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 from my notes: The course policy document for your section above.
• Reading from the textbook: Section 1.1 (pages 1–7).
• Questions due on January 22 Wednesday or ASAP thereafter in Section WBP06 (submit these here 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.)
• Discuss this in the Next item.
• Exercises from the textbook due on January 24 Friday or ASAP thereafter (submit these through MyLab in the Next item after the discussion): 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:
   • Reading from the textbook: Skim: Section 6.5 (pages 403–407).
   • Exercises due on January 24 Friday (submit these here on Canvas or in class):
     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 _____.
   • Discuss this in the Next item.
   • Exercises from the textbook due on January 27 Monday (submit these through MyLab in the Next item after the discussion): 2.2.75, 5.3.53, 5.5.13, 6.1.95, 6.2.47, 6.4.45.
2. 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 here on Canvas or in class):
     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 _____.
   • Discuss this in the Next item.
   • Exercises from the textbook due on January 29 Wednesday (submit these through MyLab in the Next item after the discussion): 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:
   • Reading from the textbook:
     • Section 7.2 (pages 441–446);
     • Section 7.4 (pages 456–460).
   • Exercises due on January 29 Wednesday (submit these here on Canvas or in class):
     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?
   • Discuss this in the Next item.
   • Exercises from the textbook due on January 31 Friday (submit these through MyLab in the Next item after the discussion): 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:
   • Reading from the textbook:
     • Section 7.3 (pages 449–453);
     • Section 7.5 (pages 463–470).
   • Exercises due on January 31 Friday (submit these here on Canvas or in class): 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.
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 3 Monday (submit these through MyLab in the Next item after the discussion): 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:
   • Reading from the textbook: Section 7.6 (pages 473–478).
   • Exercises due on February 3 Monday (submit these here on Canvas or in class): 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.
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 5 Wednesday (submit these through MyLab in the Next item after the discussion): 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:
   • 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 here on Canvas or in class):
     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___.
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 7 Friday (submit these through MyLab in the Next item after the discussion): 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:
   • 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 here on Canvas or in class):
     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?
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 10 Monday (submit these through MyLab in the Next item after the discussion): 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:
   • Reading from the textbook: Section 4.1 through Objective 3 (pages 249–255).
   • Exercises due on February 10 Monday (submit these here on Canvas or in class):
     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.)
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 12 Wednesday (submit these through MyLab in the Next item after the discussion): 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:
   • 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 here on Canvas or in class):
     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?
   • Discuss this in the Next item.
   • Exercises from the textbook due on February 14 Friday (submit these through MyLab in the Next item after the discussion): 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:
    • 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 here on Canvas or in class):
      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.)
    • Discuss this in the Next item.
    • Exercises from the textbook due on February 21 Friday (submit these through MyLab in the Next item after the discussion): 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:
    • Reading from the textbook: Section 4.5 (pages 284–291).
    • Exercises due on February 21 Friday (submit these here on Canvas or in class):
      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.
    • Discuss this in the Next item.
    • Exercises from the textbook due on February 24 Monday (submit these through MyLab in the Next item after the discussion): 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:
    • 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 here on Canvas or in class): 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.
    • Discuss this in the Next item.
    • Exercises from the textbook due on February 26 Wednesday (submit these through MyLab in the Next item after the discussion): 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:
    • 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 here on Canvas or in class): 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 _____.
    • Discuss this in the Next item.
    • Exercises from the textbook due on February 28 Friday (submit these through MyLab in the Next item after the discussion): 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:
    • Reading from the textbook: Section 8.7 Objective 1 (pages 584–587).
    • Exercises due on February 28 Friday (submit these here on Canvas or in class): 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 _____.
    • Discuss this in the Next item.
    • Exercises from the textbook due on March 3 Monday (submit these through MyLab in the Next item after the discussion): 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:
    • Reading from the textbook:
      • Section 8.6 Objective 4 (pages 580&581);
      • Section 8.7 Objective 4 (pages 591&592).
    • Reading Homework due on March 3 Monday
      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?
    • Discuss this in the Next item.
    • Exercises from the textbook due on March 5 Wednesday (submit these through MyLab in the Next item after the discussion): 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:
    • 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 here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on March 7 Friday (submit these through MyLab in the Next item 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:
    • Reading from (mostly) 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 here on Canvas or in class):
      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 1/2; 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 item.
    • Exercises from the textbook due on March 17 Monday (submit these through MyLab in the Next item 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:
    • Reading from (mostly) the textbook:
      • My notes on simplifying roots;
      • Section 9.4 (pages 634–641).
    • Exercises due on March 21 Friday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on March 24 Monday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 9.5 through Objective 1 (pages 643–645).
    • Exercises due on March 24 Monday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on March 26 Wednesday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: The rest of Section 9.5 (pages 645–647).
    • Exercises due on March 26 Wednesday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on March 28 Friday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 9.6 (pages 649–653).
    • Exercises due on March 28 Friday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on March 31 Monday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 9.8 (pages 662–667).
    • Exercises due on March 31 Monday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 2 Wednesday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 9.9 through Objective 3 (pages 670–676).
    • Exercises due on April 2 Wednesday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 4 Friday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: The rest of Section 9.9 (pages 676–678).
    • Exercises due on April 4 Friday (submit these here on Canvas or in class): 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 item.
    • Exercises from the textbook due on April 7 Monday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 10.1 through Objective 1 (pages 690–694).
    • Exercises due on April 7 Monday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 9 Wednesday (submit these through MyLab in the Next item 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:
    • 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 here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 11 Friday (submit these through MyLab in the Next item 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:
    • 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 here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 18 Friday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 10.3 (pages 716–720).
    • Exercises due on April 18 Friday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 21 Monday (submit these through MyLab in the Next item 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:
    • 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 here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 23 Wednesday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 8.1 (pages 521–528).
    • Exercises due on April 23 Wednesday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 25 Friday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 8.2 (pages 531–535).
    • Exercises due on April 25 Friday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 28 Monday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 8.3 (pages 538–546).
    • Exercises due on April 28 Monday (submit these here on Canvas or in class):
      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 item.
    • Exercises from the textbook due on April 30 Wednesday (submit these through MyLab in the Next item 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:
    • Reading from the textbook: Section 8.4 (pages 549–555).
    • Exercises due on April 30 Wednesday (submit these here on Canvas or in class): 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 item.
    • Exercises from the textbook due on May 2 Friday (submit these through MyLab in the Next item 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/.