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Intermediate Algebra

Practice Test

Intermediate AlgebraPractice Test
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Table of contents
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Chapter Review
      1. Key Terms
      2. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Chapter Review
      1. Key Terms
      2. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Chapter Review
      1. Key Terms
      2. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Chapter Review
      1. Key Terms
      2. Key Concepts
    7. Exercises
      1. Review Exercises
      2. Practice Test
  14. 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
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  15. Index

Practice Test

In the following exercises, find the distance between the points and the midpoint of the line segment with the given endpoints. Round to the nearest tenth as needed.

327.

(−4,−3)(−4,−3) and (−10,−11)(−10,−11)

328.

(6,8)(6,8) and (−5,−3)(−5,−3)

In the following exercises, write the standard form of the equation of the circle with the given information.

329.

radius is 11 and center is (0,0)(0,0)

330.

radius is 12 and center is (10,−2)(10,−2)

331.

center is (−2,3)(−2,3) and a point on the circle is (2,−3)(2,−3)

332.

Find the equation of the ellipse shown in the graph.

The figure shows an ellipse graphed on the x y coordinate plane. The ellipse has a center at (0, 0), a vertical major axis, vertices at (0, plus or minus 10), and co-vertices at (plus or minus 6, 0).

In the following exercises, ⓐ identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, and ⓑ graph the equation.

333.

4 x 2 + 49 y 2 = 196 4 x 2 + 49 y 2 = 196

334.

y = 3 ( x − 2 ) 2 − 2 y = 3 ( x − 2 ) 2 − 2

335.

3 x 2 + 3 y 2 = 27 3 x 2 + 3 y 2 = 27

336.

y 2 100 − x 2 36 = 1 y 2 100 − x 2 36 = 1

337.

x 2 16 + y 2 81 = 1 x 2 16 + y 2 81 = 1

338.

x = 2 y 2 + 10 y + 7 x = 2 y 2 + 10 y + 7

339.

64 x 2 − 9 y 2 = 576 64 x 2 − 9 y 2 = 576

In the following exercises, ⓐ identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola, ⓑ write the equation in standard form, and ⓒ graph the equation.

340.

25 x 2 + 64 y 2 + 200 x − 256 y − 944 = 0 25 x 2 + 64 y 2 + 200 x − 256 y − 944 = 0

341.

x 2 + y 2 + 10 x + 6 y + 30 = 0 x 2 + y 2 + 10 x + 6 y + 30 = 0

342.

x = − y 2 + 2 y − 4 x = − y 2 + 2 y − 4

343.

9 x 2 − 25 y 2 − 36 x − 50 y − 214 = 0 9 x 2 − 25 y 2 − 36 x − 50 y − 214 = 0

344.

y = x 2 + 6 x + 8 y = x 2 + 6 x + 8

345.

Solve the nonlinear system of equations by graphing:
{3y2−x=0y=−2x−1.{3y2−x=0y=−2x−1.

346.

Solve the nonlinear system of equations using substitution:
{x2+y2=8y=−x−4.{x2+y2=8y=−x−4.

347.

Solve the nonlinear system of equations using elimination:
{x2+9y2=92x2−9y2=18.{x2+9y2=92x2−9y2=18.

348.

Create the equation of the parabolic arch formed in the foundation of the bridge shown. Give the answer in y=ax2+bx+cy=ax2+bx+c form.

The figure shows a parabolic arch formed in the foundation of the bridge. The arch is 10 feet high and 30 feet wide.
349.

A comet moves in an elliptical orbit around a sun. The closest the comet gets to the sun is approximately 20 AU and the furthest is approximately 70 AU. The sun is one of the foci of the elliptical orbit. Letting the ellipse center at the origin and labeling the axes in AU, the orbit will look like the figure below. Use the graph to write an equation for the elliptical orbit of the comet.

The figure shows a model of an elliptical orbit around the sun on the x y coordinate plane. The ellipse has a center at (0, 0), a horizontal major axis, vertices marked at (plus or minus 45, 0), the sun marked as a foci and labeled (25, 0), the closest distance the comet is from the sun marked as 20 A U, and the farthest a comet is from the sun marked as 70 A U.
350.

The sum of two numbers is 22 and the product is −240.−240. Find the numbers.

351.

For her birthday, Olive’s grandparents bought her a new widescreen TV. Before opening it she wants to make sure it will fit her entertainment center. The TV is 55”. The size of a TV is measured on the diagonal of the screen and a widescreen has a length that is larger than the width. The screen also has an area of 1452 square inches. Her entertainment center has an insert for the TV with a length of 50 inches and width of 40 inches. What are the length and width of the TV screen and will it fit Olive’s entertainment center?

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