Chapter 2

Graphs and equations

Chapter description
In this chapter we look at different ways of solving equations.
We shall do this both by using the algebra from the first chapter and also by seeing what the solutions we find mean when we look at them graphically.
The chapter is split up into the following sections.

  1. Solving simple equations
    1. Do you need help with this? Self-Test (3)
    2. Rules for solving simple equations
    3. Solving equations involving fractions
    4. A practical application - rearranging formulas to fit different situations.

  2. Introducing graphs
    1. Self-Test (4)
    2. A reminder on plotting graphs
    3. The midpoint of the straight line joining two points
    4. Steepness or gradient
    5. Sketching straight lines
    6. Finding equations of straight lines
    7. The distance between two points
    8. The relation between the gradients of two perpendicular lines
    9. Dividing a straight line in a given ratio

  3. Relating equations to graphs: simultaneous equations
    1. What do they mean?
    2. Methods of solving simultaneous equations

  4. Quadratic equations and the graphs which show them
    1. What do the graphs which show quadratic equations look like?
    2. The method of completing the square
    3. Sketching the curves which give quadratic equations
    4. The `Formula' for quadratic equations
    5. Special properties of the roots of quadratic equations
    6. Getting useful information from "b2 -4ac"
    7. A practical example of using quadratic equations
    8. All equations are equal - but are some more equal than others?

  5. Further equations - the Remainder and Factor theorems
    1. Cubic expressions and equations
    2. Doing long division in algebra
    3. Avoiding long division - the Remainder and Factor theorems
    4. Three examples of using these theorems, and a red herring
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