Elective course in algebra - course 51,136 rubles. from SkySmart, training 64 lessons, Date: December 5, 2023.

My favorite book is Harry Potter, and I am Professor McGonagall in it. I’ll teach you how to bottle actions with numbers, how to cook a problem using a formula, and even how to seal the root of an equation. But as long as you ask questions and do your homework!

I always try to find a common language with students and gain their trust, I am in touch 24/7. In my free time I study English and German, I like to read, mainly English classics

1. 7th grade

In an elective course in algebra, a 7th grade student will be able to deepen his knowledge of the subject, repeat the topics of the school curriculum and go beyond it - work on more complex tasks.

1. Numeric expressions.
2. Expressions with variables.
3. Properties of operations on numbers.
4. Identities. Identical transformations of expressions.
5. Thematic lesson on the topic “Cinematography”.
6. The equation and its roots.
7. Linear equation with one variable.
8. Solving problems using equations.
9. Average.
10. Median as a statistical characteristic.
11. Thematic lesson “Mythbusters”.
12. What is a function?
13. Calculation of function values ​​using the formula.
14. Function graph.
15. Direct proportionality and its graph.
16. Linear function and its graph.
17. Thematic lesson on the topic “Healthy Products”.
18. Determination of degree with a natural indicator.
19. Multiplication and division of powers.
20. Exponentiation of product and degree.
21. Monomial and its standard form.
22. Multiplying monomials.
23. Raising a monomial to a power.
24. Functions y = x2 and y = x3.
25. Thematic lesson on the topic “Guinness Book of Records”.
26. Polynomial and its standard form.
27. Addition and subtraction of polynomials.
28. Multiplying a monomial by a polynomial.
29. Taking the common factor out of brackets.
30. Multiplying a polynomial by a polynomial.
31. Factoring a polynomial using the grouping method.
32. Thematic lesson on the topic “Brain”.
33. Square or cube the sum and difference of two expressions.
34. Factorization using the squared sum and squared difference formulas.
35. Multiplying the difference of two expressions by their sum.
36. Factoring the difference of squares.
37. Thematic lesson on the topic “Unusual stones and minerals.”
38. Factorization of the sum and difference of cubes.
39. Convert an entire expression to a polynomial.
40. Application of various methods for factorization.
41. Applying transformations of integer expressions.
42. Thematic lesson "Genetics".
43. Linear equations with two variables.
44. Graph of a linear equation in two variables.
45. Systems of linear equations with two variables.
46. Substitution method.
47. Addition method.
48. Thematic lesson “Myths about the present and the past.”
49. Solving problems using systems of equations.
50. Entertaining tasks.
51. Thematic lesson on the topic “KBZHU”

2. 8th grade

The purpose of the elective algebra course is to give the child the opportunity to refresh his preparation on 8th grade topics and demonstrate them on complex problems.

1. Rational expressions.
2. The main property of a fraction. Reducing fractions.
3. Adding and subtracting fractions with like denominators.
4. Adding and subtracting fractions with different denominators.
5. Thematic lesson on the topic “Currency”.
6. Multiplying fractions. Raising fractions to powers.
7. Dividing fractions.
8. Converting rational expressions.
9. Function y = k / x and its graph.
10. Thematic lesson on the topic “Photography”.
11. Real numbers.
12. Square roots. Arithmetic square root.
13. Equation x2 = a.
14. Finding approximate values ​​of the square root.
15. Function y = √x and its graph.
16. Square root of a product and a fraction.
17. Square root of a degree.
18. Properties of square arithmetic root.
19. Thematic lesson on the topic “Mnemonics”.
20. Removing the multiplier from under the root sign. Write the multiplier under the sign of the root.
21. Converting expressions containing square roots.
22. Applying the properties of square roots.
23. Thematic lesson on the topic "Physics".
24. Definition of a quadratic equation. Incomplete quadratic equations.
25. Solving quadratic equations by squaring the binomial.
26. Formula for the roots of a quadratic equation.
27. Solving problems using quadratic equations.
28. Vieta's theorem.
29. Thematic lesson on the topic “Music”.
30. Solving fractional rational equations.
31. Solving problems using rational equations.
32. Graphical method for solving equations.
33. Equations with a parameter.
34. Thematic lesson on the topic “Astronomy”.
35. Comparison of numbers. Numerical inequalities.
36. Properties of numerical inequalities.
37. Addition and multiplication of numerical inequalities.
38. Error and accuracy of approximation.
39. Thematic lesson on the topic “KBJU”.
40. Intersection and union of sets.
41. Numerical intervals.
42. Solving inequalities with one variable.
43. Thematic lesson on the topic “Resorts”.
44. Definition of a degree with a negative integer exponent.
45. Properties of a degree with an integer exponent.
46. Standard type of number.
47. Collection and grouping of statistical data.
48. Visual presentation of statistical information.
49. Thematic lesson on the topic “Meteorology”.

3. 9th grade

In individual lessons of an elective course in algebra, a teenager will try his hand at OGE tasks and in-depth topics of grade 9.

1. Function. Domain. Range of values.
2. Properties and graphs of linear functions and inverse proportionality.
3. Properties and graphs of the square and root functions.
4. Graph of a linear fractional function.
5. Roots of a square trinomial.
6. Expansion of a quadratic trinomial.
7. Functions and their properties.
8. The function y = ax2 its graph and properties.
9. Graphs of the functions y = ax2 + n and y = a (x − m) 2.
10. Plotting a graph of a quadratic function.
11. Power function y = xn.
12. Root function.
13. Degree with a rational exponent.
14. Quadratic function.
15. The whole equation is an equation and its roots.
16. Fractional rational equations.
17. Inequalities of the second degree with one variable.
18. Interval method.
19. Techniques for solving entire equations.
20. Irrational equations and inequalities.
21. Equations and inequalities with one variable.
22. Equation with two variables and its graph.
23. Graphical method for solving systems of equations.
24. Solving systems of second degree equations.
25. Solving the problem using second degree systems.
26. Systems of equations.
27. Graphical solution of systems of inequalities with two variables.
28. Additional techniques for solving systems of inequalities with two variables.
29. Equations and inequalities with two variables.
30. Sequences.
31. Arithmetic progression. Properties, formula of the nth term.
32. Arithmetic progression. Amount formula.
33. Mixed progression problems.
34. Mathematical induction.
35. Combinatorics problems.
36. Rearrangements.
37. Placements.
38. Combinations.
39. Relative frequency of a random event.
40. Probability of equally possible events.
41. Addition and multiplication of probabilities.
42. Combinatorics. Probability theory.
43. Repetition. Numeric expressions.
44. Repetition. Functions and graphics.
45. Repetition. Equations and systems of equations.
46. Repetition. Inequalities and systems of inequalities.
47. Repetition. Problems on equations and systems.
48. Repetition. Arithmetic and geometric progressions.

4. Grade 10

An elective online algebra course will challenge the student's knowledge of trigonometry, functions, equations and graphs. In classes with a teacher, he will be able to better work through his school preparation and practice solving options for the Unified State Examination.

1. Numeric function.
2. Properties of functions.
3. Inverse function.
4. Number circle.
5. Number circle on the coordinate plane.
6. Definition of sine, cosine, tangent and cotangent.
7. Trigonometric functions of a numeric argument.
8. Trigonometric functions of angular argument.
9. Reduction formulas.
10. Function y = sin x and its properties.
11. Function y = cos x and its properties.
12. Periodicity of functions y = sin x, y = cos x.
13. Transformations of graphs of trigonometric functions.
14. Functions y = tg x, y = ctg x and their properties.
15. Equations of the form cos x = a.
16. Equations of the form sin x = a and tan x = a.
17. Trigonometric equations.
18. Homogeneous trigonometric equations.
19. sin, cos sums and differences.
20. tg sums and differences.
21. Double argument formulas.
22. Sum of sines and cosines.
23. Product of sines and cosines.
24. Number sequences. Consistency limit.
25. Infinitely decreasing geometric progression.
26. Function limit.
27. Definition of derivative.
28. Calculation of derivatives.
29. Tangent equation.
30. Study on monotonicity and extrema.
31. Building graphs.
32. The largest and smallest values ​​of a function.
33. The largest and smallest values ​​of quantities.

5. Grade 11

In the 11th grade, a student in an elective algebra course will study school topics in greater depth, learn about common mistakes other teenagers make on exams, and try their hand at solving advanced-level problems.

1. The simplest word problems.
2. The simplest problems involving percentages.
3. Graphs and diagrams.
4. Probability theory.
5. Rational and irrational equations.
6. Trigonometry. Addition formulas.
7. Trigonometry. Reduction formulas.
8. Trigonometry. Converting trigonometric expressions.
9. Trigonometry. Equations with cos.
10. Trigonometry. Equations with sin and tg.
11. Properties of degrees.
12. Exponential equations.
13. Logarithms. Definition.
14. Logarithms. Transformations.
15. Logarithmic equations.
16. Substitution in formulas.
17. Derivative. Introduction.
18. Derivative. Calculation.
19. Derivative. The largest and smallest value of a function.
20. Derivative. Extremes.
21. Derivative. Study on extrema without derivative.
22. Derivative. Antiderivative.
23. Text problems. Movement in a straight line.
24. Text problems. Movement on water.
25. Text problems. Movement in a circle.
26. Text problems. Average speed. Movement of extended bodies.
27. Text problems. Tasks for work.
28. Text problems. Implicit amount of work.
29. Text problems. Concentrations.
30. Text problems. Progression.
31. Trigonometry. The simplest equations.
32. Selection of roots in trigonometric equations.
33. Trigonometry. Quadratic equations.
34. Trigonometry. Homogeneous equations.
35. Trigonometry. Fractional rational equations.
36. Trigonometry. Inequalities, DL research.
37. Trigonometry. Sum and product of trigonometric functions.
38. Trigonometry. Additional angle. Estimation method.
39. Exponential equations.
40. Logarithmic equations.
41. Equations with modulus.
42. Equations with roots.
43. Combined equations.
44. Exponential inequalities.
45. Logarithmic inequalities.
46. Inequalities with modulus.
47. Inequalities with roots.
48. Combined inequalities.
49. Rationalization method. Solving logarithmic inequalities.
50. Rationalization method. Exponential, irrational and inequalities with modulus.
51. Systems of inequalities.
52. Options. Quadratic equations.
53. Options. Linear equations.
54. Options. Quadratic function.
55. Options. Monotone.
56. Options. Limitation.
57. Options. Invariance.
58. Options. Graphic method.
59. Options. Okha method.
60. Options. f(x) = g(x). Draw f and g.
61. Logic problems.
62. Development of the analytical method.
63. Economic tasks. Interest. Introduction.
64. Economic tasks. Deposits.
65. Economic tasks. Differentiated payments.
66. Economic tasks. Annuity payments.
67. Economic tasks. Tables.
68. Economic tasks. Non-standard loans.
69. Production tasks.
70. Number theory. GCD and NOC.
71. Number theory. Divisibility and remainders.
72. Number theory. Evaluation plus example.
73. Number theory. Average.
74. Number theory. Progression.
75. Number theory. Numbers on the board.
76. Non-standard tasks.