SAT Formula Sheet

SAT Formul a Shee t
Heart of Algebra
Lines
General
Standard Form: Ax + By = C
Midpoint: M
​ = ​(____
​  1 2  2 
​,  ​____
  1 2  2 
​ )​
Point-Slope Form: (y - y1) = m(x - x1)
Distance: d
​ = ​√(​  
  ​x2​  ​ - ​x1​  ​)​ 2​ + ​​(​y2​  ​ - ​y1​  ​)​ 2​ 
Slope-Intercept Form: y = mx + b
Average Velocity: ​Vavg
​  ​= __________
​ total distance
 ​  
 
total time
​x​  ​ + ​x​  ​ ​y​  ​ + ​y​  ​
______________
​y​  ​ - ​y​  ​
Slope of a Line: m
​ = ____
​ ​x2​  ​ - ​x1​  
​ ​
2
1
Problem Solving and Data Analysis
Growth and Decay
Statistics and Probability
General Form: A
​ = P ​(1 ± r)​​ t​​
Arithmetic Mean: _____________
  
​ 
 ​
Number of Terms
Continuous Growth/Decay: A = Pert
Percent Change: _______
​ New - Old
   
​  × 100%​
Old
Sum of the Terms
Compounding Growth/Decay: A
​ = P ​​(1 ± ​__
 nr ​)  ​  ​
nt
Exclusive OR: ​P​(A or B)​ = P​(A)​ + P​(B)​ - P​(​A & B​)​
(
)​
Conditional Probability: P
​ ​(A | B)​= ______
​ P​ PA & B
   
​ 
(​ B)​
Passport to Advanced Math
Quadratics (ax2 + bx + c)
Equations of Circles
______
–b ± ​√  ​b​ 2​ - 4ac ​ 
________
 
​ 
Quadratic Formula: x​ = ​ 
2a 
Vertex of Parabola: x​ = __
​ –b
2a ​
Equation of a circle with center (h, k) and radius r:
​(x - h)​ 2​ + ​(y - k)​ 2​= ​r​ 2​
Additional Topics in Math
The Circle
Area: A = πr2
A
Circumference: C = 2πr
θ
Arc length (in degrees): L
​ ​(A, B)​= ____
​  36 ​
0  ​ o ​​  ∙ 2πr​
θ
2
Sector Area (in degrees): A
​ OB = ____
​  36 ​
0  ​ o ​​  ∙ π ​r​  ​
O
θ
B
1
Areas
Volumes
Parallelogram: A = bh
Cube: V = s3
1
2
Trapezoid: ​A = __​   ​(​b​ 1​ + ​b​ 2​)​h​
Rectangular Prism: V = lwh
1
2
Triangle: A
​ = _​   ​ bh​
Cylinder: V = πr 2h
1
​  ​
Regular Polygon: A
​ = _​   ​ aP​or A
​ = ________
​  n ​s___
   ​ 
2
 4tan​(​ 180˚
​)  ​
n   
2
Cube: SA = 6s
Sphere: V
​ = _​ 43 ​ πr​ ​ 3​
Angles
Angles and Parallel Lines
2
Sum of Interior Angles: = 180(n - 2)˚
180(n - 2)˚
Each Interior Angle: = _______
​ ​ n ​
 
​ 
Sum of Exterior Angles: = 360˚
360˚
Each Exterior Angles: = ___
​ ​ n   ​​ 
Special Right Triangles
Trigonometry: c
​ os​(90° - x)​= sin x​
Trig Ratios
Pythagorean Identities
opposite
sin x = _________
​​ 
 
 ​​  
hypotenuse
​sin​​ 2​x + ​cos​​ 2​x = 1​
adjacent
cos x = _________
​​ 
 
 ​​  
hypotenuse
​tan​​ 2​x + 1 = ​sec​​ 2​x​
opposite
sin x _________
​tan x = ____
​ cos x
   
​=  hypotenuse
​ 
 
 ​ 
​1 + ​cot​​ 2​x = ​csc​​ 2​x​
hypotenuse
1
​csc x = ____
​  sin x
   ​ = _________
​  opposite  ​ 
hypotenuse
1
​sec x = ____
​  cos x
   ​ = _________
​  adjacent  ​ 
adjacent
1
​cot x = ____
​ tan x
   ​ = ____
​ cos x
​= _______
​ opposite ​​ 
sin x  
2