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Colorful Mathematics
Mathematics 11.
Textbook
Mozaik
MS-6311 - Edition 4,
2024
296 pages
Authors: József Kosztolányi PhD, István Kovács, Klára Pintér, János Urbán PhD, István Vincze
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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 (extra-curricular topic) 34
- 6. GRAPHS - points, edges, degree 38
- 7. GRAPHS - path, trail, walk, cycle, Eulerian trail (extra-curricular topic) 48
- 8. Tree graphs (extra-curricular topic) 57
- 9. Practical applications of combinatorics 63
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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
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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
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Functions
- 1. The exponential and the logarithm function 166
- 2. Equations and functions 170
- 3. Trigonometric functions 172
- 4. Trigonometric equations, inequalities (extra-curricular topic) 176
- 5. Miscellaneous exercises (extra-curricular topic) 181
- 6. Inverse functions (extra-curricular topic) 186
- 7. A practical application of the functions 189
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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 (extra-curricular topic) 250
- 12. Conic sections and their equations in the coordinate system (extra-curricular topic) 253
- 13. Two practical applications of coordinate geometry 258
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Calculation of probability, statistics