The topics discussed are:

• Basic algebraic functions, their graphs, derivatives and their graphical meaning. In this program, all basic functions are discussed, and the main properties of their graphs are described. Later, small deviations are introduced, and the graphs of the derivative functions are built. In the end, a user can define any algebraic function and investigate its behavior. This may be done in any region of argument x, along with a graph of a derivative function. Every topic consists of a series of headings, each of which presents a number of statements (theorems) which may be checked by the student. At the end of the activity, an interactive experiment is presented, in which all the parameters of a function and the region of its investigation are defined by the user.

• Line equations, slope
• Conditions of parallelity and perpendicularity

of lines

• Distance between two points
• Midpoint of a segment, medians
• Parallelograms, triangles, areas
• Circle: canonical equation, intersection with the axes, tangent formula

The subjects:

• Finding Altitudes and Angles
• Solving Right Triangles
• Problem solving using the Law of sines
• Problem solving using the Law of cosines
• Finding a ratio between sides
• Solving a triangle, given two sides and the angle
• Solving a triangle, given three sides
• Finding the area of a triangle
• Finding the area of a parallelogram

The program combines the method of Stages ith the interactive drawing of bar diagrams and distributions.

The subjects:

• Date organizing, frequency of appearance
• Relative and accumulated frequencies
• Boundaries, center of group, average value
• Dispersion, standard deviation
• Normal distribution

The subjects:

• The laws of Logarithms
• Decimal logarithms
• Transformation of logarithms to a

different base

• Logarithmic equations
• Calculation without a calculator

The subjects:

• Arithmetic progression: a common difference
• Calculation of the n-th term
• Sum of an arithmetic progression
• Geometric progression: a common ratio
• Exercises with consecutive terms
• Sum of a geometric progression
• Sum of an infinitely decreasing geometric sequence
• Mixed sequences (arithmetic and geometric)
• General sequence: recursive relations

The subjects:

• Trigonometric functions of a single angle
• Units of angle measurement
• Fundamental identities
• Complementary identities
• Addition laws
• Double-angle formulas
• Half-angle identities
• Product-to-sum identities
• Sum-to-product identities

The subjects:

• Period of a trigonometric function
• The inverse trigonometric functions
• Proving identities and solving equations
• Proving by direct method
• Proving by reversed method
• Solving basic equations
• Reduction to the basic form
• Reduction to the square equation
• System of trigonometric equations

The subjects:

• Square equations: definitions
• Partial square equation
• Complete square equation
• Unassigned square equation
• Basic systems of square equations
• Special equations
• Irrational equations
• Square equations with parameters

The program combines the method of Stages with interactive graphical representation of a system of linear inequalities.

The subjects:

• Graphical representation of a system of inequalities
• Area, lines of boundaries, open and closed areas, system of three and more inequalities
• Constraints, minimum and maximum values in an area, optimal value, unnecessary constraint
• Actual problems: finding of maximum profit, utilization of resources, etc.

The subjects:

• Definition of Complex Numbers
• Algebraic and Trigonometric representations
• Real and Imaginary parts, Conjugate numbers
• Basic operations on Complex Numbers
• De Moivre’s Theorem, n-th Roots of Complex Numbers

The subjects:

• Limits of polynomial and root functions
• Limits of Log and Trig functions
• Derivatives of polynomial and root functions
• Derivatives of product and ratio of two functions
• Derivatives of a function of a function
• Derivatives of trigonometric functions
• Derivatives of Log and Exp functions
• Derivatives of higher orders and other topics