maths summative assessment

linear sequence

1) find the common difference, this tells you what to multiply "n" by 2) work out what to add or subtract. do the difference between the multiplied "n" and the 1 corresponding term. 3) put both bits together for the sequence: 5, 8,11,14 the expression would be 3n +2

adding or subtracting in standard form

1) make sure the powers of 10 are the same( by making a front number smaller or bigger)[p 2) add or subtract the front numbers 3) convert to standard form if necessary

the sine rule

a/sine a = b/ sine b = c/sine c you only use 2 of the equal sines e.g. b/sinB =c/sinC or a/sinA =b/sin B used if- 2 angles given plus any side or 2 sides given and any angle not enclosed by them

the cosine rule

normal form is a squared= b squared +c squared -2bc cosA or for finding the angle it is rearranged as: cosA= b squared + c squared -a squared over 2bc used if-2 sides given and the angle enclosed by them or all 3 sides are given and no angles

ratios

when reducing a ratio to its simplest form you divide both by the same number if it contains decimals or fractions multiply by 10 or more so the numbers are more easily to work with if the ration has mixed units convert to the smaller unit

the difficult rules of powers (on paper flash cards)

with negative powers turn it upside down fractional powers 1/2 means square route 1/3 means cube route and 1/4 means fourth route etc. with fractional powers always split the fraction into a root and a power

labelling the triangle

you must label the triangle properly so the letters for the angles and sides correspond( they are opposite). use lower case letters for the sides and capital letters for the angles. it doesn't matter which sides are labelled a, b, c as long as they are opposite the corresponding angle.

y= mx+ c

"m" = gradient of the line "c" = y intercept 1) rearrange into the format y=mx+c rearrange y=mx=c if you need to find a different part of the formulae when drawing go the y intercept and use the formula to work out the other points. connect with a straight line

trigonometry common values

sin 30= 1/2 sin60=route3/2 sin45=1/route2 cos 30=route3/2 cos60=1/2 cos45=1/route2 tan 30= 1/route 3 tan60= route3 tan 45=1

more trig common values

sin0 =0 sin90=1 cos0=1 sin 90=0 tan0=0

powers and roots( on paper flash cards) the easy rules

when multiplying you add the powers when dividing you subtract the powers when raising a power you multiply them anything to the power of 0=1 anything to the power of 1 is just itself in fractions apply the power to both top and bottom

quadratic sequences

1) in quadratic sequences the difference is changing so find the difference between the differences 2) divide this value by 2- this gives the coefficient of the n squared term subtract n squared from each term in the sequence this will give you a linear sequence 3) find the rule of the nth term for the linear sequence and put this on the n squared term

make triangles into formulae triangles with the trig formulas

1) label sides O,A,H 2) write down SOH CAH TOA and decide which sides are involved and use the according formula 3) turn the one you chose into a formula triangle 4) cover up the thing you want to find and write down whatever is left showing 5) translate into numbers and work it out

multiplying and dividing standard form

1) rearrange to put the front numbers together and powers of 10 together 2) multiply or divide the front numbers and multiply or divide the powers of 10 ( by adding the powers or subtracting them) 3) make sure to answer in standard form

working out questions using the trigonometry formulas

1) work out the 2 sides of the triangle that are involves and then pick the formulae which involves those 2 sides. 2) to find the angle use sin/cos/tan -1. if not a right angled triangle you may need to make it one so u can use the formulae

more on ratios

if you know the ratio and the actual size of one part you with proportional division 1) add up the parts 2) divide from the total to find one part 3) multiply to find the amounts changing ratios does occur in quite complex questions 1) write the ratio as an equation 2)turn ratios it fractions 3)solve the two equations simultaneously

Pythagoras theorem

only works for right angled triangles uses 2 sides to find the 3 basic formula= a squared = b squared = c squared c is the hypotenuse

the trigonometry formulas

sin= opposite/ hypotenuse cos= adjacent/ hypotenuse tan= opposite/ adjacent