This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f og the composite function of f and g lim f ( x) the limit of f ( x) as x tends to a dy
dx the derivative of y with respect to x f ′( x ) the derivative of f ( x) with respect to x d2 y
dx 2 the second derivative of y with respect to x f ″( x) the second derivative of f ( x) with respect to x ∫ y dx the indefinite integral of y with respect to x x →a ∫ b a y dx the definite integral of y with respect to x between the limits x = a and
x=b ex exponential function of x log a x logarithm to the base a of x ln x the natural logarithm of x, log e x sin, cos, tan the circular functions A( x, y ) the point A in the plane with Cartesian coordinates x and y [ AB] the line segment with end points A and B 3 AB the length of [ AB] ( AB ) the line containing points A and B Â the angle at A ˆ
CAB the angle between [CA ] and [ AB] ∆ABC the triangle whose vertices are A, B and C v the vector v
→ AB the vector represented in magnitude and direction by the directed line
segment from A to B a the position vector OA i, j, k unit vectors in the directions of the Cartesian coordinate axes → the magnitude of a a
→ → | AB| the magnitude of AB v⋅w the scalar product of v and w A−1 the inverse of the non-singular matrix A AT the transpose of the matrix A det A the determinant of the square matrix A I the identity matrix P( A) probability of event A P( A′) probability of the event “not A ” P( A | B ) probability of the event A given B x1 , x2 , ... observations f1 , f 2 , ... frequencies with which the observations x1 , x2 , ... occur B ( n, p ) binomial distribution with parameters n and p N(µ ,σ 2 ) normal distribution with mean µ and variance σ 2 4 X ~ B(n, p ) the random variable X has a binomial distribution with parameters
n and p X ~ N ( µ ,σ 2 ) the random variable X has a normal distribution with mean µ and
variance σ 2 µ population mean
k σ2 population variance, σ 2 = ∑ f (x − µ)
i i =1 i n σ k , where n = ∑ f i
i =1 population standard deviation x 2 sample mean
k ∑ f (x − x )
i i 2
k , where n = ∑ f i 2
sn sn standard deviation of the sample Φ 2. 2
sample variance, sn = cumulative distribution function of the standardized normal variable with
distribution N(0, 1) i =1 n i =1 Notation
Of the various notations in use, the IBO has chosen to adopt a system of notation based on the
recommendations of the International Organization for Standardization (ISO). This notation is
used in the examination papers for this course without explanation. If forms of notation other
than those listed in this guide are used on a particular examination paper, they are defined
within the question in which they appear.
Because students are required to recognize, though not necessarily use, IBO notation in
examinations, it is recommended that teachers introduce students to this notation at the earliest
opportunity. Students are not allowed access to information about this notation in the
In a small number of cases, students may ne...
View Full Document
This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.
- Fall '13
- The Land