SAT Math Memorization

point slope form

y-y1=m(x-x1)

when to use point slope form?

when given a point and the slope - USUALLY USED ON THE SAT TO SET UP EQUATIONS BASED ON GIVEN POINTS!!

when to use slope intercept form?

when given the slope and y-intercept

what is the product of the slopes of 2 perpendicular lines?

-1

what is the relationship between the slopes of perpendicular lines?

negative reciprocal

how to turn mixed number into improper fraction

Multiply the whole number by the denominator of the fractional part.

Add the numerator of the fractional part to the result from step 1.

Place this sum over the original denominator.

p% of x

p/100 times x

p% greater than x

(1 + p/100)x

p% less than x

(1 - p/100)x

percent change formula

(final value−initial value)/initial value×100%

negative percent change means...

percent decrease

positive percent change means...

percent increase

most common pythagorean triples (there are 5 total unique ones) - state what case you can use it

(3, 4, 5), (5,12,13), (7,24,25), (8,15,17) (9,40,41) ONLY USE WHEN GIVEN TWO SIDES AND FIND THE THIRD MISSING SIDE. does not apply when only given one side (e.g. shortest side = 5, does not mean the other two are certainly 12 and 13. could be others)

write minutes in terms of seconds using 2 variables "m" and "s"

m=s/60 (because 10 seconds is 1/6 minutes)

what formula should you use in a work-rate problem?

W = rt

in quadratic equations, what is the formula for sum of the solutions

-b/a

in quadratic equations, what is the formula for product of the solutions

c/a

when solving equations involving square roots, what must you do with the solutions if there are multiple?

plug each of them back in to see if they yield "valid results"

(a+b)^2

a^2 + 2ab + b^2

(a-b)^2

a^2 - 2ab + b^2

when should you use substitution in solving system of equations?

if you see a variable with no coefficient (e.g. -5x+y = -7)

when should you use elimination in solving system of equations?

if you see matching coefficients

property of two equations when system has infinitely many solutions

both equations are equivalent (e.g. 6x+4y = 10 and 3x+2y = 5)

property of two equations when system has no solutions

both equations are equivalent except for their constants (e.g. 3x+2y = 5 and 3x+2y = -4, or 3x+2y=5 and 6x+4y=-8)

because there are no two x and y values that could possibly satisfy both equations at the same time)

solutions to a system of equations is equivalent to.... on a graph

intersection points

why do you flip signs on inequalities?

because if a

symmetrical distribution means these 2 things are equal

mean and median

an outlier does not affect _____ as strongly as it affects the ______

median, mean

(since median is based on the middle values of the data set)

box and whisker plot: meaning of the line in the middle

median

how to solve: y = x+5, y = x^2 + 11x + c. in the given system of equations, c is a constant. the system has exactly one distinct real solution. what is the value of c?

the appearance of c is a hint to analyze the discriminant to find out what value would yield only one solution (set discriminant = 0)

discriminant is positive real number

two distinct real roots

discriminant = 0

one real root (repeated root) - because there is no difference between the plus zero and minus zero when you use the quadratic formula

discriminant is negative

no real roots (two complex roots)

if it says 'n' is a factor of something and it asks you to evaluate f(n) then what will the answer always be and why?

0 since it is a factor

question: "if one tray of flatbread can be made from 8 cups of flour and 6 cups of yogurt, what is the maximum number of whole trays of flatbread that can be made from 150 cups of flour and 100 cups of yogurt?"

what is the thing you must consider in the method to find the solution?

limiting factor

when solving systems of equations you can add/subtract to eliminate variables, is this the same for inequalities? how does this method apply to inequalities?

no, inequalities should NEVER be subtracted from one another. think only in terms of addition.

inequalities can be added together if their signs point in the same direction.

formula for x-coordinate of vertex in parabola

-b/2a

vertex form of parabola

y = a(x-h)^2 + k

discriminant is positive perfect square

2 real rational roots

discriminant is positive number but not perfect square

2 real roots

what is another way to find the x-value of the vertex if not using -b/2a formula?

if the function has two roots, the x-coordinate of the vertex is equal to the average of those two roots

in a quadratics question if you are given two equations, a linear equation and a quadratic, and it is given that the system has exactly one distinct real solution, how do you find the unknown value?

know that the solutions to the equation (new equation after substitution) are the solutions to the system

what are the 3 ways to find the x-intercepts when the equation of a quadratic is not in intercept form?

1. factoring (convert into intercept form)

2. quadratic formula

3. desmos graph

when it asks, what is the maximum value of y and you have a coordinate pair, what should your answer only contain?

the y value of the coordinate is your final answer

measure of an exterior angle is equal to... ***does this only apply to right triangles??

the sum of the two angles in the triangle furthest from it (applicable to all triangles)

when a line intersects two parallel lines, the following 5 statements are true

1. vertical angles are congruent

2. alternate interior angles are congruent

3. alternate exterior angles are congruent

4. corresponding angles are congruent

5. same side interior angles are supplementary

each additional side in a polygon increases the sum of the interior angles by ____

180 degrees

for any polygon, the sum of the interior angles is given by this formula

180(n-2), n=number of sides

regular polygon

polygon in which all sides and angles are equal

these 3 statements are sufficient to PROVE that two lines are parallel

1. a pair of equal corresponding angles

2. a pair of equal alternate interior angles

3. a pair of equal alternate exterior angles

altitude of triangle

same meaning as height of triangle

length of sides in 45-45-90 triangle

legs = x

hypotenuse = xroot2

length of sides in 30-60-90 triangle

short leg (side opposite 30) = x

long leg (side opposite 60) = xroot3

hypotenuse (side opposite 90) = 2x

what are the 4 triangle congruence theorems (aka the minimum amount of information needed to prove that two triangles are congruent)

SSS, SAS, ASA, AAS

similar triangles

corresponding angles are congruent, corresponding sides are proportional in the same ratio

symbol for congruence

≅

symbol for similar

what are the 3 triangle similarity theorems? (aka minimum amount of information needed to prove that two triangles are similar)

1. AA(A) - two pairs of corresponding angles are congruent

2. SAS - two pairs of corresponding sides are proportional according to the same ratio and corresponding angle between those two sides are congruent

3. SSS - all pairs of corresponding sides are proportional according to the same ratio

formula for length of arc (degrees)

(θ/360) x 2πr

formula for area of a sector (degrees)

(θ/360) x πr^2

the measure of an inscribed angle is ______

half the measure of the arc it intercepts

angles inscribed in a semicircle always measure ___ because ____

always measure 90 degrees because they always intercept half a circle

definition of line tangent to a circle

if it touches the circle at exactly one point

a radius drawn to the point of tangency is ______

perpendicular to the line

two properties for a radius that bisects a chord (splits chord into two equal parts)

1. a radius that bisects a chord is perpendicular to that chord

2. a radius that is perpendicular to a chord bisects that chord

tangent segments to a circle drawn from the same external point are _______

congruent

standard form equation of a circle in the x-y plane

what is one way for a circle to intersect the x-axis at exactly one point? describe property of the equation.

be tangent to the x-axis, must have radius that is equal to the center's distance from the x-axis

how to complete the square for circles

what is an alternative to completing the square

graph the equation on desmos to find missing values

distance formula for 2 points

if arc AB measures _______ then central angle ACB measures ____

x degrees

formula for arc length (radians)

s = rθ

formula for area of a sector (radians)

cos(90° - x°)

what does the formula mean?

sin x°

the sine of an angle is equal to the cosine of the complementary angle (non 90deg) in a right triangle

sin(90° - x°)

what does the formula mean?

cos x°

the cosine of an angle is equal to the sine of the complementary angle

cos(π/2 - θ)

sinθ

sin(π/2 - θ)

cosθ

the angle opposite the longest side in a right triangle always measures __

90 degrees

you should always use ____ to find trig values on the SAT and not the _____. why?

always use desmos, not the unit circle (because its easier to compare decimal answer from desmos with the decimal value of each answer choice, even when given exact values like root2/2 on the multiple choice)

tan(90° - x°) is referring to O/A from which angle in a right triangle?

the top angle (that is not the right angle or the other given acute angle)

if it just says triangle ABC then what can't you assume?

you can't assume that it is a right triangle (example question: In triangle ABC, the measure of angle A is equal to the measure of angle C. If cos A = 3/8 and AB=20, what is the length of segment AC?) ***you can apply cos 3/8 to the right triangle that you construct because the cos ratio simply corresponds to the specific angle. it doesn't matter that the original triangle was not a right triangle since in that case it simply couldn't be applied, but now you can draw an altitude to make it work (just like how sin 90 is always 1)

area of square

s²

perimeter of square

4s

area of rectangle

lw

perimeter of rectangle

2l + 2w

area of parallelogram

bh

definition of parallelogram

quadrilaterals in which opposite sides are parallel and equal in length

definition of rectangle

parallelogram with 4 right angles

definition of square

rectangles with 4 sides of equal length

definition of solid in geometry

3D shape

prism

solid with flat sides and two identical ends (often called bases)

right prism (the type you will encounter on the SAT)

sides perpendicular to the bases

volume of cube

s³

surface area of cube

6s²

volume of right rectangular prism

lwh

surface area of right rectangular prism

2lw + 2lh + 2wh

volume of right circular cylinder

V=πr²h

volume of any right prism

base area x height

surface area of cylinder

2πr² + 2πrh