# algebra and equations mindmap

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- Created by: Japtha Woodward
- Created on: 12-06-13 20:18

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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)

- Multiplying out Brackets

- Collecting like Terms
- 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!

- Addition and Subtraction

- Algebraic Fractions
- 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

- Constant in bracket is always 1/2 value of b
- 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

- Solving linear equations with the form ax+b=cx+d
- 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.

- Simultaneous equations

- Algebra 1

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