# algebra and equations mindmap

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• Created by: bio1423
• Created on: 12-06-13 20:18
• 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
• 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
• 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.