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Summary A continuation of Introductory Algebra, this course focus on mathematical thinking and data analysis applied to linear, quadratic, rational, logarithmic, and exponential functions. It emphasizes also on trigonometric functions, and the main trig. identities and laws. the course incorporates the use of technology in particular graph software and Microsoft Excel to graph functions and their reflections about the axes and the different outcomes when the vertical and the horizontal shift is applied. The Larson text, "Pre-Calculus" is used in this course along with MyMathLab web-based materials and Blackboard/Active Board. Emphasis on Mathematics vocabulary and concepts in English and major component of problem-solving are already developed in this course.
2- Graph the functions studied using transformation techniques like shifting (Vertical and Horizontal), stretching, and reflection. 1.7 3.1
3- Analyse problems 1.5, and solve equations (Polynomial Ch 2, Exponential Ch 3, Logarithmic Ch 3, and Trigonometry Ch 4) in a technical context using the language of Mathematics.
4- Recall and implement some fundamental formulas in Algebra and Trigonometry needed in the subsequent courses in Calculus. Ch 4 Ch5 Ch6
5- Add, subtract, and multiply Matrices, and also find their Inverses and Determinants. Ch 8
6- Simplify and write Complex Numbers in Standard Form which will be used heavily in some Engineering courses. 2.4
7- Apply the 7 methods (Algebraic, and Matrix and Methods) presented in this course to solve the Linear Systems of equations. Ch7 and Ch8
CHAPTERS
Download: PowerPoint Presentations | Vocabulary | Download PDF BOOK
Topics Covered:
Functions and Their Graphs
Polynomial and Rational Functions
Exponential and Logarithmic Function
Trigonometry
Analytic Trigonometry
Laws of Sines and Cosines
System of Equations
Matrices and determinants
Course Learning Outcomes:
1- Use the concepts delivered in this course to evaluate functions, as well as finding their Domains, Ranges Ch 1 4.2, Zeros Ch 2, and Inverses 8.3.
1.5 Analyzing Graphs of Functions PowerPoint | Vocabulary | Notes | BB VIDEO 10
1.4 Functions PowerPoint | Vocabulary | Notes | BB recording 8
0 Review Introductory Algebra
0 Review PDF | PowerPoint | Vocabulary | Notes
Objectives:
Recall and implement fundamental formulas from Introductory Algebra.
BLACKBOARD recording _1 _2 _3 _4 _5 _6 _7
1 Functions and Their Graphs
Objectives:
Familiarize with Concepts and Vocabulary
Determine if a relation is a function or not.
Find the domain and range from a graph, equation, set of points, table, word problem,...etc.
Find the Difference Quotient.
Find the function Notation (evaluate the function)
Find the value for the Piece-wise function.
Familiarize with Concepts and Vocabulary
Domain and Range of a Function using Graphs
Determine if the graph is a function using a Vertical Line Test.
Determine if the function is Odd or Even or neither.
Find the zeros of a function.
Where is the graph increasing, decreasing, or constant?
Quiz
Objectives:
1.6 Graph of Basic Functions
PowerPoint| Vocabulary| Graph Software & Video | recording_12
Objective:
Graph of basic functions:
Constant
Linear
Square root
Cube Root
Absolute Value
Quadratic Function (Parabola)
Cubic Function
Reciprocal Function
Greatest Integer
1.7 Transformation of Functions PowerPoint | Vocabulary | recording_13
Objectives:
Familiarize with Concepts and Vocabulary
Graph of Basic functions.Graph functions.
Transformation of function
1.8 Combinations of Functions and Composite Functions
PowerPoint | Vocabulary recording_14 15
Objectives:
Familiarize with Concepts and Vocabulary
Combine functions by add, subtract, multiply, and division.
Find the domain of two functions (add, subtract, multiply).
Find the domain of two divided functions.
Combine function
Find the composite function.
Find the domain of the composite function.
1.9 Inverse Functions PowerPoint Vocabulary recording_16 17
Objectives:
Familiarize with Concepts and Vocabulary
Decide whether or not the relation is a function (Vertical Line Test).
Decide whether or not the function is a one-to-one function (Horizontal Line Test). It has or not inverse.
Decided whether the two functions are Inverse of each other.
Find the inverse of pairs of points, table, function, graph, ...etc
Test 1 Chapter 1 Review recording_18 recording_19
2 Polynomial and Rational Functions
2.1 Quadratic Functions and Models نموذج التربيعية
Vocabulary PowerPoint Video recording_21
Objectives:
Familiarize with Concepts and Vocabulary
Find the degree of any Polynomial
Analyze graphs of quadratic functions
Write functions in standard form and use the result to sketch graphs of functions.
Find the minimum and maximum values of quadratic functions in real-life applications.
Quadratic functions can be used to model data to analyze consumer behavior.
Objectives:
Familiarize with Concepts and Vocabulary
Use transformations to sketch graphs of polynomial functions.
Use the Leading Coefficient Test to determine the end behavior of graphs of polynomial functions.
Find and use zeros of polynomial functions as sketching aids.
Use the Intermediate Value Theorem to help locate zeros of polynomial functions
2.3 Polynomial and Synthetic Division
Objectives:
Familiarize with Concepts and Vocabulary
Use long division to divide polynomials by other polynomials.
Use synthetic division to divide polynomials by binomials of the form (x - k)
Use the Remainder Theorem and the Factor Theorem
2.4 Complex Numbers
Vocabulary | PowerPoint recording_24 _25
Objectives:
Familiarize with Concepts and Vocabulary
Find complex solutions of quadratic equations.
Use complex conjugates to write the quotient of two complex numbers in standard form.
Use the imaginary unit "i" to write complex numbers.
Add, subtract, and multiply complex numbers.
Example 2: Finding Products and Quotients Involving the Square Root of -a
Example 1: Writing the Square Root of -a as i Square Root of a
Example 3: Simplifying Quotients Involving the Square Root of -a
Example 4: Adding and Subtracting Complex Numbers
Example 5: Multiplying Complex Numbers
Example 6: Dividing Complex Numbers
Example 7: Simplifying
2.5 Zeros of Polynomial Functions
Objectives:
Familiarize with Concepts and Vocabulary
Use the Fundamental Theorem of Algebra to determine the number of zeros of polynomial functions.
Find rational zeros of polynomial functions.
Find conjugate pairs of complex zeros.
Find zeros of polynomials by factoring.
Use Descartes’s Rule of Signs and the Upper and Lower Bound Rules to find zeros of polynomials.
2.6 Rational Functions PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
2.7 Nonlinear Inequalities
Solve polynomial inequalities.
Solve rational inequalities.
Use inequalities to model and solve real-life problems.
3 Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs
Objectives:
Familiarize with Concepts and Vocabulary
Recognize and evaluate exponential functions with base a.
Graph exponential functions and use the One-to-One Property.
Recognize, evaluate, and graph exponential functions with base e.
Use exponential functions to model and solve real-life problems.
3.2 Logarithmic Functions and Their Graphs
Objectives:
Familiarize with Concepts and Vocabulary
Recognize and evaluate logarithmic functions with base a.
Graph logarithmic functions.
Recognize, evaluate, and graph natural logarithmic functions.
Use logarithmic functions to model and solve real-life problems.
3.3 Properties of Logarithms
Objectives:
Familiarize with Concepts and Vocabulary
Use the change-of-base formula to rewrite and evaluate logarithmic expressions.
Use properties of logarithms to evaluate or rewrite logarithmic expressions.
Use properties of logarithms to expand or condense logarithmic expressions.
Use logarithmic functions to model and solve real-life problems.
3.4 Exponential and Logarithmic Equations
Objectives:
Familiarize with Concepts and Vocabulary
Solve simple exponential and logarithmic equations.
Solve more complicated exponential equations.
Solve more complicated logarithmic equations.
Use exponential and logarithmic equations to model and solve real-life problems.
3.5 Exponential and Logarithmic Models PowerPoint Vocabulary
Midterm Exam
7 Systems of Equations and Inequalities
7.1 Linear and Nonlinear Systems of Equations Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Use the method of substitution to solve systems of linear equations in two variables.
Use the method of substitution to solve systems of nonlinear equations in two variables.
Use a graphical approach to solve systems of equations in two variables.
Use systems of equations to model and solve real-life problems
7.2 Two-Variable Linear Systems Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Use the method of elimination to solve systems of linear equations in two variables.
Interpret graphically the numbers of solutions of systems of linear equations in two variables.
Use systems of linear equations in two variables to model and solve real-life problems.
7.3 Multi-variable Linear Systems
PowerPoint
7.4 Partial Fractions PowerPoint
7.5 Systems of Inequalities PowerPoint
7.6 Linear Programming. PowerPoint
8 Matrices and Determinants
8.1 Matrices and Systems of Equations Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Write matrices and identify their orders.
Perform elementary row operations on matrices.
Use matrices and Gaussian elimination to solve systems of linear equations.
Use matrices and Gauss-Jordan elimination to solve systems of linear equations. Why you should
8.2 Operations with Matrices Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Decide whether two matrices are equal.
Add and subtract matrices and multiply matrices by scalars.
Multiply two matrices.
Use matrix operations to model and solve real-life problems.
8.3 The Inverse of a Square Matrix Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Verify that two matrices are inverses of each other.
Use Gauss-Jordan elimination to find the inverses of matrices.
Use a formula to find the inverses of matrices.
Use inverse matrices to solve systems of linear equations.
8.4 The Determinant of a Square Matrix Vocabulary | PowerPoint
Objectives:
Familiarize with Concepts and Vocabulary
Find the determinants of matrices 2 x 2.
Find minors and co-factors of square matrices.
Find the determinants of square matrices.
8.5 Applications of Matrices and Determinants (Cramer’s Rule ONLY)
Objectives:
Familiarize with Concepts and Vocabulary
Use Cramer’s Rule to solve systems of linear equations.
Use determinants to find the areas of triangles.
Use a determinant to test for collinear points and find an equation of a line passing through two points.
Use matrices to encode and decode messages.
4 Trigonometry
4.1 Radian and Degree Measure
Vocabulary |PowerPoint| Recorded Lecture 1 + 2 + 3|Homework|
Notes; last slide in PowerPoint.
Objectives:
Familiarize with Concepts and Vocabulary (Radius Vs.
Radian).
Describe angles.
Use the radian measure.
Use degree measure.
Use angles to model and solve real-life problems.
Area and Circumference
arc
4.2 Trigonometric Functions: The Unit Circle
Vocabulary|PowerPoint|Recorded Lecture 1 + 2|Homework|Notes; last slide in PowerPoint.
Objectives:
Familiarize with Concepts and Vocabulary
Identify a unit circle and describe its relationship to real numbers.
Evaluate trigonometric functions using the unit circle.
Use the domain and period to evaluate sine and cosine functions.
Use a calculator to evaluate trigonometric functions.
4.3 Right Triangle Trigonometry
Vocabulary|PowerPoint|Recorded Lecture 1 + 2|Homework |Notes; last slide in PowerPoint.
Objectives:
Familiarize with Concepts and Vocabulary
Evaluate trigonometric functions of acute angles.
Use fundamental trigonometric identities.
Use a calculator to evaluate trigonometric functions.
Use trigonometric functions to model and solve real-life problems.
4.4 Trigonometric Functions of Any Angle
Vocabulary|PowerPoint|Recorded Lecture 1 |Homework |Notes; last slide in PowerPoint.
Objectives:
Familiarize with Concepts and Vocabulary
Evaluate trigonometric functions of any angle.
Find reference angles.
Evaluate trigonometric functions of real numbers.
4.5 Graphs of Sine and Cosine Functions
Vocabulary|PowerPoint|Recorded Lecture 1 + 2|Homework |Notes; last slide in PowerPoint.
Objectives: Familiarize with Concepts and Vocabulary
Sketch the graphs of basic sine and cosine functions.
Use amplitude and period to help sketch the graphs of sine and cosine functions.
Sketch translations of the graphs of sine and cosine functions.
Use sine and cosine functions to model real-life data.
4.6 Graphs of Other Trigonometric Functions * (Graphs of Sec. and Csc. functions are Optional).
Vocabulary|PowerPoint|Recorded Lecture 1 + 2|Homework |Notes; last slide in PowerPoint.
Objectives
Familiarize with Concepts and Vocabulary
Sketch the graphs of tangent functions.
Sketch the graphs of cotangent functions.
Sketch the graphs of secant and cosecant functions
4.7 Inverse Trigonometric Functions
Objectives:
Familiarize with Concepts and Vocabulary
Evaluate and graph the inverse sine function.
Evaluate and graph the other inverse trigonometric functions.
Evaluate and graph the compositions of trigonometric functions.
5 Analytic Trigonometry
Pre-5.2 Verifying Trigonometric Identities
Objectives:
1) Familiarize with Concepts and Vocabulary
2) Verify trigonometric identities.
Pre-5.3 Solving Trigonometric Equations
Objectives: Familiarize with Concepts and Vocabulary
Use standard algebraic techniques to solve trigonometric equations.
Solve trigonometric equations of quadratic type.
Solve trigonometric equations involving multiple angles.
Use inverse trigonometric functions to solve trigonometric equations.
Pre-5.4 Sum & Difference Formulas
PowerPoint|Vocabulary|Recorded Lecture 1 + 2|Homework |Notes; last slide in PowerPoint.
Objectives:
Familiarize with Concepts and Vocabulary
• Use sum and difference formulas to evaluate trigonometric functions, verify identity and solve trigonometric equations.
Pre-5.5 Multiple-Angle Formulas
Objectives:
Familiarize with Concepts and Vocabulary
Use multiple-angle formulas to rewrite and evaluate trigonometric functions.
Use power-reducing formulas to rewrite and evaluate trigonometric functions.
Use half-angle formulas to rewrite and evaluate trigonometric functions.
Use product-to-sum and sum-to product formulas to rewrite and evaluate trigonometric functions.
Use trigonometric formulas to rewrite real-life models.
6 Additional Topics in Trigonometry
6.1 The Law of Sines (AAS or ASA or SSA or ASS).
Objectives:
• Familiarize with Concepts and Vocabulary
• Use the Law of Sines to solve oblique triangles (AAS or ASA).
• Use the Law of Sines to solve oblique triangles (SSA).
• Find the areas of oblique triangles.
• Use the Law of Sines to model and solve real-life problems.
Challenge: True or false: A triangle in which two sides and an angle opposite one of them are given (SSA) always results in at least one triangle. Answer
6.2 The Law of Cosines (SSS or SAS).
Objectives
Familiarize with Concepts and Vocabulary
Use the Law of Cosines to solve oblique triangles (SSS or SAS).
Use the Law of Cosines to model and solve real-life problems
Use Heron’s Area Formula to find the area of a triangle.
:
Final Exam Vocabulary
Objectives:
Familiarize with Concepts and Vocabulary
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