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Contemporary Mathematics

Chapter Review

Contemporary MathematicsChapter Review
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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 Review

Prime and Composite Numbers
1.
Identify which of the following numbers are prime, composite, or neither:
201, 34, 17, 1, 37.
2.
Find the prime factorization of 500.
3.
Find the greatest common divisor of 80 and 340.
4.
Find the greatest common divisor of 30, 40, and 70.
5.
Find the least common multiple of 45 and 60.
6.
Bella and JJ volunteer at the zoo. Bella volunteers every 8 days, while JJ volunteers every 14 days. How many days pass between days they volunteer together?
The Integers
7.
Identify all the integers in the following list: .
8.
Plot the following on the same number line:
{1, 5, −2, 0}.
9.
What two numbers have absolute value of 18?
10.
Calculate 14 - ( - 12).
11.
Calculate ( - 19) \times 4.
12.
Calculate ( - 240) \div ( - 12).
13.
Six students rent a house together. The total monthly rent (including heat and electricity) is $3,120. If they all pay an equal amount, how much does each student pay?
Order of Operations
14.
Calculate 5 \times 3 - ( - 12).
15.
Calculate {4^2} \times 6 + {2^3}.
16.
(4 - 6) \times 2
17.
{(8 - 1)^3} - 3 \times 9
18.
120 - (51 + 12) \div {3^2}
Rational Numbers
19.
Reduce \frac{{90}}{{153}} to lowest terms.
20.
Convert \frac{430}{25} to a mixed number and reduce to lowest terms.
21.
Convert \frac{9}{5} to decimal form.
22.
Convert \frac{5}{11} to decimal form.
23.
Calculate \frac{4}{15} + \frac{9}{10} and reduce to lowest terms.
24.
Compute and reduce to lowest terms.
25.
Determine 30% of 400.
26.
18 is what percent of 40?
27.
In Professor Finnegan’s Science Fiction course, there are 60 students. Of those, 15% say they’ve read A Hitchhiker’s Guide to the Galaxy. How many of the students have read that book?
Irrational Numbers
28.
Simplify the square root by expressing it in lowest terms: \sqrt {275}.
29.
Calculate 4\sqrt {13} - 15\sqrt {13} without a calculator. If not possible, explain why.
30.
Calculate \left( {2.3\sqrt 5 } \right) \times \left( {4.2\sqrt 3 } \right) without a calculator. If not possible, explain why.
31.
Rationalize the denominator of \frac{6}{{\sqrt {22} }}, and simplify the fraction.
32.
Find the conjugate of 4\sqrt 7 + 3 and find the product of 4\sqrt 7 + 3 and its conjugate.
33.
Rationalize the denominator of \frac{3}{{8 + \sqrt {34} }} and simplify the fraction.
Real Numbers
34.
Identify the numbers of the following list as a natural number, an integer, a rational number, or a real number: \sqrt {37}, −0.43, 18, −43, 12\pi.
35.
Identify the property of real numbers illustrated here: 14 + 19 = 19 + 14.
36.
Identify the property of real numbers illustrated here: 87.4 + 0 = 87.4.
37.
Identify the property of real numbers illustrated here: 2 \times (\sqrt {31} - 12) = 2\sqrt {31} - 2 \times 12.
38.
Identify the property of real numbers illustrated here: 98 \times 41 = 41 \times 98.
39.
Use mental math to calculate 21 \times 99.
Clock Arithmetic
40.
Determine 74 modulo 9.
41.
Use clock arithmetic to calculate 13 + 25.
42.
Use clock arithmetic to calculate 4 \times 8.
43.
It is Wednesday. What day of the week will it be in 44 days?
44.
It is 4:00. What time will it be in 100 hours?
45.
Security guards with Acuriguard submit a report on campus activity every 4 days. If they make a report on a Monday, what day of the week will it be after 10 more reports?
Exponents
46.
Use exponent rules to simplify {17^8} \times {17^3}.
47.
Use exponent rules to simplify \frac{{{{15}^9}}}{{{{15}^{ - 5}}}}.
48.
Use exponent rules to simplify {(3k)^6}.
49.
Use exponent rules to simplify {\left( {\frac{y}{4}} \right)^{11}}.
50.
Use exponent rules to simplify {\left( {{{51}^3}} \right)^6}.
51.
Use exponent rules to simplify {\left( {\frac{{3{x^4}}}{5}} \right)^7}.
52.
Rewrite \frac{{{5^2}}}{{{x^4}}} without a denominator.
53.
Rewrite 16{z^{ - 9}} without negative exponents.
Scientific Notation
54.
Convert 0.0000452 to scientific notation.
55.
Convert 3.01 \times {10^5} to standard notation.
56.
Convert 42.9 \times {10^{ - 9}} to scientific notation.
57.
Calculate 4.51 \times {10^5} - 9.11 \times {10^4}.
58.
Calculate \left( {9.15 \times {{10}^3}} \right) \div \left( {3 \times {{10}^8}} \right).
59.
The Sextans Dwarf Spheroidal Galaxy has diameter 8,400 light years (ly). Express this in Scientific notation.
60.
The Reticulum II Galaxy has diameter 3.78 \times {10^2} light years (ly), while the Andromeda Galaxy has a diameter of 2 \times {10^5}. How many times bigger is the Andromeda Galaxy compared to the Reticulum II Galaxy?
Arithmetic Sequences
61.
Determine the common difference of the following sequence: {19, 13, 7, 1, -5, …}.
62.
Find the 25th term, {a_{25}}, of the arithmetic sequence with {a_1} = 13 and d = 1.7.
63.
Find the first term and the common difference of the arithmetic sequence with 8th term {b_8} = 50 and 15th term {b_{15}} = 106.
64.
Find the sum of the first 30 terms, {s_{30}}, for the arithmetic sequence with first term {a_1} = - 4 and common difference d = 3.5.
65.
Jem makes a stack of 5 pennies. Each day, Jem adds three pennies to the stack. How many pennies are in the stack after 10 days?
Geometric Sequences
66.
Determine the common ratio of the following geometric sequence: {6, 18, 54, 162, …}.
67.
Find the 6th term, {c_6}, of the geometric sequence with {c_1} = 400 and r = 0.25.
68.
Find the sum of the first 12 terms, {s_{12}}, for the geometric sequence with first term {a_1} = - 4 and common ratio r = - 1.25.
69.
Carolann and Tyler deposit $8,500 in an account bearing 5.5% interest compounded yearly. If they do not deposit any more money in that account, how much will be in the account after 15 years?
70.
The total number of ebooks sold in 2013 was 242 million ({a_1} = 242). Each year, the number of ebooks sold has declined by 3% (r = 0.97). How many ebooks were sold between 2013 and 2022?
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