Colourful Mathematics 10.
10. évfolyam, 2. kiadás (2017. 08. 22.)
Ingyenes, online hozzáférés a kiadvány digitális változatához, interaktív extra tartalmakkal.
kód: MS-6310
ára: 4 980 Ft
méret: B5, 256 oldal
tanterv: NAT2012
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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.
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