# Maths- numbers.

GCSE maths, section 1 of 6.

Teacher recommended

- Created by: carys
- Created on: 02-06-12 14:33

## Types of numbers

*Square numbers*- the difference between two square numbers are all odd.

*Cube numbers*- they're like the volumbes of cubes e.g. 2x2x2= 8

*Prime numbers*- all end in 1,3,7,9 (except 2 and 5).

**How to work out prime numbers-**

- does it end in 1,3,7,5?
- find its square root
- list all prime numbers less than this square root
- divide the number by all the prime numbers less that its square root
- if none of these divide cleanly (the answer has decimal places), the number is a prime number.

## Factors, Prime Factors, LCM and HCF

*Factors-* all the numbers that divide into the asked number (e.g. factors of 12)

*Finding Prime Factors-* any number can be broken down into a string of prime numbers all multiplied together (called "expressing it as a product of prime factors").

*Factor tree method-* Split the number into two factors. If the number is a prime number, circle it and if not split it up into more factors until you end up with all the prime factors. You can arrange them in order, smallest first.

*Lowest common multiple-* the smallest number that will divide by all the numbers in the question.

*Highest commont factor-* the biggest number that will divide into all the numbers in the question.

## Percentages

*Type 1-* "Find x% of y"- e.g. Find 15% of £46 - 0.15 x 46 = £6.90

*Type 2-* "Express x as a percentage of y" e.g. Give 40p as a percentage of £3.34"- (40 divided by 334) x 100 = 12%

*Type 3-* e.g. "a house increases in a value by 20% to £72,000. Find out what it was worth before the rise." An increase 0f 20% means that £72,000 represents 120% of the orginal value. If it was a drop of 20%, then it would represent 80%. You divide the value (£72,000) by 120% and then times it by 100.

*Percentage change-* percentage "change"= Change divided by original x 100.

## Surds

*Rational numbers-* are either a whole number, a fraction or a terminating/recurring decimal.

*Irrational numbers-* are never-ending non-repeating decimals. These are surds.

*Manipulating Surds-* Surds are expressions with irrational square roots in them. They must be used if they ask for an exact answer. There are a few simple rules to follow-

- √a x √b = √ab e.g. √2 x √3 = √2x3 = √6
- (√b)2 = b
- √a/√b = √a/b e.g. √8/√2 = √8/2 = √4 = 2
- √a + √b = do nothing!
- (a + √b)2 = (a + √b) (a + √b) = a2 + 2a√b + b

## Bounds and Reciprocals

*Upper and lower bounds of a measurement-* the real unit can be as much as half the rounded unit above or below the rounded-off value. e.g.- 2.4m to the nearest 0.1 could have a real value of anything up to 2.4m +/- 0.05m giving answers of 2.45m and 2.35m for the upper and lower bounds.

*Maximum and minimum values for calculations-* when a calcualtion is done using rounded-off values there will be a discrepancy between the calculated value and the actual value.

*Reciprocals-*

- the reciprocal of a number is "one over" the number
- you can find the reciprocal of a fraction by turning it upside down
- a number multiplied by its reciprocal gives 1
- 0 has no reciprocal because you can't divide anything by 0

## Conversions

*how to work out conversion factor-* find the conversion factor, multiply by it and divide by it, choose the common sense answer.

*Metric-imperial conversions-*

- 1kg = 2 1/4lbs
- 1m = 1 yard + 10%1
- 1 litre = 1 3/4 pints
- 1 inch = 2.5 cm
- 1 gallon = 4.5 litres
- 1 foot = 30cm
- 1 metric tonne = 1 imperial ton
- 1 mile = 1.6 km (or 5 miles = 8 km)

## nth term

*Formular*- dn + (a-d)

"a"- the first term of the sequence

"d"- the common difference between terms

*Changing difference type-* "a + (n-1)d + 1/2 (n-1) (n-2) c"

"a" = first time

"d" = the first difference (between the first and second number)

"c"- the change between one difference and the next

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