Introduction to Algebra - PowerPoint

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					Unit 1: Introduction to Algebra
1.    Introduction to Algebra
                                               Example Problem
2.    Working with Real Numbers
3.    Solving Equations and                    Use the figure and the
      Problems                                 information inside of it to
4.    Polynomials                              write an equation involving
5.    Factoring Polynomials
                                               x.
6.    Systems of Linear Equations                             7
7.    Fractions
8.    Applying Fractions
9.    Introduction to Functions            x         Rectangle Area = 21
10.   Inequalities
11.   Rational and Irrational
      Numbers
12.   Quadratic Functions



                          Unit 1: Introduction to Algebra             1
What is Algebra?
    Algebra is the most basic and fundamental
     branch of mathematics. It explains the
     laws that govern the other branches. Other
     branches of mathematics include
     arithmetic, geometry, trigonometry, and
     calculus.
                            Algebra

          Geometry       Trigonometry             Calculus




                     Unit 1: Introduction to Algebra         2
    Where does the name “Algebra”
    come from?
   The term comes from the
    title of an Arabic book - Al-
    jabr w'al-muqabala -
    written by Abu Ja'far
    Muhammad ibn Musa Al-
    Khwarizmi (who lived
    around the year 800)
                                                       This picture is taken from
    which is all about algebra                         a stamp from the former
                                                       USSR




                     Unit 1: Introduction to Algebra                    3
        Introduction to Algebra:
        why this unit important.
   Mathematics has been described as the
    universal language. In order to use a
    language successfully, you must
    understand its symbols and terminology.
    In this unit, you will be introduced to the
    terminology that shapes algebraic
    thought: variables, grouping symbols
    and the language of equations.

                  Unit 1: Introduction to Algebra   4
Introduction to Algebra
Learning Objectives
 Simplify numerical expressions and
  evaluate algebraic expressions
 Simplify expressions with and without
  grouping symbols
 Find solutions sets of equations over a
  given domain
 Translate phrases into variable
  expressions

                Unit 1: Introduction to Algebra   5
Introduction to Algebra
Learning Objectives cont.
   Translate word sentences into equations.
   Translate simple word problems into
    equations.
   Solve word problems over a given domain.
   Graph real numbers on a number line and
    compare real numbers.
   Use opposite and absolute values.



                   Unit 1: Introduction to Algebra   6
Conclusion
   This chapter provides             Example Problem Solution
    you with the necessary
    introductions and                      Use the figure and the
    practice to prepare for                information inside of it to
    successful study of                    write an equation
    algebra.                               involving x.
                                                        7

                                                                         Solution
                                       x       Rectangle Area = 21       7x = 21




                      Unit 1: Introduction to Algebra                7

				
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