Colorful Mathematics
Mathematics 11.
Textbook
Mozaik Kiadó
MS6311  Edition 1, 2015  296 pages
Authors: Csordás M.Kosztolányi J.Pintér K.dr. Urbán J.Vincze I.
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Combinatorics, graphs
 1. Fibonacci numbers 10
 2. Permutations, variations 13
 3. Combinations without repetition, Pascal's triangle 20
 4. Binomial coefficients, combination with repetition 28
 5. Miscellaneous counting exercises (extracurricular topic) 34
 6. GRAPHS  points, edges, degree 38
 7. GRAPHS  path, trail, walk, cycle, Eulerian trail (extracurricular topic) 48
 8. Tree graphs (extracurricular topic) 57
 9. Practical applications of combinatorics 63

Powers, roots, logarithms
 1. Exponentiation and computing the roots (reminder) 66
 2. Power functions and root functions 71
 3. Power with fractional (rational) exponent 74
 4. Power with irrational exponent, exponential function 80
 5. Exponential equations, simultaneous exponential equations and exponential inequalities 85
 6. The concept of the logarithm 92
 7. The logarithm function 98
 8. The logarithmic identities 102
 9. Logarithmic equations, simultaneous logarithmic equations and logarithmic inequalities . 107
 10. Practical applications 115

Applications of trigonometry
 1. Vector operations, applications (reminder) 120
 2. The dot product 125
 3. Dot product in the coordinate system 130
 4. The sine rule 134
 5. The cosine rule 139
 6. Applications of the trigonometric relations 143
 7. Addition formulae 147
 8. Applications of the addition formulae 150
 9. Trigonometric equations, inequalities 156
 10. The application of trigonometry for positioning 163

Functions
 1. The exponential and the logarithm function 166
 2. Equations and functions 170
 3. Trigonometric functions 172
 4. Trigonometric equations, inequalities (extracurricular topic) 176
 5. Miscellaneous exercises (extracurricular topic) 181
 6. Inverse functions (extracurricular topic) 186
 7. A practical application of the functions 189

Coordinate geometry
 1. Vectors in the coordinate system. Operations with vectors given with coordinates (reminder) 192
 2. The distance between two points. The angle of inclination of two vectors 195
 3. The coordinates of the point of division of a line segment. The coordinates of the centroid of a triangle 198
 4. Data defining a straight line in the coordinate system 204
 5. The equation of a straight line I. 212
 6. The equation of a straight line II. 215
 7. The intersection point, the distance and the angle of inclination of two straight lines 219
 8. The equation of a circle 225
 9. The mutual position of a circle and a straight line; the common points of two circles 233
 10. The equation of a parabola 244
 11. The parabola and the quadratic function (extracurricular topic) 250
 12. Conic sections and their equations in the coordinate system (extracurricular topic) 253
 13. Two practical applications of coordinate geometry 258

Calculation of probability, statistics