algebra and equations mindmap

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  • Maths
    • Algebra 1
      • Collecting like Terms
        • Must be to the same power
        • Must be same letter
      • Substitution
        • Replacing a letter with a number
      • Brackets
        • Multiplying out Brackets
          • Number outside bracket multiplies all inside.
          • No. outside bracket is -, signs inside bracket change.
          • To simplify expression, multiply out brackets the collect like terms.
        • Multiplying brackets together
          • FOIL
          • (a+b)2 means (a+b) x (a+b)
        • Factorisation (putting brackets in)
          • Take out the common terms
          • When brackets are X they = first expression
          • Factorising a quadratic gives 2 brackets
            • Difference of two squares:   x2 - a2 = (x-a)(x+a)
    • Algebra 2
      • Algebraic Fractions
        • Addition and Subtraction
          • Find a common denominator
          • Simplify by multiplying out the numerator
          • Simplify by collecting like terms
        • Multiplication
          • Simply multiply the numerators together, then the denominators together
          • Cancel if possilble!
    • Equations 1
      • Solving linear equations with the form ax+b=cx+d
        • Get all the x's on 1 side of the =
      • Solving linear equations with brackets
        • Multiply out the brackets first
        • Then solve like a normal equation
      • Solving quadratic equations
        • Make sure the quadratic equation is = 0
        • Then factorise it
        • From the brackets work out the TWO values of x: eg (x+2): x=-2
      • Completing the square
        • Used when quadratic equations; (x+a)2 + bx +c = 0
        • 1. Rearrange equation to form; ax2 + bx + c = 0.
          • If a is not 1, DIVIDE whole equation by a
        • 2. Write in form:    (x+b/2)2
          • Constant in bracket is always 1/2 value of b
            • Constant being the + or - no. next to x
        • Multiply out bracket, compare to original and adjust by +/- an extra amount
        • 4. Then solve equation; leave answer in surd form.
          • Put into form: (x+b/2)2 - amount needed to make same as original = 0.
      • Using equations to solve problems
        • Always show working
        • Collect like terms, and work out x
    • Equations 2
      • Simultaneous equations
        • Finding values for the letters that will make both work
        • Graph method
          • The point of intersection = solution
          • Draw the equations lines
        • Elimination method
          • If the coefficient of 1 letter is same, the letter can be removed by subtracting equations
          • If terms to eliminate have the same sign, subtract
          • If the terms to eliminate have different signs, add.
      • Solving cubic equations by trial and improvement
        • Go 1 decimal place further to determine which value it rounds to.
        • can also be used to find the root of equation
          • root of graph is point line crosses x-axis
          • lowest + no.

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