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Intermediate Algebra 2e

Practice Test

Intermediate Algebra 2ePractice 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 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, write the first five terms of the sequence whose general term is given.

320.

a n = 5 n − 3 3 n a n = 5 n − 3 3 n

321.

a n = ( n + 2 ) ! ( n + 3 ) ! a n = ( n + 2 ) ! ( n + 3 ) !

322.

Find a general term for the sequence, −23,−45,−67,−89,−1011,…−23,−45,−67,−89,−1011,…

323.

Expand the partial sum and find its value. ∑i=14(−4)i∑i=14(−4)i

324.

Write the following using summation notation. −1+14−19+116−125−1+14−19+116−125

325.

Write the first five terms of the arithmetic sequence with the given first term and common difference. a1=−13a1=−13 and d=3d=3

326.

Find the twentieth term of an arithmetic sequence where the first term is two and the common difference is −7.−7.

327.

Find the twenty-third term of an arithmetic sequence whose seventh term is 1111 and common difference is three. Then find a formula for the general term.

328.

Find the first term and common difference of an arithmetic sequence whose ninth term is −1−1 and the sixteenth term is −15.−15. Then find a formula for the general term.

329.

Find the sum of the first 25 terms of the arithmetic sequence, 5,9,13,17,21,…5,9,13,17,21,…

330.

Find the sum of the first 50 terms of the arithmetic sequence whose general term is an=−3n+100.an=−3n+100.

331.

Find the sum. ∑i=140(5i−21)∑i=140(5i−21)

In the following exercises, determine if the sequence is arithmetic, geometric, or neither. If arithmetic, then find the common difference. If geometric, then find the common ratio.

332.

14 , 3 , −8 , −19 , −30 , −41 , … 14 , 3 , −8 , −19 , −30 , −41 , …

333.

324 , 108 , 36 , 12 , 4 , 4 3 , … 324 , 108 , 36 , 12 , 4 , 4 3 , …

334.

Write the first five terms of the geometric sequence with the given first term and common ratio. a1=6a1=6 and r=−2r=−2

335.

In the geometric sequence whose first term and common ratio are a1=5a1=5 and r=4,r=4, find a11.a11.

336.

Find a10a10 of the geometric sequence, 1250,250,50,10,2,25,….1250,250,50,10,2,25,…. Then find a formula for the general term.

337.

Find the sum of the first thirteen terms of the geometric sequence, 2,−6,18,−54,162,−486…2,−6,18,−54,162,−486…

In the following exercises, find the sum.

338.

∑ i = 1 9 5 ( 2 ) i ∑ i = 1 9 5 ( 2 ) i

339.

1 − 1 5 + 1 25 − 1 125 + 1 625 − 1 3125 + … 1 − 1 5 + 1 25 − 1 125 + 1 625 − 1 3125 + …

340.

Write the repeating decimal as a fraction. 0.81—0.81—

341.

Dave just got his first full-time job after graduating from high school at age 18. He decided to invest $450 per month in an IRA (an annuity). The interest on the annuity is 6% which is compounded monthly. How much will be in Adam’s account when he retires at his sixty-fifth birthday?

342.

Expand the binomial using Pascal’s Triangle. (m−2n)5(m−2n)5

343.

Evaluate each binomial coefficient. ⓐ (81)(81)
ⓑ (1616)(1616) ⓒ (120)(120) ⓓ (106)(106)

344.

Expand the binomial using the Binomial Theorem. (4x+5y)3(4x+5y)3

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