Download MATH 108 Summer Syll..

MATH 108 – Precalculus
Professor Horwitz
Please silence and put away all electronic devices before entering class.
Email: [email protected]
Tutoring Center Hours: M,W, R 10:30 am – 6:00 pm
Tutoring Center Location: Cullimore Hall 214
This is a course designed to prepare the student for Calculus. The course will have three very specific goals,
meeting each of these goals will demonstrate your readiness for Calculus I in the fall. The first goal is to improve
your algebra skills with some more advanced topics, the second goal is to demonstrate mastery of logarithms and
logarithmic functions and the third is to demonstrate mastery of basic trigonometry and trigonometric functions.
This course is a hybrid course. Students will work primarily on ALEKS a web based mathematics site that is
designed to assist students with mathematics. The ALEKS curriculum will be divided into 9 Modules or 255 total
topics. Students will be able to login outside the normal class hours to advance their work over the course of the six
weeks. Due to the rapid pace of this summer course consistent work outside class will be essential for success
in this term.
Attendance: Students are expected to attend class. Each class is a learning experience that cannot be replicated
through simply “getting the notes.” Three unexcused absences will lower your final grade one letter grade. Four
unexcused absences will result in a failing grade for the course.
Tutoring Center: The tutoring center will be open from 10:30-6 pm on Monday, Wednesday and Thursday and is
located at Cullimore 214. Students are encouraged to use the tutoring center as needed throughout the summer
session.
Homework: Homework is an expectation of the course. All homework for the summer session is listed, by section,
below. On Friday of each week students will be assigned a progress assessment. This progress assessment will
review any of the topics that the student has completed in the course. This progress assessment must be completed by
the scheduled time or the site will close access to the assessment and students will be graded on what has been
completed.
Exams: There will be two exams and a final. All three exams will be computer based. The first two exams will be
completed on the ALEKS site. The exam will be approximately 35 questions and will last 1.5 hours. The final exam
will NOT be from the ALEKS site. This exam will last 90 minutes and will be given on the final day of the summer
session. The final exam will test your readiness for the next class.
Quizzes: The progress assessments in addition to quizzes given in this session. In addition to the progress
assessments given over each weekend, comprehensive assessments will be given during class as per the instructor.
All assessments will appear on the student’s ALEKS schedule. Students will be responsible for checking their
schedule for upcoming assessments. There will be 7-10 assessments given throughout the summer session.
Grades: Your average will be determined by averaging your scores according to the following formula:
Exam 1:
15%
Exam 2:
15%
Progress and Comprehensive Assessments: 10%
ALEKS Objectives
20%
Final Exam:
40%
Textbook: Precalculus - A Right Triangle Approach by Ratti and McWaters, 2nd Edition, ISBN-10: 0-321-64470-0.
Week 1
1.1
Linear Equations and Applications
1.1-1.2
1.2
Quadratic Rational And Radical Equations
1.4-1.5
2.1
Linear Inequalities/Absolute Value Equations
and Inequalities
1.6-1.7
2.2
ALEKS
3.1
Quiz Chapter 1
3.2
The Coordinate Plane/Lines
2.1&2.3
4.1
Functions and Graphs
2.2&2.4
4.2
ALEKS
5.1
Library of Functions/Transformations
2.6-2.7
5.1
Composite Functions/Inverse Functions
2.8-2.9
Week 2
1.1
Complete Chapter 2/Review
1.2
Quadratic Functions
3.1
2.1
Polynomial Functions/Dividing Polynomials
3.2-3.3
2.2
ALEKS/Quiz on Chapter 2
3.1
Rational Functions/
Polynomial and Rational Inequalities
3.6-3.7
3.2
Variation
3.8
4.1
Finish Chapter 3/Review
4.2
ALEKS/Quiz on Chapter 3
5.1
Catch up/Review
5.2
Exam 1
Week 3
1.1
Exponential Function/
Natural Exponential Function
4.1-4.2
1.2
Logarithmic Functions/Rules for Logs
4.3-4.4
2.1
Exponential and Logarithmic Functions
4.5
2.2
ALEKS/Quiz on Chapter 4
3.1
Angles and their Measure
5.1
3.2
Right Triangle Trigonometry
5.2
4.1
Unit Circle
5.3
4.2
ALEKS
5.1
Graphs of sin/cos
5.4
5.2
Graphs of other Trigonometric Functions
5.5
1.1
Inverse Trigonometric Functions
5.6
1.2
Double Angle and Half Angle
6.3
2.1
Verifying Identities/Sum and Difference
6.1-6.2
2.2
ALEKS/Quiz on Chapter 5
3.1
Trigonometric Equations I
6.5
3.2
Trigonometric Equations II
6.6
4.1
Law of Sines/Cosines
7.1-7.3
4.2
ALEKS/Quiz on Chapter 6
5.1
Catch Up/Review
5.2
Exam 2
Week 4
Week 5
1.1
Area of a Triangle
7.4
1.2
Polar Coordinates
7.7
2.1
Systems of Equations
8.1
2.2
ALEKS/Quiz on Chapter 7
3.1
Linear Programming
8.5
3.2
Partial Fraction
8.6
4.1
Catch up and Review
4.2
ALEKS
5.1
Final
Homework
Title
Section
Page(s)/Problems
Linear Equations and Applications
1.1-1.2
p. 93 28, 32, 36, 44, 50, 56, 60,
78, 80, 86, 92, 94
Quadratic Rational
1.4
p. 128 18, 20, 38, 42, 46, 78,
80, 100, 104, 108, 110
Factoring and Radical Equations
1.5
p. 142 8, 12, 14, 16, 20, 24, 32,
34
Linear Inequalities
1.6
p. 154 19-39 odd, 41-50
Absolute Value Equations
and Inequalities
1.7
p. 162 23-33, 71-79
The Coordinate Plane/Graphs
2.1&2.2
p. 176 14, 16
p. 188 38, 42, 44, 58, 60, 62,
64
Functions and lines
2.3&2.4
p. 203 12, 16, 28, 32, 36, 38,
40, 44, 48, 54, 56, 78, 80, 82
p. 224 9-27 odd 49-53 odd
63-66
Library of Functions/Transformations
2.6-2.7
p. 248 23-33 odd
p. 263 12, 16, 42, 44, 54
Composite Functions/Inverse Functions
2.8-2.9
p. 274 26-36 evens and 37-42
p. 287 15-23 odd 67-74
Quadratic Functions
3.1
p. 306 22, 28, 30, 54, 58, 64,
66
Polynomial Functions
3.2
p. 323 40, 42, 44, 52, 56, 58,
64, 66
Dividing Polynomials
3.3
p. 337 7-23 odd
Rational Functions
3.6
Polynomial and Rational Inequalities
3.7
p. 372 28, 36, 38, 40, 50, 54,
56, 60
p. 384 15-35 odd 52-62 all
Variation
3.8
p. 392 11-27 odd
Exponential Function/
4.1-4.2
p. 414 16, 20, 22, 24, 48, 50,
70, 72, 76, 78, 86
Natural Exponential Function
p. 425 26, 28, 30
Logarithmic Functions
4.3
p. 440 10, 14, 16, 24, 28, 30,
32, 34, 36, 38, 40, 42, 46, 50,
68, 72, 80, 94, 98
Rules for Logs
4.4
p. 453 19-28, 39-50, 51-58
Exponential and Logarithmic Functions
4.5
p. 467 23-39 odd, 60-70 evens,
98, 99, 102, 103-113
Angles and their Measure
5.1
p. 489 27-45 odd, 63-73 odd
Right Triangle Trigonometry
5.2
p. 502 10, 16, 18, 48 (Change
angle to 30 degrees), 50
(Change Angle to 60 Degrees)
Trigonometric Functions of Any Angle
5.3
p. 517 26, 28, 30, 38, 40, 58,
60, 66, 68, 70, 72
Graphs of sin/cos
5.4
p. 535 10, 20, 24, 40, 42
Graphs of other Trigonometric Functions
5.5
p. 545 27-47 odd
Inverse Trigonometric Functions
5.6
p. 555 9-21 odd 33, 41, 42, 5566
Verifying Identities
6.1
p. 572 29-39 42, 43, 53, 54, 58
Sum and Difference
6.2
p. 584 8, 16, 22, 24, 26
Double Angle and Half Angle
6.3
p. 595 13-21 odd, 43-53 odd
Trigonometric Equations I
6.5
p. 611 7-16, 39-46
Trigonometric Equations II
6.6
p. 620 7-37 all
Law of Sines
7.1
p. 634 10, 16, 22 (Leave
answers with sin(angle))
Law of Cosines
7.3
p. 642 8, 11-18, 20, 30, 38, 4143
Area of a Triangle
7.4
p. 655 7-21 odd, 31-36
Polar Coordinates
7.7
p. 693 7-21 odd, 23-38, 63, 67,
77
Systems of Equations
8.1
p. 721 58, 62, 68, 88, 94, 96,
98
Linear Programming
8.5
p. 763 31-39 odd
Partial Fraction
8.6
p. 774 21-47 odd
Week 1 –
Module #1 -- Basics (56 topics)
Simplifying a fraction
Ordering fractions
Addition or subtraction of fractions with different denominators Fraction multiplication
Fraction division
Fractional part of a circle
Converting a fraction to a percentage
Converting a percentage to a fraction
Converting between percentages and decimals
Percentage of a whole number
Finding the sale price given the original price and percent discount Finding the original price given the sale price and percent discount Solving a proportion of the form x/a = b/c
Word problem on proportions: Problem type 1
Absolute value of a number
Operations with absolute value
Integer addition: Problem type 2
Integer subtraction
Integer multiplication and division
Signed fraction multiplication: Advanced
Signed fraction addition: Advanced
Signed decimal addition with three numbers
Evaluating expressions with exponents: Problem type 1
Exponents and order of operations
Integers and rational numbers
Rational and irrational numbers
Evaluating a linear expression in two variables
Additive property of equality with integers Multiplicative property of equality with signed fractions Solving a two-step equation with integers
Solving a two-step equation with signed fractions
Solving an equation to find the value of an expression
Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear equation with several occurrences of the variable:
Variables on both sides and fractional coefficients Solving a linear equation with several occurrences of the variable: Variables on both sides and distribution
Solving a linear equation with several occurrences of the variable: Variables on both sides and two distributions Solving a linear equation with several occurrences of the
variable: Fractional forms with binomial numerators Solving a word problem with two unknowns using a linear equation
Solving a decimal word problem using a linear equation with the variable on both sides
Solving a decimal word problem using a linear equation of the form Ax + B = C
Solving a fraction word problem using a linear equation with the variable on both sides
Solving a linear inequality: Problem type 2
Solving a linear inequality: Problem type 3
Solving a linear inequality: Problem type 4
Solving an equation involving absolute value: Basic
Solving an equation involving absolute value: Advanced
Solving an inequality involving absolute value: Basic
Solving a system of linear equations using elimination with multiplication and addition
Solving equations written in factored form
Finding the roots of a quadratic equation with leading coefficient 1
Finding the roots of a quadratic equation with leading coefficient greater than 1
Solving a quadratic equation needing simplification
Writing a quadratic equation given the roots and the leading coefficient
Applying the quadratic formula: Exact answers
Solving a word problem using a quadratic equation with rational roots
Solving a word problem using a quadratic equation with irrational roots
Module 2 Linear Functions (41 topics)
Set builder and interval notation
Union and intersection of intervals
Reading a point in the coordinate plane
Plotting a point in the coordinate plane
Introduction to functions: Notation and graphs
Sum, difference, and product of two functions
Domain and range from ordered pairs
Domain and range from the graph of a continuous function
Domain and range from the graph of a piecewise function
Range of a real-valued function
Writing an equation for a function after a vertical translation
Writing an equation for a function after a vertical and horizontal translation Classifying the graph of a function
Evaluating a piecewise-defined function
Graphing a piecewise-defined function
Finding a solution to a linear equation in two variables
Identifying solutions to linear equations in two variables
Y-intercept of a line
Finding x- and y-intercepts of a line given the equation: Advanced
Finding the slope of a line given its equation
Determining the slope of a line given its graph
Graphing a line given the x- and y-intercepts
Graphing a line given its equation in slope-intercept form
Graphing a line given its equation in standard form
Graphing a vertical or horizontal line
Graphing a line through a given point with a given slope
Graphing an equation involving absolute value in the plane: Advanced Writing an equation of a line given the y-intercept and another point Writing the equation of a line given
the slope and a point on the line Writing the equations of vertical and horizontal lines through a given point
Writing the equation of the line through two given points
Slopes of parallel and perpendicular lines: Problem type 1
Slopes of parallel and perpendicular lines: Problem type 2
Writing an equation and drawing its graph to model a real-world situation Application problem with a linear function: Problem type 1
Application problem with a linear function: Problem type 2 Interpreting the graphs of two functions
Finding the x-intercept(s) and the vertex of a parabola
Graphing a parabola of the form y = ax2 Graphing a parabola of the form y = (x-a)2 + c Graphing a parabola of the form y = ax2 + bx + c
Week 2 –
Module #3 -- Exp and Poly (30 topics)
Introduction to the product rule of exponents Product rule with negative exponents Quotients of expressions involving exponents Product rule with positive exponents
Power rule with positive exponents
Ordering numbers with positive exponents
Writing a positive number without a negative exponent
Writing a negative number without a negative exponent
Power rule with negative exponents: Problem type 1
Ordering numbers with negative exponents
Evaluating a quadratic expression in one variable
Simplifying a sum or difference of three univariate polynomials
Degree of a multivariate polynomial
Multiplying binomials with leading coefficients of 1
Squaring a binomial: Univariate
Multiplication involving binomials and trinomials in two variables
Polynomial long division: Problem type 1
Greatest common factor of two multivariate monomials
Least common multiple of two monomials
Factoring a quadratic with leading coefficient 1
Factoring a quadratic with leading coefficient greater than 1
Factoring a difference of squares
Factoring with repeated use of the difference of squares formula
Factoring a sum or difference of two cubes
Factoring a product of a quadratic trinomial and a monomial
Completing the square
Graphing a simple cubic function
Inferring properties of a polynomial function from its graph
Using a graphing calculator to solve a word problem involving a polynomial of degree 3
Using a graphing calculator to solve a word problem involving a local extremum of a polynomial function
Exam 1 – Modules 1-3
Week 3 –
Module #4 -- Radicals (21 topics)
Square root of a perfect square
Square root of a rational perfect square
Square root simplification
Square root addition
Square root multiplication
Simplifying a radical expression: Problem type 1
Simplifying a radical expression: Problem type 2
Simplifying a product of radical expressions
Simplifying a product of radical expressions using the distributive property Rationalizing the denominator of a radical expression
Rationalizing the denominator of a radical expression using conjugates Solving a radical equation that simplifies to a linear equation: One radical Solving a radical equation that
simplifies to a linear equation: Two radicals Domain of a square root function
Cube root of an integer
Converting between radical form and exponent form
Rational exponents: Basic
Rational exponents: Negative exponents and fractional bases
Rational exponents: Powers of powers
Solving a quadratic equation using the square root property: Problem type 1 Odd root property
Module #5 -- Rational Exp (27 topics)
Ordering fractions with variables
Ratio of multivariate polynomials
Simplifying a ratio of polynomials: Problem type 1
Simplifying a ratio of polynomials: Problem type 2
Multiplying rational expressions: Problem type 1
Multiplying rational expressions: Problem type 2
Dividing rational expressions: Problem type 1
Complex fraction: Problem type 1
Adding rational expressions with common denominators
Adding rational expressions with different denominators: ax, bx
Adding rational expressions with different denominators: Multivariate
Adding rational expressions with different denominators: x+a, x+b
Partial fraction decomposition
Solving a rational equation that simplifies to a linear equation: Problem type 1 Solving a rational equation that simplifies to a linear equation: Problem type 2 Solving a rational
equation that simplifies to a linear equation: Problem type 3 Solving a rational equation that simplifies to a quadratic equation: Problem type 1 Solving a rational equation that
simplifies to a quadratic equation: Problem type 2 Solving a rational equation that simplifies to a quadratic equation: Problem type 3 Algebraic symbol manipulation
Word problem on direct variation
Word problem on inverse variation
Word problem on inverse proportions
Word problem involving multiple rates
Quotient of two functions
Sketching the graph of a rational function: Problem type 1
Sketching the graph of a rational function: Problem type 2
Week 4 –
Module #6 Logs and Expon (21 topics)
Composition of two functions: Basic
Composition of two functions: Advanced
Inverse functions: Problem type 1
Inverse functions: Problem type 2
Converting between logarithmic and exponential equations Evaluating a logarithmic expression
Basic properties of logarithms
Change of base for logarithms: Problem type 1
Change of base for logarithms: Problem type 2
Solving an exponential equation: Problem type 1
Solving an exponential equation: Problem type 2
Solving a logarithmic equation: Problem type 1
Solving a logarithmic equation: Problem type 2
Solving a word problem using an exponential equation: Problem type 1 Solving a word problem using an exponential equation: Problem type 2 Solving a word problem using an
exponential equation: Problem type 3 Solving a word problem using an exponential equation: Problem type 4 Sketching the graph of an exponential function: Basic
Sketching the graph of an exponential function: Advanced
Sketching the graph of a logarithmic function
Translating the graph of a logarithmic or exponential function
Exam 2 – Modules 4-6
Week 5 –
Module #7 -- Trigonometry (23 topics)
Arc length and area of a sector of a circle
Area involving rectangles and circles: Advanced problem Converting between degree and radian measure: Problem type 1 Coterminal angles
Sketching an angle in standard position
Sine, cosine, and tangent ratios
Using a trigonometric ratio to find a side length in a right triangle
Using a trigonometric ratio to find an angle measure in a right triangle
Finding trigonometric ratios given a right triangle
Common angles and trigonometric functions
Finding values of trigonometric functions given information about an angle: Problem type 1 Finding values of trigonometric functions given information about an angle:
Problem type 2 Finding values of trigonometric functions given information about an angle: Problem type 3 Sketching the graph of a sine or cosine function: Problem type 1
Sketching the graph of a sine or cosine function: Problem type 2
Values of inverse trigonometric functions
Composition of a trigonometric function and an inverse trigonometric function: Problem type 1 Composition of a trigonometric function and an inverse trigonometric function:
Problem type 2 Composition of a trigonometric function and an inverse trigonometric function: Problem type 3 Cofunction identities
Double-angle identities: Problem type 1
Solving a basic trigonometric equation involving sine or cosine
Solving a basic trigonometric equation involving tangent, cotangent, secant, or cosecant
Module #8 -- Geometry (16 topics)
Perimeter of a square or a rectangle
Area of a square or a rectangle
Area of a piecewise rectangular figure
Finding the side length of a rectangle given its perimeter or area Finding the perimeter or area of a rectangle given one of these values Circumference and area of a circle
Perimeter involving rectangles and circles Volume of a rectangular prism
Volume of a cylinder
Volume of a cone
Volume of a sphere
Surface area of a cube or a rectangular prism Surface area of a cylinder
Pythagorean Theorem
Distance between two points in the plane Midpoint of a line segment in the plane
Week 6 –
Module #9 Advanced Topics (20 topics)
Plotting a point in polar coordinates
Converting rectangular coordinates to polar coordinates
Converting polar coordinates to rectangular coordinates
Converting an equation written in rectangular coordinates to one written in polar form Converting an equation written in polar form to one written in rectangular coordinates
Estimating a limit numerically
Finding limits from a graph
Finding limits for a piecewise-defined function
Finding a limit by using the limit laws: Problem type 1
Finding a limit by using the limit laws: Problem type 2
Finding a limit by using the limit laws: Problem type 3
Squeeze Theorem
Determining points of discontinuity from a graph
Determining a parameter to make a function continuous
Limits at infinity and graphs
Limits at infinity and rational functions
Infinite limits and graphs
Infinite limits and rational functions
Finding a limit of a trigonometric function by using continuity
Finding a limit by using special trigonometric limits
Final Exam – Modules 1-9