Maths y9 eoy

Question	Answer
standard form:	e.g. 999000000 = 9.99x10^8 0.08 = 8x10^-2 Image: Mobile upload (image/jpeg)
adding and subtracting standard form	convert each number first, add them together and convert back to standard form e.g. 6x10^3 + 7.6x10^2= 6.76x10^3 4x10^3 - 5.2x10^2= 3.48x10^3
multiplying and dividing standard form	no need to convert just multiply or divide the first numbers and add or subtract the powers. e.g. 4x10^3 x 2x10^2= 8x10^5 8x10^7 / 4x10^3= 2x10^4
significant figures	remember that if its for example 1sf then consider wether the second one is above or below 5 to decide wether to round the 1st sf e.g. 15200(1sf)=20000 0.06270(2sf)=0.06300
multiplying decimals	ignore the 0. and just multiply the number after the 0. e.g. 0.23x0.9=0.207 0.3x0.67=0.201
dividing decimals	make the decimals whole numbers and divide them. the answer for the decimals is the same for the whole numbers. e.g. 2.4/0.6=4 1.8/0.03=60
surds	number in root factor tree of roots one root has to be prime divide the none prime one and remove the root root325=root25xroot13 =5root13
Solving equations	equation will look like this ax-bx=c e.g. 6x-2x=40 4x=40 x=10
rearranging equations	equation will look like this ax+b=x+c rearrange to put the x’s on the same side but remember CHANGE SIDE CHANGE SIGN e.g. 4x+5=x+14 4x-x=-5+14 3x=9 x=3
expanding brackets	multiply all numbers inside the brackets by the number outside and remove the brackets in the answer e.g. 3(2x+5)= 6x+15
rearranging equations 2	you will be given a question with two brackets that equal each other that you have to expand. expand the brackets then put both x’s on the same side. IMPORTANT: for the answer start with x= so the x has been eliminated. next is the fraction, the number that was with the x goes at the bottom of the fraction. the number left over goes as the numerator. e.g. 4(2x+3)=5(3x-2) 8x+12=15x-10 15x-8x=-10+12 7x=22 x= 22/7 3(2x+9)=2(4x-1) 6x+27=8x-2 6x-8x=-27-2 -2x=-29 x= 29/2
double brackets	use FOIL (first outside inside last) e.g. (x+4)(x+3) x^2+3x+4x+12 x^2 +7x+12
rearranging formulae: changing the subject	move all letters away onto the other side from the letter that you want to make the subject. CHANGE THE SIDE CHANGE THE SIGN e.g. subject:q p= 3q^2+r//s ps=3q^2+r ps-r=3q^2 ps-r/3=q^2 rootps-r/3=q subject:q p=z(q/r + t)^2 p/z=(q/r+t)^2 rootp/z=q/r+t rootp/z -t=q/r r(rootp/z -t) Image: Mobile upload (image/jpeg)
inequalities	greater than, less than, greater than or equal to, less than or equal to intervals use inequalities to represent a range of values. the inequalities set the boundaries of the interval 1_<x_<12 you would describe this as: “x lies between 1 and 12. it includes both 1 and 12.” you would draw this as black circles on either side of the number line. there are 3 ways to show an interval 1)list the values as if they are integers 2)using inequalities/ describing 3) a number line dark circle in number line means that number is included. hollow circle means that it isn’t included. if there is only one greater than or less than then the blank space for a circle will just be an arrow on one side.
angles in polygons	angle relationships(picture) how to find angles exterior=360/no of sides interior=180-exterior exterior=180-interior sum=(no of sides-2)x180 interior=sum/sides sides=sum/interior sum/180=sides-2 sum=interior x sides sides= 360/ exterior Image: Mobile upload (image/jpeg)
quadratic sequences	find 1st difference(difference between terms) find 2nd difference(difference between 1st) half the 2nd dif to get the coefficient. the coefficient is the first part of the nth term. put n above terms. and put coefficient above them. find difference between the coefficient n and the terms. difference will create a linear sequence that comes at the end of the nth term if all terms are same then that number goes at the end instead. so the nth term of a quadratic sequence is: coefficient +linear nth term
data handling	raw data is the original data and all of the data collected to find the median of raw data do. (NUMBER OF DATA+1) divided by 2= nth position for even number of data ADD MIDDLE PAIR AND DIVIDE BY 2 =nth position do this for frequency tables\/ Image: Mobile upload (image/jpeg)
Question Text	Answer Text
Question Text	Answer Text
hierarchy of operations	leave roots unless you can simplify them. when adding numbers with powers, convert them into normal numbers before adding them. USE BIDMAS e.g. _//5^2+3x^3_/-27 _//25+3x-3 _//25+-9 _//16 _/16=4 ^3_/10^2+5^2 ^3_/100+25 ^3_/125=5
multiplying indices	Rule: a^m x a^n=a^m+n multiply the normal numbers together but add the powers together e.g. 3^6 x 3^11= 3^17 2k^3 x 4k^2= 8k^5

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	Created by toby gorner over 6 years ago