* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Square Numbers
Survey
Document related concepts
History of logarithms wikipedia , lookup
Ethnomathematics wikipedia , lookup
Law of large numbers wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Infinitesimal wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Positional notation wikipedia , lookup
Large numbers wikipedia , lookup
Real number wikipedia , lookup
Transcript
Revision: The Bare essentials Factors: Numbers that divide into other numbers. Look for pairs of numbers e.g. Factors of 12 are 1x12 2x6 3x4 = 1,2,3,4,6,12 Multiples: Answers to the times tables. First 5 multiples of 5 are 5,10,15,20,25. Square Numbers: Times a number by itself to give a square number. Can also form a square from it. Square numbers: 1,4,9,16,25,36,49,64,81,100 3x3=9 so 9 is a square number. 4x4=16 so 16 is a square number. Shown as 42 =16 Cube Numbers: Times a number by itself and then itself again. Cube numbers are: 1,8,27,64,125,216 3x3x3=27 so 27 is a cube number. Square Root: Opposite of squaring. Means what number times itself? 4 = 2 (as 2x2=4) 25 = 5 (as 5x5=25) 64 = 8 (as 8x8=64) Prime Numbers: Only has 2 factors (numbers that go into them). Numbers that go in are only 1 and the number itself. Factors of 7 are only 1 and 7 so it’s a prime number so are 2,3,5,7,11,13,17,19… Even numbers can’t be prime as 2 goes into them. 1 is not a prime number. Rotational Symmetry: Order is how many times it looks the same in one complete rotation. Start 1 2 3 4 Order = 4 as looks the same 4 times. Triangles: Equilateral Same sides 2 sides same Same angles Scalene All different 2 angles same 60 60 Rounding Off: Isosceles 60 1 Significant figure = one number then zeros 234 to 1 sig fig = 200 ( 1 number then 0s) 48752 to 1 sig fig = 40000 Estimating: Round to 1 sig fig then do calculation. 234 x 65 = 200 x 70 = 14000 Make the numbers easy to use first even if you are allowed to use a calculator. Fractions of amounts: Divide amount by bottom number then times by top. 2 1 2 of £150 = 150 ÷ 5 = £30 ( that’s 5 5 of £150) then £30 x 2 = £60 ( 5 ) If ½ or ¼ or ¾, then ÷ 2 for a half and ÷ 2 again for ¼. Percentage of Amounts: Always out of 100. Find 1% by dividing by 100, then multiply up. Find 12% of £150, Do £150 ÷ 100 = £1.50 ( 1%) then times up by 12 e.g £1.50 x 12 = £18. Remember ÷ 100 to give 1% then multiply it up. Remember to add amount on if it asks for the new price not just the increase. Top ÷ bottom Fractions e.g. 2 16 9 40 X 100 Decimals 2 ÷ 16 9 ÷ 40 Percentages 0.125 X 100 12.5% 0.225 X 100 22.5% Probability: Always out of 1. Usually write as a fraction but also as a decimal or percentage. List outcomes to see how many there are. Flick a coin and role a dice: 1H 2H 3H 4H 5H 6H 1T 2T 3T 4T 5T 6T (12 outcomes) Coordinates: along first, then up or down. (x,y) 5 -3,2 4 3 -5 –4 –3 –2 –1 -2 -3 -5,-4 3,4 2 1 1 2 3 4 5 3,-3 -4 -5 Angles acute obtuse reflex 180º Angles add up to 360 º Angles add up to 180 º 360° Congruent: Same shape, same size 90° Powers: Shows how many numbers to times together. 22 means 2 x 2 = 4 23means 2 x 2 x 2 = 8 24means 2 x 2 x 2 x 2 = 16 Not 2 x 4 Ratio: Shows how to share out things. Method 1 Method 2 Find how many shares there are. Count out the quantity in the ratio Divide amount by this total to find given until all used up then add up. the amount in one share then multiply out. Example: 20 sweets in the ratio 4:1 between Tom and Daniel 4 + 1 = 5 ( total number of shares) Tom Daniel 16 sweets 4 sweets 20 sweets ÷ 5 = 4 sweets ( number of sweets in one share) Tom gets 4 x 4 sweets = 16 sweets Daniel gets 1 x 4 sweets = 4 sweets Example Range = biggest – smallest 2,8,3,5,9,3 range=9-2=7 Mode = Most often or common one mode=3 Mean = Total of all numbers ÷ How many numbers you have mean=30÷6=5 Median = middle number (put in order first then cross off from each end) (If 2 middle numbers take the mean e.g. the number that would be between them) Can’t have 2 numbers for the median.2 3 3 5 8 9 median = 4 4 Common Conversions to Learn Fraction 1 2 1 4 3 4 1 5 1 3 1 10 Decimal Percentage 0.5 50% 0.25 25% 0.75 75% 0.20 20% 0.33 33.3% 0.10 10% Perimeter: Distance round the outside. Imagine you are walking around it, how far have you gone all the way round? Area = ½ x base x height height width Area = length x width length Volume: Space inside. Volume = length x width x height base