Angol nyelvű matematika

Colourful Mathematics 10. Az MS-2310 Sokszínű matematika 10. c. kötet angol nyelvű változata MS-6310
10. évfolyam, 2. kiadás (2017. 08. 22.)
kód: MS-6310
ára: 4 980 Ft
méret: B5, 256 oldal
tanterv: NAT 2012
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A kiadvány az MS-2310 Sokszínű matematika 10. c. kötet angol nyelvű változata. This book is the English version of the Hungarian market leader textbook titled Sokszínű matematika 10.
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Mathematical reasoning10
1. What does it imply?10
2. The pigeonhole principle21
3. Arrangement (ordering) problems29
4. Picking problems32
Computing the root36
1. Rational numbers, irrational numbers36
2. The identities (laws) of the square root40
3. Applying the identities (laws) of the square root44
4. The nth root of numbers50
5. The identities (laws) of the nth root .53
The quadratic equation60
1. The quadratic equation and function60
2. The quadratic formula64
3. The zero product form. The relation between the roots and the coefficients69
4. Equations of higher degree which can be reduced to quadratic equations74
5. Quadratic inequalities80
6. Parametric quadratic equations (higher level courseware)84
7. Equations involving square roots90
8. Quadratic simultaneous equations96
9. Arithmetic and geometric mean101
10. Extreme value exercises (higher level courseware)106
11. Problems leading to quadratic equations110
Widening the knowledge about circles116
1. Reminder116
2. The theorem of the central and inscribed/tangent-chord angles117
3. The theorem of inscribed angles; the arc of viewing angles121
4. The theorem of inscribed quadrilaterals (higher level courseware)125
The similarity transformation and its applications129
1. Parallel intercepting lines, parallel intercepting line segments (higher level courseware)129
2. The angle bisector theorem (higher level courseware)135
3. The transformation of central dilation (or homothety)137
4. The similarity transformation141
5. Similarity of figures; the simple cases of similar triangles143
6. A few applications of similarity147
7. The ratio of the area of similar planar figures154
8. The ratio of the volume of similar solids158
Trigonometric functions of acute angles161
1. Determining distances with the help of similarity161
2. Trigonometric functions of acute angles164
3. Relations between the trigonometric functions of acute angles168
4. Trigonometric functions of special angles172
5. Determining several data of a triangle with the help of trigonometric functions175
6. Calculations in the plane and in space with the help of trigonometric functions180
1. The concept of a vector; the sum and the difference of vectors; scalar multiplication of vectors (reminder)184
2. Expressing vectors as the sum of components in different directions188
3. Applying vectors in the plane and in space194
4. Vectors in the coordinate system, the coordinates of a vector, operations with vectors given with coordinates199
Trigonometric functions204
1. The definition and the simple properties of the sine and the cosine function204
2. The graph of the sine function209
3. The graph of the cosine function, equations, inequalities214
4. The tangent and the cotangent function221
5. Compound exercises and applications .228
6. Geometric applications232
Calculation of probability238
1. Events238
2. Operations with events243
3. Experiments, frequency, relative frequency, probability248
4. The classical model of probability ..251
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: Website offers more help material for processing with the course book.

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