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Mathematics
Mathematics · Grade 10
34/34 weeks ready · M. A. Mirzaahmedov, Sh. N. Ismailov, A. Q. Amanov (algebra and analysis), B. Q. Haydarov (geometry). Mathematics Grade 10, Parts 1 and 2, 1st edition. EXTREMUM PRESS, Tashkent, 2017
Chapter I
Sets and logic
1
Sets and operations on them
1. The concept of a set, operations on sets, the complement of a set
Quiz (8)
Homework
2
Statements and logical operations
2. Statements: negation, conjunction and disjunction
3. Logical equivalence and laws of logic
Quiz (8)
Homework
3
Implication, predicates and quantifiers
4. Implication, converse, inverse and contrapositive
5. Predicates and quantifiers
Quiz (8)
Homework
4
Correct reasoning and problem solving
6. Laws of correct reasoning; sophisms and paradoxes
7. Problem solving: sets and logic
Quiz (8)
Homework
Chapter II
Percentages, equations and inequalities
5
Simple and compound interest
8. Simple and compound interest
Quiz (8)
Homework
6
Percentage problems
9. Problem solving: percentages and interest
Quiz (8)
Homework
7
Rational equations
10. Simple rational equations and systems
Quiz (8)
Homework
8
Irrational equations
11. Simple irrational equations and systems
Quiz (8)
Homework
9
Exponential equations
12. Simple exponential equations and systems
Quiz (8)
Homework
10
Approximate solving and rational inequalities
13. Solving equations approximately
14. Simple rational inequalities and systems
Quiz (8)
Homework
11
Irrational inequalities
15. Simple irrational inequalities
Quiz (8)
Homework
Geometry
Planimetry review and introduction to stereometry
12
The logic of planimetry and problem-solving methods
16. The logical structure of planimetry
17. Geometric problems and methods of solving them
Quiz (8)
Homework
13
Planimetry review
18. Practice and applications: planimetry
Quiz (8)
Homework
14
Polyhedra and solids of revolution
19. Solid figures and polyhedra
20. Solids of revolution: cylinder, cone and sphere
Quiz (8)
Homework
15
Surface area problems
21. Practice and applications: polyhedra and solids of revolution
Quiz (8)
Homework
16
Lines, planes and sections in space
22. Lines and planes in space
23. Polyhedra and constructing their simple sections
Quiz (8)
Homework
17
Practice with lines and planes in space
24. Practice and applications: lines and planes in space
Quiz (8)
Homework
Chapter III
Elementary functions and equations
18
Function, monotonicity and extrema
25. Relations and mappings; the function
26. Monotonicity, greatest and least values of elementary functions
Quiz (8)
Homework
19
Linear and quadratic models
27. Linear and quadratic models
Quiz (8)
Homework
20
Periodic processes, sine and cosine
28. Periodic processes and observing them
29. The functions y = sin x, y = cos x and modelling with them
Quiz (8)
Homework
21
The simplest trigonometric equations
30. The simplest trigonometric equations
Quiz (8)
Homework
22
Trigonometric inequalities and graph transformations
31. The simplest trigonometric inequalities
32. Transformations of graphs
Quiz (8)
Homework
23
Parametric graphs and the exponential function
33. Graphs of simple functions given parametrically
34. The exponential function and its graph
Quiz (8)
Homework
24
Exponential inequalities and the logarithm
35. Directly solvable exponential inequalities
36. The logarithm, the logarithmic function, simplest logarithmic equations and inequalities
Quiz (8)
Homework
25
Exponential and logarithmic models
37. Modelling with exponential and logarithmic functions
Quiz (8)
Homework
Chapter IV
Complex numbers
26
Complex numbers and operations on them
38. Complex numbers, operations on them, and representing a complex number
Quiz (8)
Homework
27
The trigonometric form of a complex number
39. Complex numbers of the form r(cos φ + i sin φ) and re^(iφ)
40. Product and quotient of complex numbers in trigonometric form
Quiz (8)
Homework
28
Roots of complex numbers
41. Extracting the square root of a complex number
Quiz (8)
Homework
Geometry
Parallelism and perpendicularity in space
29
Mutual position of lines in space
42. Mutual position of lines in space
Quiz (8)
Homework
30
Parallelism of a line and a plane, and of two planes
43. Mutual position of a line and a plane in space
44. Mutual position of planes in space
Quiz (8)
Homework
31
Parallel projection and parallelism problems
45. Parallel projection in space
46. Practice and applications: parallelism
Quiz (8)
Homework
32
Perpendicular lines and planes, obliques, distance
47. Perpendicular lines and planes in space
48. Perpendicular, oblique and distance in space
Quiz (8)
Homework
33
Three perpendiculars and perpendicular planes
49. The theorem of three perpendiculars
50. Perpendicular planes in space
Quiz (8)
Homework
34
Orthogonal projection and perpendicularity in practice
51. Orthogonal projection in space and its use in engineering
52. Practice and applications: perpendicularity
Quiz (8)
Homework
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