# ACT & SAT Math Formula & Notes Sheet

## Preview text

ACT & SAT Math Formula & Notes Sheet
by Mario’s Math Tutoring (YouTube Channel)

Distance:​ Midpoint: ​

​ d = √(x2 − x1) 2 + (y2 − y1)2
M = ( x 1+2 x 2 , y 1+2 y 2 )

Slope:​

​m = yx 22−−xy 11

Pythagorean Theorem:​ multiples of these)

a 2 + b2 = c2 (Common ​Pythagorean Triples:​ ​3-4-5​, ​5-12-13​, ​8-15-17​, ​7-24-25​ or

SOH CAH TOA
sin θ = ohpyppoostietenusisdee

cos θ = ahdyjapcoetennt ussidee

tan θ = aodpjpaocseintet ssiiddee

csc θ =

1 sinθ

sec θ

=

1 secθ

cot

θ

=

1 tanθ

sin 2θ + cos 2θ = 1

sin(90 − θ) = cosθ cos(90 − θ) = sinθ

Standard Form of the Equation of a Circle: (x − h)2 + (y − k)2 = r2
(h,k) Center of the circle and r is radius

Equations of Parabolas:

y = ax2 + bx + c

remember

x=

−b 2a

is the x-coordinate

of vertex and is the axis of symmetry.

y = a(x − h)2 + k vertex form (h,k) vertex y = a(x − p)(x − q) intercept form (p,0),(q,0) x-intercepts

Expected Value:
n
∑ x iP (x i)
i=1
(Sum up the outcome of an event multiplied the
probability of it happening for each possible outcome.)

Imaginary Numbers: i = √− 1 i2 = − 1

Average(mean):

Average

=

T otal # Items

Feel free to copy, share, & distribute this ACT/SAT study sheet giving attribution to Mario’s Math Tutoring(YouTube Channel)

ACT & SAT Math Formula & Notes Sheet

by Mario’s Math Tutoring (YouTube Channel)

Probability:

P

=

# Successes T otal P ossible Outcomes

Logs:
log bx = n

is equivalent to bn = x

Arc Length:

arc length =

θ 360

(2πr)

Rules of Exponents:

xm • xn = xm+n

xxmn = xm−n (xm)n = xm·n

x0 = 1

x−m

=

1 xm

xm/n = √n xm or (√n x)m

Area of Sector:

area of sector =

θ 360

(πr2 )

Quadratic Formula & Discriminant: If ax2 + bx + c = 0 then
x = −b±√b2−4ac
2a
if b2 − 4ac ≻ 0 then 2 real solutions if b2 − 4ac = 0 then 1 real solutions if b2 − 4ac ≺ 0 then 0 real solutions, 2 imaginary

Special Right Triangles:

Area of Circle:
A = πr2

Circumference of Circle:
C = 2πr or C = πd

Volume of Cylinder:
V = πr2h

*Free ACT & SAT Math Video Tutorials available on Mario’s Math Tutoring YouTube Channel to help boost your scores.*

amount of change
Percent of Change = original amount
Feel free to copy, share, & distribute this ACT/SAT study sheet giving attribution to Mario’s Math Tutoring(YouTube Channel)

ACT & SAT Math Formula & Notes Sheet
by Mario’s Math Tutoring (YouTube Channel)

Other Topics helpful to know/study: ● Similar triangles ● Proportions ● Order of Operations (PEMDAS) ● Fractions & Mixed Numbers ● Imaginary & Complex Numbers ● Square Roots & Radicals ● Greatest Common Factor (GCF) ● Least Common Multiple (LCM) ● Isosceles & Equilateral Triangles ● Laws of Logic & Conditional Statements ● Functions ● Inequalities & Special Cases ● Foiling Binomials & Factoring ● Equations of Lines(y=mx + b) ● Multiplication Counting Principle ● Perimeter & Area Problems ● Writing Linear Combinations ● Scientific Notation ● Permutations, Combinations & Factorials ● Systems of Equations ● Translating Sentences into Equations ● Absolute Value Equations & Inequalities ● Quadrilaterals ● One to One Property of Exponents ● Circles & Angles

● Law of Sines & Law of Cosines ● Median, Mean, Mode, basic Statistics ● Angle Problems, Parallel lines cut by
Transversal ● Rewriting Equations “in terms of” ● Piecewise Functions ● Unit Conversions ● Multiplying Matrices & Basics of Matrices ● Unit Circle ● Direct Variation ● Extended Ratios ● Graphing Parabolas ● Percentages ● Types of Numbers (Rational, Irrational, etc.) ● Venn Diagrams ● Rationalizing Denominators ● Completing the Square ● Solving Radical Equations ● Graphing Lines & Inequalities ● Polynomials - Zeros, Factors, Remainders ● Polynomial Long Division ● Rational Exponents ● Exponential Functions
*Free videos covering all these topics available on ​Mario’s Math Tutoring YouTube Channel*

Feel free to copy, share, & distribute this ACT/SAT study sheet giving attribution to Mario’s Math Tutoring(YouTube Channel)