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    Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)
    Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)
    Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)
    Ebook460 pages1 hour

    Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)

    By John Parnell

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    About this ebook

    One of the best ways to succeed in Algebra is to practice taking real test questions. This ebook contains over 1,000 problems on Algebra divided into thirty-two chapters. Try the problems. Check your answers. With a little Practice, Practice, Practice, you’ll be Perfect, Perfect, Perfect. Good Luck!
    LanguageEnglish
    PublisherJohn Parnell
    Release dateAug 13, 2010
    ISBN9781452336510
    Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)
    Author

    John Parnell

    About the author: Mr. Parnell holds teaching certification in physics, chemistry, biology, general science, mathematics, and business and distributed education. Over the course of forty years of teaching, he has taught students from the sixth grade through graduate school. In addition, Mr. Parnell has taught for the New York State Research Foundation preparing students for the SAT exam in mathematics.

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      Book preview

      Practice Makes Perfect in Mathematics - John Parnell

      Practice Makes Perfect in Mathematics:

      Algebra

      Volume 2 of 2

      Over 1,000 Practice Problems

      John E. Parnell, B.S., M.S.

      Certified Math and Science Teacher

      Published by Tutor Turtle Press at Smashwords.com.

      © 2010 by John E. Parnell

      Smashwords Edition, License Notes

      This ebook is licensed for your personal enjoyment only. This ebook may not be re-sold or given away to other people. If you would like to share this book with another person, please purchase an additional copy for each person you share it with. If you’re reading this book and did not purchase it, or it was not purchased for your use only, then you should return to Smashwords.com and purchase your own copy. Thank you for respecting the hard work of this author.

      Discover all the titles in the Practice Makes Perfect in Mathematics series by John E. Parnell at Smashwords.com:

      Practice Makes Perfect in Mathematics: Algebra (2 Volumes)

      Practice Makes Perfect in Mathematics: Integrated Algebra

      Practice Makes Perfect in Mathematics: Geometry

      Practice Makes Perfect in Mathematics: Algebra II and Trigonometry

      Practice Makes Perfect in Mathematics: Precalculus

      FORWARD

      One of the best ways to succeed in Algebra is to practice taking real test questions. This ebook contains over 1,000 problems on Algebra divided into thirty-two chapters. Try the problems. Check your answers. With a little Practice, Practice, Practice, you’ll be Perfect, Perfect, Perfect. Good Luck!

      Table of Contents

      Volume 2

      Unit 4: Introduction to Graphing (Algebra I)

      Chapter 35: The Real Number Line

      Chapter 36: The Coordinate Plane

      Chapter 37: The Equation of a Line

      Chapter 38: Systems of Equations and Inequalities

      Chapter 39: The Equation of a Parabola

      Unit 5: More Graphing Techniques (Algebra II)

      Chapter 40: The Equation of a Circle

      Chapter 41: Systems of 1st and 2nd Degree Equations

      Chapter 42: Inequalities

      Chapter 43: Ellipses & Hyperbolas

      Chapter 44: Exponentials and Logarithms

      Chapter 45: The Complex Coordinate Plane

      Unit 6: Probability

      Chapter 46: Outcomes, Sample Spaces & Tree Diagrams

      Chapter 47: Combinations & Arrangements

      Chapter 48: The Probability of an Event

      Chapter 49: Permutations with Repetitions

      Chapter 50: Combinations and the Combinations Formula

      Chapter 51: Probability of Combined Events

      Chapter 52: Binomial Expansions

      Chapter 53: Bernoulli Experiments

      Unit 7: Statistics

      Chapter 54: Data Sets: Mean, Median, Mode, & Percentiles

      Chapter 55: Displaying Data

      Chapter 56: Mean, Standard Deviation, and the Normal Distribution

      Chapter 57: Regressions and Curve Fitting

      Unit 8: Matrices

      Chapter 58: Matrix Operations

      Chapter 59: Matrix Models

      Unit 9: Sequences, Series, and Summation Notation

      Chapter 60: Sequences

      Chapter 61: Arithmetic Sequences

      Chapter 62: Geometric Sequences

      Chapter 63: Recursive Rules for Sequences

      Chapter 64: Arithmetic Series

      Chapter 65: Geometric Series

      Chapter 66: Summation (Sigma) Notation

      Volume 1

      Unit 1: Number Systems

      Chapter 1: Integers and Rational Numbers

      Chapter 2: Properties of Real Numbers

      Chapter 3: Decimals, Fractions & Percentages

      Chapter 4: Scientific Notation

      Chapter 5: Irrational Numbers, Square Roots, and Powers

      Chapter 6: Factorials

      Chapter 7: Properties of Finite Number Systems

      Chapter 8: Exponents and Logarithms

      Chapter 9: Complex Numbers

      Unit 2: Introduction to Algebra (Algebra I)

      Chapter 10: Evaluating Algebraic Expressions

      Chapter 11: Addition & Subtraction of Polynomials

      Chapter 12: Solving Linear Equations in One Variable

      Chapter 13: Inequalities

      Chapter 14: Multiplication of Polynomials

      Chapter 15: Factoring Polynomials

      Chapter 16: Rational Expressions & Division of Polynomials

      Chapter 17: Solving Quadratic Equations by Factoring

      Chapter 18: Ratios, Proportions, & Direct Variation

      Chapter 19: Solving Systems of Equations & Inequalities

      Chapter 20: Word Problems

      Chapter 21: Adding & Subtracting Algebraic Fractions

      Chapter 22: Solving Linear Equations with Algebraic Fractions

      Chapter 23: Simplifying Algebraic Expressions by Factoring

      Unit 3: Intermediate Algebra (Algebra II)

      Chapter 24: The Quadratic Formula

      Chapter 25: Solving Systems of Equations

      Chapter 26: Algebraic Fractions & Linear Equations

      Chapter 27: Radical Expressions & Equations

      Chapter 28: Exponential Equations

      Chapter 29: Logarithms

      Chapter 30: Roots of Quadratic Equations

      Chapter 31: Absolute Value

      Chapter 32: Inverse Variation

      Chapter 33: Relations and Functions

      Chapter 34: Summations

      Answers to Questions

      Unit 4: Introduction to Graphing (Algebra I)

      Chapter 35: The Real Number Line

      Chapter 36: The Coordinate Plane

      Chapter 37: The Equation of a Line

      Chapter 38: Systems of Equations and Inequalities

      Chapter 39: The Equation of a Parabola

      Unit 5: More Graphing Techniques (Algebra II)

      Chapter 40: The Equation of a Circle

      Chapter 41: Systems of 1st and 2nd Degree Equations

      Chapter 42: Inequalities

      Chapter 43: Ellipses & Hyperbolas

      Chapter 44: Exponentials and Logarithms

      Chapter 45: The Complex Coordinate Plane

      Unit 6: Probability

      Chapter 46: Outcomes, Sample Spaces & Tree Diagrams

      Chapter 47: Combinations & Arrangements

      Chapter 48: The Probability of an Event

      Chapter 49: Permutations with Repetitions

      Chapter 50: Combinations and the Combinations Formula

      Chapter 51: Probability of Combined Events

      Chapter 52: Binomial Expansions

      Chapter 53: Bernoulli Experiments

      Unit 7: Statistics

      Chapter 54: Data Sets: Mean, Median, Mode, & Percentiles

      Chapter 55: Displaying Data

      Chapter 56: Mean, Standard Deviation, and the Normal Distribution

      Chapter 57: Regressions and Curve Fitting

      Unit 8: Matrices

      Chapter 58: Matrix Operations

      Chapter 59: Matrix Models

      Unit 9: Sequences, Series, and Summation Notation

      Chapter 60: Sequences

      Chapter 61: Arithmetic Sequences

      Chapter 62: Geometric Sequences

      Chapter 63: Recursive Rules for Sequences

      Chapter 64: Arithmetic Series

      Chapter 65: Geometric Series

      Chapter 66: Summation (Sigma) Notation

      Unit 4: Introduction to Graphing (Algebra I)

      Chapter 35: The Real Number Line

      1. Which inequality is represented by the graph below?

      -3 <x 4

      -3 <x< 4

      -3 x 4

      -3 x< 4

      2. Which graph represents the inequality 1 x < 4?

      3.

      Which inequality is represented in the graph?

      4 x 2

      4 <x< 2

      4 <x 2

      4 x< 2

      4. Which inequality is represented by the graph below?

      x>-1

      x<-1

      x -1

      x -1

      5. Which graph represents the open sentence -5 x < 0?

      6. Which inequality is represented by the graph below?

      -2 x< 3

      -2 x 3

      -2 <x< 3

      -2 <x 3

      7. Which inequality is represented by the graph below?

      -5 <x< 6

      -5 x 6

      -5 x< 6

      -5 <x 6

      8. Let x and y be numbers such that 0 < x < y < 1, and let d = x - y. Which graph could represent the location of d on the number line?

      9.

      Which inequality is represented in the accompanying graph?

      -4 <x< 2

      -4 x< 2

      -4 <x 2

      -4 x 2

      10. Which point on the accompanying number line best represents the position of ?

      A

      B

      C

      D

      Answers to Chapter 35: The Real Number Line

      Chapter 36: The Coordinate Plane

      1. Which diagram represents the graph of the statement x 3?

      2. Find the area of the triangle formed by the intersection of the lines:

      x+y= 8

      y= ½x 1

      x= 2

      3. The coordinates of ABC are A(0,4), B(6,0), and C(0, 0). Find the area of ABC.

      12

      16

      24

      36

      4. If the coordinates of the vertices of ABC are A(3, 2), B(7, 2), and C(5, 5), what is the area of the triangle?

      10

      14

      20

      28

      5. Pentagon RSTUV has coordinates R (1, 4), S (5, 0), T (3, -4), U ( 1, 4), and V ( 3, 0).

      (a) What is an equation of the line of symmetry of pentagon RSTUV ?

      (b) What is the area of triangle RVS?

      (c) What is the area of trapezoid STUV ?

      (d)  What is the area of pentagon RSTUV ?

      6.

      In the diagram, parallelogram ABCD has vertices A(2, 1), B(8, 1), C(11, 5), and D(5, 5). What is the area of parallelogram ABCD?

      12

      24

      40

      48

      7.

      Find the number of square units in the area of parallelogram ABCD.

      10

      14

      28

      56

      8. Which graph represents the inequality x ≥ 3?

      9.

      The graph of which inequality is shown in the diagram?

      y> ½x+ 1

      y ½x+ 1

      y< ½x+ 1

      y ½x+ 1

      10.

      In the diagram, ABCD is a parallelogram with vertices A(2, 0), B(7, 0), C(10, 3), and D(5, 3). What is the area of parallelogram ABCD?

      15

      21

      27

      10.5

      11. Pentagon RSTUV has coordinates R(1, 4), S(5, 0), T(3, 4), U( 1, 4), and V( 3, 0). What is an equation for the line of symmetry of pentagon RSTUV ?

      12.

      If x = -3 and y = 2, which point on the accompanying graph represents (-x, - y)?

      P

      Q

      R

      S

      13. John left his home and walked 3 blocks to his school, as shown in the accompanying graph.

      What is one possible interpretation of the section of the graph from point B to point C?

      John arrived at school and stayed throughout the day.

      John waited before crossing a busy street.

      John returned home to get his mathematics homework.

      John reached the top of a hill and began walking on level ground.

      14. In the accompanying graph, if point P has coordinates (a,b), which point has coordinates (-b,a)?

      A

      B

      C

      D

      Answers to Chapter 36: The Coordinate Plane

      Chapter 37: The Equation of a Line

      1. What is the slope

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