|Objective:||This course covers some of the basic topics in Algebra. Topics covered in algebra are equations and inequalities, graphs, functions and types of functions and also sequences and series. There will be expanding binomial terms with integer powers by using Binomial Theorem. In conclusion, students will learn basic concepts in each topic and how to apply respective formulas, sketch some graphs, and also solve the different types of problems.|
|Student Learning Time:||160 hours|
Final Examination: 50%
Fundamentals of Algebra
Real numbers, polynomials, factoring polynomials, rational expressions, integer exponents, rational exponents and radicals.
Equations and Inequalities
Equations: linear equations, quadratic equations, radical equations, polynomial equations. Inequalities: linear, quadratic, rational and polynomial inequalities. Equations and Inequalities involving absolute value.
Functions, domain and range, graphs of functions and transformations of functions. Types of functions and their graphs: quadratic functions, polynomial functions, rational functions. Composite and inverse functions. Exponential and logarithmic functions and their graphs.
Polynomial Division and Partial Fractions
Dividing polynomials, synthetic division, remainder theorem and Factor theorem. Rational root theorem. Partial fraction decomposition: Distinct roots, repeated roots, non-real roots (second order polynomial).
Sequences and Series
Introduction to summation (sigma) notation. Sequences and series. Arithmetic sequences and geometric sequences and series. The binomial theorem. Pascal’s Triangle. Mathematical induction.
At the completion of the subject, students should be able to: