# MATH-1100-ES31, MATH-1100-FC09, and MATH-1100-LN09

Welcome to the permanent home page for Sections ES31, FC09, and LN09 of MATH-1100 (Intermediate Algebra) at Southeast Community College in the Fall term of 2021. I am Toby Bartels, the instructor.

• Course policies (DjVu).
• Class hours: Tuesdays and Thursdays from 2:30 PM to 3:50 in ESQ 103, the Nebraska City Learning Center, LNK V08, or at LifeSize meeting 10354350.
• Final exam time: December 16 Thursday from 2:30 PM to 4:10 or by appointment.

## Contact information

I am often available outside of those times; feel free to send a message any time.

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 MyLabs, integrated into Canvas, on which many of the assignments appear.

### Rational expressions

1. General review:
• Section 1.1 (pages 1–7);
• Skim: Section 6.5 (pages 403–407).
• Reading Homework due on August 26 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 blanks with simpler equations: If AB = 0, then _____ or _____.
• Problem Set from the textbook due on August 31 Tuesday: 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:
• Reading Homework due on August 31 Tuesday:
1. Fill in the blank with a vocabulary word: A _____ 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 ___.
3. Fill in the blank: To divide by a rational expression, multiply by its _____.
• Problem Set from the textbook due on September 2 Thursday: 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, 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.
• Reading from (mostly) the textbook:
• Section 7.3 (pages 449–453);
• Section 7.4 (pages 456–460);
• Section 7.5 (pages 463–470).
• Reading Homework due on September 2 Thursday:
• 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?
• Problem Set from the textbook due on September 7 Tuesday: 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, 7.4.13, 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.
4. Complex rational expressions:
• Reading from the textbook: Section 7.6 (pages 473–478).
• Reading Homework due on September 7 Tuesday: 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.
• Problem Set from the textbook due on September 9 Thursday: 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.
5. 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);
• Reading Homework due on September 9 Thursday:
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___.
• Problem Set from the textbook due on September 14 Tuesday: 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.
6. Word problems with division:
• Skim: Section 6.7 (pages 417–421);
• Read: The rest of Section 7.8 (pages 494–502).
• Reading Homework due on September 14 Tuesday:
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?
• Problem Set from the textbook due on September 16 Thursday: 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 1–6, is available after class on September 23 Thursday and due before class on September 28 Tuesday.

### Systems and roots

1. 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).
• Reading Homework due on September 16 Thursday:
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.
• Problem Set from the textbook due on September 21 Tuesday: 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.
2. Word problems with multiple variables:
• 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).
• Reading Homework due on September 21 Tuesday:
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.)
• Problem Set from the textbook due on September 23 Thursday: 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.
3. Mixture problems:
• Reading from the textbook: Section 4.5 (pages 284–291).
• Reading Homework due on September 28 Tuesday:
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.
• Problem Set from the textbook due on September 30 Thursday: 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.
4. Roots:
• Reading from (mostly) the textbook:
• Skim: Section 9.1 (pages 616–619);
• Section 9.2 (pages 620–626);
• My notes on roots.
• Reading Homework due on September 30 Thursday:
1. In the expression nb, the real number b is the _____, and the natural number n is the _____.
2. Under which of the following conditions is nb (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.
3. Write nb using a fractional exponent.
4. Assuming that m/n is a rational number in lowest terms, write bm/n using only roots and powers with integer exponents.
• Problem Set from the textbook due on October 5 Tuesday: 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.
• Reading from (mostly) the textbook:
• My notes on simplifying roots;
• Section 9.4 (pages 634–641);
• Optional: Section 9.3 (pages 628–632).
• Reading Homework due on October 5 Tuesday:
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 nanb exists (as a real number), express it as a single root.
3. Assuming that m√(nb) exists (as a real number), express it as a single root.
• Problem Set from the textbook due on October 7 Thursday: 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.
6. Arithmetic with roots:
• Reading from the textbook: Section 9.5 (pages 643–647).
• Reading Homework due on October 7 Thursday:
1. As 2x + 3x = 5x, so 2√7 + 3√7 = _____.
2. As (x + 2)(x + 3) = x2 + 5x + 6, so (3x + 2)(3x + 3) = _____.
3. While x2 doesn't simplify, (√x)2 = _____.
• Problem Set from the textbook due on October 12 Tuesday: 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.
• Reading from the textbook: Section 9.6 (pages 649–653).
• Reading Homework due on October 12 Tuesday:
1. To rationalize the denominator of a/√b, multiply top and bottom by _____.
2. To rationalize the denominator of a/3b, 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 _____.
• Problem Set from the textbook due on October 14 Thursday: 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.
• Reading from the textbook: Section 9.8 (pages 662–667).
• Reading Homework due on October 14 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 _____.
• Problem Set from the textbook due on October 21 Thursday: 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.
9. Complex numbers:
• Reading from the textbook: Section 9.9 (pages 670–678).
• Reading Homework due on October 21 Thursday:
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.
• Problem Set from the textbook due on October 26 Tuesday: 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, 9.9.81, 9.9.89, 9.9.95, 9.9.141.
Quiz 2, covering the material in Problem Sets 7–15, is available after class on October 28 Thursday and due before class on November 2 Tuesday.

• Reading from (mostly) the textbook:
• Reading Homework due on October 26 Tuesday:
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?
• Problem Set from the textbook due on October 28 Thursday: 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.
• Reading from (mostly) the textbook:
• Reading Homework due on November 2 Tuesday:
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.
• Problem Set from the textbook due on November 4 Thursday: 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.
3. Fancy equations:
• Reading from the textbook: Section 10.3 (pages 716–720).
• Reading Homework due on November 4 Thursday:
1. To turn 3x2 + 3x = 1 into a quadratic equation, substitute u = ___.
2. To turn 1/x2 + 1/x = 1 into a quadratic equation, substitute u = ___.
• Problem Set from the textbook due on November 9 Tuesday: 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.
4. Word problems with quadratic equations and roots:
• Subsection 10.1.4 (pages 697–699);
• Subsection 10.2.3 (pages 711&712).
• Reading Homework due on November 9 Tuesday:
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?
• Problem Set from the textbook due on November 11 Thursday: 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.
5. Relations:
• Section 8.1 (pages 521–528);
• Section 8.2 (pages 531–535).
• Reading Homework due on November 11 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 _____.
• Problem Set from the textbook due on November 16 Tuesday: 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.
6. Functions:
• Reading from the textbook: Section 8.3 (pages 538–546).
• Reading Homework due on November 16 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.
• Problem Set from the textbook due on November 18 Thursday: 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.
7. Graphs of functions:
• Reading from the textbook: Section 8.4 (pages 549–555).
• Reading Homework due on November 18 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.
• Problem Set from the textbook due on November 23 Tuesday: 8.4.17, 8.4.19, 8.4.22, 8.4.31, 8.4.33, 8.4.37, 8.4.39, 8.4.51.
8. Compound inequalities:
• Reading from (mostly) the textbook:
• Skim: Section 2.8 (pages 148–157);
• My notes on inequalities;
• Section 8.6 (pages 574–581).
• Reading Homework due on November 23 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.
• Problem Set from the textbook due on November 30 Tuesday: 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.
9. Absolute value:
• Reading from (mostly) the textbook:
• Reading Homework due on November 30 Tuesday: 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 _____.
• Problem Set from the textbook due on December 2 Thursday: 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.
Quiz 3, covering the material in Problem Sets 16–24, is available after class on December 2 Thursday and due before class on December 7 Tuesday.

## Quizzes

1. Rational expressions:
• Review date: September 23 Thursday (in class).
• Date due on MyLab: September 28 Tuesday (before class).
• Corresponding problems sets: 1–6.
• 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.
2. Systems and roots:
• Review date: October 28 Thursday (in class).
• Date due on MyLab: November 2 Tuesday (before class).
• Corresponding problems sets: 7–15.
• 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.