MATH-1100-WBP02

Welcome to the permanent home page for Section WBP02 of MATH-1100 (Intermediate Algebra) at Southeast Community College in the Fall semester of 2024. I am Toby Bartels, your instructor.

Course administration

Canvas page (where you must log in).
Help with DjVu (if you have trouble reading the DjVu files on this page).
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 10:30 to 11:30, and
- by appointment,
in room U9C and over Zoom meeting 610-024-2876.

Feel free to send a message at any time, even nights and weekends (although I'll be slower to respond then).

Readings

The official textbook for the course is the 4th Edition of Elementary & Intermediate Algebra written by Sullivan et al and published by Prentice-Hall (Pearson). You will automatically get an online version of this textbook through Canvas, although you can use a print version instead if you like. This comes with access to Pearson MyLab, integrated into Canvas, on which many of the assignments appear.

Rational expressions

General review:
- Reading from the textbook:
  - Section 1.1 (pages 1–7);
  - Skim: Section 6.5 (pages 403–407).
- Exercises due on August 21 Wednesday (submit these 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 August 23 Friday (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, 2.2.75, 5.3.53, 5.5.13, 6.1.95, 6.2.47, 6.4.45.
Rational expressions:
- Reading from (mostly) the textbook:
  - My notes on rational expressions;
  - Section 7.1 (pages 433–439).
- Exercises due on August 23 Friday (submit these 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 August 26 Monday (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.
Multiplying and dividing rational expressions:
- Reading from the textbook:
  - Section 7.2 (pages 441–446);
  - Section 7.3 (pages 449–453).
- Exercises due on August 26 Monday (submit these on Canvas):
  1. Fill in the blank: To divide by a rational expression, multiply by its _____.
  2. 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 August 28 Wednesday (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, 7.3.17, 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.
Adding and subtracting rational expressions:
- Reading from the textbook:
  - Section 7.4 (pages 456–460);
  - Section 7.5 (pages 463–470).
- Exercises due on August 28 Wednesday (submit these on Canvas):
  1. 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.
  2. What is the least common denominator of 1/8 and 5/18?
- Exercises from the textbook due on August 30 Friday (submit these through MyLab): 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, 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.
Complex rational expressions:
- Reading from the textbook: Section 7.6 (pages 473–478).
- Exercises due on August 30 Friday (submit these 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 September 4 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.
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 September 4 Wednesday (submit these 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 September 6 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.
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 September 6 Friday (submit these 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 September 9 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.

Quiz 1, covering the material in Problem Sets 1–7, is available on September 13 Friday and due on September 16 Monday.

Systems of equations and inequalities

Systems of equations:
- Reading from the textbook: Section 4.1 through Objective 3 (pages 249–255).
- Exercises due on September 9 Monday (submit these 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 September 11 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.
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 September 11 Wednesday (submit these on Canvas):
  1. Fill in the blanks:
    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 September 13 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.
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 September 18 Wednesday (submit these 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 September 20 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.
Mixture problems:
- Reading from the textbook: Section 4.5 (pages 284–291).
- Exercises due on September 20 Friday (submit these 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 September 23 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.
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 September 23 Monday (submit these 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 September 25 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.
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 September 25 Wednesday (submit these 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 September 27 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.
Absolute-value equations:
- Reading from the textbook: Section 8.7 Objective 1 (pages 584–587).
- Exercises due on September 27 Friday (submit these 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 September 30 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.
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 September 30 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?
- Exercises from the textbook due on October 2 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.

Quiz 2, covering the material in Problem Sets 8–15, is available on October 11 Friday and due on October 16 Wednesday.

Roots and radicals

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 October 2 Wednesday (submit these 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.
- Exercises from the textbook due on October 4 Friday (submit these through MyLab): 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.
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, expressed using radicals instead of fractional exponents.
- Exercises due on October 4 Friday (submit these 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. Look at the Power Rule given on page 629 of the textbook, and check it when a = −1, r = 2, and s = 1/2. Is the rule correct in this case?
- Exercises from the textbook due on October 7 Monday (submit these through MyLab): 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.
Simplifying radical expressions:
- Reading from (mostly) the textbook:
  - My notes on simplifying roots;
  - Section 9.4 (pages 634–641).
- Exercises due on October 7 Monday (submit these 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.
- Exercises from the textbook due on October 9 Wednesday (submit these through MyLab): 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.
Adding and subtracting radical expressions:
- Reading from the textbook: Section 9.5 through Objective 1 (pages 643–645).
- Exercises due on October 9 Wednesday (submit these 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.)
- Exercises from the textbook due on October 11 Friday (submit these through MyLab): 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.
Multiplying radical expressions:
- Reading from the textbook: The rest of Section 9.5 (pages 645–647).
- Exercises due on October 18 Friday (submit these 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.)
- Exercises from the textbook due on October 21 Monday (submit these through MyLab): 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.
Dividing radical expressions:
- Reading from the textbook: Section 9.6 (pages 649–653).
- Exercises due on October 21 Monday (submit these 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 _____.
- Exercises from the textbook due on October 23 Wednesday (submit these through MyLab): 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.
Radical equations:
- Reading from the textbook: Section 9.8 (pages 662–667).
- Exercises due on October 23 Wednesday (submit these 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 _____.
- Exercises from the textbook due on October 25 Friday (submit these through MyLab): 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.
Complex numbers:
- Reading from the textbook: Section 9.9 through Objective 3 (pages 670–676).
- Exercises due on October 25 Friday (submit these 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.
- Exercises from the textbook due on October 28 Monday (submit these through MyLab): 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.
Advanced operations on complex numbers:
- Reading from the textbook: The rest of Section 9.9 (pages 676–678).
- Exercises due on October 28 Monday (submit these 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.
- Exercises from the textbook due on October 30 Wednesday (submit these through MyLab): 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.

Quiz 3, covering the material in Problem Sets 16–24, is available on November 1 Friday and due on November 4 Monday.

Quadratic equations and functions

Quadratic equations:
- Reading from the textbook: Section 10.1 through Objective 1 (pages 690–694).
- Exercises due on October 30 Wednesday (submit these on Canvas):
  1. Solve x² = q² for x.
  2. Assuming that c ≠ 0, solve x² = c for x in the complex-number system.
- Exercises from the textbook due on November 1 Friday (submit these through MyLab): 10.1.19, 10.1.21, 10.1.23, 10.1.25, 10.1.27, 10.1.29, 10.1.31, 10.1.33.
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 November 6 Wednesday (submit these 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?
- Exercises from the textbook due on November 8 Friday (submit these through MyLab): 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.
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 November 8 Friday (submit these 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.
- Exercises from the textbook due on November 11 Monday (submit these through MyLab): 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.
Fancy equations:
- Reading from the textbook: Section 10.3 (pages 716–720).
- Exercises due on November 11 Monday (submit these 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 = ___.
- Exercises from the textbook due on November 13 Wednesday (submit these through MyLab): 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.
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 November 13 Wednesday (submit these 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?
- Exercises from the textbook due on November 15 Friday (submit these through MyLab): 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.
Graphs:
- Reading from the textbook: Section 8.1 (pages 521–528).
- Exercises due on November 15 Friday (submit these 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.
- Exercises from the textbook due on November 18 Monday (submit these through MyLab): 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.
Relations:
- Reading from the textbook: Section 8.2 (pages 531–535).
- Exercises due on November 18 Monday (submit these 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 _____.
- Exercises from the textbook due on November 20 Wednesday (submit these through MyLab): 8.2.27, 8.2.29, 8.2.31, 8.2.33, 8.2.39, 8.2.45, 8.2.49, 8.2.53.
Functions:
- Reading from the textbook: Section 8.3 (pages 538–546).
- Exercises due on November 20 Wednesday (submit these on Canvas):
  1. 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 ____.
  2. 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.
- Exercises from the textbook due on November 22 Friday (submit these through MyLab): 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.
Graphs of functions:
- Reading from the textbook: Section 8.4 (pages 549–555).
- Exercises due on November 22 Friday (submit these on Canvas): Fill in the blanks with mathematical expressions:
  1. If (3, 5) is a point on the graph of a function f, then f(___) = ___.
  2. If g(2) = 4 for a function g, then _____ is a point on the graph of g.
- Exercises from the textbook due on November 25 Monday (submit these through MyLab): 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.

Quiz 4, covering the material in Problem Sets 25–33, is available on November 25 Monday and due on December 2 Monday.

Quizzes

Rational expressions:
- Date available: September 13 Friday.
- Date due: September 16 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 on Canvas, at least one intermediate step for each result.
Systems of equations and inequalities:
- Date available: October 11 Friday.
- Date due: October 16 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 on Canvas, at least one intermediate step for each result except #1.
Roots and radicals:
- Date available: November 1 Friday.
- Date due: November 4 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 on Canvas, at least one intermediate step for each result, and at last two intermediate steps in #6.
Quadratic equations and functions:
- Date available: November 25 Monday.
- Date due: December 2 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 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

There is a comprehensive final exam at the end of the term. (You'll arrange to take it some time December 9–13.) To speed up grading at the end of the term, the exam is multiple choice and filling in blanks, with no partial credit.

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 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 TBA).

The final exam will be 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!

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2024 November 1. Toby reserves no legal rights to them.

The permanent URI of this web page is https://tobybartels.name/MATH-1100/2024FA/.