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 administration
- 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.
Contact information
I am often available outside of those times;
feel free to send a message any time.
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 MyLabs, 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).
- Reading Homework due on August 26 Thursday:
- 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.
- 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.
- Rational expressions:
- Reading from (mostly) the textbook:
- 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.
- 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.
- 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.
- 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.
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
- 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.
- 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.)
- 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.
- 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.
- 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 nth 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.
- Write
n√b
using a fractional exponent.
- 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.
- 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
√(x2)
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.
- 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.
- Arithmetic with roots:
- Reading from the textbook: Section 9.5 (pages 643–647).
- Reading Homework due on October 7 Thursday:
- As 2x + 3x = 5x,
so 2√7 +
3√7 =
_____.
- As (x + 2)(x + 3) =
x2 + 5x + 6,
so
(3√x + 2)(3√x + 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.
- 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√(b2),
multiply top and bottom by _____.
- 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.
- 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: i2 = ___
(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.
- 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.
Quadratic equations and functions
- Quadratic equations:
- Reading from (mostly) the textbook:
- Reading Homework due on October 26 Tuesday:
- Assuming that c > 0,
solve x2 = c for x.
- Starting from x2 + 2px,
what do you add to complete the square?
- 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.
- The quadratic formula:
- Reading from (mostly) the textbook:
- Reading Homework due on November 2 Tuesday:
- Assuming that a ≠ 0,
solve
ax2 + bx + c = 0
for x.
- 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.
- Fancy equations:
- Reading from the textbook: Section 10.3 (pages 716–720).
- Reading Homework due on November 4 Thursday:
- To turn
3√x2 +
3√x =
1
into a quadratic equation,
substitute u = ___.
- 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.
- 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 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.
- 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.
- 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.
- 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.
- 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:
- |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.
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
- 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.
Final exam
A comprehensive final exam
is on December 16 Thursday from 2:30 PM to 4:10.
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
were written by Toby Bartels, last edited on 2021 December 6.
Toby reserves no legal rights to them.
The permanent URI of this web page
is
http://tobybartels.name/MATH-1100/2021FA/.
