mathinschool.com
numbers and algebraic expressions
logic, sets, intervals
absolute value
function and its properties
linear function
quadratic function
polynomials
rational function
exponential function
logarithm
number sequences
limits of sequences and functions
derivative and integral of functions
trigonometry
plane geometry
analytic geometry
solid geometry
combinatorics
probability
elements of statistics
kropki game

Sets are generally denoted by Capital Letters: A, B, C, ... Elements in the set represent lowercase letters: a, b, c, ... a ∈ A - a is an element in set A e.g. 2 ∈ N, 1/3 ∈ W, a ∉ A - a is not an element in set A e.g. 2/3 ∉ N, square root of 7 ∉ C, ∅ - empty set (has no elements), A = B - sets A and B are equal (have the same elements), A ⊆ B - set A is contained in B, set A is a subset of B e.g. A = {1, 2}, B = {1, 2, 3}, A ⊆ B. There are two ways to define sets: 1. list every elements e.g. A = {1, 5, 8}, B = {c, d, k}, C = {sister, brother, aunt}, 2. write a formula describing features of elements only in this set, A = {x ∈ R: x*2} - sef of real numbers less than 2, B = {x ∈ C: x^2 = 4} - set of integer numbers such that their square power equals 4.