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Gravity
A collection of terms, concepts, and especially formulas that are important to know before going into the ACT
Terms in this set (128)
quadratic formula
[-b ± √(b² - 4ac)] / (2a)
slope formula
(y2- y1) / (x2- x1)
rationals
fractions (anything expressible as a ratio of integers)
order of operations
PEMDAS (Parentheses (grouping symbols - inside to outside) / Exponents / Multiply & Divide (Left to right) / Add & Subtract(Left to right))
Arithmetic Sequences
t1, t1+ d, t1+2d, ...
Geometric Sequences
t1, t1· r, t1· r², ...
percentages
part = (percent / 100) x whole; is/of=%/100
average or mean
sum of terms / number of terms
average speed
total distance / total time
sum
average x (number of terms)
mode
value in the list that appears most often
median
middle value in the list after values are put in numerical order
fundamental counting principle
if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.
probability
number of desired outcomes / number of total outcomes
adding exponents
x^a · x^b = x^(a+b)
subtracting exponents
x^a / x^b = x^(a-b)
negative exponents
1 / x^b = x^(-b)
multiplying exponents
(x^a)^b = x^(a·b)
x^0
1
roots
√(xy) = √x · √y
FOIL
(x+a)(x+b) = x² + (b+a)x + ab
difference of squares
a² -b² = (a+b)(a-b)
a² + 2ab + b²
(a+b)²
a² - 2ab + b²
(a-b)(a-b)
distance formula
√[(x2- x1)² + (y2- y1)²)]
midpoint formula
[(x1+ x2)/2 , (y1+ y2)/2]
intersecting lines
opposite angles are equal (each pair of angles along the same line add to 180 degrees)
area of triangle
area = (1/2)bh
angles of triangle
add up to 180 degrees
length of triangle sides
length of 1 side is always less than the sum of the other 2
equilateral
three equal sides, all angles = 60 degrees
isosceles
2 equal sides, 2 equal angles
similar
same shape, corresponding angles are equal, corresponding sides are in proportion
full circle
= 360 degrees
length of arc
r * angle (in radians); s=r * theta
rectangle area
length * width
parallelogram area
base * height
rectangular solid volume
length * width * height
right cylinder volume
pi · r² · h
equation of circle
(x - h)² + (y - k)² = r² ; (h,k) is the center
logarithms
y = log(little b)x means b^y = x
complex numbers
a + bi
special sin cos relationship
sin^2(angle) + cos^2(angle) = 1
trapezoid area
[(base1 + base2) / 2] · h
direct variation
y=kx
inverse variation
y=k/x
slope-intercept form
y=mx+b
point-slope form
y - y1= m(x - x1)
standard form
Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative
Dividing by a negative number in an inequality
must reverse the inequality symbol
Graphing < or > on a coordinate plane
dotted line
Graphing ≥ or ≤ on a coordinate plane
solid line
Graphing ≥ or > on a coordinate plane
shade upwards or to the right
Graphing ≤ or < on a coordinate plane
shade downwards or to the left
chord
The distance from one point on the circle to another point on the circle.
sector
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
arc
Part of a circle connecting two points on the circle; could be minor (less than 180 degrees - needs 2 letters to name it) or major (greater than or equal to 180 degrees - needs 3 letters to name it)
Central Angle
An angle whose vertex is the center of the circle; equal to the degree measurement of the intercepted arc it creates
Pythagorean Theorem
a²+b²=c² (c=hypotenuse, only true for right triangles)
Slope formula [between 2 points (x₁,y₁) and (x₂, y₂)]
y2 - y1/ x2-x1
Logarithm Formula: log base x = y
b to the y power equals x
sin
opposite/hypotenuse
cos
adjacent/hypotenuse
tan
opposite/adjacent
Mean
Add all numbers, divide by number of numbers.
Median
The middle number from small to large, choose median.
FOIL
First, Outer, Inner, Last
Number of degrees in n-sided polygon
(n-2)(180)
Percent Formula
is/of = %/100
acute angle
an angle less than 90 degrees but more than 0 degrees
adjacent angles
are a pair of angles with a common vertex and a common side, but no common interior points
area
the number of square units needed to cover a flat surface
circle
a closed plane figure made up of all the points the same distance from the center; radius from center to point on circle (1/2 d); diameter from point to point through center (2r)
circumference
the distance around a circle; C = 2*pi*r; C = pi * d
complementary angles
two angles whose sum is a right angle (90 degrees)
cube
a three-dimensional shape with six square or rectangular sides
diameter
the length of a straight line passing through the center of a circle and connecting two points on the circumference
equilateral triangle
A triangle with all sides congruent.
obtuse angle
an angle between 90 and 180 degrees
parallel lines
coplanar lines that do not intersect
parallelogram
a quadrilateral whose opposite sides are both parallel and equal in length
perpendicular lines
Two lines that intersect to form right angles
polygon
a closed plane figure bounded by straight sides
quadrilateral
a four-sided polygon
right triangle
a triangle with one right angle
supplementary angles
Two angles whose sum is 180 degrees
volume
the amount of 3-dimensional space occupied by an object
Area of a square
A=side²
Area of a circle
A=πr²
Volume of a cube
V=s³
Fahrenheit to Celsius
C = 5/9 (F-32)
Celsius to Fahrenheit
F= 9/5 (C+32)
a³-b³
(a-b)(a²+ab+b²)
a³+b³
(a+b)(a²-ab+b²)
undefined slope
vertical line
zero slope
horizontal line
Infinitely many solutions
when the system of equations has the same slope and y-intercept
One solution
when the system of equations has different slopes and possibly the same y-intercept
No solution
when the system of equations has the same slope but different y-intercepts
Elimination method
solving systems by adding or subtracting equations to eliminate a variable (sometimes requires that one or both equations be multiplied by a LCM)
Solution of the system of linear equations
Any ordered pair in a system that makes all the equations true
Graphing method
Graphing the system of equations and finding the point at which they intersect
Substitution method
Replacing one variable with an equivalent expression containing the other variable
Absolute value equation
A V-shaped graph that points upward or downward
translation
transformation of a graph that is a shift of a graph horizontally, vertically, or both, which results in a graph of the same shape and size, but in a different position.
Area of a sector
x°/360 times (πr²), where x is the degrees in the angle
Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Sn=n(a1+an)/2
arithmetic sum; n is the # of terms
An=a1+(n-1)d
arithmetic series; d is the common difference
An=a₁r^(n-1)
geometric series; r is the common ratio (what one term is multiplied by in order to get the next term)
Sn=a1(1-r^n)/(1-r)
geometric sum; r is the common ratio and cannot equal zero
S=a1/(1-r)
geometric infinite sum
reflection
transformation resulting in a mirror image over a particular line (usually the x-axis or y-axis)
dilation
transformation that changes the size of a graph (stretch or compress)
rotation
transformation that "spins" a graph around a particular point
parabola
the graph of a quadratic equation
cosecant
csc = 1/sin
secant
sec = 1/cos
cotangent
cot = 1/tan
y=asin(b*theta)
a: amplitude; b: # of cycles from 0 to 2pi; period: 2pi/b; starts at zero
y=acos(b*theta)
a: amplitude; b: # of cycles from 0 to 2pi; period: 2pi/b; starts at max
Law of Cosines
c^2 = a^2 + b^2 - 2abcosC; b^2 = a^2 + c^2 - 2accosB; a^2 = b^2 + c^2 - 2bccosA; used with SAS or SSS
Law of Sines
sinA / a = sinB / b = sinC / c; used with AAS or ASA or SSA
45-45-90 triangle
hypotenuse = √2 * leg
30-60-90 triangle
hypotenuse = 2 * shorter leg; longer leg = √3 * shorter leg
to convert from radians to degrees
multiply by 180/pi
to convert from degrees to radians
multiply by pi/180
an angle with a vertex on a circle
creates an intercepted arc that is twice the degree of that angle
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