Maths revision

Maths revision

Numbers (ARITHMETICS
1. Putting numbers in ascending order (whole numbers & decimals)
  1. 1. Put them in groups according to how many digits they have smallest to biggest amount.
    1. 2. Then order each of those groups in numbers according to the digits for example: 1,3,8,9 23,34,67,84, 100,135,654,879, 1134,2335,4657,7685
  2. decimals: 1. group the numbers according to how many zero's there are after the decimal point.
    1. 2. Than compare the numbers within the groups by looking at the number after each last zero that is after the decimal point and the number which is the smallest goes first as it's asscanding order.
      1. The most amount of zero's of decimal groups is the smallest decimals so the smallest amount or no amount of zero's after the decimal point is the biggest number.
2. Adding and subtracting decimals:
  1. 1. same as normal method expect the digits should be lined to the decimal place
    1. 2. Once there all lined do the same way you would either add or subract normally.
      1. when subtracting put the biggest decimal above first if it helps imagine the decimals as pounds.
      2. 2. multiplying decimals you must move the decimal place which is already there and if the decimal point moves places and there's no number than you must add a zero.
        multiplying other numbers like 300 split the number for example you can divide by three than put a decimal at the end of the number if it's not already a decimal and move it two places to the right.
        Dividing a number by ten you move the invisible decimal one place to the left for decimals you divide using the actual decimal which is VISIBLE andivide by moving it one decimal to the left. for divide you do not need to keep the zero if it's on the right hand side, on the left you must add a zero to fill it in
        2.when dividing with normal numbers that are not 100 than split the number and repate the process however instead of adding two 0's move the decimal point two places to the left. when it comes to decimals you must turn the number into a whole number by x's it by 10 100 or 100's all numbers should be on the left than divide how you would normally using the bus stop method and than add that decimal place according how many digits there were on after the decimal point for both of the decimal numbers that were used before.
3. Multiplying & dividing by 10 100 100's (whole numbers & decimals)
  1. 1. To multiply by 10 you must add a single 0 on whole numbers with two digits however you can also imagine a decimal point at the end of the number and move the decimal point along one place to the right the the same will apply if you're mulitplying by 100 0r 1000 expect you move it along two or three decimal point as there are two or three zero's.
4. multiplying without a calculator(CHINESE METHOD)
  1. Dividing without a calculator for whole numbers and decimals (BUS STOP METHOD)
    1. 1.Draw the bus stop method diagram and on the outside write the divider even it has two digits than write the number that's getting divided on the inside if a decimal than decimal point on top where the answer will be and also inside the diagram to.
      1. 2. than work it starting from the number closet to the divider our if the number doesn't go into that particlar number than carry that number to the other one to make a 2 digit number on the next one. same goes to reminders carry them on.
        3. place the numbers on top of the bus stop line that will be you're answer. If there's a reminder on the last digit than just carry it avove on top of the bus stop line and add it into you're answer like you would for the addtion method. the above is you're answer.
  2. 1. split the digits and put them in a grid make sure to draw digonal lines.
    1. 2. Once you have done that from the bottom right times each digit if the digit is a single digit than add a zero ahead for example an 8 is 08
      1. 3. Once that is done you start from the bottom right using the digonal lines as a guide. IF THE NUMBER ADDED HAS TWO DIGIT CARRY ONE ON TO THE RIGHT the remaining numbers that you had addedis you're answer.
        for decimals just x the number so it turns to a whole number and than do the same Chinese method and how ever much amount of digits there were after the decimal point put a decimal point so that's how much digits there are, make sure to have the same amount of digits from both number
5. approximates to one DP (decimal place) & sp (significant place)
  1. 1. Rounding to one DP you have to: first find out weather it's to one or two decmal place and circle the 2nd or ist number after the decimal point
    1. 2. Look at the number next to the circle number that will be the decider. If the decider is 5 or more than round it up one and if the decider is four or less then round it one. you have to get rid of the remaining numbers after the 2 or 1 number that is mean;t to be rounded off. if the decider is 9 than rounded of would be ten so than carry 10 to the digit ahead.
  2. ( 1 or... Significant place)
    1. 1. look at the digits whatever number that is after a zero or the first number of th(this zero must in the beginning of the decimal and not after a whole number digit)l if there isn't a 0. Than you look at the number next to it on thr right that will be the decider weather you round up or down. The remaining digits you get rid as you'll only need the amount of digits it says in the question. If the signifcant figure is the first digit of a whole number than fill in the rest of the remaining digits in 0 also fill in the gaps of any decimal points with a 0.
6. LCM & HCM
  1. LCm: to find the lcm you must find the smallest number that aill divide all the numbers you are given to find this out you write the timetables of the given numbers and look for the lowest mulitply in all the timetables written likewise you do the same for HCM however you look for the biggest number rather than the smallest
7. Ratio
  1. give the ratio in his simplist form well you have to look at both numbers and see what they times by both should times by same number and keep simplyfing until it cannot be done xample
  2. dividing in a given ratio well you first add the two ratios than you use that new number and divide the other number and then you mulitply one part by the ratio to get you're new ratio for example
Graphs
Shapes & area
Angles & geometry
Measures
statistics & probabilty
Algebra
1. square numbers: when you square a number you multiply it by itself. all square numbers answers are positive reguardless if you're doing two minus whole numbers or not
2. Cube numbers: when you times a number by itself than by itself again. cube numbers can give posative and negative answers
3. other powers: the littel number on the right of a whole number or decimal can be any number but you times it by that many times like you would for sqaure or cube it's the same method just diffrent numbers to multply it with. the little number is called the power of index. you read this as somethimg to power of something 3 to the power of 5
4. Power rules: rule one when you multiply you add the powers. example
  1. ruke two: when dividing you subtract the powers (the small numbers on the top right of a normal number) example
    1. rue 3: when raising (numbers in brackets) one power to another you multiply.
      1. rule 4: anything with the power 1 on a normal number just keep the numbers the same,
        anything to the power zero the answer is always 1
        if the big number is one than you just make the answer one regardless what the power maybe
5. Simplifying Terms
  1. abc means a x b x c and 3a means 3xa
    1. k x k x k x k means k4
      1. (gn)2 g x g x n x n the brackets mean both letters are squared, g x g x n x n
        (-3) you do the ame -3 x-3= 9
6. collecting and simplyfing terms
  1. = and + make a -
    1. + and a - makes -
      1. = and = makes a +
        + and a + makes a +
  2. 1. circle individual terms rembering to put a plus or minuse infront of each individual for all or as many as you can an example
    1. 1. Now ithat it's a lot more clearer you add up or take away the like terms to make a similoar equation using the like terms which are the letter that repersent a number
7. expanding brackets
  1. fitst you times what's outsside the brackets in the inside of the brackets on each digits to make a new equation
  2. then circle the new equations with the pkus or minus in front and simplkyf if you can then work oyt the answer example
  3. watch out for minus signs and collect like terms at the end
8. factorings ( adding brackets in algerbnra equations)
9. inequalities and equalties
calculator methods to use in exam
Fractions
1. Equivilant fractions and simplyfing (cancelling down)
  1. To simpligy you must 1. you must multiply the numorter and demonitor to make the even number which is asked in the questions the top and bottom should be timed same. you make a fracyion equvilant so the denimontor is even and easier to divide.
  2. To simplyfy fractions you divide the top and botom till it can longer be divided. an easier way to do this is look at the denomintor and numonayor and look for the lowest common factor that both can be divided and make that into the fraction in nthe right order if the nu,bers are ecen then repeate the process again until not completly dimplified. or you can go through the first ten times tvle and think if it can be divided and the lowest term will be the simplistexample
2. iconverting mixed fractions nto fractions look at the denominators of all the fractions than
  1. 1. you have to times the mixed number by the demoniator then add the numerator that will be you're new numerator the demoniator stays the same only the numerator changes
3. Converting fractions to mixed numbers
  1. divide top by bottom you write the whole number as the big number and the reminder goes into the numerator
4. ordering fractions:
  1. for all the fractions look at the denominator and write down the timetable for each and find the LCM change all the demoniators than times the same you did for the bottpm on the top than order remeber to put the orginal fractioms in the answer not the converted ones that's just to help you line your's and the orginal together to make it clearer to see what ti write in the answer
5. adding and subtracting fractions
  1. when nymbers on the bottom is the same tjhan just add or subtract tht top and keep the nottom you havve yo cancrl thr answer down if it can/
  2. when numbers of a fractiomn the denominators aere nit the same than you must must find the denominators lowest commen muliply and then do what you did for the bottom top to the times than continue normally as yiou would remerbing ti cancelling down the answer if you can/
  3. when adding and subtracting with mixed nymbers you must convert them into normal fractiomns by getting the whole number and times it by denominator and than add the numerator to make the new numerator and than proceed if the bottom are not same number than find LCM and do top as bottom and subtract or minuse if you want to turn the answer back into a mixed number than divide top my bottom the reminder will be the whole number
6. mulitplying and dividing fractions:
  1. when multiplying improper or normal fractions times top and bottom to get you're answer. you can then cancel down. if possibel cancel down the fractions in teh sum first to find the answer
  2. when having fraction of a number than you mist turn the number into a fraction by putting the numerator as number and the denominator always as 1 than times as normal
  3. when dividing you turn teh second fraction upside down and tomes the two fractions to get youre answer and simplyf if asked.
  4. when dividng with fractions and whole numbers do the same do the numebr over 1 as a fraction and than flip the second fraction and times normaaly but simply the fractions first if ou can
  5. qhen multiplying or dividing mix numbers you must tur the mixed number into a fraction and proceed how you would.
percentage decimals and fractions
1. fraction - decimal top divided by bottom gives you a decimal
2. decimal to percantage x by 100
3. percantage to decimal you have to divide by 100
4. decimal to fractions you must you divide top by bottom and than you must decide if you need to times over 10 100 1000 you know by looking at amount of digits after the decimal points if tehre's two then you do 100
5. to find out the percantage of something
  1. 1. divide the percentage by 100 than and then you will have a decimal get that decimal than times it by the second number that needs to be found the the new decimal is you're answert exampke
6. increase or decrese of a percentage
  1. 1. first you need work out 1% of something you need to divide the whole number by 100 than you get a decimal that you times on howver much perecnt needs to be time than add or decerse that in the orginal number depending on waht the questions asking yiou for example

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