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Intermediate Algebra 2e

Review Exercises

Intermediate Algebra 2eReview Exercises
  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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    10. Key Concepts
    11. 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. Key Terms
    7. Key Concepts
    8. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    9. Key Concepts
    10. 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. Key Terms
    11. Key Concepts
    12. 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. Key Terms
    11. Key Concepts
    12. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    8. Key Concepts
    9. 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. Key Terms
    7. Key Concepts
    8. 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

Review Exercises

Sequences

Write the First Few Terms of a Sequence

In the following exercises, write the first five terms of the sequence whose general term is given.

240.

an=7n5an=7n5

241.

an=3n+4an=3n+4

242.

an=2n+nan=2n+n

243.

an=2n+14nan=2n+14n

244.

an=(−1)nn2an=(−1)nn2

Find a Formula for the General Term (nth Term) of a Sequence

In the following exercises, find a general term for the sequence whose first five terms are shown.

245.

9,18,27,36,45,9,18,27,36,45,

246.

−5,−4,−3,−2,−1,−5,−4,−3,−2,−1,

247.

1e3,1e2,1e,1,e,1e3,1e2,1e,1,e,

248.

1,−8,27,−64,125,1,−8,27,−64,125,

249.

13,12,35,23,57,13,12,35,23,57,

Use Factorial Notation

In the following exercises, using factorial notation, write the first five terms of the sequence whose general term is given.

250.

an=4n!an=4n!

251.

an=n!(n+2)!an=n!(n+2)!

252.

an=(n1)!(n+1)2an=(n1)!(n+1)2

Find the Partial Sum

In the following exercises, expand the partial sum and find its value.

253.

i=17(2i5)i=17(2i5)

254.

i=135ii=135i

255.

k=044k!k=044k!

256.

k=14(k+1)(2k+1)k=14(k+1)(2k+1)

Use Summation Notation to write a Sum

In the following exercises, write each sum using summation notation.

257.

13+19127+181124313+19127+1811243

258.

48+1216+202448+1216+2024

259.

4+2+43+1+454+2+43+1+45

Arithmetic Sequences

Determine if a Sequence is Arithmetic

In the following exercises, determine if each sequence is arithmetic, and if so, indicate the common difference.

260.

1,2,4,8,16,32,1,2,4,8,16,32,

261.

−7,−1,5,11,17,23,−7,−1,5,11,17,23,

262.

13,9,5,1,−3,−7,13,9,5,1,−3,−7,

In the following exercises, write the first five terms of each arithmetic sequence with the given first term and common difference.

263.

a1=5a1=5 and d=3d=3

264.

a1=8a1=8 and d=−2d=−2

265.

a1=−13a1=−13 and d=6d=6

Find the General Term (nth Term) of an Arithmetic Sequence

In the following exercises, find the term described using the information provided.

266.

Find the twenty-fifth term of a sequence where the first term is five and the common difference is three.

267.

Find the thirtieth term of a sequence where the first term is 16 and the common difference is −5.−5.

268.

Find the seventeenth term of a sequence where the first term is −21−21 and the common difference is two.

In the following exercises, find the indicated term and give the formula for the general term.

269.

Find the eighteenth term of a sequence where the fifth term is 1212 and the common difference is seven.

270.

Find the twenty-first term of a sequence where the seventh term is 1414 and the common difference is −3.−3.

In the following exercises, find the first term and common difference of the sequence with the given terms. Give the formula for the general term.

271.

The fifth term is 17 and the fourteenth term is 53.

272.

The third term is −26−26 and the sixteenth term is −91.−91.

Find the Sum of the First n Terms of an Arithmetic Sequence

In the following exercises, find the sum of the first 30 terms of each arithmetic sequence.

273.

7,4,1,−2,−5,7,4,1,−2,−5,

274.

1,6,11,16,21,1,6,11,16,21,

In the following exercises, find the sum of the first fifteen terms of the arithmetic sequence whose general term is given.

275.

an=4n+7an=4n+7

276.

an=−2n+19an=−2n+19

In the following exercises, find each sum.

277.

i=150(4i5)i=150(4i5)

278.

i=130(−3i7)i=130(−3i7)

279.

i=135(i+10)i=135(i+10)

Geometric Sequences and Series

Determine if a Sequence is Geometric

In the following exercises, determine if the sequence is geometric, and if so, indicate the common ratio.

280.

3,12,48,192,768,3072,3,12,48,192,768,3072,

281.

5,10,15,20,25,30,5,10,15,20,25,30,

282.

112,56,28,14,7,72,112,56,28,14,7,72,

283.

9,−18,36,−72,144,−288,9,−18,36,−72,144,−288,

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

284.

a1=−3a1=−3 and r=5r=5

285.

a1=128a1=128 and r=14r=14

286.

a1=5a1=5 and r=−3r=−3

Find the General Term (nth Term) of a Geometric Sequence

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.

287.

Find a9a9 given a1=6a1=6 and r=2.r=2.

288.

Find a11a11 given a1=10,000,000a1=10,000,000 and r=0.1.r=0.1.

In the following exercises, find the indicated term of the given sequence. Find the general term of the sequence.

289.

Find a12a12 of the sequence, 6,−24,96,−384,1536,−6144,6,−24,96,−384,1536,−6144,

290.

Find a9a9 of the sequence, 4374,1458,486,162,54,18,4374,1458,486,162,54,18,

Find the Sum of the First n terms of a Geometric Sequence

In the following exercises, find the sum of the first fifteen terms of each geometric sequence.

291.

−4,8,−16,32,−64,128−4,8,−16,32,−64,128

292.

3,12,48,192,768,30723,12,48,192,768,3072

293.

3125,625,125,25,5,13125,625,125,25,5,1

In the following exercises, find the sum

294.

i=187(3)ii=187(3)i

295.

i=1624(12)ii=1624(12)i

Find the Sum of an Infinite Geometric Series

In the following exercises, find the sum of each infinite geometric series.

296.

113+19127+1811243+1729113+19127+1811243+1729

297.

49+7+1+17+149+1343+49+7+1+17+149+1343+

In the following exercises, write each repeating decimal as a fraction.

298.

0.80.8

299.

0.360.36

Apply Geometric Sequences and Series in the Real World

In the following exercises, solve the problem.

300.

What is the total effect on the economy of a government tax rebate of $360$360 to each household in order to stimulate the economy if each household will spend 60%60% of the rebate in goods and services?

301.

Adam just got his first full-time job after graduating from high school at age 17. He decided to invest $300$300 per month in an IRA (an annuity). The interest on the annuity is 7%7% which is compounded monthly. How much will be in Adam’s account when he retires at his sixty-seventh birthday?

Binomial Theorem

Use Pascal’s Triangle to Expand a Binomial

In the following exercises, expand each binomial using Pascal’s Triangle.

302.

(a+b)7(a+b)7

303.

(xy)4(xy)4

304.

(x+6)3(x+6)3

305.

(2y3)5(2y3)5

306.

(7x+2y)3(7x+2y)3

Evaluate a Binomial Coefficient

In the following exercises, evaluate.

307.


(111)(111)
(1212)(1212)
(130)(130)
(83)(83)

308.


(71)(71)
(55)(55)
(90)(90)
(95)(95)

309.


(11)(11)
(1515)(1515)
(40)(40)
(112)(112)

Use the Binomial Theorem to Expand a Binomial

In the following exercises, expand each binomial, using the Binomial Theorem.

310.

(p+q)6(p+q)6

311.

(t1)9(t1)9

312.

(2x+1)4(2x+1)4

313.

(4x+3y)4(4x+3y)4

314.

(x3y)5(x3y)5

In the following exercises, find the indicated term in the expansion of the binomial.

315.

Seventh term of (a+b)9(a+b)9

316.

Third term of (xy)7(xy)7

In the following exercises, find the coefficient of the indicated term in the expansion of the binomial.

317.

y4y4 term of (y+3)6(y+3)6

318.

x5x5 term of (x2)8(x2)8

319.

a3b4a3b4 term of (2a+b)7(2a+b)7

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