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Are these all the algebra topics I need to know before starting calculus?

  1. Nov 26, 2008 #1
    The free textbook I'm using is from http://www.totallyfreemath.com/
    I'm not allowed to direct link to the book. Free Math -> View Book Online -> accept terms

    Here are the topics covered not including chapter 1:

    Solving Equations and Inequality:

    2-1 Algebraic Notation and Terminology
    2-2 Evaluating Algebraic Expressions
    2-3 Algebraic Addition and Subtraction
    2-4 The Addition and Subtraction Property of Equality
    2-5 The Multiplication and Division Property of Equality
    2-6 Solving Linear Equations Ans
    2-7 Solving Literal Equations and Formulas
    2-8 Word Problems
    2-9 Solving Linear Inequalities

    Polynomials and Exponents:

    3-1 Exponents-I
    3-2 Products of Algebraic Expressions
    3-3 Exponents-II
    3-4 Exponents-III
    3-5 Scientific Notation

    Factoring and Solution of Quadratic Equations by Factoring:

    4-1 Common Factors
    4-2 Factoring Trinomials of the Form x2 + bx + c
    4-3 Factoring Trinomials of the Form ax2 + bx + c
    4-4 Factoring the Difference of Two Squares and Perfect Square Trinomials
    4-5 Other Types of Factoring
    4-6 Factoring: A General Strategy
    4-7 Solving Quadratic Equations by Factoring
    4-8 Applications of the Quadratic Equation

    Rational Expressions, Ratio and Proportion:

    5-1 Rational Numbers and Rational Expressions
    5-2 Simplifying Rational Expressions
    5-3 The Quotient of Two Polynomials
    5-4 Ratio and Proportion

    Operations with Rational Expressions:

    6-1 Multiplication and Division of Rational Expressions
    6-2 Addition and Subtraction of Rational Expressions
    6-3 Addition and Subtraction of Rational Expressions
    6-4 Complex Fractions
    6-5 Rational Equations
    6-6 Rational Expression Applications

    Linear Equations in Two Variables:

    7-1 Ordered Pairs and the Rectangular Coordinate System
    7-2 Graphs of Linear Equations
    7-3 The Slope of a Line
    7-4 The Equation of a Line
    7-5 Graphing Linear Inequalities in Two Variables
    7-6 Functions Defined by Linear Equations in Two Variables

    Systems of Linear Equations:

    8-1 Solutions of Systems of Linear Equations by Graphing
    8-2 Solutions of Systems of Linear Equations by Elimination
    8-3 Solutions of Systems of Linear Equations by Substitution
    8-4 Applications of Systems of Linear Equations Ans
    8-5 Solving Systems of Linear Inequalities by Graphing

    Roots and Radicals:

    9-1 Principal Roots
    9-2 Product Property for Radicals
    9-3 Quotient Property for Radicals
    9-4 Sums and Differences of Radicals
    9-5 Further Operations with Radicals
    9-6 Fractional Exponents
    9-7 Equations Involving Radicals

    Solutions of Quadratic Equations:

    10-1 Solutions of Quadratic Equations by Extracting the Roots Ans
    10-2 Solutions of Quadratic Equations by Completing the Square Ans
    10-3 Solutions of Quadratic Equations by the Quadratic Formula Ans
    10-4 Complex Solutions to Quadratic Equations
    10-5 The Graphs of Quadratic Equations in Two Variables-Quadratic Functions

    *phew*... Does that cover all topics, or is there a lot more to know? I know I've read around here about needing trigonometry and geometry before starting calculus. This is going to take a lot of self discipline...

    I'm probably going to buy a book or software that can teach me calculus (if there are any) if I make it through the pre-requisites. A lot of times I google up topics and watch youtube teachers since the book can be very vague and lacking explanation.
  2. jcsd
  3. Nov 26, 2008 #2


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    Gold Member

    A LOT of calculus problems require trigonometric knowledge, and a good handle on different trigonometric identities. From the theoretical side there's no actual trigonometry going on, but in practice you need to deal with trigonometric functions all the time in calculus, so you'll need to know what's going on with them.

    You don't really need a lot of geometry... as long as you know how to calculate the area of a circle and a rectangle and a triangle, and maybe some 3-d shapes, but those can be picked up as you go along.

    You probably will want to practice factoring higher order polynomials (rational root theorem, etc.). On occasion you'll need to factor a cubic or quartic (if you're unlucky) polynomial and will need to know how to find the first couple linear factors
  4. Nov 28, 2008 #3
    I'd also say the algebra of logarithms. That's what my Calc I students tend to forget the most.
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