# Maths revision cards

- Mathematics
- NumberAlgebraGraphsRatios and proportionsGeometry and MeasuresPythagoras and TrigonometryProbability and Statistics
- GCSE
- AQA

- Created by: Elanac
- Created on: 24-11-16 16:49

## Types of Number and BODMAS

**Intergers - A whole number.**

**Rational numbers** come in 3 different forms:

1) **Intergers**

2) **Fractions**

3) **Terminating or recurring decimals**

**Irrational numbers** are **never-ending, non-repeating decimals.** **Square roots of +v****e intergers** are **either intergers or irrational.**

**3.14159**....... is also **irrational.**

**BODMAS**

**B**rackets **- O**ther **- D**ivision **- M**ultiplication **- A**ddition **- S**ubtraction.

This is the **order** in which **these operations should be done.**

## Multiples, Factors and Prime Factors

The **Multiples **of a number are the times table of a number.

The **Factors** of a number are all the numbers that divide into a number.

A **Prime Number** is a number which doesn't divide by anything apart from itself and 1.

Finding the prime factors - The Factor Tree

EXAMPLE: 420

So... 42 10

420 = 2 x 2 x 3 x 5 x 7

7 6 2 5

2 3

## LCM and HCF

LCM - 'Least Common Multiple'

The **smallest **number that will **divide by all** the numbers in the question.

HCF - 'Highest Common Factor'

The **biggest** number that will **divide into all** the numbers in the question.

## Fractions

**Cancelling Down**

To cancel down or simplify a fraction, divide the top and bottom by the same number, til they won't go further.

**Multiplying**

Cancel the fraction down first if you can and then multiply the top and bottom numbers seperately

**Dividing**

Turn the second fraction upside down and then multiply.

## Fractions

**Common denominators**

Find the LCM and then multiply the top numbers by the opposite denominator.

**Adding and subtracting**

Make sure the denominator is the same

Combine the top lines and do simple addition or subtraction

**Expressing as a fraction**

EXAMPLE: Write 180 as a fraction of 80.

Just write the first number over the second and then cancel down.

180 = 9

80 4

## Fractions, Decimals and Percentages

Fractions, decimals and percentages are simply three different ways of expressing a proportion of something.

Divide x by 100

Fraction ~~ ~~ Decimal ~~ ~~ Percentage

e.g. 7 is 7 =0.35 x100 =35%

20 divided

by 20

## Estimating

Estimating square roots

1) Find two square numbers, one either side of the number you're given

2) Decide which number it's closest to, and make a sensible estimate of the digit after the decimal point.

## Bounds

When a measurement is rounded to a given unit, the actual measurement can be anything up to half a unit bigger or smaller.

When a measurement is truncated to a given unit, the actual measurement can be up to a whole unit bigger but not smaller.

## Standard Form

Any number can be written in standard form.

A x 10*

A must be a number between 1 and 10

* is just the number of times the decimal place moves

RULES:

1) The front number must be between 1 and 10

2) The power of 10,*, is how far the decimal point moves.

3) * is +ve for big numbers, * is -ve for small numbers.

## Standard Form

**Multiplying and divinding standard form.**

1) Rearrange to put the front numbers and the powerss of 10 together

2) Multiply or divide the front numbers, and use the power rules to multiply or divide the powers of 10.

3) Make sure your answer is in standard form.

**Adding and subtracting standard form.**

1) Make sure the powers of 10 are the same

2) Add or subtract the front numbers

3) Convert the answer to standard form.

## Algebra Basics

+ + makes +

+ - makes -

- + makes -

- - makes +

1) abc means a x b x c

2) gn* means g x n x n

3) (gn)* means g x g x n x n

4) p(q - r)* means p x (q - r) x (q - r)

## Algebra Basics

A term is a collection of numbers, letters and brackets, all multiplied/divided together.

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