MATH-1100-LN04&WBP06

Handouts are stored on this page in DjVu format; see the DjVu help if you have trouble reading these files. (They're avaialable in PDF on Canvas; see the link for your section immediately below.)

Course administration

For Section LN04

• Canvas page (where you must log in).
• Official syllabus (DjVu).
• Course policies (DjVu).
• Class hours: Mondays, Wednesdays, and Fridays from 10:00 to 10:50 in room U107.
• Final exam: May 16 Friday from 10:00 to 11:40 in room U107.

For Section WBP06

• Canvas page (where you must log in).
• Official syllabus (DjVu).
• Course policies (DjVu).
• Class hours: Online only.
• Final exam time: By appointment only.

Contact information

• Name: Toby Bartels, PhD.
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours:
  • on Mondays, Wednesdays, and Fridays from 1:00 PM to 2:00,
  • on Tuesdays and Thursdays from 2:30 PM to 3:30, and
  • by appointment,
  in room U9C and over Zoom meeting 610-024-2876.

Readings

Try to read this introduction before the first day of class:

• Objectives:
  • Understand what to expect from this course;
  • Know how to submit assignments.
• Reading:
  • The course policy document for your section above;
  • Section 1.1 (pages 1–7) from the textbook.
• Questions due on January 22 Wednesday or ASAP thereafter in Section WBP06 (submit these on Canvas):
  1. If you need to submit an assignment that can't be easily typed (such as a graph, a table, or a complicated mathematical expression), so that you find that you have to write it out by hand, how will you send me a picture of that?
  2. How will you get the final exam proctored? (Lincoln Testing Center, ProctorU, etc).
  You can change your mind about these later! (But let me know if you change your mind about #2.)
• Exercises from the textbook due on January 24 Friday or ASAP thereafter (submit these through MyLab): O.1.1, O.1.2, O.1.3, O.1.4, O.1.5, O.1.6, O.1.7, O.1.8, O.1.10.

Rational expressions

1. General review:
   • Objectives:
     • Review multiplying polynomials;
     • Review factoring techniques;
     • Review solving equations by factoring.
   • Reading from (mostly) the textbook:
     • Skim: Section 6.5 (pages 403–407);
     • Optional: my online factoring review.
   • Exercises due on January 24 Friday (submit these in class or on Canvas):
     1. Fill in the blank with a plural vocabulary word: In the product (3x − 2)(x + 4) = 3x² + 10x − 8, the polynomials 3x − 2 and x + 4 are the _____ of the polynomial 3x² + 10x − 8.
     2. Fill in the blanks with simpler equations: If AB = 0, then _____ or _____.
   • Exercises from the textbook due on January 27 Monday (submit these through MyLab): 2.2.75, 5.3.53, 5.5.13, 6.1.95, 6.2.47, 6.4.45.
2. Rational expressions:
   • Objectives:
     • Identify rational expressions;
     • Evaluate rational expressions;
     • Find when rational expressions are defined;
     • Simplify rational expressions.
   • Reading from (mostly) the textbook:
     • My notes on rational expressions;
     • Section 7.1 (pages 433–439).
   • Exercises due on January 27 Monday (submit these in class or on Canvas):
     1. Fill in the blank with a vocabulary word: A(n) _____ expression is the result of dividing two polynomials.
     2. Fill in the blank with a number (or a kind of number): The result of evaluating a rational expression is undefined if and only if the denominator evaluates to _____.
   • Exercises from the textbook due on January 29 Wednesday (submit these through MyLab): 7.1.21, 7.1.23, 7.1.25, 7.1.27, 7.1.29, 7.1.31, 7.1.33, 7.1.35, 7.1.37, 7.1.39, 7.1.41, 7.1.43, 7.1.45, 7.1.47, 7.1.49, 7.1.51, 7.1.85.
3. Multiplying and dividing rational expressions:
   • Objectives:
     • Multiply rational expressions;
     • Find the reciprocal of a rational expression;
     • Divide rational expressions;
     • Find common denominators of rational expressions;
     • Rewrite rational expressions to have common denominators.
   • Reading from the textbook:
     • Section 7.2 (pages 441–446);
     • Section 7.4 (pages 456–460).
   • Exercises due on January 29 Wednesday (submit these in class or on Canvas):
     1. Fill in the blank: To divide by a rational expression, multiply by its _____.
     2. Fill in the blank: The _____ _____ _____ of two rational expressions is the lowest-degree polynomial that is a multiple of both of the original expressions' denominators.
     3. What is the least common denominator of 1⁄8 and 5⁄18?
   • Exercises from the textbook due on January 31 Friday (submit these through MyLab): 7.2.31, 7.2.33, 7.2.35, 7.2.37, 7.2.39, 7.2.41, 7.2.43, 7.2.45, 7.2.47, 7.2.49, 7.2.51, 7.4.13, 7.4.17, 7.4.19, 7.4.23, 7.4.25, 7.4.35, 7.4.39, 7.4.43, 7.4.47, 7.4.51, 7.4.53, 7.4.57, 7.4.69, 7.5.45, 7.5.47, 7.5.49.
4. Adding and subtracting rational expressions:
   • Objectives:
     • Add rational expressions with the same denominator;
     • Subtract rational expressions with the same denominator;
     • Add rational expressions with different denominators;
     • Subtract rational expressions with different denominators.
   • Reading from the textbook:
     • Section 7.3 (pages 449–453);
     • Section 7.5 (pages 463–470).
   • Exercises due on January 31 Friday (submit these in class or on Canvas): For which of the following operations between rational expressions do you need to get a common denominator? (Say Yes or No for each.)
     1. Addition.
     2. Subtraction.
     3. Multiplication.
     4. Division.
   • Exercises from the textbook due on February 3 Monday (submit these through MyLab): 7.3.17, 7.3.23, 7.3.29, 7.3.31, 7.3.35, 7.3.41, 7.3.43, 7.3.49, 7.3.55, 7.3.61, 7.3.65, 7.3.73, 7.3.89, 7.5.51, 7.5.53, 7.5.55, 7.5.57, 7.5.59, 7.5.61, 7.5.63, 7.5.65, 7.5.67, 7.5.95.
5. Complex rational expressions:
   • Objectives:
     • Identify complex rational expressions;
     • Simply complex rational expressions;
     • Compare two methods to simplify complex rational expressions.
   • Reading from the textbook: Section 7.6 (pages 473–478).
   • Exercises due on February 3 Monday (submit these in class or on Canvas): Fill in the blanks with one word each:
     1. A rational expression with rational subexpressions inside it is called a _____ rational expression.
     2. If you simplify a rational expression by Method I (from Objective 1 on pages 474–476 of the textbook), then you divide the _____ and _____ after simplifying them separately.
     3. If you simplify a rational expression by Method II (from Objective 2 on pages 477&478 of the textbook), then you multiply the numerator and denominator by the _____ _____ _____ of the subexpressions.
   • Exercises from the textbook due on February 5 Wednesday (submit these through MyLab): 7.6.11, 7.6.13, 7.6.25, 7.6.27, 7.6.39, 7.6.41, 7.6.43, 7.6.45, 7.6.47, 7.6.49, 7.6.51.
6. Rational equations:
   • Objectives:
     • Review solving polynomial equations;
     • Identify rational equations;
     • Solve rational equations;
     • Check rational equations for extraneous solutions;
     • Compare two methods to solve rational equations.
   • Reading from (mostly) the textbook:
     • Skim: Section 6.6 (pages 409–415);
     • My notes on rational equations;
     • Section 7.7 (pages 481–490);
     • Section 7.8 through the beginning of Objective 1 (pages 493&494).
   • Exercises due on February 5 Wednesday (submit these in class or on Canvas):
     1. Fill in the blank with an appropriate term: A _____ equation is an equation where both sides are rational expressions.
     2. True or false: After solving a rational equation, even if you're sure that you didn't make any mistakes, you generally still need to check your solutions.
     3. Fill in the blanks with appropriate variables: If A/‍B = C/‍D, then A___ = B___.
   • Exercises from the textbook due on February 7 Friday (submit these through MyLab): 7.7.15, 7.7.17, 7.7.19, 7.7.21, 7.7.23, 7.7.25, 7.7.27, 7.7.29, 7.7.31, 7.7.33, 7.7.47, 7.7.49, 7.7.51, 7.7.53, 7.8.19, 7.8.21, 7.8.29.
7. Word problems with division:
   • Objectives:
     • Set up word problems involving proportions;
     • Set up word problems involving similar triangles;
     • Set up word problems involving rates of work;
     • Set up word problems involving uniform motion;
     • Solve word problems using rational equations once they're set up.
   • Reading from the textbook:
     • Skim: Section 6.7 (pages 417–421);
     • Read: The rest of Section 7.8 (pages 494–502).
   • Exercises due on February 7 Friday (submit these in class or on Canvas):
     1. True or false: If the angles in two geometric figures are equal, then their corresponding lengths are also equal.
     2. True or false: If the angles in two geometric figures are equal, then their corresponding lengths are proportional.
     3. If a job can be completed in 4 hours, then what is the rate at which the job is completed, in jobs per hour?
   • Exercises from the textbook due on February 10 Monday (submit these through MyLab): 7.8.41, 7.8.43, 7.8.45, 7.8.47, 7.8.49, 7.8.51, 7.8.53, 7.8.55, 7.8.57, 7.8.61, 7.8.67, 7.8.69, 7.8.73, 7.8.79.

Systems of equations and inequalities

8. Systems of equations:
   • Objectives:
     • Test solutions of systems of equations;
     • Graph systems of linear equations;
     • Solve simple systems of linear equations by graphing.
   • Reading from the textbook: Section 4.1 through Objective 3 (pages 249–255).
   • Exercises due on February 10 Monday (submit these in class or on Canvas):
     1. Answer Yes or No: Suppose that you have a system of equations and a point that might be a solution. If the point is a solution to one equation in the system but not a solution to another equation in the system, then is that point a solution to the system of equations?
     2. Given a system of two equations in the two variables x and y, if the graphs of the two equations intersect at (and only at) the point (3, 5), then what is the solution of the system? (Give explicitly the value of x and the value of y.)
   • Exercises from the textbook due on February 12 Wednesday (submit these through MyLab): 4.1.17, 4.1.19, 4.1.21, 4.1.39, 4.1.41, 4.1.43, 4.1.45, 4.1.59, 4.1.61, 4.1.63, 4.1.65.
9. Solving systems of equations:
   • Objectives:
     • Solve systems of linear equations in two or three variables;
     • Compare two methods for solving systems of linear equations;
     • Classify systems of linear equations (with the same number of equations as variables) as consistent or inconsistent, and dependent or independent.
   • Reading from (mostly) the textbook:
     • Section 4.2 through Objective 1 (pages 260–264);
     • Section 4.3 through Objective 1 (pages 268–272);
     • My notes on systems of equations.
   • Exercises due on February 12 Wednesday (submit these in class or on Canvas):
     1. Fill in the blanks with one vocabulary word each:
        1. If a system of equations has no solutions, then the system is _____;
        2. If a system of linear equations has the same number of variables as equations, then it is _____ if and only if it has exactly one solution.
     2. Consider the system of equations consisting of x + 3y = 4 (equation 1) and 2x + 3y = 5 (equation 2).
        1. If I solve equation (1) for x to get x = 4 − 3y and apply this to equation (2) to get 2(4 − 3y) + 3y = 5 (and continue from there), then what method am I using to solve this system?
        2. If instead I multiply equation (1) by −2 to get −2x − 6y = −8 and combine this with equation (2) to get −3y = −3 (and continue from there), then what method am I using to solve this system?
   • Exercises from the textbook due on February 14 Friday (submit these through MyLab): 4.2.13, 4.2.15, 4.2.17, 4.2.23, 4.2.25, 4.2.35, 4.2.37, 4.2.39, 4.2.41, 4.3.13, 4.3.15, 4.3.17, 4.3.27, 4.3.29, 4.3.31, 4.3.35, 4.3.47, 4.3.49, 4.3.55.
10. Word problems with multiple variables:
    • Objectives:
      • Set up linear equations with multiple variables to model complementary and supplementary angles;
      • Set up linear equations with multiple variables to model uniform motion;
      • Solve word problems involving multiple linear equations in multiple variables once they're set up.
    • Reading from the textbook:
      • Section 4.1 Objective 4 (pages 256&257);
      • Section 4.2 Objective 2 (page 265);
      • Section 4.3 Objective 2 (page 273);
      • Section 4.4 (pages 277–282).
    • Exercises due on February 19 Wednesday (submit these in class or on Canvas):
      1. If an angle has a measure of x°, while its complement has a measure of y°, then what equation holds between x and y?
      2. If an angle has a measure of x°, while its supplement has a measure of y°, then what equation holds between x and y?
      3. If d is the distance travelled by an object travelling at a constant speed r for a period of time t, then what equation holds between d, r, and t? (Write this equation without using division.)
    • Exercises from the textbook due on February 21 Friday (submit these through MyLab): 4.2.53, 4.3.69, 4.3.71, 4.4.9, 4.4.11, 4.4.13, 4.4.15, 4.4.19, 4.4.23, 4.4.25, 4.4.27, 4.4.29, 4.4.31, 4.4.33, 4.4.35.
11. Mixture problems:
    • Objectives:
      • Make tables to model mixture problems;
      • Set up systems of linear equations to model mixture problems;
      • Solve mixture problems.
    • Reading from the textbook: Section 4.5 (pages 284–291).
    • Exercises due on February 21 Friday (submit these in class or on Canvas):
      1. Suppose that you have c children, paying $1 each, and a adults, paying $5 each; write down an algebraic expression for the total amount paid by these people, in dollars.
      2. Suppose that you have x kilograms of an item worth $1/‍kg and y kilograms of an item worth $5/‍kg; write down an algebraic expression for the total value of these items, in dollars.
      3. Suppose that you have x litres of a 1% solution (by volume) and y litres of a 5% solution; write down an algebraic expression for the total volume of the pure solute, in litres.
      4. Suppose that you have p pennies (worth 1 cent each) and n nickels (worth 5 cents each); write down an algebraic expression for the total value of these coins, and indicate what unit you are using for this value.
    • Exercises from the textbook due on February 24 Monday (submit these through MyLab): 4.5.9, 4.5.11, 4.5.13, 4.5.15, 4.5.17, 4.5.19, 4.5.21, 4.5.23, 4.5.25, 4.5.27, 4.5.29, 4.5.35, 4.5.37.
12. Compound inequalities:
    • Objectives:
      • Review linear inequalities;
      • Determine the truth or falsehood of a compound statement from the truth and/or falsehood of the constituent statements;
      • Express the solution set of a compound inequality in interval notation;
      • Solve compound statements by solving the individual statements;
      • Solve linear compound inequalities directly.
    • Reading from (mostly) the textbook:
      • Skim: Section 2.8 (pages 148–157);
      • My notes on inequalities;
      • Section 8.6 through Objective 3 (pages 574–580).
    • Exercises due on February 24 Monday (submit these in class or on Canvas): Which of these statements are always true and which are always false?
      1. x ≤ 4 and x > 5;
      2. x ≥ 2 or x < 3;
      3. 7 ≤ x < 6.
    • Exercises from the textbook due on February 26 Wednesday (submit these through MyLab): 8.6.43, 8.6.45, 8.6.47, 8.6.49, 8.6.51, 8.6.53, 8.6.55, 8.6.57, 8.6.59, 8.6.67, 8.6.69, 8.6.71, 8.6.73, 8.6.81, 8.6.83, 8.6.85, 8.6.87, 8.6.89, 8.6.91, 8.6.93.
13. Absolute-value inequalities:
    • Objectives:
      • Evaluate absolute values;
      • Test absolute-value statements;
      • Convert absolute-value inequalities into compound inequalities or compound statements;
      • Solve simple absolute-value inequalities.
    • Reading from (mostly) the textbook:
      • Section 8.7 introduction (page 584);
      • Section 8.7 Objectives 2&3 (pages 588–591);
      • My notes on absolute-value problems.
    • Exercises due on February 26 Wednesday (submit these in class or on Canvas): Fill in the blanks with inequalities (possibly compound) that don't involve absolute values:
      1. |‍u| < a is equivalent to _____.
      2. |‍u| ≤ a is equivalent to _____.
      3. |‍u| > a is equivalent to _____ or _____.
      4. |‍u| ≥ a is equivalent to _____ or _____.
    • Exercises from the textbook due on February 28 Friday (submit these through MyLab): 8.7.69, 8.7.71, 8.7.73, 8.7.75, 8.7.77, 8.7.85, 8.7.87, 8.7.89, 8.7.91.
14. Absolute-value equations:
    • Objectives:
      • Convert absolute-value equations into compound statements;
      • Solve simple absolute-value equations;
      • Solve equations between absolute values.
    • Reading from the textbook: Section 8.7 Objective 1 (pages 584–587).
    • Exercises due on February 28 Friday (submit these in class or on Canvas): Fill in the blanks with equations that don't involve absolute values:
      1. If a ≥ 0, then |‍u| = a is equivalent to _____ or _____.
      2. |‍u| = |‍v| is equivalent to _____ or _____.
    • Exercises from the textbook due on March 3 Monday (submit these through MyLab): 8.7.43, 8.7.47, 8.7.49, 8.7.51, 8.7.53, 8.7.55, 8.7.57, 8.7.59, 8.7.61, 8.7.63, 8.7.65, 8.7.103, 8.7.105, 8.7.107, 8.7.109.
15. Word problems with inequalities and absolute values:
    • Objectives:
      • Set up compound inequalities to model situations where a quantity is bounded;
      • Set up absolute-value inequalities to model situations where a quantity's variation is bounded.
    • Reading from the textbook:
      • Section 8.6 Objective 4 (pages 580&581);
      • Section 8.7 Objective 4 (pages 591&592).
    • Exercises due on March 3 Monday (submit these in class or on Canvas):
      1. Suppose that a and b are real numbers, with a ≤ b. If x must lie between a and b, inclusive, then what compound inequality expresses this fact?
      2. Suppose that c and e are real numbers, with e > 0. If x is meant to take the value c, with a tolerance of e, then what absolute-value inequality expresses this fact?
    • Exercises from the textbook due on March 5 Wednesday (submit these through MyLab): 8.6.101, 8.6.103, 8.6.105, 8.6.107, 8.6.109, 8.7.121, 8.7.123, 8.7.125, 8.7.127.

Roots and radicals

16. Roots:
    • Objectives:
      • Define real roots with odd indices;
      • Define principal roots with even indices;
      • Identify when a root is defined in the real-number system;
      • Evaluate rational roots of rational numbers.
    • Reading from (mostly) the textbook:
      • Skim: Section 9.1 (pages 616–619);
      • Section 9.2 through Objective 2 (pages 620–623);
      • My notes on roots.
    • Exercises due on March 5 Wednesday (submit these in class or here on Canvas):
      1. In the expression ⁿ√b, the real number b is the _____, and the natural number n is the _____.
      2. Under which of the following conditions is ⁿ√b (the principal real nth root of b) defined (as a real number)? Answer Yes or No for each.
         1. When n is even and b is positive;
         2. When n is even and b is negative;
         3. When n is odd and b is positive;
         4. When n is odd and b is negative.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 7 Friday (submit these through MyLab in the Next assignment after the discussion): 9.1.33, 9.1.35, 9.1.37, 9.2.37, 9.2.39, 9.2.41, 9.2.43, 9.2.45, 9.2.47, 9.2.49, 9.2.51, 9.2.101, 9.2.103, 9.2.105, 9.2.111.
17. Fractional exponents:
    • Objectives:
      • Convert an expression with a rational exponent to one with a power and/or a root;
      • Evaluate rational powers of rational numbers with rational exponents;
      • Test alleged rules of exponentiation.
    • Reading from the textbook:
      • The rest of Section 9.2 (pages 623–626);
      • Section 9.3 (pages 628–632);
      • Warning: Some of the rules listed on page 629 under "The Laws of Exponents" are not correct as stated, where a and b can be any real numbers and r and s can be any rational numbers. It's safer to learn these rules only when a and b are both positive (or r and s are both integers). In the next reading, I'll give some rules that you can safely use in all situations involving real numbers, expressed using radicals instead of fractional exponents.
    • Exercises due on March 7 Friday (submit these in class or here on Canvas):
      1. Write ⁿ√b using a fractional exponent.
      2. Assuming that m/‍n is a rational number in lowest terms, write b^m/‍n using only roots and powers with integer exponents.
      3. Consider the Power Rule as stated on page 629 of the textbook: (a^r)^s = a^r⋅s, where a is a real number and r and s are rational numbers. Check this rule when a is −1, r is 2, and s is ½; what do you get for the left-hand side and the right-hand side in this example? Is the rule correct in this case?
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 17 Monday (submit these through MyLab in the Next assignment after the discussion): 9.2.73, 9.2.75, 9.2.93, 9.2.95, 9.2.97, 9.2.99, 9.2.109, 9.2.113, 9.4.37, 9.4.39, 9.4.133, 9.3.69, 9.3.71, 9.3.75.
18. Simplifying radical expressions:
    • Objectives:
      • Simplify a root of a power;
      • Simplify a root when the radicand has a power as a factor;
      • Simplify a root of a power when the index and exponent don't match;
      • Simplify a root of a root;
      • Know when absolute values can be removed.
    • Reading from (mostly) the textbook:
      • My notes on simplifying roots;
      • Section 9.4 (pages 634–641).
    • Exercises due on March 21 Friday (submit these in class or here on Canvas):
      1. Simplify √x² without using roots or fractional exponents and without making any assumptions about x (besides that it's a real number).
      2. Assuming that ⁿ√a ⁿ√b exists (as a real number), express it as a single root.
      3. Assuming that ^m√ⁿ√b exists (as a real number), express it as a single root.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 24 Monday (submit these through MyLab in the Next assignment after the discussion): 9.2.53, 9.2.55, 9.2.57, 9.2.107, 9.4.41, 9.4.43, 9.4.45, 9.4.47, 9.4.49, 9.4.119, 9.4.121, 9.4.123, 9.4.125, 9.4.127, 9.4.129, 9.4.131, 9.3.65, 9.3.87.
19. Adding and subtracting radical expressions:
    • Objectives:
      • Identify like terms in a radical expression;
      • Add radical expressions;
      • Take the opposite of a radical expression;
      • Subtract radical expressions.
    • Reading from the textbook: Section 9.5 through Objective 1 (pages 643–645).
    • Exercises due on March 24 Monday (submit these in class or here on Canvas):
      1. As 2x + 3x = 5x, so 2√7 + 3√7 = _____.
      2. As (x + 2)(x + 3) = x² + 5x + 6, so (³√7 + 2)(³√7 + 3) = _____. (Remember that (³√7)² = ³√49.)
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 26 Wednesday (submit these through MyLab in the Next assignment after the discussion): 9.5.19, 9.5.21, 9.5.23, 9.5.25, 9.5.27, 9.5.29, 9.5.31, 9.5.33, 9.5.41.
20. Multiplying radical expressions:
    • Objectives:
      • Multiply roots;
      • Raise a root to a power;
      • Multiply radical expressions;
      • Raise a radical expressions to a power.
    • Reading from the textbook: The rest of Section 9.5 (pages 645–647).
    • Exercises due on March 26 Wednesday (submit these in class or here on Canvas):
      1. While x² doesn't simplify, (√x)² = _____.
      2. As (x + 2)(x + 3) = x² + 5x + 6, so (√x + 2)(√x + 3) = _____. (Use the previous result to simplify.)
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 28 Friday (submit these through MyLab in the Next assignment after the discussion): 9.5.49, 9.5.51, 9.5.53, 9.5.55, 9.5.57, 9.5.63, 9.5.65, 9.5.67, 9.5.69, 9.5.71, 9.5.75, 9.5.109.
21. Dividing radical expressions:
    • Objectives:
      • Rationalize a denominator that's a root;
      • Rationalize a denominator with two terms, one rational and one a square root;
      • Rationalize a denominator with two terms, each a square root;
      • Take the reciprocal of a radical expression;
      • Divide radical expressions.
    • Reading from the textbook: Section 9.6 (pages 649–653).
    • Exercises due on March 28 Friday (submit these in class or here on Canvas):
      1. To rationalize the denominator of a/‍√b, multiply top and bottom by _____.
      2. To rationalize the denominator of a/‍³√b, multiply top and bottom by _____.
      3. To rationalize the denominator of a/‍³√b², multiply top and bottom by _____.
      4. To rationalize the denominator of a/‍(√b + c), multiply top and bottom by _____.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on March 31 Monday (submit these through MyLab in the Next assignment after the discussion): 9.6.13, 9.6.15, 9.6.17, 9.6.19, 9.6.21, 9.6.23, 9.6.25, 9.6.27, 9.6.29, 9.6.31, 9.6.33, 9.6.37, 9.6.41, 9.6.47, 9.6.51, 9.6.61.
22. Radical equations:
    • Objectives:
      • Identify the root in a radical equation;
      • Solve radical equations with odd-indexed roots;
      • Solve radical equations with even-indexed roots;
      • Solve radical equations with multiple roots.
    • Reading from the textbook: Section 9.8 (pages 662–667).
    • Exercises due on March 31 Monday (submit these in class or here on Canvas):
      1. Fill in the blank with an appropriate term: A _____ equation is an equation where one or both sides are radical expressions.
      2. True or false: After solving a radical equation, even if you're sure that you didn't make any mistakes, you generally still need to check your solutions.
      3. Fill in the blank with an equation that doesn't involve radicals: If a ≥ 0, then √u = a is equivalent to _____.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 2 Wednesday (submit these through MyLab in the Next assignment after the discussion): 9.8.17, 9.8.19, 9.8.23, 9.8.33, 9.8.39, 9.8.43, 9.8.47, 9.8.51, 9.8.55, 9.8.57, 9.8.61, 9.8.105.
23. Complex numbers:
    • Objectives:
      • Graph a complex number on the complex-number plane;
      • Take the principal square root of a negative number;
      • Add complex numbers;
      • Subtract complex numbers;
      • Multiply complex numbers.
    • Reading from the textbook: Section 9.9 through Objective 3 (pages 670–676).
    • Exercises due on April 2 Wednesday (submit these in class or here on Canvas):
      1. Fill in the blank with a number: i² = ___ (where i is the imaginary unit).
      2. Fill in the blank with an algebraic expression: If a is a positive real number, then √−a = ___. (Write this so that the expression doesn't include any root operations whose outputs are imaginary.)
      3. True or false: Every real number is also a complex number.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 4 Friday (submit these through MyLab in the Next assignment after the discussion): 9.9.25, 9.9.27, 9.9.29, 9.9.33, 9.9.35, 9.9.37, 9.9.39, 9.9.41, 9.9.43, 9.9.45, 9.9.51, 9.9.53, 9.9.55, 9.9.57.
24. Advanced operations on complex numbers:
    • Objectives:
      • Take the complex conjugate of a complex number;
      • Take the absolute value of a complex number;
      • Take the reciprocal of a complex number;
      • Divide complex numbers;
      • Raise a complex number to a power.
    • Reading from the textbook: The rest of Section 9.9 (pages 676–678).
    • Exercises due on April 4 Friday (submit these in class or here on Canvas): Suppose that a and b are real numbers.
      1. What is the complex conjugate of a + bi?
      2. Write the reciprocal of a + bi with only real denominators.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 7 Monday (submit these through MyLab in the Next assignment after the discussion): 9.9.81, 9.9.83, 9.9.85, 9.9.87, 9.9.89, 9.9.95, 9.9.97, 9.9.99, 9.9.101, 9.9.141.

Quadratic equations and functions

25. Quadratic equations:
    • Objectives: TBA.
    • Reading from the textbook: Section 10.1 through Objective 1 (pages 690–694).
    • Exercises due on April 7 Monday (submit these in class or here on Canvas):
      1. Solve x² = q² for x.
      2. Assuming that c ≠ 0, solve x² = c for x in the complex-number system.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 9 Wednesday (submit these through MyLab in the Next assignment after the discussion): 10.1.19, 10.1.21, 10.1.23, 10.1.25, 10.1.27, 10.1.29, 10.1.31, 10.1.33.
26. Completing the square:
    • Objectives: TBA.
    • Reading from (mostly) the textbook:
      • Section 10.1 Objectives 2&3 (pages 694–697);
      • My notes on solving quadratic equations.
    • Exercises due on April 9 Wednesday (submit these in class or here on Canvas):
      1. Starting from x² + 2px, what do you add to complete the square?
      2. Starting from x² + bx, what do you add to complete the square?
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 11 Friday (submit these through MyLab in the Next assignment after the discussion): 10.1.45, 10.1.47, 10.1.49, 10.1.51, 10.1.53, 10.1.55, 10.1.57, 10.1.59, 10.1.61, 10.1.63, 10.1.65, 10.1.67.
27. The quadratic formula:
    • Objectives: TBA.
    • Reading from (mostly) the textbook:
      • Section 10.2 through Objective 2 (pages 702–711);
      • My notes on classifying solutions to quadratic equations.
    • Exercises due on April 16 Wednesday (submit these in class or here on Canvas):
      1. Assuming that a ≠ 0, solve ax² + bx + c = 0 for x in the complex-number system.
      2. Fill in the blank with a vocabulary word: The _____ of ax² + bx + c is b² − 4ac.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 18 Friday (submit these through MyLab in the Next assignment after the discussion): 10.2.23, 10.2.25, 10.2.27, 10.2.29, 10.2.31, 10.2.33, 10.2.35, 10.2.37, 10.2.39, 10.2.41, 10.2.43, 10.2.45, 10.2.47, 10.2.49.
28. Fancy equations:
    • Objectives: TBA.
    • Reading from the textbook: Section 10.3 (pages 716–720).
    • Exercises due on April 18 Friday (submit these in class or here on Canvas):
      1. To turn ³√x² + ³√x = 1 into a quadratic equation, substitute u = ___.
      2. To turn 1/‍x² + 1/‍x = 1 into a quadratic equation, substitute u = ___.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 21 Monday (submit these through MyLab in the Next assignment after the discussion): 10.2.71, 10.2.73, 10.2.75, 10.3.49, 10.3.51, 10.3.53, 10.3.55, 10.3.57, 10.3.59.
29. Word problems with quadratic equations and roots:
    • Objectives: TBA.
    • Reading from the textbook:
      • Section 10.1 Objective 4 (pages 697–699);
      • Section 10.2 Objective 3 (pages 711&712).
    • Exercises due on April 21 Monday (submit these in class or here on Canvas):
      1. Pythagorean Theorem: If a, b, and c are the lengths of the sides of a right triangle, with c the length of the side opposite the right angle, then what equation holds between a, b, and c?
      2. If x² = 4, where x is the length of a road in miles, then what is the length of the road?
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 23 Wednesday (submit these through MyLab in the Next assignment after the discussion): 10.1.75, 10.1.77, 10.1.83, 10.1.95, 10.1.97, 10.1.99, 10.2.87, 10.2.89, 10.2.93.
30. Graphs:
    • Objectives: TBA.
    • Reading from the textbook: Section 8.1 (pages 521–528).
    • Exercises due on April 23 Wednesday (submit these in class or here on Canvas):
      1. The two number lines that mark the coordinates in a rectangular coordinate system are the coordinate _____, and the point where they intersect is the _____.
      2. A point on a graph that is also on a coordinate axis is a(n) _____ of that graph.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 25 Friday (submit these through MyLab in the Next assignment after the discussion): 8.1.17, 8.1.19, 8.1.21, 8.1.23, 8.1.25, 8.1.33, 8.1.39, 8.1.45, 8.1.49, 8.1.53, 8.1.55, 8.1.57.
31. Relations:
    • Objectives: TBA.
    • Reading from the textbook: Section 8.2 (pages 531–535).
    • Exercises due on April 25 Friday (submit these in class or here on Canvas):
      1. The ordered pairs (a, b) and (c, d) are equal if and only if ___ = ___ and ___ = ___.
      2. If (3, 5) is on the graph of a relation, then 3 belongs to the _____ of the relation, and 5 belongs to its _____.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 28 Monday (submit these through MyLab in the Next assignment after the discussion): 8.2.27, 8.2.29, 8.2.31, 8.2.33, 8.2.39, 8.2.45, 8.2.49, 8.2.53.
32. Functions:
    • Objectives: TBA.
    • Reading from the textbook: Section 8.3 (pages 538–546).
    • Exercises due on April 28 Monday (submit these in class or here on Canvas):
      1. Fill in the blank with a number: A function can be interpreted as a relation in which each element of the domain is related to ____ element(s) of the range.
      2. Fill in the blanks with variables: Given an equation in the variables x and y (in that order) and assuming that it can be solved for ___, the equation represents y as a function of x if and only if there is at most one solution for each value of ____.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on April 30 Wednesday (submit these through MyLab in the Next assignment after the discussion): 8.3.35, 8.3.37, 8.3.39, 8.3.41, 8.3.43, 8.3.45, 8.3.47, 8.3.49, 8.3.51, 8.3.53, 8.3.55, 8.3.57, 8.3.59, 8.3.73, 8.3.75, 8.3.77, 8.3.79.
33. Graphs of functions:
    • Objectives: TBA.
    • Reading from the textbook: Section 8.4 (pages 549–555).
    • Exercises due on April 30 Wednesday (submit these in class or here on Canvas): Fill in the blanks with mathematical expressions:
      1. Fill in the blank with a geometric word: The graph of a relation is the graph of a function if and only if every _____ line goes through the graph at most once.
      2. If (3, 5) is a point on the graph of a function f, then f(___) = ___.
      3. If g(2) = 4 for a function g, then _____ is a point on the graph of g.
    • Discuss this in the Next assignment.
    • Exercises from the textbook due on May 2 Friday (submit these through MyLab in the Next assignment after the discussion): 8.4.17, 8.4.19, 8.4.22, 8.4.31, 8.4.33, 8.4.37, 8.4.39, 8.4.51, 10.2.77.

Quizzes

1. Rational expressions:
   • Review date: February 14 Friday.
   • Date due: February 17 Monday.
   • Corresponding problems sets: 1–7.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work here on Canvas, at least one intermediate step for each result.
2. Systems of equations and inequalities:
   • Review date: March 17 Monday.
   • Date due: March 19 Wednesday.
   • Corresponding problems sets: 8–15.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work here on Canvas, at least one intermediate step for each result except for those in #1, #4, and the first part of #7.
3. Roots and radicals:
   • Review date: April 11 Friday.
   • Date due: April 14 Monday.
   • Corresponding problems sets: 16–24.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work here on Canvas, at least one intermediate step for each result, and at last two intermediate steps in #6.
4. Quadratic equations and functions:
   • Review date: May 2 Friday.
   • Date due: May 5 Monday.
   • Corresponding problems sets: 25–33.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work here on Canvas, at least one intermediate step for each result. For #3, use any method and solve in the complex-number system. For #8, include a table of values.

Final exam

For the exam, you may use one sheet of notes that you wrote yourself; please take a scan or a picture of this (both sides) and submit it here on Canvas. However, you may not use your book or anything else not written by you. You certainly should not talk to other people! Calculators are allowed (although you shouldn't really need one), but not communication devices (like cell phones).

The exam consists of questions similar in style and content to those in the practice exam (DjVu).

Even for Section WBP06, the final exam is proctored. If you're near any of the three main SCC campuses (Lincoln, Beatrice, Milford), then you can schedule the exam at one of the Testing Centers; it will automatically be ready for you at Lincoln, but let me know if you plan to take it at Beatrice or Milford, so that I can have it ready for you there. If you have access to a computer with a webcam and mike, then you can take it using ProctorU for a small fee; let me know if you want to do this so that I can send you an invitation to schedule it. If you're near Lincoln, then we may be able to schedule a time for you to take the exam with me in person. If none of these will work for you, then contact me as soon as possible!

The permanent URI of this web page is https://tobybartels.name/MATH-1100/2025SP/.