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Contemporary Mathematics

Chapter Test

Contemporary MathematicsChapter Test
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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. 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
    13. Chapter 13
  17. Index

Chapter Test

1 .
Perform the indicated operation for the expression: ( 3 x 2 + 2 x + 1 ) − ( x 2 − 2 + 2 ) + x ( 3 x + 11 )
2 .
Solve the linear equations using properties of equations: x ( x − 2 ) + = 9 x + x ( x − 6 )
3 .
It costs 55 cents for a stamp. Construct a linear equation and solve how much it cost to buy 50 stamps.
4 .
Solve the formula A = ( b 1 + b 2 ) 2 h for h .
5 .
Solve the inequality − 2 x < − 6 , graph the solution on the number line, and write the solution in interval notation.
6 .
Construct a linear inequality to solve the application: Bella wants to buy a round of shakes for her friends. It will cost $4.75 per shake, including tip and tax. Her budget is $50. What is the maximum number of friends Bella can buy shakes for?
7 .
Manneken Pis is a famous statue in Brussels, Belgium. It is 24 inches tall and weighs 37.5 pounds. The average man is 69 inches tall and weighs 198 pounds. Is Manneken Pis proportional to the average male?
8 .
Graph y = 1 4 x + 1 by plotting points.
9 .
Graph the linear inequality: y ≥ 2 x + 7
10 .
Graph and list the solutions to the quadratic equation x 2 − 36 = 0 .
11 .
Solve x 2 − 49 = 0 by factoring.
12 .
Solve x 2 + 5 x + 2 = 0 using the quadratic formula.
13 .
Evaluate the function f ( x ) = − 3 x + 21 at the values f ( − 2 ) , f ( − 1 ) , f ( 0 ) , f ( 1 ) , and f ( 2 ) .
14 .
Use the vertical line test to determine if the given graph represents a function. A function is plotted on an x y coordinate plane. The x and y axes range from negative 10 to 10, in increments of 1. The function passes through the points, (negative 8, negative 1), (negative 4.5, 1), (negative 1.5, negative 1), (1.5, 1), (4.5, negative 1), and (7.5, 1). Note: all values are approximate.
15 .
Use the graph shown to find the domain and the range. Four points are plotted on an x y coordinate plane. The x and y axes range from negative 10 to 10, in increments of 1. The points are plotted at the following coordinates: (negative 7, 1), (negative 2, negative 3), (0, 5), and (4, 6).
16 .
Graph 2 y = x − 4 using the intercepts.
17 .
Use the slope formula to find the slope of the line between (1, 4) and (3, 5).
18 .
Identify the slope and y -intercept of y − 2 3 x = 1 .
19 .
Graph the line of y = 2 3 x + 1 using its slope and y -intercept.
The equation C = 4.50 + 15 p , models the cost of visiting the Cat Café in San Diego for one hour. C , in dollars, is the total cost and the cost per person, p , is $15 plus a $4.50 reservation fee.
20 .
Find the payment for two people.
21 .
Find the payment for five people.
22 .
Interpret the slope and C -intercept of the equation.
23 .
Graph the equation.
24 .
Solve the system of equations by graphing.
{ y − 3 x = 3 y = − 6 x + 12
25 .
Solve the system of equations by substitution.
{ y = 5 x − 5 − 3 x + y = − 3
26 .
Solve the systems of equations by elimination.
{ y = 1 3 x − 6 y = x − 3
27 .
Anna goes to the concession stand at a movie theater. She buys 5 popcorns and 4 large sodas and pays a total of $60. During intermission, Isabelle goes to the concession stand. She buys 1 popcorn and 2 large sodas and pays a total of $18. What is the cost of one popcorn, and the cost of one large soda?
28 .
Solve the systems of linear equations by graphing.
{ y > 1 3 x − 1 y < x − 3
Juliette is selling fresh lemonade and cupcakes. She sells a cup of lemonade for $2 and a cupcake for $3. She needs to make at least $100 to donate to the local cat sanctuary. She needs to sell at least 20 cups of lemonade.
29 .
Write a system of inequalities to model this situation.
30 .
Graph the system.
31 .
Could she sell 30 cups of lemonade and 10 cupcakes and make $100?
32 .
Could she sell 20 cups of lemonade and 30 cupcakes and make $100?
A toy maker makes exactly two toys out of wood; the Box ( x ) and the Bat ( y ). He makes $5 per Box and $6 per Bat. Each Box requires 30 ounces of wood, and each Bat requires 45 ounces of wood. Today the toy maker has 270 ounces of wood available. The toy maker also only makes 8 wooden toys per day. To maximize profit, how many of each wooden toy should the toy maker make?
33 .
Find the objective function.
34 .
Write the constraints as a system of inequalities.
35 .
Graph of the system of inequalities.
36 .
Find the value of the objective function at each corner point of the graphed region.
37 .
To maximize profit, how many of each toy should the toymaker make?
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