MATH-1100-ES31

Welcome to the permanent home page for Section ES31 of MATH-1100 (Intermediate Algebra) at Southeast Community College in the Fall term of 2019. I am Toby Bartels, the instructor.

Here is material about the administration of the course:

Canvas page (where you must log in for full access, available while the course is in session).
Help with DjVu (if you have trouble reading the files below).
Official syllabus (DjVu).
Course policies (DjVu).
Class hours: Tuesdays and Thursdays from 9:30 to 10:50 in ESQ 105.

Information to contact me:

Name: Toby Bartels.
Canvas messages.
Email: TBartels@Southeast.edu.
Voice mail: 1-402-323-3452.
Text messages: 1-402-805-3021.
Office hours: Mondays and Wednesdays from 10:00 to 12:30 and by appointment in ESQ 112.
Online availability: Fridays from 10:30 to 12:30 and by appointment.

I am often available outside of those times; feel free to send a message any time and to check for me in the office whenever it's open.

Required resources

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).

Textbook access (DjVu instructions).

Rational expressions and inequalities

General review:
- Reading from the textbook:
  - Section 1.1 (pages 1–7);
  - Skim: Section 6.5 (pages 403–407);
  - Skim: Section 7.1 (pages 433–439);
  - Skim: Section 7.2 (pages 441–446);
  - Skim: Section 7.3 (pages 449–453).
- Exercises due August 29 Thursday:
  1. Fill in the blank: In the product (3x − 2)(x + 4) = 3x² + 10x − 8, the polynomials (3x − 2) and (x + 4) are the _____ of the polynomial 3x²2 +10x − 8.
  2. Fill in the blank: The quotient of two polynomials is called a _____ _____.
- Exercises from the textbook due September 3 Tuesday on MyLab: 2.2.75, 5.3.53, 5.5.13, 6.1.95, 6.2.47, 6.4.45, 7.1.85.
Adding rational expressions:
- Reading from (mostly) the textbook:
  - My notes on rational expressions;
  - Section 7.4 (pages 456–460);
  - Section 7.5 (pages 463–470).
- Exercises due September 3 Tuesday:
  - 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.
  - What is the least common denominator of 1/8 and 5/18?
- Exercises from the textbook due September 5 Thursday on 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 September 5 Thursday: Fill in the blanks:
  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 Subsection 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 Subsection 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 September 10 Tuesday on 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 subsection 1 (pages 493&494);
- Exercises due September 10 Tuesday:
  1. Fill in the blank with an appropriate term: A rational equation is an equation where both sides are _____ expresions.
  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 September 12 Thursday on 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);
  - The rest of Section 7.8 (pages 494–502).
- Exercises due September 12 Thursday:
  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 September 17 Tuesday on 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.
Compound inequalities:
- Reading from (mostly) the textbook:
  - Skim: Section 2.8 (pages 148–157);
  - My notes on inequalities;
  - Section 8.6 (pages 574–581).
- Exercises due September 17 Tuesday: 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 September 19 Thursday on 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, 8.6.101, 8.6.103, 8.6.105, 8.6.107, 8.6.109.
Absolute value:
- Reading from (mostly) the textbook:
  - My notes on absolute-value problems;
  - Section 8.7 (pages 584–592).
- Exercises due September 19 Thursday: Fill in the blanks with equations or 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 _____.
  5. If a ≥ 0, then |u| = a is equivalent to _____ or _____.
  6. |u| = |v| is equivalent to _____ or _____.
- Exercises from the textbook due September 24 Tuesday on 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, 8.7.69, 8.7.71, 8.7.73, 8.7.75, 8.7.77, 8.7.85, 8.7.87, 8.7.89, 8.7.91, 8.7.103, 8.7.105, 8.7.107, 8.7.109, 8.7.121, 8.7.123, 8.7.125, 8.7.127.

Quiz/Exam 1, covering the material above, is on October 1 Tuesday.

Systems and roots

Systems of equations:
- Reading from (mostly) the textbook:
  - My notes on systems of equations;
  - Section 4.1 through subsection 3 (pages 249–255);
  - Section 4.2 through subsection 1 (pages 260–264);
  - Section 4.3 through subsection 1 (pages 268–272).
- Exercises due September 24 Tuesday:
  1. A system of equations with at least one solution is _____.
  2. A system of equations with no solution is _____.
  3. 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.
- Exercises from the textbook due September 26 Thursday on 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, 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:
  - Subsection 4.1.4 (pages 256&257);
  - Subsection 4.2.2 (page 265);
  - Subsection 4.3.2 (page 273);
  - Section 4.4 (pages 277–282).
- Exercises due September 26 Thursday:
  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 October 3 Thursday on 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 October 3 Thursday:
  1. 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.
  2. 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.
  3. 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.
  4. 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.
- Exercises from the textbook due October 8 Tuesday on 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.
Roots:
- Reading from (mostly) the textbook:
  - Skim: Section 9.1 (pages 616–619);
  - Section 9.2 (pages 620–626);
  - My notes on roots.
- Exercises due October 8 Tuesday:
  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 nth root of b) defined (as a real number)?
    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.
    (Since ⁿ√b is defined under more than one of these conditions, list all of these conditions that work).
  3. Write ⁿ√b using a fractional exponent.
  4. Assuming that m/n is a rational number in lowest terms, write b^m/n using only roots and powers with integer exponents.
- Exercises from the textbook due October 10 Thursday on 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, 9.2.51, 9.2.73, 9.2.75, 9.2.93, 9.2.95, 9.2.97, 9.2.99, 9.2.109, 9.2.111, 9.2.113, 9.2.47, 9.2.49, 9.2.101, 9.2.103, 9.2.105.
Simplifying radical expressions:
- Reading from (mostly) the textbook:
  - My notes on simplifying roots;
  - Section 9.4 (pages 634–641);
  - Optional: Section 9.3 (pages 628–632).
- Exercises due October 10 Thursday:
  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 October 15 Tuesday on MyLab: 9.4.37, 9.4.39, 9.4.133, 9.3.69, 9.3.71, 9.3.75, 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.
Arithmetic with roots:
- Reading from the textbook: Section 9.5 (pages 643–647).
- Exercises due October 15 Tuesday:
  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) = _____. (Use that (³√7)² = ³√49.)
  3. While x² doesn't simplify, (√7)² = _____.
- Exercises from the textbook due October 17 Thursday on MyLab: 9.5.21, 9.5.25, 9.5.31, 9.5.33, 9.5.41, 9.5.53, 9.5.65, 9.5.67, 9.5.71, 9.5.75, 9.5.109.
Dividing radical expressions:
- Reading from the textbook: Section 9.6 (pages 649–653).
- Exercises due October 17 Thursday:
  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 October 24 Thursday on 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 October 24 Thursday:
  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 October 29 Tuesday on 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 (pages 670–678).
- Exercises due October 29 Tuesday:
  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) = ___.
  3. True or false: Every real number is also a complex number.
- Exercises from the textbook due October 31 Thursday on MyLab: 9.9.25, 9.9.33, 9.9.27, 9.9.29, 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, 9.9.81, 9.9.89, 9.9.95, 9.9.141.

Quiz/Exam 2, covering the material above, is on November 5 Tuesday.

Quadratic equations and functions

Quadratic equations:
- Reading from (mostly) the textbook:
  - Section 10.1 (pages 690–699);
  - My notes on solving quadratic equations.
- Exercises due October 31 Thursday:
  1. Assuming that c > 0, solve x² = c for x.
  2. Starting from x² + 2px, what do you add to complete the square?
  3. Starting from x² + bx, what do you add to complete the square?
- Exercises from the textbook due November 7 Thursday on 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, 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 (pages 702–712);
  - My notes on classifying solutions to quadratic equations.
- Exercises due November 7 Thursday:
  1. Assuming that a ≠ 0, solve ax² + bx + c = 0 for x.
  2. Fill in the blank with a vocabulary word: The _____ of ax² + bx + c is b² − 4ac.
- Exercises from the textbook due November 12 Tuesday on 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 November 12 Tuesday:
  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 November 14 Thursday on MyLab: 10.3.49, 10.3.51, 10.3.53, 10.3.55, 10.3.57, 10.3.59.
Relations:
- Reading from the textbook:
  - Section 8.1 (pages 521–528);
  - Section 8.2 (pages 531–535).
- Exercises due November 14 Thursday:
  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.
  3. The set of input values of a binary relation is its _____, and the set of output values is its _____.
- Exercises from the textbook due November 19 Tuesday on 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, 8.2.27, 8.2.29, 8.2.31.
Functions:
- Reading from the textbook: Section 8.3 (pages 538–546).
- Exercises due November 19 Tuesday:
  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 ____.
  3. 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 November 21 Thursday on 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 November 21 Thursday: 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 November 26 Tuesday on 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.
Linear functions:
- Reading from the textbook:
  - Section 8.5 (pages 560–568);
  - Optional: Section 9.7 (pages 655–659).
- Exercises due November 26 Tuesday:
  1. A _____ function is a function whose graph is a line.
  2. Every line in a coordinate plane is the graph of a function except for _____ lines.
  3. Identify which of the following functions are linear. (Say Yes or No for each one.)
    - f(x) = 3x − 2;
    - g(x) = 3/x + 2;
    - h(x) = 3/2.
- Exercises from the textbook due December 3 Tuesday on MyLab: 8.5.19, 8.5.21, 8.5.23, 8.5.25, 8.5.31, 8.5.33, 8.5.47, 8.5.49, 8.5.51, 8.5.57, 8.5.63.
Quadratic functions:
- Reading from (mostly) the textbook:
  - Section 10.4 (pages 724–733);
  - Section 10.5 (pages 736–746);
  - My notes on quadratic functions.
- Exercises due December 3 Tuesday: Suppose that f(x) = ax² + bx + c for all x.
  1. Fill in the blank with the name of a geometric shape: The graph of a f is a _____.
  2. Fill in the blanks with algebraic formulas: The vertex of this graph has the coordinates (___, ___).
- Exercises from the textbook due December 5 Thursday on MyLab: 10.4.17, 10.4.19, 10.4.21, 10.4.23, 10.5.15, 10.5.17, 10.5.23, 10.5.25, 10.5.27, 10.5.29, 10.5.63, 10.5.65.

Quiz/Exam 3, covering the material above, is on December 5 Thursday.

Final

A comprehensive final exam is on December 13 Friday from 1:00 PM to 3:00 PM. The exam will consist of questions similar in style and content to those in the practice final exam (DjVu).

This web page and the files linked from it (except for the official syllabus and the textbook access instructions) were written by Toby Bartels, last edited on 2019 December 5. Toby reserves no legal rights to them.

The permanent URI of this web page is https://tobybartels.name/MATH-1100/2019FA/.