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Gravity
Commonly tested terms and formulas on standardized tests such as SAT, ACT, and SSAT.
Terms in this set (20)
PERCENT INCREASE/DECREASE
Difference of amounts/Original amount x 100
SUM OF ANGLES IN A POLYGON
(n-2) x 180
"n" refers to number of sides
AREA OF A SECTOR
Degrees of the angle/360 x Area of circle
i.e. A fraction of the area
LENGTH OF AN ARC
Degrees of the angle/360 x Circumference of circle
i.e. A fraction of the circumference
GROUP RATIO
Given amount/Sum of parts = Amount of individual part.
RELATED RATIO
Set the ratio of items into fractions. Find the common item. Change both fractions so that the common item shares the same number (like a common denomiator). Compare the desired items.
PERMUTATION
nPr. Order matters. It's the total possible arrangements of
n
number of items, taking
r
random items at a time.
e.g. How many batting line-ups of 13 players can be made taking 9 players at a time?
13 nPr 9 = 259459200
COMBINATION
nCr. Order does not matter. It's the total possible ways
n
number of items can be combined, taking
r
random items at at time.
e.g. How many committes of 3 people can be made from a group of 5 people?
5 nCr 3 = 10
FACTORIAL
n! It's the total possible ways
n
number of items can be combined. All items are used.
e.g. How many ways can 5 books be arranged on a shelf?
5! = 5x4x3x2x1 = 120
AVERAGE OF CONSECUTIVE NUMBERS
Sum of 1st and last numbers in the series/2.
e.g. What is the average of the even integers from 5 to 105?
5 + 105 = 110
110/2 = 55
DIRECT PROPORTION (direct variation)
As one variable (x) increases, the other variable (y) increases at the same rate.
x=yk or x/y=k, where k is a constant.
INVERSE PROPORTION (indirect variation)
As one variable (x) increases, the other variable (y)decreases at the same rate.
y = k/x or, more commonly used, yx = k, where k is a constant.
DISTANCE FORMULA
The square root of: (x2-x1)^2 + (y2+y1)^2
PYTHAGOREAN TRIPLES
Special right triangles that have integers as side lengths. A very common one is the 3-4-5. A less common one is the 5-12-13. Look for triangles with multiples of these as well.
ANSWER GENERATED SUBSTITUTION
Test takers use this substitution method by plugging the answer choices into the question to find the correct answer. Questions of this type usually ask for a single variable.
PERFECT SQUARES
(a+b)^2=a^2+2ab+b^2
(a-b)^2=a^2-2ab+b^2
DIFFERENCE OF SQUARES
(a+b)(a-b)=(a^2-b^2)
FRACTIONAL EXPONENT
a^m/n
m=exponent n=index
CHORD
A line through a circle that doesn't pass through the center.
TWO-EVENT PROBABILITY
1st event affects the probability of the 2nd event. Desired/All possible outcomes x (Desired-1)/(All possible outcomes-1)
e.g. - What is the probability of picking 2 jacks without replacement from a deck of cards?
4/52 x 3/51 = 1/221
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