functions.

13.

f(x)=2 x 3 +5 x 2 6x9 f(x)=2 x 3 +5 x 2 6x9

14.

f(x)=4 x 4 +8 x 3 +21 x 2 +17x+4 f(x)=4 x 4 +8 x 3 +21 x 2 +17x+4

15.

f(x)=4 x 4 +16 x 3 +13 x 2 15x18 f(x)=4 x 4 +16 x 3 +13 x 2 15x18

16.

f(x)= x 5 +6 x 4 +13 x 3 +14 x 2 +12x+8 f(x)= x 5 +6 x 4 +13 x 3 +14 x 2 +12x+8

Given the following information about a polynomial function, find the function.

17.

It has a double zero at x=3 x=3and zeros at x=1 x=1and x=2 x=2. Its y-intercept is (0,12). (0,12).

18.

It has a zero of multiplicity 3 at x= 1 2 x= 1 2 and another zero at x=3 x=3. It contains the point (1,8). (1,8).

Use Descartes’ Rule of Signs to determine the possible number of positive and negative solutions.

19.

8 x 3 21 x 2 +6=0 8 x 3 21 x 2 +6=0

For the following rational functions, find the intercepts and horizontal and vertical asymptotes, and sketch a graph.

20.

f(x)= x+4 x 2 2x3 f(x)= x+4 x 2 2x3

21.

f(x)= x 2 +2x3 x 2 4 f(x)= x 2 +2x3 x 2 4

Find the slant asymptote of the rational function.

22.

f(x)= x 2 +3x3 x1 f(x)= x 2 +3x3 x1

Find the inverse of the function.

23.

f(x)= x2 +4 f(x)= x2 +4

24.

f(x)=3 x 3 4 f(x)=3 x 3 4

25.

f(x)= 2x+3 3x1 f(x)= 2x+3 3x1

Find the unknown value.

26.

y yvaries inversely as the square of x xand when x=3, x=3, y=2. y=2.Find y yif x=1. x=1.

27.

y yvaries jointly with x xand the cube root of z. z. If when x=2 x=2and z=27, z=27, y=12, y=12,find y yif x=5 x=5and z=8. z=8.

Solve the following application problem.

28.

The distance a body falls varies directly as the square of the time it falls. If an object falls 64 feet in 2 seconds, how long will it take to fall 256 feet?

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