 # Angol nyelvű matematika MS-6311

## Colourful Mathematics 11.

11. évfolyam, 3. kiadás (2020. 09. 02.)
Mozaik Kiadó
méret: 170x240 mm
terjedelem: 296 oldal
4 980 Ft
3 984 Ft (20% osztálykedvezménnyel)*
Kosárba * Legalább 15 példány megrendelése esetén 20% kedvezményt tudunk biztosítani 2021.03.31 és 2021.10.15 között.
 A kiadvány az MS-2311 Sokszínű matematika 11. c. kötet angol nyelvű változata. This book is the English version of the Hungarian market leader textbook titled Sokszínű matematika 11.
Kapcsolódó kiadványok
 A kiadvány digitális változata a könyvben levő kóddal ingyenesen elérhető*A kiadvány hátsó borítójának belső oldalán található egyedi kóddal a kiadvány digitálisan is elérhető. Az aktivált kódokkal DÍJMENTES hozzáférést biztosítunk a kiadvány mozaWeb Home változatához az aktiválástól számított minimum egy éves időtartamra. A kódok csak egyszer aktiválhatók.
Mintaoldalak    Tartalomjegyzék
 Combinatorics, graphs 10 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 Powers, roots, logarithms 66 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 120 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 166 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 Coordinate geometry 192 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 Calculation of probability, statistics 264 1. Classical probability model 264 2. Sampling with replacement 273 3. Sampling without replacement (extra-curricular topic) 280 4. Probabilistic games on graphs (extra-curricular topic) 286 5. Reality and statistics 293
A kiadvány bevezetője
 Guide to use the course book. The notations and highlights used in the book help with acquiring the courseware. - The train of thought of the worked examples show samples how to understand the methods and processes and how to solve the subsequent exercises. - The most important definitions and theorems are denoted by colourful highlights. - The parts of the courseware in small print and the worked examples noted in claret colour help with deeper understanding of the courseware. These pieces of knowledge are necessary for the higher level of graduation. - Figures, the key points of the given lesson, review and explanatory parts along with interesting facts of the history of mathematics can be found on the margin. The difficulty level of the examples and the appointed exercises is denoted by three different colours: Yellow: drilling exercises with basic level difficulty; the solution and drilling of these exercises is essential for the progress. Blue: exercises the difficulty of which corresponds to the intermediate level of graduation. Claret: problems and exercises that help with preparing for the higher level of graduation. These colour codes correspond to the notations used in the Colourful mathematics workbooks of Mozaik Education. The workbook series contains more than 3000 exercises which are suitable for drilling, working on in lessons and which help with preparing for the graduation. The end results of the appointed exercises can be found on the following website: www.mozaik.info.hu. Website www.mozaweb.hu offers more help material for processing with the course book.

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