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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

Understanding Percent
1.
Convert 0.45 to percent form.
2.
What is 70% of 200?
3.
Rewrite the fraction \frac{{240}}{{100}} as a percentage.
4.
20 is what percent of 500?
Discounts, Markups, and Sales Tax
5.
An item with a retail price of $250.00 is on sale for 30% off. What is the sale price of the item? Round to the nearest penny.
6.
The sales price of an item is $38.50 after a 40% discount. What was the retail price of the item? Round to the nearest penny.
7.
A retailer buys an item for $1,000.00 and has a 65% markup. What is the retail price of the item? Round to the nearest penny.
8.
The sale price of an item is $46.00 and the retail price is $65.00. What is the percent discount? Round to two decimal places.
9.
The retail price of an item is $345.38 and sales tax in the region is 8.25%. How much is the sales tax?
Simple Interest
10.
$3,000 is invested in a 5-year CD earning 2.25% interest. How much is the CD worth in 5 years?
11.
A $4,000.00 simple interest loan is taken out for 3 years at 12.5%. How much is owed when the loan comes due?
12.
A $10,000 loan with annual simple interest of 14.9% is taken out for 90 days. How much is due in 90 days?
13.
A simple interest loan for $20,000 is taken out at 13.9% annual interest rate. A partial payment of $13,500.00 is made 30 days into the loan period. After this payment, what will the remaining balance be?
14.
Find the present value of an investment with future value of $15,000 if the investment earns 3.55% simple interest for 10 years?
Compound Interest
15.
Find the future value after 20 years of $15,000 deposited in an account bearing 4.26% interest compounded quarterly.
16.
What is the effective annual yield for an account bearing 3.21% interest compounded quarterly? Round to two decimal places if necessary.
17.
Find the present value of $100,000 in an account bearing 5.25% interest compounded daily after 30 years.
Making a Personal Budget
18.
In budgeting, what is the difference between an expense that is a need and an expense that is a want?
19.
Apply the 50-30-20 budget philosophy to a monthly income of $6,000.00.
20.
Create the budget for a person with the following income and bills, and determine how much the income exceeds or falls short of the expenses:
Job = $5,250, Side job = $550, rent = $1,150.00, utilities = $150.00, internet = $39.99, student loans = $375.00, food = $550.00, bus and subway = $112.00, credit cards = $200.00, entertainment = $400.00, clothing = $150.00.
21.
In question 20, the budget for a person was created. Can the person afford to buy a car if the monthly payments will be $365.50, monthly car insurance will be $114.75, and gasoline will be $200.00?
Methods of Savings
22.
Why is a CD less flexible than a money market account?
23.
Which is likely to have the highest interest rate, a savings account, CD, or money market account?
24.
$3,000 is deposited in a money market account bearing 3.88% interest compounded monthly. How much is the account worth in 15 years?
25.
Refer to question 24. What is the return on investment for the money market account? Round to two decimal places, if necessary.
26.
$300 is deposited monthly in an ordinary annuity that bears 6.5% interest compounded monthly. How much is in the annuity after 30 years?
27.
How much must be deposited quarterly in an account bearing 4.89% interest compounded quarterly for 30 years so the account has a future value of $500,000?
Investments
28.
Why is investing in a stock riskier than in a mutual fund?
29.
Which investment offers high rates of return with reduced risk?
30.
Which investment offer a fixed rate of return over time?
31.
Which is the riskiest investment?
32.
How much is earned on a 10-year bond with issue price of $1,000 that pays 3.9% annually?
33.
Henri’s employer matches up to 6% of salary for IRA contributions. Henri’s annual income is $52,500. If Henri wants to deposit $3,000 annually in his IRA, how much in matching funds does the employer deposit in the IRA?
34.
How much must be deposited quarterly in a mutual fund that is expected to earn 11.2% interest compounded quarterly if the account is to be worth $1,000,000 after 38 years?
35.
Lorraine purchases stocks for $5,000. The stocks paid dividends by reinvesting the dividends in stock. She sold the stock for $13,750 after 6 years. What was Lorraine’s annual return on that investment? Round to two decimal places if necessary.
36.
What are two ways stocks earn money?
The Basics of Loans
37.
What is an installment loan?
38.
An installment loan with monthly payments has an outstanding balance of $3,560. If the annual interest rate is 9%, how much interest will be paid that month?
39.
A loan for $42,000 is taken out for 6 years at 7.5% interest. What are the payments for that loan?
40.
The total interest paid on a loan was $4,500. The loan had an origination fee of $400.00, a $125.00 processing fee, and a filing fee of $250.00. How much was the cost of financing for that loan?
41.
Using the amortization table below, what is the remaining balance after payment 25?
A spreadsheet labeled as amortization schedule calculator. The sheet calculates the repayment for the loan amount of $17,500.00 for an interest rate of 8.25 percent annually and the monthly payment is $356.93. The factors include calculations such as month, payment, principal, interest, total, and interest and balance.
Understanding Student Loans
42.
If a college program takes 5 years, how long is the student’s eligibility period for student loans?
43.
What is the funding gap for a student with cost of college equal to $35,750 and non-loan financial aid of $24,150?
44.
What is the maximum amount of federal subsidized and unsubsidized loans for a dependent student in their third year of an undergraduate data science program?
45.
A single person has gross income of $28,500. Their poverty guideline is $12,000. What is their discretionary income?
Credit Cards
46.
The billing cycle for a credit card goes from March 15 to April 14. The balance at the start of the billing cycle is $450.00. The list of transactions on the card is below. Find the average daily balance for the billing cycle.
Date Activity Amount
15-Mar Billing Date Balance $450.00
21-Mar Movie $50.00
28-Mar Gasoline $65.00
31-Mar Snacks $15.50
1-Apr Dinner $63.60
1-Apr Payment $300.00
1-Apr Gasoline $48.90
9-Apr Plane Tickets $288.50
47.
The average daily balance for Greg’s last credit card statement was $1,403.50. The card charges 15.9% interest. If the billing cycle for that statement was 30 days, how much interest is Greg charged?
48.
The billing cycle for a credit card goes from March 15 to April 14. The balance at the start of the billing cycle is $450.00. The list of transactions on the card is below. The interest rate is 15.9%. What is the balance due at the end of the billing cycle?
Date Activity Amount
15-Mar Billing Date Balance $450.00
21-Mar Movie $50.00
28-Mar Gasoline $65.00
31-Mar Snacks $15.50
1-Apr Dinner $63.60
1-Apr Payment $300.00
1-Apr Gasoline $48.90
9-Apr Plane Tickets $288.50
Buying or Leasing a Car
49.
Name three common fees when leasing a car.
50.
Name three common fees when buying a car.
51.
If the cost of a car is $35,500, and the residual value of the car after 3 years is $27,800, what is the monthly depreciation for the car?
52.
What is the annual interest rate if the money factor is 0.000045?
53.
What is the payment for a lease on a car if the price of the car is $29,900, the residual price of the car is $16,500, the lease is for 24 months, and the APR is 8.9%?
Renting and Homeownership
54.
Name two advantages of renting a residence.
55.
Name two advantages of buying a home.
56.
What is PMI?
57.
What are the monthly payments for a 25-year mortgage for $165,000 at 4.8% interest, not including escrow?
58.
What are the monthly payments, including escrow, for a 25-year mortgage for $165,000 at 4.8% interest, if the property taxes are $5,200 annually, the homeowner’s insurance is $825 every 6 months, and the PMI is $45 per month?
Income Tax
59.
What is the maximum gift that a person can receive that is an exemption on federal income taxes?
60.
Find the gross income if a person earns $51,500 at their full-time job, they earn $5,300 for contracted services, and $5,000 in gambling winnings.
61.
Find adjusted gross income for a person with a gross income of $67,850, if they had a $2,000 gift, they paid $1,000 in mortgage interest, $4,250 in property taxes, and they contributed $750 to a qualifying charity.
62.
How much SSI is paid by a person with an annual income of $183,500?
63.
How much in FICA taxes are paid from a person’s paycheck with gross income of $3,450?
64.
How much in federal income tax does a person filing single pay if their taxable income is $205,240? Use the tax table below.
Bracket Lower Income Limit Upper Income Limit Tax Rate
1 0 $10,275 10%
2 $10,276 $41,775 12%
3 $41,776 $89,075 22%
4 $89,076 $170,050 24%
5 $170,051 $215,950 32%
6 $215,951 $539,900 35%
7 $539,901 37%
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