Section 1
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area of rectangle/rhombus/parallelogram
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Date created
Mar 14, 2020
Cards (102)
Section 1
(50 cards)
area of rectangle/rhombus/parallelogram
A=bh
square
rectangle and rhombus
Rhombus
4 equal sides + big four
Area of a circle
A=πr²
Surface area of a cube formula
6s^2
given a system of equations, what does it mean when you solve and get an equation that is always true?
the equations are all for the same line
How do quartiles divide a list?
Q1, median, Q3, divide a list into 4 equal (in terms of number of points) groups
square of a difference
(a-b)^2 = a^2 - 2ab + b^2
concentration
amount of solute/total amount of solution (not amount of solute over amount of water)
Sum of Angles in a Regular Polygon
find the sum of the angles by using (n-2)180, then divide by n to find the measure of each individual angle
Circumference of a circle
C=2πr C=πd
Formula for arc length
arc length/2πr = angle/360
solving most quadratics on GRE
1) get everything equal to zero 2) divide by any GCF 3)factor 4) use zero product property to create two linear equations equal to zero, solve
The sum of the angles in a quadrilateral is
360°
Percent of a population between each standard deviation, from -2SD to +2SD
2% -2SD 14% -1SD 34% mean 34% +1SD 14% +2SD 2%
Power Rule (to raise a power to a power)
multiply the exponents
"or" or "is" in word problems
=
Parallelogram Properties
1) opposite sides are parallell. 2) opposite sides are congruent. 3) opposite angles are congruent. 4) consequtive angles are supplementary. 5) diagonals bisect each other.
Volume of a rectangular solid
(length)(width)(height)
A is 50 more than B
A=B+50
measure of inscribed angle
1/2 the measure of the intercepted arc
30-60-90 triangle (half an equilateral triangle)
1:√3:2
Fraction Exponent
The denominator becomes the root, the numerator becomes the power
sum of angles in n sides polygon
(n-20x180
difference of two squares
a² - b² = (a + b)(a - b)
Area of a square
A=s²
Pythagorean triplits
(3,4,5)(5,12,13)(8,15,17)(7,24,25)
volume of cube
V=s^3
isosceles triangle
equal bases, opposite angles equal
velocity of objects moving in the same direction
subtract, the velocity is the rate at which the gap is closing if they are growing closer, the velocity is the rate at which the gap is growing if they are moving further apart
sum of squares
(a+b)^2 = a^2+2ab+b^2
how do you find the 1st and 3rd quartile?
they are the medians of each half of the list on either side of the median
Average velocity
total distance/total time (add distances and times from each leg)
A is 50 less than B
A=B-50
Surface area of a rectangular solid
2lw + 2wh + 2lh
Area of a trapezoid
A=1/2(b1+b2)h
interquartile range
The difference between the upper and lower quartiles. the middle 50 percent of a population
degree of an angle inscribed in a semicircle
90
Area of a triangle
A=1/2bh
Product Rule (to multiply exponents)
Keep the base and add the powers
isosceles right triangle
sides = 1:1:√2 angles = 45:45:90
equilateral triangle
all equal sides, all 60 degree angles
trapezoid
A quadrilateral with exactly one pair of parallel sides
Area of a sector
area of sector/πr² = angle/360
rectangle
all 90 degree angles + big four
Negative Exponents
any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power
symmetrical trapezoid
equal legs; equal angles on each side; equal diagonals
what do the lines on a box plot represent?
the max, min, and three quartile numbers (Q1, median, Q3)
Quotient Rule (to divide exponents)
to divide, keep the base and subtract the powers
Velocity of objects moving in opposite directions
add, if they are going towards each other the velocity is the velocity at which the gap is closing, if they are moving away from each other the velocity is the rate at which the gap is growing
Section 2
(50 cards)
how to get the x or y intercept from a line's equation
plug 0 in for y to get the x intercept, and for x to get the y intercept
Probability that either A or B will happen? ex, if the probability that A occurs is is .4, the probability either of them occur is .6, and the probability they both occur is .25, what is the probability that B occurs?
peither a or b =pA + pB - (pB and B) The probability that either will occur individually minus the probability that they both do ex. .6 = 0.4 + pb - 0.25 pB=0.15
Method for problems where members of a group are placed into two different kinds of categories (i.e. age and city of origin)
double helix method: each one category is spread over columns, one over rows, plus a totals row and column
the amount of possible combinations when choosing a group (in any order) from a larger group
nCr n = number in big group r = number in small group nCr = n!/r1
two main causes for an undefined (not real) solution?
the square root of a negative and division by 0
if b is between 0 and 1, is the square root of b greater than or less than b?
yes
how to count the number of factors of a large number for odds? evens?
to find the number of factors of N: 1) find the prime factorization of N 2) list the exponents of primes 3)add one to each = a new list 4) product of new list = # of factors for odd factors, just discount the factors of 2 in the first list for even, find the total number and subtract the number of odds
standard deviation
a computed measure of how much scores vary around the mean score
given a system of equations, what does it mean when you solve and get an equation that is never true?
the equations are parallel
how to tell if a number is divisible by 3
if the sum of its digits is divisible by 3
solving absolute value equation
-isolate expression in absolute value -set it equal to the positive and negative of whatever is on the other side of the equation -solve both -check for extraneous solutions
how to take the root of a root ex. cube root of a square root
multiply roots answer 6th root
finding the equation of a line given a single point and the slope?
plug the point in for x and y, plug in the intercept, solve for b (the intercept)
if b > 1, then is the square root of b greater than or less than b?
less
the nth term of any arithmetic sequence
a of n = a of 1 + d (n-1), where d is the number that is added each term and a is the remained when any term is divided by d
adding inequalities
we can add inequalities when the inequality signs are the same
Slopes of Perpendicular Lines
Slopes are negative reciprocals or each other
on a coordinate plane, the equation of a circle with center 0,0
x^2 + y^2 = r^2
equation of y axis?
x = 0
Raising a root to a power
When raising a root to another power, simply convert the root to power form and multiply the exponents. For example: (√a) to 2 = (a½) to 2 = a (½·2) = a to 1 = a roots and powers of the same level cancel each other out, leaving only the base. ∜a to 4 = a
finding the distance between two points on the coordinate plane
slope triangle to find rise and run, then Pythagorean theorem (leg^2 + leg^2 = hypotenuse^2). Hypotenuse = distance
Is zero an integer?
yes
when checking a solution to an absolute value equation, what happens if the absolute value of an expression turns out to be equal to a negative number?
this means that the solution is an extraneous solution. An absolute value cannot be equal to a negative number
how to tell if a number is divisible by 9
if the sum of its digits is divisible by 9
multiplication and division in an inequality?
multiplying and dividing by a positive number works the same as with equations multiplying or dividing by a negative number reverses the order of the inequality
as compounding period decreases, what happens to amount of interest earned?
it increases
Compound interest formula (non annual compounding)
A=(P/n)(r^yn) A=Amount P=Principal r=Multiplier y=years n = how many times in a year the the interest is compounded (ex. compounded quarterly, n = 4)
choosing a combination out of a larger group (when order does not matter) ex. J is allowed to invite 3 friends on a camping trip. if J has th10 friends, how many ways can she invite 3 of them?
n!/r!(n-r)! ex answer: 10!/3!(10-3)! 120
how to add a sequence of evenly spaced integers
pair the numbers by first and last to produce pairs of a constant sum. then multiply by the number of pairs. [n(n+1)]/2
Precent increase formula
[(new value-original value)/original value] x 100
slope-intercept form
y=mx+b, where m is the slope and b is the y-intercept of the line.
Work Rate with multiple workers
Work = Individual Rate x Number of Workers x Time
when should you include the negative square root?
if the square root sign is written by the test maker, consider positive roots only
equation of vertical line?
x = k (where k is the x intercept)
how to tell if a number is divisible by 6
it must be divisible by 2 and 3
general form of horizontal line?
y=k (where k is the y intercept, or the "height" of the line )
how to get ride of roots in the denominator?
if the fraction has a single root in the denominator, we rationalize by multiplying by that root over itself. if the denominator of the fraction contains addition or subtraction involving a radical expression, we multiple the conjugate of the denominator over itself (use the difference of two squares to get a square minus a square
Units Digit Question
1) Look for repeating pattern, usually 4 2) Figure out where the pattern will be at the desired power *Only need to consider single digit product*
prime numbers between 1 and 60
1, 3, 7, 11, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59
finding the equation of a line given 2 points
use the points to find the slope, plug the slope into slope intercept form as well as one of the points, then solve for b
1/ (a/b) = ?
b/a
equation of x axis?
y = 0
multiplying and dividing inequalities?
can't do it
addition and subtraction in an inequality?
the same as with equations
how to solve proportional reasoning questions when working with formulas (given a formula, told some variables will be multiplied by some number, asked what some variable would be multiplied by as a result)
set every variable equal to one, then make the changes described by the questions
Compound Interest Formula (annual)
A=P(r^y) A=Amount P=Principal r=Multiplier y=years
slop formula
y2-y1/x2-x1
potential results when solving a system of two equations with two unknowns
one solution (intersect point), infinite solutions (same line), no solutions (parallel line)
Volume of a cylinder
V = πr^2h
Subtracting inequalities
we can subtract inequalities when the inequality signs are in the opposite directions (the resultant inequality follows the sign of the initial inequality
Section 3
(2 cards)