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My Maths GCSE Manual

A book with

simplified version of how to do all the boring shit you gotta do for your maths

GCSE

Prime Factors

This is that thing with the factor tree.

Once you’ve split two numbers up into their prime factors, its super

easy to find the HCF and LCM.

Here’s an example:

·

The prime factors of 12 are 2*2*3, and the prime

factors of 28 are 2*2*7

·

They have 2*2 in common, so this is the HCF of 12 and

28 (2*2=4, obvs, so the HCF is 4).

·

The LCM is basically the HCF multiplied by whatever

numbers they do not have in common- hence 2*2*3*7, which is 84, so the LCM is

84. Simples.

Indices

Here are some basic rules about Indices that you need to memorise:

Surds

Generally, treat surds like algebra, as if ‘square root 2’ was simply

‘x’.

However, you need to be able to simplify and expand surds, too.

Here’s how you can do that:

·

SqRt44= SqRt4 * SqRt11= 2 * SqRt11

·

What I have done above is find the highest square

number factor of the surd

·

This demonstrates how you can split a surd into any of

its factors

·

equally, when multiplying to surds, you multiply them

as you would if they were ordinary numbers (hence SqRt2 * SqRt3= SqRt6)

·

However, SqRt2+SqRt6 does not equal SqRt8. you can

only multiply or divide in this manner.

·

remember that SqRt2*SqRt2= SqRt4=2

Standard Form

·

A number between 1 and 10 * a power of 10

·

e.g. 3600 in standard form is 3.6 *10^3 (note: the

power of ten is equal to the number of digits in the original number following

the first digit)

·

another e.g. 0.0012 in standard form is 1.2 *10^-3

A more complex example:

·

(2.8 * 10^4)/(7*10^2)à (2.8/7) * (10^4/10^2)=

0.4 * 10^2= 4*10=40

Adding and subtracting fractions

·

multiply them by one another’s denominators

·

add ‘em

Converting recurring decimals

·

literally just divide the fraction using the busstop

method, and it will become quickly evident whether it is a recurring decimal or

not…

·

e.g. 4/9à 9 goes into four 0

times, so you carry over to get 40. 9 goes into 40 four times, with a remainder

of four etc.

quadratic formula

·

in a quadratic equation, you label the expression

a,b,c

·

e.g. x^2+11x+24=0à a=1 (b/c 1x^2),

b=11, c=24

·

Then you substitute them into this formula, which you

should try n memerise:

Pythagoras

·

you know this

graphical inequalities

·

when

expressed on number line, a filled circle= // or equal to, an empty

circle= less/greater

·

when expressed on a graph, you must find the line of

the inequality- hence, if the inequality is x

·

If the inequality is // or equal to, then the line

will be a single line, if it is simply greater/less than (not equal to) the

line should be a dotted line.

·

You must then shade the appropriate area- the side of

the line that makes sense with the inequality

Simultaneous equations

·

first of all, you need to find a way to cancel out one

of the algebraic letters (if you have ‘2y’ in both expressions, you might take

one away from the other, to cancel out the 2y). You might need to multiply the

equations to make them cancel out. You cancel out by adding or subtracting one

equation from the other.

·

Now you should have one equation. Solve it, and find

the unknown.

·

You substitute this unknown back into one of the

original equations to find the other unknown.

·

Done baby ;)

Simultaneous Graphs

Fill this

in omfg you lazy shit

Area of circles

·

Pi*radius^2

·

So an area of a sector of a circle is the angle of the

arc q divided by 360 *Pi *radius^2 à q/360 * (Pi*radius^2)

Circumference of circles

·

Pi*diameter

·

so the length of an arc is just à q/360* (pi*d)

Volume of a cylinder

·

are of the face*height

Surface area of a cylinder

·

(2Pi*radius^2) + (2Pi*radius *height)

Volumes of pyramids

·

1/3*Base-area*height

Volume of a sphere

·

V= 4/3*Pi * Radius^3

Stratified Sampling

·

To find a stratified sample, you do the number of

people you want to sample*the total, and divide it by the number of people from

the group that you are sampling.

·

e.g. there are 10 kids in class A and 20 in class B. I

want to take a stratified sample of 5 kids. Hence, I do 5*30 and divide it my

10 to get my sample for class A.

Cumulative frequency

·

With cumulative frequency, you add the frequency each

time

·

when plotting a cumulative frequency graph, always use

the upper bound on the Y axis

Box Plots

Fill this in motherfucker

Histograms

·

The frequency of each range in a histogram can be

found by finding the area of that bar

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