When you multiply an expression with powers you add the powers.
When you divide an expression with powers you minus the powers.
When one powers in a bracket and the others outside you multiply the powers.
When an expression doesnt have a poweri it is powered to 1.
When a power is less than 1 ( a fraction) you do the root of the number but the root number is the denominator.
When you simplify with poweers generally a^-n=1/a^n.
To change a negative power to a positive power you switch the fraction so its the other way. When a number/letter powered needs simplifying you split the power into a numerator and a denomenator put the fraction in the bracket and the numerator outside and then solve the expression.
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Functions
A function is an operation or series of operation that transforms a set of numbers into a different set.
A composite function is a function which is then followed by another. fg(x) ... you do the function closest to x first.
The inverse function is the function that will undo it and return it to the input. f^-1(x)=...
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Linear Graphs
The equation of a straight line is y=mx+c where m and c are numbers.
C is the y intercept and m is the gradient.
To work out the gradient you do the height of the triangle divided by the width.
The gradient can be negative if going high left to low right.
To find the perpendicular lines equation you do y=mx+c but then do the inverse of mx and for +c you find the y inecept (second in the bracket).
A perpendicular line has a gradient -1/m if the gradient is m or vise versa.
Parrellell lines have the same gradient but a different y intecept.
Parrellell line y intecept is determined by the difference between (x,y) when put into the equation and solved.
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Constructions
A construction can be where you bisect an angle or line at an exact point using lines to construct your point.
It can also be to get an exact distance all the way around a line or shape using staright lines and curves, you do this by using construction lines.
To make construction linees you need a compass, ruler , protractor and pencil.
Most exam questions ask you to shade in an area where an object may or not be able to go so read the question carefully and shade as you go along.
A locus is the area where you have drawn and constucted from earlier instructions.
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Factorising
To factorise a quadratic you find the two multiples of the single number and that add up to make the numberx, the letter goes in the brackets and then you + the two numbers
If the numbers are both positive you add.
If the numbers are both negative then you minus.
If the numbered letter is negative then both the numbers are minus.
If the sign of the number is negative then one of the numbers will be add and the other minus it just depends on which ones add to make the number, you write it so every pair has both neagtive and both positive.
Whenyou factorise the difference of ttwo squares you do x^2 - y^2 (x+y)(x-y).
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Factorising 2
To factorise a triple bracket you need to do the first two brackets in xfactor method and then bracket answer and do the same. simplify this answer to get the single line answer.
You should have cubed, squared, single x, and number.
You do the same method for two brackets and expand so you can simploify them first.
To simplify an algerbraic fraction you need to find the quadratics that fit into it and, factorise the fraction and then cancel out and or simplify to reach the final result.
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