Pre-Calculus 101 serves as a preparation course for Calculus I and an introduction for students to the basic mathematical concepts and skills needed to understand more advanced mathematical concepts of calculus using graphical and analytical methods
Instructor: Dr. Abeer Yasin
Course Duration: 4 months
Pre-Calculus 101 serves as a preparation course for Calculus I and an introduction for students to the basic mathematical concepts and skills needed to understand more advanced mathematical concepts of calculus using graphical, analytical, numerical and verbal representations of functions and relations. The course begins with a basic algebra review followed by an intensive study of polynomials, rational, exponential, logarithmic and trigonometric functions and their graphs. Students will explore the six trigonometric ratios and their applications to real life problems and will graph sinusoids to use them in modeling natural phenomena and to explore the relationship between trig functions and their inverses. The course provides students with the skills to prove, evaluate and analyze trigonometric identities and to solve systems of equations of linear nature composed of two or three variables. An introduction to matrices and their use in solving systems of equations will provide the students with an algebraic tool in solving systems of equations of higher order. The course concludes with an introduction to basic principles of probability and statistics where the student will be able to define and use permutations, combinations and calculate the probability of an event.
After successfully completing this course, students will be able to:
Define and work with real numbers, exponents, complex numbers, equations and inequalities.
Graph linear equations and quadratic equations.
Obtain an inverse of a function
Solve exponential and logarithmic functions
Graph trigonometric functions
Apply the law of sine and cosine to solve real life applications of trigonometric nature
Solve systems of linear equations in two variables using three different approaches
Solve linear inequalities and systems of linear inequalities
Solve systems of equations in more than three variables using matrices
Distinguish between an arithmetic sequence and a geometric sequence
Determine the use of permutation versus combination in probability nature problems.
Lesson 1: Topics from Algebra
This lesson will introduce you to real numbers, exponents and radicals, algebraic expressions, equations, complex numbers and inequalities.
Lesson 2: Functions and Graphs
This lesson will discuss the rectangular coordinate system which will later be used for graphing equations representing straight lines. The lesson will also define the function, its graphs, operations on functions and quadratic functions.
Lesson 3: Polynomial and Rational Functions
Lesson 3 will introduce the student to polynomial functions of order greater than 2, discuss the properties of polynomials and their zeros under the classification of rational and complex zeros and properties of rational functions.
Lesson 4: Inverse, Exponential and Logarithmic Functions
Lesson 4 will discuss inverse functions, exponential functions, logarithmic function and their properties. The lesson will also discuss in more detail the exponential and logarithmic functions and their solutions.
Lesson 5: Trigonometric functions
This lesson will focus on angles, trigonometric functions of angles and real numbers, values of trigonometric functions and their graphs.
Lesson 6: Analytic Trigonometry
Lesson 6 will introduce the student to trigonometric identities, trigonometric equations, the addition and subtraction formulas of trigonometric functions, multiple angle formulas and the inverse trigonometric functions.
Lesson 7: Applications of Trigonometry
In this lesson the student learns the law of sine and the law of cosines and their real life applications as well as vectors and properties of the dot product and its applications in real life examples.
Lesson 8: Systems of Equations and Inequalities
Lesson 8 introduces the student to systems of linear equations in two variables and the different method used to obtain a solution of the system. The lesson also discusses systems of inequalities and their solutions. Systems of equations of more than one variable will be introduced with the matrix system approach as a method of solution. The student will learn about matrices, algebra of matrices, the inverse of a matrix, the determinant of a matrix and properties of determinants.
Lesson 9: Sequences, Series and Probability
This lesson will introduce the student to infinite sequences and the summation notation followed by arithmetic sequences, geometric sequences and their summation. A brief introduction to probability, the binomial theorem, permutations and combinations will also be discussed.
Suggested textbook: Earl W. Swokowski and Jeffery A. Cole. Pre-Calculus Functions and Graphs. 11th edition ( 2008 ) Thomson Brooks/Cole, ISBN-13: 978-0-495-10837-5
level of difficulty:
minimum class size:
Available online by appointment
|| Pre-Calculus 101
|| live session
||Pre-Calculus 101 serves as a preparation course for Calculus I and an introduction for students to the basic mathematical concepts and skills needed to understand more advanced mathematical concepts of calculus using graphical and analytical methods
total duration: 1h 0m over 1 session(s)
| Abeer Yasin
description of :
Courses taught on- ground and online:
Fundamentals of Mathematics
Elementary Probability and Statistics
Advanced Business Statistics
Business Mathematics and Economics
Business Statistics and Research
Statistics and Probability
Research and Statistics
Probability and Statistics for Engineers
Mathematics for Medical Students
SPSS and Statistics
Linear Algebra I
Ordinary Differential Equations
Partial Differential Equations
Fundamentals of Accounting I
Fundamentals of Accounting II
Principles of Macroeconomics
Principles of Microeconomics
Quantitative Reasoning for Business (Graduate, Research)
Doctoral Dissertation Courses
DOC 733 A
DOC 734 A
DOC 734 B
Microsoft power point
Latex MiKTeX (2.7)
SPSS Statistical Software.
Graph Pad Prism Statistical Software.
MedCalc Statistical Software
Analyze it for Microsoft Excel Statistical Software
Math Magic Personal 3.64
Equation Conversion Manager
Project Kick Start
LMS Chart Maker
Assistat (Statistical Assistance, v 7.6 beta)
AM Statistical Software (product of the American Institutes of Research, v 0.06)
StatEasy (v 0.4
PQRS (Probabilities, Quantiles and Random Samples)
WinIDAMS (Validation, Manipulation and Statistical Analysis of Data, v 1.3, UNESCO)
InStat (Statistical Services Center, v 3.036)
Mathematics and Engineering:
Nonlinear Partial Differential Equations.
P-Laplace Operator and Applications in Engineering and Medicine
Pure and Applied Mathematics in Medicine:
Statistics and Applied Mathematics in Medicine:
Glomerular Filtration Rate estimation (e-GFR).
Cystatin C and Nephrology.
Cystatin C and Cardiology
GDF-15 (Growth Differentiation Factor-15)
Beta Trace Protein
Modeling of Mathematical Phenomena in Nephrology and Cardiology
's preferred teaching style:
Online-Virtual class room