Practice Makes Perfect in Mathematics: Algebra (Volume 2 of 2)
By John Parnell
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About this ebook
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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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