- Canvas page (where you must log in).
- Help with DjVu (if you have trouble reading the DjVu files on this page).
- 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.

- Name: Toby Bartels, PhD.
- Canvas messages.
- Email: TBartels@Southeast.edu.
- Voice mail: +1-402-323-3452.
- Text messages: +1-402-805-3021.
- Office hours:
- Mondays, Wednesdays, and Fridays from 1:00 PM to 2:00,
- Tuesdays and Thursdays from 10:30 to 11:30, and
- by appointment,

- General review:
- Reading from the textbook:
- Section 1.1 (pages 1–7);
*Skim*: Section 6.5 (pages 403–407).

- Reading Homework due on August 26 Thursday:
- Fill in the blank:
In the product
(3
*x*− 2)(x + 4) = 3*x*^{2}+ 10*x*− 8, the polynomials (3*x*− 2) and (*x*+ 4) are the _____ of the polynomial 3*x*^{2}2 +10*x*− 8. - Fill in the blanks with simpler equations:
If
*A**B*= 0, then _____ or _____.

- Fill in the blank:
In the product
(3
- 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.

- Reading from the textbook:
- Rational expressions:
- Reading from (mostly) the textbook:
- My notes on rational expressions;
- Section 7.1 (pages 433–439);
- Section 7.2 (pages 441–446).

- Reading Homework due on August 31 Tuesday:
- Fill in the blank with a vocabulary word: A _____ expression is the result of dividing two polynomials.
- 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 ___.
- 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:
- Adding rational expressions:
- 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.

- Reading from (mostly) the textbook:
- Complex rational expressions:
- Reading from the textbook: Section 7.6 (pages 473–478).
- Reading Homework due on September 7 Tuesday: Fill in the blanks:
- A rational expression with rational subexpressions inside it is called a _____ rational expression.
- 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.
- 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.

- 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:
- Fill in the blank with an appropriate term: A _____ equation is an equation where both sides are rational expressions.
- 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.
- 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.

- Reading from (mostly) the textbook:
- 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).

- Reading Homework due on September 14 Tuesday:
- True or false: If the angles in two geometric figures are equal, then their corresponding lengths are also equal.
- True or false: If the angles in two geometric figures are equal, then their corresponding lengths are proportional.
- 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.

- Reading from the textbook:

- 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:
- A system of equations with at least one solution is _____.
- A system of equations with no solution is _____.
- 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.

- Reading from (mostly) the textbook:
- 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).

- Reading Homework due on September 21 Tuesday:
- If an angle has a measure of
*x*°, while its*complement*has a measure of*y*°, then what equation holds between*x*and*y*? - If an angle has a measure of
*x*°, while its*supplement*has a measure of*y*°, then what equation holds between*x*and*y*? - 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.)

- If an angle has a measure of
- 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.

- Reading from the textbook:
- Mixture problems:
- Reading from the textbook: Section 4.5 (pages 284–291).
- Reading Homework due on September 28 Tuesday:
- 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. - 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. - 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. - 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.

- Suppose that you have
- 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.

- 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:
- In the expression
^{n}√*b*, the real number*b*is the _____, and the natural number*n*is the _____. - Under which of the following conditions
is
^{n}√*b*(the principal real*n*th root of*b*) defined (as a real number)? Answer Yes or No for each.- When
*n*is even and*b*is positive; - When
*n*is even and*b*is negative; - When
*n*is odd and*b*is positive; - When
*n*is odd and*b*is negative.

- When
- Write
^{n}√*b*using a fractional exponent. - Assuming that
*m*/*n*is a rational number in lowest terms, write*b*^{m/n}using only roots and powers with integer exponents.

- In the expression
- 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:
- 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).

- Reading Homework due on October 5 Tuesday:
- Simplify
√(
*x*^{2})*without*using roots or fractional exponents and without making any assumptions about*x*(besides that it's a real number). - Assuming that
^{n}√*a*^{n}√*b*exists (as a real number), express it as a single root. - Assuming that
^{m}√(^{n}√*b*) exists (as a real number), express it as a single root.

- Simplify
√(
- 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.

- Reading from (mostly) the textbook:
- Arithmetic with roots:
- Reading from the textbook: Section 9.5 (pages 643–647).
- Reading Homework due on October 7 Thursday:
- As 2
*x*+ 3*x*= 5*x*, so 2√7 + 3√7 = _____. - As (
*x*+ 2)(*x*+ 3) =*x*^{2}+ 5*x*+ 6, so (^{3}√*x*+ 2)(^{3}√*x*+ 3) = _____. - While
*x*^{2}doesn't simplify, (√*x*)^{2}= _____.

- As 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.

- Dividing radical expressions:
- Reading from the textbook: Section 9.6 (pages 649–653).
- Reading Homework due on October 12 Tuesday:
- To rationalize the denominator of
*a*/√*b*, multiply top and bottom by _____. - To rationalize the denominator of
*a*/^{3}√*b*, multiply top and bottom by _____. - To rationalize the denominator of
*a*/^{3}√(*b*^{2}), multiply top and bottom by _____. - To rationalize the denominator of
*a*/(√*b*+*c*), multiply top and bottom by _____.

- To rationalize the denominator of
- 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.

- Radical equations:
- Reading from the textbook: Section 9.8 (pages 662–667).
- Reading Homework due on October 14 Thursday:
- Fill in the blank with an appropriate term: A _____ equation is an equation where one or both sides are radical expressions.
- 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.
- 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.

- Complex numbers:
- Reading from the textbook: Section 9.9 (pages 670–678).
- Reading Homework due on October 21 Thursday:
- Fill in the blank with a number: i
^{2}= ___ (where i is the imaginary unit). - Fill in the blank with an algebraic expression:
If
*a*is a positive real number, then √(−*a*) = ___. - True or false: Every real number is also a complex number.

- Fill in the blank with a number: i
- 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.

- Quadratic equations:
- Reading from (mostly) the textbook:
- Section 10.1 through Subsection 3 (pages 690–697);
- My notes on solving quadratic equations.

- Reading Homework due on October 26 Tuesday:
- Assuming that
*c*> 0, solve*x*^{2}=*c*for*x*. - Starting from
*x*^{2}+ 2*p**x*, what do you add to complete the square? - Starting from
*x*^{2}+*b**x*, what do you add to complete the square?

- Assuming that
- 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:
- The quadratic formula:
- Reading from (mostly) the textbook:
- Section 10.2 through Subsection 2 (pages 702–711);
- My notes on classifying solutions to quadratic equations.

- Reading Homework due on November 2 Tuesday:
- Assuming that
*a*≠ 0, solve*a**x*^{2}+*b**x*+*c*= 0 for*x*. - Fill in the blank with a vocabulary word:
The _____
of
*a**x*^{2}+*b**x*+*c*is*b*^{2}− 4*a**c*.

- Assuming that
- 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.

- Reading from (mostly) the textbook:
- Fancy equations:
- Reading from the textbook: Section 10.3 (pages 716–720).
- Reading Homework due on November 4 Thursday:
- To turn
^{3}√*x*^{2}+^{3}√*x*= 1 into a quadratic equation, substitute*u*= ___. - To turn 1/
*x*^{2}+ 1/*x*= 1 into a quadratic equation, substitute*u*= ___.

- To turn
- 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.

- Word problems with quadratic equations and roots:
- Reading from the textbook:
- Subsection 10.1.4 (pages 697–699);
- Subsection 10.2.3 (pages 711&712).

- Reading Homework due on November 9 Tuesday:
- 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*? - If
*x*^{2}= 4, where*x*is the length of a road in miles, then what is the length of the road?

- Pythagorean Theorem:
If
- 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.

- Reading from the textbook:
- Relations:
- Reading from the textbook:
- Section 8.1 (pages 521–528);
- Section 8.2 (pages 531–535).

- Reading Homework due on November 11 Thursday:
- The two number lines that mark the coordinates in a rectangular coordinate system are the coordinate _____, and the point where they intersect is the _____.
- A point on a graph that is also on a coordinate axis is a(n) _____ of that graph.
- 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.

- Reading from the textbook:
- Functions:
- Reading from the textbook: Section 8.3 (pages 538–546).
- Reading Homework due on November 16 Tuesday:
- 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.
- 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 ____. - 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.

- 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:
- If (3, 5) is a point on the graph of a function
*f*, then*f*(___) = ___. - If
*g*(2) = 4 for a function*g*, then _____ is a point on the graph of*g*.

- If (3, 5) is a point on the graph of a function
- 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.

- 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?
*x*≤ 4 and*x*> 5;*x*≥ 2 or*x*< 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.

- Reading from (mostly) the textbook:
- Absolute value:
- Reading from (mostly) the textbook:
- My notes on absolute-value problems;
- Section 8.7 (pages 584–592).

- Reading Homework due on November 30 Tuesday:
Fill in the blanks with equations or inequalities (possibly compound)
that
*don't*involve absolute values:- |
*u*| <*a*is equivalent to _____. - |
*u*| ≤*a*is equivalent to _____. - |
*u*| >*a*is equivalent to _____ or _____. - |
*u*| ≥*a*is equivalent to _____ or _____. - If
*a*≥ 0, then |*u*| =*a*is equivalent to _____ or _____. - |
*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.

- Reading from (mostly) the textbook:

- 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.

- 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.

- Quadratic equations and functions:
- Review date: December 2 Thursday (in class).
- Date due on MyLab: December 7 Tuesday (before class).
- 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. For #3, use any method and solve in the complex number system. For #8, include a table of values.

This web page and the files linked from it were written by Toby Bartels, last edited on 2021 September 7. Toby reserves no legal rights to them.

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