Prior Knowledge:

Description	Equation and Variables
Area of a Parallelogram	A = bh, "b" is base and "h" is height
Area of a Triangle	A = 1/2bh, "b" is base and "h" is height
Area of a Trapezoid	A = 1/2(a+b)h, "a" and "b" are parallel sides and "h" is height
Area of a Circle	A = πr², "r" is the radius of the circle
Circumference of a Circle	C = 2πr, "r" is the radius of a circle C = πd, "d" is the diameter of a circle
Volume of a Cuboid	V = lwh, "l" is length, "w" is width, "h" is height
Volume of a Cylinder	V = πr²h, "r" is radius, "h" is height
Volume of a Prism	V = Ah, "A" is area of the polygon, "h" is height
Area of a curved surface of a Cylinder	A = 2πr²h, "r" is radius, "h" is height
Distance between two points (x₁, y₁) and (x₂, y₂)	d = sqrt((x₁-x₂)²+(y₁-y₂)²), (x₁, y₁) and (x₂, y₂) are coordinates of the points
Coordinates of the midpoint on a line segment that has (x₁, y₁) and (x₂, y₂) as endpoints	((x₁+x₂)/2, (y₁+y₂)/2), (x₁, y₁) and (x₂, y₂) are coordinates of the endpoints

Topic 1: Number and Algebra

Description	Equation and Variables	Use/Additional Info:
Solving for value of nth term of an arithmetic sequence The sum of n terms in an arithmetic sequence	u_n = u₁+(n-1)d, "u₁" is the first term, "d" is the common difference S_n = n/2(2u₁+(n-1)d) OR S_n = n/2(u₁+u_n), "u₁" is the first term, "u_n" is the nth term, "d" is the common difference
The value of the nth term of a geometric sequence The sum of n terms in a finite geometric sequence The sum of an infinite geometric sequence	$u_{n} = u_{1} r^{n - 1}$ , "u₁" is the first term, "r" is the common ratio $S_{n} = \frac{u_{1} (r^{n} - 1)}{r - 1} = \frac{u_{1} (1 - r^{n})}{1 - r}, r \neq 1$ , $S_{\infty} = \frac{u_{1}}{1 - r}, \|r\| < 1$
Compound interest formula	$F V = P V \times {(1 + \frac{r}{100 k})}^{k n}$ , "FV" is final value, "PV" is principle/present value, "k" number of compounding periods per year, "r"% is the annual interest rate
Definition of a logarithm Logarithm addition Logarithm subtraction Logarithms and exponents Logarithm division	$a^{x} = b \Leftrightarrow x = \log_{a} (b), a, b > 0, a \neq 1$ $\log_{a} x y = \log_{a} x + \log_{a} y$ $\log_{a} \frac{x}{y} = \log_{a} x - \log_{a} y$ $\log_{a} (x^{m}) = m \log_{a} (x)$ $\log_{a} x = \frac{\log_{b} x}{\log_{b} a}$
Binomial Theorem n∈ℕ	${(a + b)}^{n} = a^{n} +^{n} C_{1} a^{n - 1} b + . . . +^{n} C_{r} a^{n - r} b^{r} + . . . + b^{n}$	Consider using Pascal's triangle instead of combinations for smaller n values
Combinations Equation	$^{n} C_{r} = \frac{n!}{r! (n - r)!}$ , "n" is the total number of items, "r" is the number of items chosen	Order DOES NOT matter
HL ONLY
Permutations Equation	$^{n} P_{r} = \frac{n!}{(n - r)!}$ , "n" is the total number of items, "r" is the number of items chosen	Order MATTERS
Extension of the Binomial Theorem	${(a + b)}^{n} = a^{n} (1 + n (\frac{b}{a}) + \frac{n (n - 1)}{2!} {(\frac{b}{a})}^{2} + . . .)$
Complex numbers	$z = a + b i$	This form is most useful for addition and subtraction of complex numbers
Modulus-argument (polar) and exponential (Euler) form	$z = r (\cos θ + i \sin θ) = r e^{i θ} = r c i s θ$	Most useful for division and multiplication
De Moivre's theorem	${[r (\cos θ + i \sin θ)]}^{n} = r^{n} (\cos n θ + i \sin n θ) = r^{n} e^{i n θ} = r^{n} c i s n θ$	Use to help find roots of an imaginary polynomial

Topic 2: Functions

Description	Equation and Variables	Use/Additional Info:
Equations of a straight line Gradient (slope) formula	$y = m x + c; a x + b y + d = 0; y - y_{1} = m (x - x_{1})$ $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
Axis of symmetry of the graph of a quadratic	$f (x) = a x^{2} + b x + c \Rightarrow a x i s o f s y m m e t r y i s x = - \frac{b}{2 a}$
Solutions of a quadratic (Quadratic formula)	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}, a \neq 0$
Discriminant of a quadratic	$∆ = b^{2} - 4 a c$	If discriminant is less than 0, roots are imaginary
Exponential and logarithmic functions	$a^{x} = e^{x \ln a}; \log_{a} a^{x} = x = a^{\log_{a} x} w h e r e a, x > 0, a \neq 1$
HL ONLY
Sum and product of the roots of a polynomial function	$S u m i s \frac{- a_{n - 1}}{a_{n}}; p r o d u c t i s \frac{{(- 1)}^{n} a_{0}}{a_{n}}$	Easy method for finding roots of high power polynomials

Topic 3: Geometry and Trigonometry

Description	Equation and Variables	Use/Additional Info:
Distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂)	$d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2} + {(z_{1} - z_{2})}^{2}}$
Coordinates of the midpoint of a line segment with endpoints (x₁, y₁, z₁) and (x₂, y₂, z₂)	$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}, \frac{z_{1} + z_{2}}{2})$
Volume of a right-pyramid	$V = \frac{1}{3} A h$ , "A" is the area of the base, "h" is the height
Volume of a right cone	$V = \frac{1}{3} {πr}^{2} h$ , "r" is the radius of the base, "h" is the height
Area of the curved surface of a cone	$A = πrl$ , "r" is the radius of the base, "l" is the slant height
Volume of a sphere	$V = \frac{4}{3} {πr}^{3}$ , "r" is the radius
Surface area of a sphere	$A = 4 {πr}^{2}$ , "r" is the radius
Sine rule	$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Cosine rule	$c^{2} = a^{2} + b^{2} - 2 a b \cos C; \cos C = \frac{a^{2} + b^{2} - c^{2}}{2 a b}$
Area of a triangle	$A = \frac{1}{2} a b \sin C$
Length of an arc	$l = r θ$ , "r" is radius, "θ" is the central angle
Area of a sector	$A = \frac{1}{2} r^{2} θ$ , "r" is radius, "θ" is the central angle
Identity for tanθ	$\tan θ = \frac{\sin θ}{\cos θ}$
Pythagorean identity	$\cos^{2} θ + \sin^{2} θ = 1$
Double angle identities	$\sin 2 θ = 2 \sin θ \cos θ$ $\cos 2 θ = \cos^{2} θ - \sin^{2} θ = 2 \cos^{2} θ - 1 = 1 - \sin^{2} θ$
HL ONLY
Reciprocal trigonometric identities	$\sec θ = \frac{1}{\cos θ}$ $\cos e c θ = cscθ = \frac{1}{sinθ}$
Pythagorean identities	$1 + \tan^{2} θ = \sec^{2} θ$ $1 + \cot^{2} θ = {cosec}^{2} θ$
Compound angle identities	$\sin (A \pm B) = \sin A \cos B \pm \sin B \cos A$ $\cos (A \pm B) = \cos A \cos B \mp \sin A \sin B$ $\tan (A \pm B) = \frac{\tan A \pm \tan B}{1 \mp 2 \tan A \tan B}$	useful for adding non-standard angles on non-calculator exams
Tan double angle identity	$\tan 2 θ = \frac{2 \tan θ}{1 - \tan^{2} θ}$
Magnitude of a vector	$\|\overset{⇀}{v}\| = \sqrt{{v_{1}}^{2} + {v_{2}}^{2} + {v_{3}}^{2}}, w h e r e \overset{⇀}{v} = (\begin{matrix} \begin{matrix} v_{1} \\ v_{2} \end{matrix} \\ v_{3} \end{matrix})$
Scalar product	$\overset{⇀}{v} \cdot \overset{⇀}{w} = v_{1} w_{1} + v_{2} w_{2} + v_{3} w_{3}, w h e r e \overset{⇀}{v} = (\begin{matrix} \begin{matrix} v_{1} \\ v_{2} \end{matrix} \\ v_{3} \end{matrix}) a n d \overset{⇀}{w} = (\begin{matrix} \begin{matrix} w_{1} \\ w_{2} \end{matrix} \\ w_{3} \end{matrix})$ $\overset{⇀}{v} \cdot \overset{⇀}{w} = \|v\| \|w\| \cos θ$ , where θ is the angle between v and w
Angle between two vectors	$\cos θ = \frac{\overset{⇀}{v} \cdot \overset{⇀}{w}}{\|v\| \|w\|}$
Vector equation of a line	$\overset{⇀}{r} = \overset{⇀}{a} + λ \overset{⇀}{b}$
Parametric form of the equation of a line	$x = x_{0} + λ l, y = y_{0} + λ m, z = z_{0} + λ n$
Cartesian equations of a line	$\frac{x - x_{0}}{l} = \frac{y - y_{0}}{m} = \frac{z - z_{0}}{n}$
Vector Product
Area of a parallelogram
Vector equation of a plane
Equation of a plane (using normal vectors)
Cartesian equation of a plane

Topic 4: Statistics and Probability

Description	Equation and Variables	Use/Additional Info:
Interquartile range		Use IQR x 1.5 subtracted from Q1 and added to Q2 to determine the range of values that are not classified as outliers
Mean, $\bar{x}$ , of a data set
Probability of an event A
Complementary events
Combined events
Mutually exclusive events
Conditional probability
Independent events
Expected value of a discrete random variable X
Binomial distribution X~B(n, p)
Mean
Variance
Standardized normal variable
HL ONLY
Bayes' Theorem
Variance σ²
Standard deviation σ
Linear transformation of a single random variable
Expected value of a continuous random variable X
Variance
Variance of a discrete random variable X
Variance of a continuous random variable X

Topic 5: Calculus

Description	Equation and Variables	Use/Additional Info:
Derivative of xⁿ
Integral of xⁿ
Area between a curved y = f(x) and the x-axis, f(x) > 0
Standard Derivatives
Chain rule
Product rule
Quotient rule
Acceleration
Distance travelled from t₁ to t₂
Displacement from t₁ to t₂
Standard integrals
Area enclosed by a curved and the x-axis
HL ONLY
Derivative of f(x) from first principles
More standard derivatives
More standard integrals
Integration by parts
Area of a region enclosed by a curved and y-axis
Volume of revolution about the x or y-axes
Euler's method
Integrating factor for y' + P(x)y = Q(x)
Maclaurin series
Maclaurin series for special functions

Editors

RuY2718 - 1014 words.
joeClinton - 5 words.

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Annotated List of Formulas

Prior Knowledge:

Topic 1: Number and Algebra

Topic 2: Functions

Topic 3: Geometry and Trigonometry

Topic 4: Statistics and Probability

Topic 5: Calculus

Editors