gcse maths 'number' notes

8/10/2019 GCSE Maths 'Number' Notes

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T4: Prime Factors

A prime number is a number that can only be divided by itself and 1. Prime numbers have two factors, which iswhy 1 is not a prime number.Prime numbers are the building blocks of mathematics. All other numbers can be written as products of prime

numbers.

2 120

3 60

2 20

2 10

5 5

Done. 1

120

= 23 x 3 x 5

Highest Common Factor

Express each number as a product of its prime factors (table) and write in index form

Multiply all the factors they have in common. Do the opposite to what the name suggests and pick the lowestpowers.

Lowest Common Multiple

Express each number as a product of its prime factors (table) and write in index form

Multiple by all the factors. Do the opposite to what the name suggests and pick the highest powers.

T4: Approximating to a number of Decimal Places

The first decimal place is the first number after the decimal point.

Rule: If the next number is 5 or more, round up

If the next number is less than 5, leave it

T4: Approximating to a number of Significant Figures

The first significant figure is the first digit that is not zero. Any zeros afterwards are counted as significant figures.Rule:

Start counting at the first non-zero digit to the specified amount

Look at the next number (the first unwanted digit)

If the number is less than 5, leave it

If the number is 5 or more, round up

Put in enough zeros to keep the number approximately the same size

T4: Percentage Increase or Decrease

A percentage increase or decrease is always given as a percentage of the original amount. This is also thecause for percentage profit or loss.

% change = change % original x 100% change = increase, decrease, profit, loss

T4: Reverse Percentage (original amount)

Start with final amount and work backwards to find original.


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State percentage given

Find 1%

Find 100%

T4: Percentages and Finance

There are two types of interest:

Simple Interest: added amount stays the sameCompound Interest: added amount changes yearly

Key Words:Appreciation: something going up in valueDepreciation: something going down in value

T4: Indices

Rules Multiplying

o Add the powers: amxan=am+no X3xX6=X9

Dividingo Subtract the powers: am/an=am-no X9/X3=X6

Brackets

o Multiply the inside power with the outside power: (am)n=amno (X5)6=X30

Power of 1

o

Just the number: a1=a Power of 0

o Always 1: a0=1

Negative Powerso Flip it: a-n=1/an

Fractional Powerso Generally, find the something-root of big number using the denominator, and then square (or something)

the answer by the numerator

T6: Standard Form

This is a way of writing very large and very small numbers: Ax10n

Ordinary to Standard

Large Numbers (positive n) / Small Numbers (negative n)o Place the decimal point so that A is at least 1 and less than 10o Find n. This is the number of places the decimal point has moved (or needs to move)

Standard to Ordinary

Move the decimal so many places to the right or left depending on the value of n.o Negative indices are easier because the number is equivalent to the number of zeros before the first significant

figure

o

Positive indicesneed to work out what it is with 10 and guess from there


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Adding, Subtracting, Multiplying and Dividing SIF Numbers

Multiplying and Dividingrules for indicesAdding and Subtractingchange to ordinary number, do as normal, change back

T6: Recurring Decimals into Fractions

A recurring decimal is a decimal that never ends and has a repeated pattern, e.g. 0.147147147...

Method: Let x equal the recurring digit1 digit recurring = x101(and so on)

T6: Surds

Rational numbers can be expressed as an exact fractionIrrational numbers cannot be expressed as an exact fraction

A surd is a square root that cannot be written as a fraction

Multiplying Surds:4 x 9 = 2 x 3 = 6 = 36 = 4x9Rule: a x b = ab

Dividing Surds:100/25 = 10/5 = 2 = 4 = 100/25Rule: a/b = a/b

Another important rulea x a = a2= a

Adding or Subtracting SurdsNeed the same square root, or need to rewrite the surd

Rationalising the DenominatorThe denominator is not allowed to be a surd

o Multiply top and bottom by the surdo Simplify if possible

T6: Fractions

Equivalent Fractions:Multiplying/dividing the numerator and the denominator by the same number

Improper Fractions:22 thirds = 7 and 1 third2 and 1 quarter = 9 quarters

Adding/SubtractingNeed common denominator

MultiplyingMultiply numerators. Multiply denominators. Simplify.

DividingTurn divisor upside-down and multiply

gcse maths 'number' notes

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