Angol nyelvű matematika

Colourful Mathematics 9. Az MS-2309 Sokszínű matematika 9. c. kötet angol nyelvű változata MS-6309
9. évfolyam, 1. kiadás (2015. 09. 11.)
kód: MS-6309
ára: 4 980 Ft
méret: B5, 276 oldal
tanterv: NAT 2012
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A kiadvány az MS-2309 Sokszínű matematika 9. c. kötet angol nyelvű változata. This book is the English version of the Hungarian market leader textbook titled Sokszínű matematika 9.
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Combinatorics, sets10
1. The meaning of expressions in the mathematical language10
2. Let us count up!15
3. Sets21
4. Set operations26
5. Order of sets, inclusion-exclusion principle32
6. Number lines, intervals36
7. Graphs38
Algebra and arithmetics44
1. Usage of letters in mathematics44
2. Exponentiation48
3. Exponentiation to integer index52
4. Standard index form of numbers55
5. Integral expressions (polynomials)58
6. Special algebraic products60
7. Methods of factorisation66
8. Operations with algebraic fractions68
9. Divisibility74
10. Greatest common divisor (GCD), least common multiple (LCM)80
11. Number systems83
1. The Cartesian coordinate system, point sets88
2. Linear functions92
3. The absolute value function96
4. The quadratic function102
5. The square root function106
6. Linear fractional functions110
7. The integral part, the fractional part and the algebraic sign function (higher level courseware)116
8. More examples of functions (higher level courseware)120
9. Systematization of function transformations124
Triangles, quadrilaterals, polygons128
1. Points, straight lines, planes and their mutual position .128
2. A few basic geometric concepts (reminder)129
3. About the triangles (reminder)133
4. The relation between the sides and the angles of the triangle135
5. The relation between the sides of a right-angled triangle136
6. About the quadrilaterals (reminder)139
7. About the polygons143
8. Special point sets .145
9. The inscribed circle of a triangle149
10. The circumscribed circle of a triangle151
11. Thales’ theorem and some of its applications .153
12. Circumscribed quadrilaterals, circumscribed polygons (higher level courseware)157
Equations, inequalities, simultaneous equations160
1. The concept of equation, identity160
2. Solving equations graphically164
3. Solving equations with examining the domain and the range166
4. Solving equations with factorisation169
5. Solving equations with elimination, with the “balance method”173
6. Inequalities177
7. Equations and inequalities containing absolute value182
8. Parametric equations (higher level courseware)188
9. Solving problems with equations I191
10. Solving problems with equations II195
11. First-order simultaneous equations (system of equations) in two variables199
12. Solving problems with simultaneous equations (systems of equations)204
13. Linear systems of equations in more than two unknowns (higher level courseware)209
14. Practical exercises213
Congruent transformations216
Congruent transformations 1. The concept of geometric transformation, examples of geometric transformations216
2. Line reflection (reflection about a straight line) in the plane218
3. Axially symmetric figures221
4. Point reflection in the plane225
5. Centrally symmetric figures228
6. Applications of point reflection231
7. Rotation about a point in the plane236
8. Applications of rotation about a point I .239
9. Applications of rotation about a point II244
10. Parallel translation. Vectors246
11. Operations with vectors251
12. Congruence of figures256
1. The representation of data260
2. The description of data264
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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