meth

Percent of

(part/whole)

Area of a circle

Area = πr²

DIFFERENCE

Difference is the result of subtraction

DIGITS

Digits are to numbers what letters are to words. There are only 10 possible digits, 0 through 9

Area of a trapezoid

[ (a + b) / 2 ] (height)

THE WORD "OF"

"Of" always means multiply.

Probability

(# things you want) / total possibilities

Indirect Proportion

(A1 / A2) = (B1/ B2)

Direct Proportion:

(A1 / A2) = (B1 / B2 ) or y = kx

Percent change (this works for both percent increase and percent decrease)

(difference/original) x 100

Volume of a rectangular solid

(length)(width)(height)

Number of degrees in an n-sided shape

(n - 2) (180)

INTERQUARTILE RANGE

(never been on a real test yet) a measure of variability, based on dividing a data set into quartiles. Q1 is the "middle" value in the first half of the rank-ordered data set. Q2 is the median value in the set. Q3 is the "middle" value in the second half of the rank-ordered data set. The interquartile range is equal to Q3 minus Q1.

Distance

(rate)(time) job = (rate)(time)

0! =

1

the probability of an event NOT happening

1 - the probability of that event

PEMDAS

1) Parentheses, 2) Exponents, 3) Multiplication, 4) Division, 5) Addition, 6) Subtraction

Sneak way of doing easier Standard Deviation (Average Standard Deviation)

1) find the mean. 2) add up all the distances from the mean, then divide by the number of terms.

basic geometrical concepts

180 degrees in a line, 360 degrees in a quadrilateral, 360 degrees in a circle, all radii of a circle are equal 180 degrees in a triangle, trapezoids have two parallel sides, vertical angles are congruent, perpendicular lines have slopes that are negative reciprocals of each other

Prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 Song: Two, three, five, and SEVEN Then will be ELEVEN ThrEE, FOUR, six, and SEVEN BE-FORE one is HEAVEN ThrEE, FOUR, six, one, nine... BE-FORE seven this time Three after all the ACTORS Except when a FACTOR Nine after the SAME Except for four, LAME (2, 3, 5, 7, 11 31, 41, 61, 71 17, 37, 47, 67, 97 13, 23, 43, 53, 73, 83 19, 29, 59, 79, 89)

Circumference of a circle

2πr

Special Right Triangles

30/60/90 (x, x√3, 2x) and 45/45/90 ( x, x, x√2 )

34/14/2 RULE

34%, 14%, and 2% represent the likelihood that a value will fall into each given region. Example: What is the likelihood that a value within a group of values with a mean of 10 and a standard deviation of 2 equals 5? If the mean is 10, then one standard deviation below the mean is 10 - 2 = 8, which creates a 34% chance that a value from the group falls between 10 and 8. A second standard deviation to the left would be 8 - 2 = 6, meaning that there's a 14% chance that a particular value would fall between 8 and 6. More than two standard deviations to the left of the mean would be all values below 6. The graph tells us that these values have a 2% likelihood. The number 5 falls into this group, so 2% would be the answer.

equilateral triangles have what angles

60/60/60 degrees

Surface area of a cube

6s²

CIRCLES, RADII, INTERNAL ANGLES AND PROPORTIONALITY

All radii of a circle are equal. Angles formed in the center of a circle have the same measure on the arc. Angles formed inside the circumference of a circle have double the measure on the arc -https://www.drivecms.com/uploads/mcelroytutoring.com/Screen%20Shot%202016-09-14%20at%205.20.14%20PM.png

Arithmetic and Geometric Sequences

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference. tn = t1 + (n - 1)d -- tn is the nth term, t1 is the first term, and d is the common difference. A geometric sequence is a sequence with the ratio between two consecutive terms constant. This ratio is called the common ratio. tn = t1 . r^(n - 1) -- tn is the nth term, t1 is the first term, and r is the common ratio

CONSECUTIVE INTEGERS

Consecutive integers are integers in order from least to greatest, for example 1,2,3

TRIANGLE SIMILARITY AND LEG PROPORTIONALITY

If two triangles share two of the same angles (AA), or two sides and an angle (SAS), then they are similar . The proportion of distance that you travel along the one leg of a triangle is equal to the proportion of distance that you travel along both other legs. similar means: one is an enlargement of the other.

MEAN, MEDIAN, MODE

Mean is the same as average. Median is the number in the middle after rearranging from low to high. MODE is quite simply the number that appears the MOST. Multiple modes are possible if there is a tie for greatest frequency

permutation OR combination (Probability)

P: for lists (order matters) C: for groups (order doesn't matter) Combinations sound simpler than permutations, and they are. You have fewer combinations than permutations. Example: Combination: Picking a team of 3 people from a group of 10. C(10,3) = 10!/(7! · 3!) = 10 · 9 · 8 / (3 · 2 · 1) = 120. Permutation: Picking a President, VP and Waterboy from a group of 10. P(10,3) = 10!/7! = 10 · 9 · 8 = 720.

Compound Interest Formula

P=principle, r = interest rate, and t=unit of time: Total =P(1+r)^t

REMAINDER

Remainder is the whole number that's left over after division. For example 8/3 equals 2 remainder 2. Remainder is particularly helpful on pattern and sequence problems.

MULTIPLES

The MULTIPLES of x are the ANSWERS I get when I MULTIPLY x by another INTEGER. For example the multiples of 5 are 5,10,15,20 etc. as well as 0 (a multiple of everything because anything times zero is zero) as well as -5, -10, -15 and other NEGATIVE MULTIPLES

FACTORS

The factors of x are the answers I get when I divide x by another integer. For example the factors of 60 are 30, 20,15,12,10,6,5,4,3,2,1, as well as -5,-6,-10 etc

MAXIMUM AREA OF A TRIANGLE WITH FIXED LEGS, OR A RECTANGLE WITH A FIXED PROPORTION

The maximum area of a triangle with two fixed legs is a right triangle. The maximum area of a rectangle with fixed proportion is a square (which is a specific form of right triangle).

PRODUCT

The result of multiplication

Volume of a cylinder

V = πr²h when r = radius and h = height. (π = approximately 3.14)

Area of a triangle =

[ (base)(height) / 2 ]

The Third Side Rule for Triangles

a − b < c < a + b if c represents the "third side" and b and a represent the lengths of the other two sides. the value of the third (unknown) side of a triangle must lie between the sum and difference of the other two sides .

Pythagorean Theorem

a2 + b2 = c2 with a, b, and c representing the base, height and hypotenuse of a right triangle. Also, just in case, the Super Pythagorean Theorem for 3-D shapes (helps for determining the diagonal of a rectangular solid): a2 +b2 +c2 = d2

Exponent rules

a^b ×a^c=a^(b+c) a^b ÷a^c = a^(b−c) (a^b)^c = a^(bc) (2a^b)^c = 4a^(bc) a^b × c^b = ac^b a^b ÷ c^b = (a/c)^b

The degree measure of an arc formed by an angle with its vertex on a circle

double the measure of the angle, or equal the measure of the circle if the vertex is on the center of the circle. https://www.drivecms.com/uploads/mcelroytutoring.com/Screen%20Shot%202016-09-14%20at%205.20.14%20PM.png

perform a "prime factorization" of a number

find a series of prime numbers that multiplies together to equal that number). The prime factorization of 18, for example, is 3 x 3 x 2

two-group problems

group 1 + group 2 - both + neither = total where group 1 = the number of entities in one of the two groups group 2 = the number of entities in the other group both = the number of entities in both groups neither = the number of entities in neither group total = the total number of entities

absolute value inequalities

https://www.purplemath.com/modules/absineq.htm TRICKS: "| x + 2 | < -1". But can an absolute value ever be negative, let alone be less than a negative? No! So there is no solution to this inequality; it doesn't even make sense. if you're given something like "| x - 2 | > -3", the solution would, naturally, be "all x" or "all real numbers", since the absolute value, being itself positive or zero, must then always be greater than any negative number.

Sum

means the result of addition

Composite numbers

not prime

circle proportionality equation

part/whole = inner angle/360 = arc/2πr = area of sector/πr² the (part/whole) ratio of a circle is going to be the same value, regardless of the type of measurement (angle, area, or arc):

PYTHAGOREAN TRIPLES

particular types of Right Triangles that just happen to have exact integers as sides. 3/4/5, 5/12/13, 6/8/10, 7/24/25, 8/15/17

probability of A or B

probability of A + probability of B - probability of A and B

The Formula for a Line

slope intercept y = mx + b format standard form Ax + By = C point-slope format: y-y₁ = m(x-x₁) the slope equation (y₂- y₁) / (x₂- x₁)

Average

total / # of things, or (Average)(# of things) = total

Problems with Three Groups

venn diagram!!!

INTEGERS

whole numbers, including zero and negative whole numbers.

NUMBER PROPERTIES

x² is always positive, if xy = 0 then either x = 0 or y = 0 or both, (fraction)^>1 is always going to become smaller, that a (negative)^even = positive, (negative)^odd = odd .

3 Quadratic Identities (unfactored to factored form)

x² −y² = (x+y)(x−y) x² +2xy+y² =(x+y)² x² −2xy+y² =(x−y)²