Catalog / Mathematics Cheatsheet
Mathematics Cheatsheet
A comprehensive mathematics cheat sheet covering essential formulas, concepts, and techniques from basic arithmetic to calculus and statistics. This resource is designed for students, educators, and professionals seeking a quick reference guide.
Basic Arithmetic & Algebra
Arithmetic Operations
|
Addition |
a + b = c |
|
Subtraction |
a - b = c |
|
Multiplication |
a * b = c |
|
Division |
a / b = c (b ≠ 0) |
|
Exponents |
an (a to the power of n) |
|
Order of Operations |
PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) |
Algebraic Formulas
|
Quadratic Formula |
x = (-b ± √(b2 - 4ac)) / 2a |
|
Difference of Squares |
a2 - b2 = (a + b)(a - b) |
|
Perfect Square Trinomial |
(a + b)2 = a2 + 2ab + b2 |
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Binomial Theorem |
(a + b)n = ∑ (n choose k) an-k bk |
|
Laws of Exponents |
am * an = am+n |
|
Logarithms |
logb(x) = y ⟺ by = x |
Geometry & Trigonometry
Basic Geometry Formulas
|
Area of a Rectangle |
A = l * w (length * width) |
|
Area of a Triangle |
A = 0.5 * b * h (base * height) |
|
Area of a Circle |
A = πr2 (r = radius) |
|
Circumference of a Circle |
C = 2πr |
|
Volume of a Sphere |
V = (4/3)πr3 |
|
Volume of a Cylinder |
V = πr2h (h = height) |
Trigonometric Functions
|
Sine (sin) |
sin(θ) = Opposite / Hypotenuse |
|
Cosine (cos) |
cos(θ) = Adjacent / Hypotenuse |
|
Tangent (tan) |
tan(θ) = Opposite / Adjacent |
|
Cosecant (csc) |
csc(θ) = 1 / sin(θ) |
|
Secant (sec) |
sec(θ) = 1 / cos(θ) |
|
Cotangent (cot) |
cot(θ) = 1 / tan(θ) |
|
Pythagorean Identity |
sin2(θ) + cos2(θ) = 1 |
Calculus
Differentiation Rules
|
Power Rule |
d/dx (xn) = nxn-1 |
|
Constant Rule |
d/dx (c) = 0 |
|
Product Rule |
d/dx [f(x)g(x)] = f’(x)g(x) + f(x)g’(x) |
|
Quotient Rule |
d/dx [f(x)/g(x)] = [g(x)f’(x) - f(x)g’(x)] / [g(x)]2 |
|
Chain Rule |
d/dx [f(g(x))] = f’(g(x)) * g’(x) |
|
Derivative of sin(x) |
d/dx [sin(x)] = cos(x) |
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Derivative of cos(x) |
d/dx [cos(x)] = -sin(x) |
|
Derivative of ex |
d/dx [ex] = ex |
Integration Rules
|
Power Rule |
∫ xn dx = (xn+1) / (n+1) + C (n ≠ -1) |
|
Integral of 1/x |
∫ (1/x) dx = ln|x| + C |
|
Integral of ex |
∫ ex dx = ex + C |
|
Integral of sin(x) |
∫ sin(x) dx = -cos(x) + C |
|
Integral of cos(x) |
∫ cos(x) dx = sin(x) + C |
|
Integration by Parts |
∫ u dv = uv - ∫ v du |
Statistics & Probability
Descriptive Statistics
|
Mean |
μ = (∑xi) / n (Average of values) |
|
Median |
Middle value when data is sorted |
|
Mode |
Most frequent value |
|
Variance |
σ2 = ∑((xi - μ)2) / n |
|
Standard Deviation |
σ = √(σ2) (Square root of variance) |
|
Range |
Max(x) - Min(x) |
Probability
|
Probability of an Event |
P(A) = Number of favorable outcomes / Total number of outcomes |
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Conditional Probability |
P(A|B) = P(A ∩ B) / P(B) |
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Independent Events |
P(A ∩ B) = P(A) * P(B) |
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Bayes’ Theorem |
P(A|B) = [P(B|A) * P(A)] / P(B) |
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Expected Value |
E[X] = ∑ [x * P(x)] |
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Variance of a Random Variable |
Var(X) = E[(X - E[X])²] |