# maths, proportion, formulae, sequences and inequalities

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- Created by: Japtha Woodward
- Created on: 15-06-13 17:56

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- maths
- Number patterns
- Sequences
- each number is a term
- eg. Square no.s, Cube no.s, powers of 2, trisngular no.s etc.

- finding the nth term
- nth term of a linear sequence is an+b
- a = common difference
- So, if the nth term is the first term, add in value of first term.
- e.g. 3 = 2 x 1 + b
- b = 1
- nth term is 2n + 1

- use it to find b

- nth term of a linear sequence is an+b

- Sequences
- Inequalities
- solved in a similar way to equations
- Dividing by a negative reverses direction of inequality
- On a number line
- solid circle means included
- hollow circle means excluded

- Graphs of inequalities
- A graph is used to find a region containing the values that satisfy an equation
- the line of the inequality is the boundary
- An excluding boundary is a dotted line
- Including boundary is solid.

- Used in linear programming
- Usd to solve allocation problems

- Formulae
- Need to be able to write a formula for given information
- Using formulae
- Describes relationship between 2 or more variables
- Must have an = in it

- Substituting into formula
- Similar to substituting into expressions
- replace letters with the values given
- work out value on calculator

- rearranging formulae
- subject of a formula is the letter on its own on one side of =
- What you do to one side, do to the other
- Collect all of subject terms that appear together

- Quadratic formulae
- Used when completing the square and factorisation don't work.
- x= -b+ sqrt b2 - 4ac/2a

- Proportion
- Direct Proportion
- As one increases, so does the oher
- Graph goes through the origin
- Graph is a straight line

- Inverse proportion
- When y is multiplied by a number, x is divided by that number
- graphs of y against x go to infinity when one of them Is 0.
- A curve

- Variation
- include statements such as 'd varies as the square of x'
- E.g, the value of a diamond varies directly with the square of its weight
- So, is a diamond weighing 5g is 2500, ow heavy is one worth 5000

- 1. change sentence into proportionality statement
- So, is a diamond weighing 5g is 2500, ow heavy is one worth 5000

- 2. replace proportionality symbol wit = k to make an equation. V=kw2
- 3. substitute in values in question
- rearrange to find value of k
- 5. put k value back into equation, now answer

- Direct Proportion

- Number patterns
- Proportion
- Direct Proportion
- As one increases, so does the oher
- Graph goes through the origin
- Graph is a straight line

- Inverse proportion
- When y is multiplied by a number, x is divided by that number
- graphs of y against x go to infinity when one of them Is 0.
- A curve

- Variation
- include statements such as 'd varies as the square of x'
- E.g, the value of a diamond varies directly with the square of its weight
- 1. change sentence into proportionality statement
- 2. replace proportionality symbol wit = k to make an equation. V=kw2
- 3. substitute in values in question
- rearrange to find value of k
- 5. put k value back into equation, now answer

- Direct Proportion

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