the distributive property:<\/span><\/p>\n \n \n \n <\/p>\n
<\/p>\n
fast fractions<\/b><\/p>\n
\nfor example: <\/p>\n
<\/p>\n
exponents and roots<\/b><\/p>\n
laws for combining:<\/span><\/p>\n <\/p>\n
<\/p>\n
<\/p>\n
1 and 0 as bases: <\/span><\/p>\n\n1 raised to any power is 1. 0 raised to any nonzero power is 0 <\/i><\/li>\nany nonzero number to the power of 0 is 1, e.g. <\/i><\/li>\n<\/ul>\n fractions as exponents: <\/span><\/p>\n <\/p>\n
negative exponents:<\/span><\/p>\n <\/p>\n
negative bases:<\/span><\/p>\n\nwith an even exponent: positive result<\/i><\/li>\nwith an odd exponent: negative result<\/i><\/li>\n<\/ul>\n <\/p>\n
roots <\/b><\/p>\n
estimating roots:<\/span><\/p>\nto estimate square roots of numbers that aren\u2019t perfect squares, just examine the nearby perfect squares. for example, to find , you know that and , so find must be between 7 and 8.<\/i><\/p>\n
cube roots: <\/span><\/p>\n a number that, when cubed, equals n. e.g.: \n <\/i><\/p>\n
simplifying roots: <\/span><\/p>\nseparate the number into its prime factors, and take out matching pairs. e.g.:<\/i><\/p>\n
<\/i><\/p>\n
<\/i><\/p>\n
adding roots: <\/span><\/p>\nroots can be added like variables. e.g.:<\/i><\/p>\n
<\/i><\/p>\n
<\/p>\n
prime numbers and integers<\/b><\/p>\n\n1 is not a prime. <\/i><\/li>\n2 is the smallest prime and the only even prime.<\/i><\/li>\nan integer is any counting number including negative numbers (e.g. -3, -1, 2, 7\u2026but not 2.5)<\/i><\/li>\n<\/ul>\n <\/p>\n
ratios <\/b><\/p>\n
ratios let us compare the proportions of two quantities. <\/i><\/p>\n
if there is a 2:5 ratio of boys to girls at a school, that means that for every 5 girls, there are 2 boys. so there could be 2 boys and 5 girls, 20 boys and 50 girls, 200 boys and 500 girls, etc. <\/i><\/p>\n
ratios are given by x:y, x to y, or x\/y. if a question says \u201cfor every x there is\/are a y,\u201d you are most likely dealing with a ratio question. ratios can also be x:y:z.<\/i><\/p>\n
ratios can be simplified like fractions. 3:6 is the same as 1:2. <\/i><\/p>\n
remember that if there is a 2:5 ratio of boys to girls at a school, the ratio of boys to total students is 2:(5 + 2) = 2:7. so 2\/7 of the students are boys. <\/i><\/p>\n
<\/p>\n
percentages<\/b><\/p>\n
the meaning of \u201cpercent\u201d<\/span><\/p>\n <\/p>\n
calculating percentages<\/span><\/p>\n <\/p>\n
percent change<\/span><\/p>\n <\/p>\n
<\/p>\n
divisibility<\/b><\/p>\n
3 : sum of digits divisible by 3<\/i><\/p>\n
4 : the last two digits of number are divisible by 4<\/i><\/p>\n
5 : the last digit is either a 5 or zero<\/i><\/p>\n
6 : even number and sum of digits is divisible by 3<\/i><\/p>\n
8 : if the last three digits are divisible by 8<\/i><\/p>\n
9: sum of digits is divisible by 9<\/i><\/p>\nalgebra<\/h2>\n
<\/p>\n
foil<\/b><\/p>\n
first, outer, inner, last:<\/span><\/p>\n <\/p>\n
common patterns to memorize:<\/span><\/p>\n <\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
cross-multiplication<\/b><\/p>\n
<\/p>\n
<\/p>\n
quadratic equations:<\/b><\/p>\n
for <\/i> , where a is not 0, if you can factor it to <\/i> , then the solutions are -y and z. for example:<\/i><\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
or <\/p>\n
<\/p>\n
geometry<\/h2>\n <\/p>\n
angles <\/b><\/p>\n
a right angle is made up of 90 degrees <\/i><\/p>\n
a straight line is made up of 180 degrees. <\/i><\/p>\n
if two lines intersect, the sum of the resulting four angles equals 360<\/i><\/p>\n
<\/p>\n
circles<\/b><\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
triangles<\/b><\/p>\n
general:<\/span><\/p>\n <\/p>\n
side a – side b < side c<\/em><\/p>\nside a + side b > side c<\/em><\/p>\n<\/em>right triangles:<\/span><\/p>\n where c is the hypotenuse.<\/i><\/p>\n
a 45\u02da-45\u02da-90\u02da triangle has sides in a ratio of x : x : x\u221a2, with x\u221a2 as the hypotenuse<\/i><\/p>\n
a 30\u02da-60\u02da-90\u02da triangle has sides in a ratio of x : x\u221a3 : 2x, with the 1x side opposite the 30 degree angle and 2x as the hypotenuse<\/i><\/p>\n
certain right triangles have sides with all integer lengths. these sets of numbers are called pythagorean triples, and you should memorize some of them: 3-4-5, 5-12-13, and 8-15-17. a multiple of a pythagorean triple is also a pythagorean triple (e.g., 6-8-10).<\/i><\/p>\n
<\/p>\n
squares<\/b><\/p>\n
, where s = side<\/p>\n
<\/p>\n
<\/p>\n
rectangles<\/b><\/p>\n
, where l = length and w = width<\/p>\n
<\/p>\n
<\/p>\n
trapezoids<\/b><\/p>\n
<\/p>\n
<\/p>\n
polygons<\/b><\/p>\n
, where n = # of sides<\/p>\n
<\/p>\n
<\/h2>\ncoordinate geometry<\/h2>\n <\/p>\n
slope-intercept form<\/b><\/p>\n
, where m is the slope and b is the y-intercept.<\/i><\/p>\n
<\/p>\n
slope<\/b><\/p>\n
<\/p>\n
<\/p>\n
the distance formula<\/b><\/p>\n
<\/p>\n
<\/p>\n
word problems<\/h2>\n <\/p>\n
sequences<\/b><\/p>\n
<\/p>\n
<\/p>\n
probability<\/b><\/p>\n
<\/p>\n
<\/p>\n
averages<\/b><\/p>\n
mean<\/span>:<\/p>\n <\/p>\n
median:<\/span><\/p>\nthe middlemost value when numbers are arranged in ascending order; for an even count of numbers, take the average of the middle two<\/i><\/p>\n
mode:<\/span><\/p>\nthe number that occurs most frequently in a list or set<\/i><\/p>\n
<\/p>\n
distance, rate, and time<\/b><\/p>\n
, <\/p>\n
<\/p>\n
counting<\/b><\/p>\n
combination:<\/span><\/p>\n <\/p>\n
when the order does not matter\u2014for example, picking any 3 friends from a group of 5.<\/i><\/p>\n
permutation:<\/span><\/p>\n <\/p>\n
when the order does matter\u2014for example, how many ways you could order 3 letters from the word party?<\/i><\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
below is a list of formulas and math facts you\u2019ll need if you\u2019re looking to ace sat math. a lot of it should be old hat for you at this point\u2014after all, you study this stuff in school, right?\u2014but it\u2019s definitely handy to have it all in one place for reference, and there are some […]<\/p>\n","protected":false},"author":42,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[],"ppma_author":[24883],"acf":[],"yoast_head":"\n
important sat math formulas and facts<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n