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

Examples: x^4 - 2x^3 + 5x * 0, -2x^3 + 3x^2 - 4 ≤ 0, x(x-3)^2 (x+4)^3 * 0. Solving the polynomial inequalities: 1. Write the polynomial in factored form. 2. Read roots. 3 Read multiplicity of roots. 4. Mark roots on x-axis. 5. Draw approximate graph of the polynomial begin always from right side -- from up if the polynomial begins positive number, -- from down if the polynomial begins negative number. 6. Graph "crosses" x-axis for roots of odd multiplicity. Graph "bounces" back from x-axis for roots of even multiplicity. 7. Mark green for signs: *, ≤ part of a graph belowe x-axis. For signs: *, ≥ part of a graph above x-axis. 8. For signs: ≤, ≥ draw full circe in roots. For signs: *, * draw open circe in roots. 9. Draw interval correspond to green part of a graph. 10. Write solution.