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Mathematics 11.

Table of contents
Combinatorics, graphs
1. Fibonacci numbers
2. Permutations, variations
3. Combinations without repetition, Pascal's triangle
4. Binomial coefficients, combination with repetition
5. Miscellaneous counting exercises (extra-curricular topic)
6. GRAPHS - points, edges, degree
7. GRAPHS - path, trail, walk, cycle, Eulerian trail (extra-curricular topic)
8. Tree graphs (extra-curricular topic)
9. Practical applications of combinatorics
Powers, roots, logarithms
Applications of trigonometry
Functions
Coordinate geometry
Calculation of probability, statistics

Combinatorics, graphs

1. Fibonacci numbers
2. Permutations, variations
3. Combinations without repetition, Pascal's triangle
4. Binomial coefficients, combination with repetition
5. Miscellaneous counting exercises (extra-curricular topic)
6. GRAPHS - points, edges, degree
7. GRAPHS - path, trail, walk, cycle, Eulerian trail (extra-curricular topic)
8. Tree graphs (extra-curricular topic)
9. Practical applications of combinatorics

Powers, roots, logarithms

1. Exponentiation and computing the roots (reminder)
2. Power functions and root functions
3. Power with fractional (rational) exponent
4. Power with irrational exponent, exponential function
5. Exponential equations, simultaneous exponential equations and exponential inequalities
6. The concept of the logarithm
7. The logarithm function
8. The logarithmic identities
9. Logarithmic equations, simultaneous logarithmic equations and logarithmic inequalities
10. Practical applications

Applications of trigonometry

1. Vector operations, applications (reminder)
2. The dot product
3. Dot product in the coordinate system
4. The sine rule
5. The cosine rule
6. Applications of the trigonometric relations
7. Addition formulae
8. Applications of the addition formulae
9. Trigonometric equations, inequalities
10. The application of trigonometry for positioning

Functions

1. The exponential and the logarithm function
2. Equations and functions
3. Trigonometric functions
4. Trigonometric equations, inequalities (extra-curricular topic)
5. Miscellaneous exercises (extra-curricular topic)
6. Inverse functions (extra-curricular topic)
7. A practical application of the functions

Coordinate geometry

1. Vectors in the coordinate system. Operations with vectors given with coordinates (reminder)
2. The distance between two points. The angle of inclination of two vectors
3. The coordinates of the point of division of a line segment. The coordinates of the centroid of a triangle
4. Data defining a straight line in the coordinate system
5. The equation of a straight line I.
6. The equation of a straight line II.
7. The intersection point, the distance and the angle of inclination of two straight lines
8. The equation of a circle
9. The mutual position of a circle and a straight line; the common points of two circles
10. The equation of a parabola
11. The parabola and the quadratic function (extra-curricular topic)
12. Conic sections and their equations in the coordinate system (extra-curricular topic)
13. Two practical applications of coordinate geometry

Calculation of probability, statistics

1. Classical probability model
2. Sampling with replacement
3. Sampling without replacement (extra-curricular topic)
4. Probabilistic games on graphs (extra-curricular topic)
5. Reality and statistics
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