SAT Formulas
Sum of the First n Positive Integers: n(n+1)/2
Sum of the First n Odd Integers: n^2
Sum of the First n Even Integers: n(n+1)
Angle Sum of a Triangle: 180 degrees
Special Right Triangles:
45-45-90: In a 45-45-90 right triangle, the hypotenuse is √2 times the length of each leg.
30-60-90: In a 30-60-90 right triangle, the hypotenuse is twice the length of the shorter leg, and the
longer leg is √3 times the length of the shorter leg.
Distance, Rate, and Time: d = rt
Midpoint Formula: ((x1 + x2)/2, (y1 + y2)/2)
Slope Formula: m = (y2 - y1) / (x2 - x1)
Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
Perimeter and Area of a Rectangle: Perimeter = 2(length + width), Area = length x width
Volume and Surface Area of a Sphere:
Volume = (4/3)πr^3
Surface Area = 4πr^2
Volume and Surface Area of a Cone:
Volume = (1/3)πr^2h
Surface Area = πr^2 + πr√(r^2 + h^2)
Volume and Surface Area of a Cylinder:
Volume = πr^2h
Surface Area = 2πr^2 + 2πrh
Distance Formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
Law of Sines: (a/sin(A)) = (b/sin(B)) = (c/sin(C))
Law of Cosines: c^2 = a^2 + b^2 - 2ab cos(C)