(2019-2020 academic year,
Classes start on October 1)

Items:

Physics (grades 7-11);

Olympiad physics (grades 7-11) admission based on test results * ;

Mathematics (grades 2-11);

Olympiad mathematics (grades 2-11) admission based on test results * ;

Informatics (grades 9-11);

Robotics (grades 2-6);

Programming (grades 2-8);

Medical Biophysical Engineering (grades 7-9);

Russian language (grades 9-11).

Participants of the courses will be able to repeat the material they passed at school and fill in the gaps in knowledge, get acquainted with the format of the Unified State Exam and prepare for passing exams and performing at the Olympiads.

Our advantages:

Convenient location;

Classes in groups of up to 15 people;

The best teachers with extensive experience of working with students;

The programs were approved by the Academic Council of MIPT;

Payment is monthly;

Physics

7th grade
1. Physical quantities, measurement of physical quantities. Measurement accuracy and error.
2. Mechanical movement. Speed, calculation of the path and travel time.
3. Graphic method for solving problems.
4. Body mass, density.
5. Gravity, body weight. The addition of forces.
6. Force of friction. Friction at rest and sliding.
7. Pressure of solids, liquids and gases. Pascal's law. Hydraulic Press.
8. Calculation of pressure on the bottom and walls of the vessel. Communicating vessels.
9. Atmospheric pressure.
10. Archimedean force. Swimming conditions tel. Aeronautics.
11. Mechanical work, power.
12. Simple mechanisms. Leverage rule. Moment of power.
13. Center of gravity of the body, conditions of balance of bodies.
14. "Golden rule" of mechanics. Efficiency of simple mechanisms.
15. Energy, the law of conservation of energy.

8th grade
1. Mechanical movement. Fundamentals of kinematics.
2. Average speed and average density.
3. Vectors in physics. Addition of vectors.
4. Relativity of speeds.
5. Body trajectory. Dependence of the coordinates and velocity of the body on time.
6. Thermal phenomena. Temperature. Internal energy.
Thermal conductivity. Quantity of heat. Heat capacity.
7. Specific heat of combustion. Aggregate states of matter. Specific heat of fusion. Specific heat of vaporization.
8. Heat balance.
9. Humidity. Absolute and relative air humidity.
10. Electrical phenomena. Electric charge. Charge conservation law.
11. Conductors and dielectrics.
12. Direct current. Electrical circuits. Sources of current.
Voltage. Ammeter. Voltmeter. Resistance. Parallel and series connection of conductors. 13. Work and current power. Thermal effect of the current. Joule-Lenz law.
14. Optics. The law of rectilinear light propagation. The law of reflection. Construction of an image in a flat mirror.
15. The law of refraction of light. Full internal reflection.

Grade 9
1 Kinematics
1.1 Kinematics of a material point
1.2 Rectilinear equal alternating motion
1.3 Uniform movement of the body in a circle
2 Dynamics and conservation laws in mechanics
2.1 Newton's laws
2.2 The law of conservation of energy
2.3 Law of conservation of momentum
2.4 Oscillatory and wave processes, sound
3 Thermal phenomena
3.1 Structure of matter, molecular theory
3.2 Thermal phenomena
3.3 Phase transitions
4 Electrical and magnetic phenomena
4.1 Electrifying bodies
4.2 Direct current
4.3 Magnetism
5 Optics
5.1 Geometric optics
6 Quantum phenomena
7 Basics of conducting experimental work

Grade 10
1. Kinematics. Body movement at an angle to the horizon. Conservation law in kinematics.
2. Dynamics. Strength. Newton's laws.
3. Centripetal acceleration. Body movement in a circle.
4. Impulse. Impulse change law. Impulse conservation law.
5. Molecular kinetic theory. Perfect gas.
6. Equation of state of ideal gas. Internal energy. Temperature.
7. Isoprocesses. Adiabatic process.
8. Work in thermodynamics. Cycles. Cycle efficiency.
9. The first law of thermodynamics.
10. Heat capacity. Molar heat capacity.
11. The law of conservation in thermodynamics.
12. Electric field. Coulomb's law.
13. Electric field strength. The principle of superposition of fields. Power lines.
14. Potential. Potential difference. Voltage.
15. Intensity and potential of the field of a uniformly charged infinite plane and a uniformly charged sphere.
16. Conductors and dielectrics in an electric field. Capacitors.
17. The energy of the electric field. The movement of charged particles in an electric field.
18. Direct current. Electromotive force (EMF). Ohm's law for a complete circuit. Kirchhoff rules.
19. Work and current power. Joule-Lenz law.
20. Magnetic field. Vector of magnetic induction. Magnetic field of the current.
21. Ampere's law. Lorentz force. EMF Induced in a Conductor.
22. Movement of charged particles in a magnetic field.

Grade 11
1. Foundations of molecular kinetic theory. Perfect gas.
2. Equation of state of ideal gas. Internal energy. Temperature.
3. Work in thermodynamics. Cycles. Coefficient of performance (COP) cycles. The first law of thermodynamics. Heat capacity. Molar heat capacity.
4. Phase transitions. Heat balance.
5. Air humidity. Saturated and unsaturated steam.
6. Electrostatics. Field strength and potential of a uniformly charged infinite plane and a uniformly charged sphere.
7. Capacitors. D.C. Electromotive force (EMF). Ohm's law for a complete circuit. Kirchhoff rules.
8. Joule-Lenz law. Work and power in an electrical circuit.
9. Magnetic field. Vector of magnetic induction. The movement of charged particles in an electromagnetic field.
10. Ampere's law. Lorentz force.
11. Magnetic flux. Inductance. EMF Induced in a Conductor. The law of electromagnetic induction. Lenz's rule.
12. Mechanical vibrations. Mathematical pendulum. Spring-loaded pendulum. Energy transformations during oscillatory motion.
13. Oscillatory circuit. Energy transformations during oscillatory motion.
14. Geometric optics. Refraction of light. Thin lenses.
15. Wave optics. Interference. Diffraction.
16. Mechanics. Kinematics. Kinematic equations for displacement and velocity. Equally accelerated movement.
17. The movement of a body thrown at an angle to the horizon. Energy conservation law in kinematic problems.
18. Dynamics. Newton's laws.
19. Statics. Moment of power. Equilibrium conditions for solids.
20. Elements of quantum physics.

Maths

    2nd grade


    1. Techniques for oral addition and subtraction of two-digit numbers. Record addition and subtraction of two-digit numbers in a column. Addition and subtraction of two-digit numbers with a transition through the digit.
    2. Combination property of addition. Subtracting the amount from the number. Subtracting a number from a sum. Using addition and subtraction properties to streamline calculations.
    3. Multiplication and division of natural numbers.
    4. Special cases of multiplication and division with 0 and 1.
    5. The travel property of multiplication.
    6. Multiplication table. Tabular multiplication and division of numbers.
    7. Combination property of multiplication. Multiplication and division by 10 and by 100. Multiplication and division of round numbers.
    9. The order of performing actions in expressions containing addition, subtraction, multiplication and division (with and without parentheses).
    10. Distribution property of multiplication. The rule for dividing a sum by a number. Outside of table multiplication and division. Oral techniques outside of multiplication and division tables. Using the properties of multiplication and division to streamline calculations.


    1. Analysis of the problem, construction of graphical models, planning and implementation of the solution.
    2. Composite tasks in 2-4 actions for all arithmetic operations within 1000.
    3. Problems with letter data. Tasks for calculating the length of a polyline; the perimeter of the triangle and quadrilateral; area and perimeter of rectangle and square.
    4. Addition and subtraction of the studied values \u200b\u200bwhen solving problems.

    Geometric shapes and sizes... Point, line, ray, segment. Parallel and intersecting lines.
    1. Polyline, the length of the polyline. Perimeter of the polygon.
    2. Plane. Angle. Straight, acute and obtuse angles. Perpendicular straight lines.
    3. Rectangle. Square. Properties of the sides and corners of the rectangle and square. Creation of rectangle and square on checkered paper according to the specified lengths of their sides.
    4. Rectangular parallelepiped, cube. Circle and circle, their center, radius, diameter.
    Compass. Drawing patterns from circles using a compass.
    5. Composing figures from parts and dividing figures into parts. Intersection of geometric shapes.
    6. Units of length.
    7. The perimeter of the rectangle and square.
    8. Area of \u200b\u200ba geometric figure. Direct comparison of figures by area. Measurement of area. Units of area (square centimeter, square decimeter, square meter) and the ratio between them. The area of \u200b\u200bthe rectangle. Square area. Squares of shapes composed of rectangles and squares.
    9. Conversion, comparison, addition and subtraction of homogeneous geometric values.


    1. Reading and writing numerical and literal expressions containing addition, subtraction, multiplication and division (with and without parentheses). Calculation of the values \u200b\u200bof the simplest letter expressions for given letter values.


    1. Operation. Object and result of the operation.
    2. Operations on objects, figures, numbers. Direct and reverse operations.
    Finding unknowns: the object of the operation, the operation being performed, the result of the operation.
    3. Program of action. Algorithm. Linear, branched and cyclic algorithms.
    Compilation, recording and execution of algorithms of various types.
    4. Reading and filling in the table. Analysis of table data.
    5. An ordered search of options. Line networks. Paths. Opportunity tree.

    Grade 3

    Numbers and arithmetic operations with them
    1. Count in thousands. Digits and classes: class of units, class of thousands, class of millions, etc. Numbering, comparison, addition and subtraction of multidigit numbers
    (within 1,000,000,000,000). Representation of a natural number as a sum of bit terms.
    2. Multiplication and division of numbers by 10, 100, 1000, etc. Written multiplication and division (without remainder) of round numbers.
    3. Multiplication of a multivalued number. Writing multiplication in a column.
    Multidigit division. Record division by angle.
    Oral addition, subtraction, multiplication and division of multidigit numbers in cases that can be reduced to actions within 100. Simplification of calculations with multidigit numbers based on the properties of arithmetic operations.
    Construction and use of algorithms for the studied cases of oral and written actions with multi-digit numbers.
    The order of performing actions with and without brackets.

    Working with word problems. Analysis of the problem, construction of graphic models and tables, planning and implementation of the solution. Search for different solutions. 1. Composite tasks in 2-4 actions with natural numbers on the meaning of addition, subtraction, multiplication and division, difference and multiple comparison of numbers. 2. Tasks containing the relationship between quantities, of the form a \u003d b c: tasks for movement, tasks for work, tasks for cost. 3. Classification of simple problems of the studied types. A general way to analyze and solve a compound problem.
    4. Tasks to determine the beginning, end and duration of the event.
    5. Tasks to find numbers by their sum and difference.
    6. Tasks for calculating the areas of figures made up of rectangles and squares.
    7. Addition and subtraction of the studied values \u200b\u200bwhen solving problems.


    1. Rectangular parallelepiped, cube, their vertices, edges and faces. Creation of a sweep and a model of a cube and rectangular parallelepiped.
    2. Units of length: millimeter, centimeter, decimeter, meter, kilometer, the ratio between them.
    3. Conversion of geometric values, comparison of their values, addition, subtraction, multiplication and division by a natural number.
    4. Formula. Formulas for the area and perimeter of a rectangle. Formulas for the area and perimeter of a square.
    5. Formula for the volume of a rectangular parallelepiped. The formula for the volume of a cube.

    Algebraic representations.
    1. Equation. Root of the equation. Many roots of the equation. Compound equations that reduce to a chain of simple ones.
    2. Units of mass: gram, kilogram, centner, ton, the ratio between them.

    Mathematical language and elements of logic.
    1. A lot. Element of the set. The signs ∈ and ∉. Setting a set by listing its elements and a property.
    2. Empty set and its designation: Ø. Equal sets. Euler-Venn diagram.
    3. Subset. The signs ⊂ and ⊄. Intersection of many. ∩ sign. Intersection properties of sets. Union of sets. ∪ sign. Union properties of sets.
    4. Classification of elements of a set by property. Streamlining and systematization of information in reference books.
    5. Solving problems for an ordered enumeration of options using tables and a tree of possibilities.

    4th grade

    Numbers and arithmetic operations with them.
    1. Evaluation and estimation of the amount, difference, product, quotient.
    2. Checking the correctness of the calculations.
    3. Fractions. A visual representation of fractions using geometric shapes and on the number ray. Comparison of fractions with the same denominator and fractions with the same numerators.
    4. Division and fractions.
    5. Finding a part of a number, a number by its part and a part that one number is from another.
    6. Addition and subtraction of fractions with the same denominators.
    7. Correct and incorrect fractions. Mixed numbers. Isolation of a whole part from an irregular part. Improper fraction representation of a mixed number. Addition and subtraction of mixed numbers (with the same fractional denominators).
    8. Construction and use of algorithms for the studied cases of actions with fractions and mixed numbers.
    9. Expression and its meaning. Procedure for performing actions.

    Working with word problems. Independent analysis of the problem, building models, planning and implementing the solution. Search for different solutions. Correlation of the obtained result with the condition of the problem, assessment of its likelihood. Checking the task.
    1. Composite tasks in 2-5 actions with natural numbers for all arithmetic operations, difference and multiple comparison. Addition, subtraction and differential comparison of fractions and mixed numbers.
    2. Tasks to find the share of the whole and the whole by its share.
    3. Three types of problems for fractions: finding a part of a number, a number by its part and a fraction that one number is from another.
    4. Tasks for speed, time, distance.
    5. Tasks to calculate the area of \u200b\u200ba right-angled triangle and the areas of figures.

    Geometric shapes and sizes.
    1. Developed corner. Adjacent and vertical corners. The central angle and the angle inscribed in the circle.
    2. Measurement of angles. Protractor. Plotting corners with a protractor.
    3. Units of area: square millimeter, square centimeter, square decimeter, square meter, ar, hectare, the ratio between them.
    4. Study of the properties of geometric shapes using measurements.
    5. Conversion, comparison, addition and subtraction of homogeneous geometric values.
    Multiplication and division of geometric quantities by a natural number.

    Algebraic representations. Inequality. Many solutions to inequality. Severe and non-strict inequality. Signs ≥, ≤. Double inequality.

    Working with information and data analysis. Pie, bar and line charts, motion graphs: reading, interpreting data, plotting.
    1. Working with text: checking understanding; highlighting the main idea, significant comments and examples illustrating them; note-taking.

    Grade 5

    Integers
    1. A series of natural numbers. Decimal notation for natural numbers. Rounding off natural numbers.
    2. Coordinate beam.
    3. Comparison of natural numbers. Addition and subtraction of natural numbers.
    4. Multiplication and division of natural numbers.
    5. Divisors and multiples of natural numbers. Greatest common divisor. Least common multiple. Divisibility criteria.
    6. Prime and composite numbers. Decomposition of numbers into prime factors.
    7. Solving word problems by arithmetic methods.

    Fractions.
    1. Ordinary fractions. The main property of a fraction. Finding a fraction of a number. Finding a number by the value of its fraction. Right and wrong fractions. Mixed numbers. Reducing fractions to NOZ.
    2. Comparison of ordinary fractions and mixed numbers. Arithmetic operations with ordinary fractions and mixed numbers.
    3. Decimal fractions. Comparison and rounding of decimal fractions. Arithmetic operations with decimal fractions. Representation of a decimal fraction as a fraction and a fraction as a decimal.
    4. Proportion. The main property of proportion. Direct and inverse proportional relationships.

    Solving word problems using arithmetic methods.
    1. Translation of the problem statement into mathematical language. Methods for working with the simplest mathematical models.
    2. Drawing up literal expressions and formulas according to the conditions of the problems; Working with expressions and formulas, numeric substitutions, performing the corresponding calculations.
    Solving word problems by the algebraic method.

    Rational numbers.
    1. Positive, negative numbers and the number zero.
    2. Opposite numbers. The absolute value of a number.
    3. Integers. Rational numbers. Comparison of rational numbers. Arithmetic operations with rational numbers. Properties of addition and multiplication of rational numbers.
    Coordinate line. Coordinate plane.

    The quantities. Dependencies between quantities.
    1. Units of length, area, volume, mass, time, speed.
    2. Examples of dependencies between quantities. Representation of dependencies in the form of formulas. Calculations by formulas.

    Numeric and literal expressions. Equations.
    1. Numerical expressions. The value of a numeric expression. The order of actions in numerical expressions. Literal expressions. Expansion of brackets. Similar terms, bringing similar terms. Formulas.
    2. Equations. Root of the equation. Basic properties of equations. Solving word problems using equations.

    Geometric figures. Measurement of geometric quantities.
    1. Segment. Segment creation. Line segment length, broken line. Measuring the length of a segment, building a segment of a given length. Perimeter of the polygon. Plane. Straight. Ray.
    2. Angle. Types of angles. The degree measure of the angle. Measuring and plotting angles with a protractor.
    3. Rectangle. Square. Triangle. Types of triangles. Circumference and circle. Circumference.

    6th grade

    1. Elements of logic.
    2. The concept of denial.
    3. Variable. Variable expressions.
    4. Number line. Negative numbers. The concept of a negative number and actions with it. The absolute value of a number.
    5. Rational numbers and decimal fractions.
    6. Fractions. Actions and expressions with fractions.
    7. Tasks for movement.
    8. The concept of average values. Average.
    9. The concept of relationship. Scale. The concept of proportion and the main property of proportion. Actions with proportions and their transformation.
    10. Dependencies between quantities. Direct and inverse proportionality and their graphs. Solving problems using proportions.
    11. Concept of interest. Percentage growth. Interest problems.
    12. Coefficient. Similar terms. Expression transformations.
    13. Linear equations. Graphs of dependence of quantities.
    14. Solving problems with applied content by the method of equations.
    15. Logical following and equivalence. Denial of following. Reverse statements.
    16. Images and definitions of geometric concepts.
    17. Properties of geometric shapes.
    18. Measurement of geometric values. Length, area, volume.

    7th grade

    1. Fractions. Actions with fractions 2. Modulus of number. The geometric meaning of the module.
    3. A lot. Elements of the set. Subset.
    4. Determination of the degree with a natural indicator. Multiplication and division of degrees.
    5. Monomial. Actions with monomials. Identities.
    6. Polynomial. Calculating the values \u200b\u200bof a polynomial and its standard form. Actions with polynomials.
    7. Equations. Roots of linear equations in one variable. Solving problems using equations.
    8. Factorization. Proof of identities. Solving equations.
    9. Function. Formula. Calculating the values \u200b\u200bof a function using a formula. Function graph. Mutual arrangement of graphs of functions.
    10. Linear equations with two variables and their graphs.
    11. Systems of equations. Methods for solving systems of equations. Graphical way. Solving problems using systems of equations.
    12. Initial geometric concepts. Line, point, ray, segment. Corners. Measurement of angles.
    13. Signs of parallelism of two lines. Axiom of parallel lines.
    14. Vector. Types and equality of vectors. Actions with vectors. The projection of the vector onto the coordinate axis.
    15. Triangles. Signs of equality of triangles.
    16. Relationship between sides and angles of a triangle. Right triangle.
    17. Circumference. The length and area of \u200b\u200bthe circle. Ball.
    18. Elements of combinatorics. Counting the number of options. Combinations with repetitions. Statistical characteristics.
    19. The probability of occurrence of events. The classical scheme for determining the probability.

    8th grade

    1. Monomials. Polynomials. Actions with polynomials. Abbreviated multiplication formulas. Expression transformations.
    Degree with a natural indicator.
    2. Function. Formula. Calculating the values \u200b\u200bof a function using a formula. Function graph.
    3. Square roots. Approximate extraction of arithmetic square roots. Exact and approximate values.
    Function y \u003d x1 / 2 and its graph.
    4. Transformations of expressions containing a root.
    5. Function y \u003d 1 / x and its graph. Quadratic function and its graph.
    6. Quadratic equations. Full square selection method.
    7. Module number.
    8. Linear function. Linear function graph. Plot of the modulus of a linear function.
    9. Parameters in equations.
    Logical enumeration in problems with a parameter.
    10. Elements of number theory.
    11. Severability. Divisibility criteria. Prime and composite numbers. The main theorem of arithmetic.
    12. Decomposition into prime factors. Greatest common divisor (GCD). Least Common Multiple (LCM).
    14. Triangles. The problem of dividing a segment.
    15. Figures on a plane. Areal considerations.

    Grade 9

    1. Rational equations. Selection of roots. Range of permissible values \u200b\u200b(ODZ). Equivalent transitions. Quadratic equations.
    Biquadratic equations. Cubic equations.
    2. Parameters in rational equations. Logical enumeration in problems with a parameter. Parameters in quadratic equations.
    3. Right-angled triangle. Medians, bisectors, and heights in a triangle. Triangle area formulas.
    4. Rational inequalities. The method of intervals.
    5. Parameters in rational equations and inequalities.
    6. Trapezium.
    7. Systems of nonlinear equations.
    8. Solving problems using systems of equations.
    9. Irrational equations. ODZ in irrational equations. Equivalent transitions.
    10. Equations with modulus.
    11. Irrational inequalities. Inequalities with the module.
    11. Quadrangles.
    12. Parameters in irrational equations and inequalities.
    13. Problems of segment division
    14. Sets. Statements. Theorems.
    15. Sets on the plane.
    16. Areal considerations when solving planimetric problems.
    17. Numerical sequence. Arithmetic and geometric progressions.
    18. Circles.
    19. Different tasks for planimetry.

    Grade 10

    1. Decomposition of a polynomial into sets. Cubic equations. Rational equations. Rational inequalities.
    The method of intervals. Irrational equations. Equations with modulus.
    2. Method of rationalization for irrational inequalities and inequalities with modulus.
    3. Cube. Prism. Parallelepiped. Pyramid. Sections in stereometry.
    4. Geometric ideas for solving problems with parameters.
    5. Functions and their properties. Inverse function. Parity, periodicity.
    6. Perpendicularity of lines and planes. Three perpendicular theorem.
    7. Trigonometric functions. Trigonometric circle. Basic trigonometric formulas.
    8. Trigonometric equations.
    9. Selection of roots in trigonometric equations.
    10. Planimetry. Sine and cosine theorems.
    11. Various stereometric problems on the topic: sections, perpendicularity of lines and planes.
    12. Systems of trigonometric equations.
    13. Trigonometric inequalities.
    14. Inverse trigonometric functions.
    15. Areal considerations in solving geometric problems on a plane.
    16. Angle between crossed lines. The angle between a straight line and a plane.
    17. Numerical sequence. Sequence limit.
    18. Derivative.
    19. Vectors.

    Grade 11

    1. Indicative functions. Exponential equations.
    2. Logarithms. Logarithmic equations.
    3. The angle between crossing lines. The angle between a straight line and a plane.
    The distance between crossing lines.
    4. Solution of cubic rational equations. Rational inequalities. The method of intervals.
    Rationalization method in modulus inequalities, with a root, as well as in exponential and logarithmic inequalities.
    6. Vectors and coordinates in space. Solution of stereometric problems by the coordinate method.
    Vector method for solving stereometric problems.
    7. Sphere. Ball. Cylinder. Cone.
    9. Inscribed and described spheres.
    10. Systems of equations; rational and irrational inequalities (including problems with a parameter).
    11. Sections, perpendicularity of lines and planes.
    12. Repetition: trigonometric equations and inequalities, exponential and logarithmic equations and inequalities
    (including tasks with a parameter).
    13. Solving planimetric problems using algebraic and trigonometric methods.
    14. Elements of number theory. Divisibility. Divisibility criteria. Prime and composite numbers. The main theorem of arithmetic.
    Prime factorization.
    15. Elements of financial mathematics.

    Olympiad physics

    Olympiad mathematics

    Informatics

    Theoretical


    1) Mathematical theory of information. The amount of information.

    2) The theory of information coding. Coding algorithms.

    3) Representation of numerical information. Number systems. Types of number systems. Algorithms for translating numbers.

    4) Representation of numerical information in a computer. Computer arithmetic.

    5) Presentation of text information. Code tables.

    6) Presentation of graphic and sound information.

    7) Fundamentals of the device of computer networks. Network addressing.

    8) Strategy for solving problems "Dynamic programming"

    9) Algebra of logic. Logical operations. The laws of the algebra of logic.

    10) Logical expressions. Simplification of logical expressions.

    11) Analysis of logical expressions.

    12) Systems of logical equations. Solution methods.

    13) Fundamentals of game theory. Search for a winning strategy on the game tree.


    Programming


    1) Formal description of the programming language: syntax diagrams, Backus-Naur notation forms.

    2) Language base: variables, types, assignment. Program structure, language operators.

    3) Features of input and output.

    4) Branching operators. Case analysis strategies.

    5) Operators of the cycle.

    6) Processing of sequences of elements. Standard templates. Typical tasks and methods for their solution.
    Types of correct initialization.

    7) Processing character data.

    8) Working with strings.

    9) Arrays of data. Features of processing arrays.

    10) Algorithms for finding an element in an array and sorting an array.

    11) Processing of multidimensional arrays.

    12) Description of algorithms in the form of functions and procedures. Name localization principle.
    Methods for passing parameters by value and by reference.

    13) Recursion. Drawing up recursive algorithms. Tracing recursive algorithms.


    Unified State Exam


    1) Features of the conduct, verification and appeal of the Unified State Exam in Informatics.

    2) Registration of solutions to the tasks of the second part of the exam.

    3) Examples of tasks from previous years and methods of solving them.

    4) Conducting and analyzing trainings.


    In grades 10 and 11, the list of topics is almost the same, but different degrees of depth and pace of passage.
    Informatics. Teachers


    Merzlyakov Vasily Vladimirovich

    Head of the Department

    Graduated from the Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University and

    Faculty of Pedagogical Education, Moscow State University MV Lomonosov with honors.

    Has extensive experience working with gifted children.

    Unified State Exam Expert.

    Works with specialized groups in grades 10-11.

    Vladimir
    Vladimirovich Usatyuk

    Teacher of informatics at the boarding school. A. N. Kolmogorov (SSC MSU).

    Programmer researcher at Paragon Software.

    Physics teacherGOBU "Phystech- lyceum» nameP.L.Kapitsa.

    The total work experience is 36 years. Teaching experience - 33 years.

    Three times Soros teacher,

    Seven times laureate"All-Russian competition of teachers of physics and mathematics" in the nomination "Mentor of Future Scientists",

    Honorary Worker of General Education of the Russian Federation,

    Winner of the competition for the best teachers in Russia 2006,

    Awarded the medal "People's Recognition of Pedagogical Labor"

    Honored teacher of the Russian Federation.

    Russian language

    • Grade 9
    • Grade 10
    • Grade 11

    Robotics

    Purpose: Teach a child to solve technical and technological issues and give engineering knowledge in accordance with age.

    The robotics course is aimed at professional orientation and acquaintance of children in the field of prototyping, 3D modeling, electronics, soldering and programming of microcontrollers, as well as the basics of mechanics and mechartonics. After completing this course, the child will form the correct picture of the world and the correct direction in further education.
    The entire course is designed for lessons lasting 5 years and students up to the 7th grade.
    Classes are held once a week for 2 astronomical hours.
    For a better and more effective mastering of the material received in the classroom, children are organized into groups in accordance with the class of students at school. The conduct of the classes is adapted in accordance with the intellectual development and age of the child.
    Education is carried out from grade 2 to grade 6 inclusive.

    Programming

    2-3 class
    Basics of arithmetic in Python:

    • Arithmetic operations.
    • Fractions.
    • Measure.
    • Units.
    • Share of the number.
    Basics of layout in Python:
    • Concept of point, line, angle.
    • Simple shapes.
    • Perimeter.
    • Area.
    • Number beam.
    • Coordinate plane.
    4th grade
    Solving problems in Python:
    • Arithmetic operations: repetition and reinforcement.
    • Fractions and operations with fractions.
    • Simple equations.
    • The processes of motion of one body (speed, time, distance),
    • Work processes (labor productivity, time, workload)
    Advanced layout in Python:
    • Draw simple shapes with given dimensions
    • Regular polygons.
    • Spirals.
    • Circle and circle elements.
    • Objects of rotation: ball, cylinder, cone.
    • Rotation, translation, scaling
    Grade 5
    Basics of algebra and geometry in Python:
    • Fractions and decimals: repetition and reinforcement.
    • Equations and formulas.
    • Numbers and scales.
    • Area and volume of figures
    • Charts
    Python Programming Basics:
    • Logic elements and logical operations
    • Branching operators.
    • Loop operators.
    • Creation of scenes and objects.
    6th grade
    Modeling dynamic scenes in Python:
    • Graphic primitives
    • Relationships and proportions
    • Perpendicular and parallel lines
    • Creating simple objects
    • Movement of simple objects
    • Interaction of objects with each other
    Advanced Python Programming:
    • Variable types
    • Basic operators
    • Coordinate relationship methods
    • Creating your own functions
    • Touch, drag and drop
    7th grade
    The beginnings of probability theory in Python:
    • Combinatorial elements
    • Random phenomena
    • The probability of a random event
    • Formula for adding probabilities
    • The formula for multiplying probabilities
    The beginnings of statistics in Python:
    • Data collection
    • Data processing
    • Data exploration
    • Simple statistical analysis
    • Linear function and its graphs
    • Data visualization
    • UML Modeling Basics
    • Basic UML Elements
    • Linking UML Elements
    • Simple UML Models
    8th grade
    Modeling processes in Python:
    • Parameters
    • Power function
    • Equations and inequalities
    • Optimization basics
    • Software Engineering in UML
    • Objects and Classes
    • Object Oriented Programming Principles
    • Process models in UML

    Medical Biophysical Engineering

    Creation

    In our classes, children get acquainted with the wonderful world of ceramics.

    Ceramics is one of the oldest types of artistic creation. Plasticity of clay, its ubiquity, ability
    in combination with water, take any forms, as well as the property of hardening as a result of hardening in fire - they determined its important
    value in human life.

    The lesson program has a specific goal - to help children fall in love with the art of ceramics, to acquaint them with the features and properties
    its various types. In the course of the lesson, students get acquainted with the manufacture of products by hand - modeling a folk toy,
    rope technique for making ceramic products, making tiles and decorating, forming a product on a shuttle
    using a template, drying, decorating, firing.

    Children get acquainted with the basics of ceramics, with many techniques of working with clay, they begin to solve more complex problems in their work:
    emotionally - figurative expression of life impressions, associative perception of an artistic image.

    You can work with clay directly with your hands, without special tools, which significantly expands the horizons of self-expression.
    Clay is very plastic, pliable, but with its own character. Take the clay in your hands and feel the handshake of a friend.

    The classes are taught by a professional ceramic artist.

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The Moscow Institute of Physics and Technology is a higher educational institution of the Russian Federation that trains highly qualified specialists in various fields of modern science and technology. It's no secret that many applicants dream of going to MIPT. This university has a long history and honors its traditions, never lowering educational standards. Each applicant will find a suitable specialty, from the Faculty of Radio Engineering and Cybernetics to the Faculty of Biological and Medical Physics. Recently, MIPT signed a cooperation agreement with Ecole Polytechnique, which will allow successful students to continue their studies in France.

An MIPT graduate is undoubtedly a specialist in demand. And his knowledge is a benchmark for many students of technical universities in the country. However, it should be said that the competitive situation has not changed for many years: to be confident in your enrollment, you need to have a score close to 300 out of 300 possible, since many applicants are winners and prize-winners of All-Russian Olympiads or holders of 100 points on the Unified State Exam in a specialized subject.

But one should not think about the unattainability of a budgetary place at the Moscow Institute of Physics and Technology, each applicant has the opportunity to enter. However, school knowledge is clearly not enough here. For 10 years, the teachers of the Unified State Examination Center have been preparing schoolchildren for the successful passing of the Unified State Exam and admission to MIPT. Working in small groups, up to 9 people, allows the teacher to make virtually individual training with each student.

(2019-2020 academic year,
Classes start on October 1)

Items:

Physics (grades 7-11);

Olympiad physics (grades 7-11) admission based on test results * ;

Mathematics (grades 2-11);

Olympiad mathematics (grades 2-11) admission based on test results * ;

Informatics (grades 9-11);

Robotics (grades 2-6);

Programming (grades 2-8);

Medical Biophysical Engineering (grades 7-9);

Russian language (grades 9-11).

Participants of the courses will be able to repeat the material they passed at school and fill in the gaps in knowledge, get acquainted with the format of the Unified State Exam and prepare for passing exams and performing at the Olympiads.

Our advantages:

Convenient location;

Classes in groups of up to 15 people;

The best teachers with extensive experience of working with students;

The programs were approved by the Academic Council of MIPT;

Payment is monthly;

Physics

7th grade
1. Physical quantities, measurement of physical quantities. Measurement accuracy and error.
2. Mechanical movement. Speed, calculation of the path and travel time.
3. Graphic method for solving problems.
4. Body mass, density.
5. Gravity, body weight. The addition of forces.
6. Force of friction. Friction at rest and sliding.
7. Pressure of solids, liquids and gases. Pascal's law. Hydraulic Press.
8. Calculation of pressure on the bottom and walls of the vessel. Communicating vessels.
9. Atmospheric pressure.
10. Archimedean force. Swimming conditions tel. Aeronautics.
11. Mechanical work, power.
12. Simple mechanisms. Leverage rule. Moment of power.
13. Center of gravity of the body, conditions of balance of bodies.
14. "Golden rule" of mechanics. Efficiency of simple mechanisms.
15. Energy, the law of conservation of energy.

8th grade
1. Mechanical movement. Fundamentals of kinematics.
2. Average speed and average density.
3. Vectors in physics. Addition of vectors.
4. Relativity of speeds.
5. Body trajectory. Dependence of the coordinates and velocity of the body on time.
6. Thermal phenomena. Temperature. Internal energy.
Thermal conductivity. Quantity of heat. Heat capacity.
7. Specific heat of combustion. Aggregate states of matter. Specific heat of fusion. Specific heat of vaporization.
8. Heat balance.
9. Humidity. Absolute and relative air humidity.
10. Electrical phenomena. Electric charge. Charge conservation law.
11. Conductors and dielectrics.
12. Direct current. Electrical circuits. Sources of current.
Voltage. Ammeter. Voltmeter. Resistance. Parallel and series connection of conductors. 13. Work and current power. Thermal effect of the current. Joule-Lenz law.
14. Optics. The law of rectilinear light propagation. The law of reflection. Construction of an image in a flat mirror.
15. The law of refraction of light. Full internal reflection.

Grade 9
1 Kinematics
1.1 Kinematics of a material point
1.2 Rectilinear equal alternating motion
1.3 Uniform movement of the body in a circle
2 Dynamics and conservation laws in mechanics
2.1 Newton's laws
2.2 The law of conservation of energy
2.3 Law of conservation of momentum
2.4 Oscillatory and wave processes, sound
3 Thermal phenomena
3.1 Structure of matter, molecular theory
3.2 Thermal phenomena
3.3 Phase transitions
4 Electrical and magnetic phenomena
4.1 Electrifying bodies
4.2 Direct current
4.3 Magnetism
5 Optics
5.1 Geometric optics
6 Quantum phenomena
7 Basics of conducting experimental work

Grade 10
1. Kinematics. Body movement at an angle to the horizon. Conservation law in kinematics.
2. Dynamics. Strength. Newton's laws.
3. Centripetal acceleration. Body movement in a circle.
4. Impulse. Impulse change law. Impulse conservation law.
5. Molecular kinetic theory. Perfect gas.
6. Equation of state of ideal gas. Internal energy. Temperature.
7. Isoprocesses. Adiabatic process.
8. Work in thermodynamics. Cycles. Cycle efficiency.
9. The first law of thermodynamics.
10. Heat capacity. Molar heat capacity.
11. The law of conservation in thermodynamics.
12. Electric field. Coulomb's law.
13. Electric field strength. The principle of superposition of fields. Power lines.
14. Potential. Potential difference. Voltage.
15. Intensity and potential of the field of a uniformly charged infinite plane and a uniformly charged sphere.
16. Conductors and dielectrics in an electric field. Capacitors.
17. The energy of the electric field. The movement of charged particles in an electric field.
18. Direct current. Electromotive force (EMF). Ohm's law for a complete circuit. Kirchhoff rules.
19. Work and current power. Joule-Lenz law.
20. Magnetic field. Vector of magnetic induction. Magnetic field of the current.
21. Ampere's law. Lorentz force. EMF Induced in a Conductor.
22. Movement of charged particles in a magnetic field.

Grade 11
1. Foundations of molecular kinetic theory. Perfect gas.
2. Equation of state of ideal gas. Internal energy. Temperature.
3. Work in thermodynamics. Cycles. Coefficient of performance (COP) cycles. The first law of thermodynamics. Heat capacity. Molar heat capacity.
4. Phase transitions. Heat balance.
5. Air humidity. Saturated and unsaturated steam.
6. Electrostatics. Field strength and potential of a uniformly charged infinite plane and a uniformly charged sphere.
7. Capacitors. D.C. Electromotive force (EMF). Ohm's law for a complete circuit. Kirchhoff rules.
8. Joule-Lenz law. Work and power in an electrical circuit.
9. Magnetic field. Vector of magnetic induction. The movement of charged particles in an electromagnetic field.
10. Ampere's law. Lorentz force.
11. Magnetic flux. Inductance. EMF Induced in a Conductor. The law of electromagnetic induction. Lenz's rule.
12. Mechanical vibrations. Mathematical pendulum. Spring-loaded pendulum. Energy transformations during oscillatory motion.
13. Oscillatory circuit. Energy transformations during oscillatory motion.
14. Geometric optics. Refraction of light. Thin lenses.
15. Wave optics. Interference. Diffraction.
16. Mechanics. Kinematics. Kinematic equations for displacement and velocity. Equally accelerated movement.
17. The movement of a body thrown at an angle to the horizon. Energy conservation law in kinematic problems.
18. Dynamics. Newton's laws.
19. Statics. Moment of power. Equilibrium conditions for solids.
20. Elements of quantum physics.

Maths

    2nd grade


    1. Techniques for oral addition and subtraction of two-digit numbers. Record addition and subtraction of two-digit numbers in a column. Addition and subtraction of two-digit numbers with a transition through the digit.
    2. Combination property of addition. Subtracting the amount from the number. Subtracting a number from a sum. Using addition and subtraction properties to streamline calculations.
    3. Multiplication and division of natural numbers.
    4. Special cases of multiplication and division with 0 and 1.
    5. The travel property of multiplication.
    6. Multiplication table. Tabular multiplication and division of numbers.
    7. Combination property of multiplication. Multiplication and division by 10 and by 100. Multiplication and division of round numbers.
    9. The order of performing actions in expressions containing addition, subtraction, multiplication and division (with and without parentheses).
    10. Distribution property of multiplication. The rule for dividing a sum by a number. Outside of table multiplication and division. Oral techniques outside of multiplication and division tables. Using the properties of multiplication and division to streamline calculations.


    1. Analysis of the problem, construction of graphical models, planning and implementation of the solution.
    2. Composite tasks in 2-4 actions for all arithmetic operations within 1000.
    3. Problems with letter data. Tasks for calculating the length of a polyline; the perimeter of the triangle and quadrilateral; area and perimeter of rectangle and square.
    4. Addition and subtraction of the studied values \u200b\u200bwhen solving problems.

    Geometric shapes and sizes... Point, line, ray, segment. Parallel and intersecting lines.
    1. Polyline, the length of the polyline. Perimeter of the polygon.
    2. Plane. Angle. Straight, acute and obtuse angles. Perpendicular straight lines.
    3. Rectangle. Square. Properties of the sides and corners of the rectangle and square. Creation of rectangle and square on checkered paper according to the specified lengths of their sides.
    4. Rectangular parallelepiped, cube. Circle and circle, their center, radius, diameter.
    Compass. Drawing patterns from circles using a compass.
    5. Composing figures from parts and dividing figures into parts. Intersection of geometric shapes.
    6. Units of length.
    7. The perimeter of the rectangle and square.
    8. Area of \u200b\u200ba geometric figure. Direct comparison of figures by area. Measurement of area. Units of area (square centimeter, square decimeter, square meter) and the ratio between them. The area of \u200b\u200bthe rectangle. Square area. Squares of shapes composed of rectangles and squares.
    9. Conversion, comparison, addition and subtraction of homogeneous geometric values.


    1. Reading and writing numerical and literal expressions containing addition, subtraction, multiplication and division (with and without parentheses). Calculation of the values \u200b\u200bof the simplest letter expressions for given letter values.


    1. Operation. Object and result of the operation.
    2. Operations on objects, figures, numbers. Direct and reverse operations.
    Finding unknowns: the object of the operation, the operation being performed, the result of the operation.
    3. Program of action. Algorithm. Linear, branched and cyclic algorithms.
    Compilation, recording and execution of algorithms of various types.
    4. Reading and filling in the table. Analysis of table data.
    5. An ordered search of options. Line networks. Paths. Opportunity tree.

    Grade 3

    Numbers and arithmetic operations with them
    1. Count in thousands. Digits and classes: class of units, class of thousands, class of millions, etc. Numbering, comparison, addition and subtraction of multidigit numbers
    (within 1,000,000,000,000). Representation of a natural number as a sum of bit terms.
    2. Multiplication and division of numbers by 10, 100, 1000, etc. Written multiplication and division (without remainder) of round numbers.
    3. Multiplication of a multivalued number. Writing multiplication in a column.
    Multidigit division. Record division by angle.
    Oral addition, subtraction, multiplication and division of multidigit numbers in cases that can be reduced to actions within 100. Simplification of calculations with multidigit numbers based on the properties of arithmetic operations.
    Construction and use of algorithms for the studied cases of oral and written actions with multi-digit numbers.
    The order of performing actions with and without brackets.

    Working with word problems. Analysis of the problem, construction of graphic models and tables, planning and implementation of the solution. Search for different solutions. 1. Composite tasks in 2-4 actions with natural numbers on the meaning of addition, subtraction, multiplication and division, difference and multiple comparison of numbers. 2. Tasks containing the relationship between quantities, of the form a \u003d b c: tasks for movement, tasks for work, tasks for cost. 3. Classification of simple problems of the studied types. A general way to analyze and solve a compound problem.
    4. Tasks to determine the beginning, end and duration of the event.
    5. Tasks to find numbers by their sum and difference.
    6. Tasks for calculating the areas of figures made up of rectangles and squares.
    7. Addition and subtraction of the studied values \u200b\u200bwhen solving problems.


    1. Rectangular parallelepiped, cube, their vertices, edges and faces. Creation of a sweep and a model of a cube and rectangular parallelepiped.
    2. Units of length: millimeter, centimeter, decimeter, meter, kilometer, the ratio between them.
    3. Conversion of geometric values, comparison of their values, addition, subtraction, multiplication and division by a natural number.
    4. Formula. Formulas for the area and perimeter of a rectangle. Formulas for the area and perimeter of a square.
    5. Formula for the volume of a rectangular parallelepiped. The formula for the volume of a cube.

    Algebraic representations.
    1. Equation. Root of the equation. Many roots of the equation. Compound equations that reduce to a chain of simple ones.
    2. Units of mass: gram, kilogram, centner, ton, the ratio between them.

    Mathematical language and elements of logic.
    1. A lot. Element of the set. The signs ∈ and ∉. Setting a set by listing its elements and a property.
    2. Empty set and its designation: Ø. Equal sets. Euler-Venn diagram.
    3. Subset. The signs ⊂ and ⊄. Intersection of many. ∩ sign. Intersection properties of sets. Union of sets. ∪ sign. Union properties of sets.
    4. Classification of elements of a set by property. Streamlining and systematization of information in reference books.
    5. Solving problems for an ordered enumeration of options using tables and a tree of possibilities.

    4th grade

    Numbers and arithmetic operations with them.
    1. Evaluation and estimation of the amount, difference, product, quotient.
    2. Checking the correctness of the calculations.
    3. Fractions. A visual representation of fractions using geometric shapes and on the number ray. Comparison of fractions with the same denominator and fractions with the same numerators.
    4. Division and fractions.
    5. Finding a part of a number, a number by its part and a part that one number is from another.
    6. Addition and subtraction of fractions with the same denominators.
    7. Correct and incorrect fractions. Mixed numbers. Isolation of a whole part from an irregular part. Improper fraction representation of a mixed number. Addition and subtraction of mixed numbers (with the same fractional denominators).
    8. Construction and use of algorithms for the studied cases of actions with fractions and mixed numbers.
    9. Expression and its meaning. Procedure for performing actions.

    Working with word problems. Independent analysis of the problem, building models, planning and implementing the solution. Search for different solutions. Correlation of the obtained result with the condition of the problem, assessment of its likelihood. Checking the task.
    1. Composite tasks in 2-5 actions with natural numbers for all arithmetic operations, difference and multiple comparison. Addition, subtraction and differential comparison of fractions and mixed numbers.
    2. Tasks to find the share of the whole and the whole by its share.
    3. Three types of problems for fractions: finding a part of a number, a number by its part and a fraction that one number is from another.
    4. Tasks for speed, time, distance.
    5. Tasks to calculate the area of \u200b\u200ba right-angled triangle and the areas of figures.

    Geometric shapes and sizes.
    1. Developed corner. Adjacent and vertical corners. The central angle and the angle inscribed in the circle.
    2. Measurement of angles. Protractor. Plotting corners with a protractor.
    3. Units of area: square millimeter, square centimeter, square decimeter, square meter, ar, hectare, the ratio between them.
    4. Study of the properties of geometric shapes using measurements.
    5. Conversion, comparison, addition and subtraction of homogeneous geometric values.
    Multiplication and division of geometric quantities by a natural number.

    Algebraic representations. Inequality. Many solutions to inequality. Severe and non-strict inequality. Signs ≥, ≤. Double inequality.

    Working with information and data analysis. Pie, bar and line charts, motion graphs: reading, interpreting data, plotting.
    1. Working with text: checking understanding; highlighting the main idea, significant comments and examples illustrating them; note-taking.

    Grade 5

    Integers
    1. A series of natural numbers. Decimal notation for natural numbers. Rounding off natural numbers.
    2. Coordinate beam.
    3. Comparison of natural numbers. Addition and subtraction of natural numbers.
    4. Multiplication and division of natural numbers.
    5. Divisors and multiples of natural numbers. Greatest common divisor. Least common multiple. Divisibility criteria.
    6. Prime and composite numbers. Decomposition of numbers into prime factors.
    7. Solving word problems by arithmetic methods.

    Fractions.
    1. Ordinary fractions. The main property of a fraction. Finding a fraction of a number. Finding a number by the value of its fraction. Right and wrong fractions. Mixed numbers. Reducing fractions to NOZ.
    2. Comparison of ordinary fractions and mixed numbers. Arithmetic operations with ordinary fractions and mixed numbers.
    3. Decimal fractions. Comparison and rounding of decimal fractions. Arithmetic operations with decimal fractions. Representation of a decimal fraction as a fraction and a fraction as a decimal.
    4. Proportion. The main property of proportion. Direct and inverse proportional relationships.

    Solving word problems using arithmetic methods.
    1. Translation of the problem statement into mathematical language. Methods for working with the simplest mathematical models.
    2. Drawing up literal expressions and formulas according to the conditions of the problems; Working with expressions and formulas, numeric substitutions, performing the corresponding calculations.
    Solving word problems by the algebraic method.

    Rational numbers.
    1. Positive, negative numbers and the number zero.
    2. Opposite numbers. The absolute value of a number.
    3. Integers. Rational numbers. Comparison of rational numbers. Arithmetic operations with rational numbers. Properties of addition and multiplication of rational numbers.
    Coordinate line. Coordinate plane.

    The quantities. Dependencies between quantities.
    1. Units of length, area, volume, mass, time, speed.
    2. Examples of dependencies between quantities. Representation of dependencies in the form of formulas. Calculations by formulas.

    Numeric and literal expressions. Equations.
    1. Numerical expressions. The value of a numeric expression. The order of actions in numerical expressions. Literal expressions. Expansion of brackets. Similar terms, bringing similar terms. Formulas.
    2. Equations. Root of the equation. Basic properties of equations. Solving word problems using equations.

    Geometric figures. Measurement of geometric quantities.
    1. Segment. Segment creation. Line segment length, broken line. Measuring the length of a segment, building a segment of a given length. Perimeter of the polygon. Plane. Straight. Ray.
    2. Angle. Types of angles. The degree measure of the angle. Measuring and plotting angles with a protractor.
    3. Rectangle. Square. Triangle. Types of triangles. Circumference and circle. Circumference.

    6th grade

    1. Elements of logic.
    2. The concept of denial.
    3. Variable. Variable expressions.
    4. Number line. Negative numbers. The concept of a negative number and actions with it. The absolute value of a number.
    5. Rational numbers and decimal fractions.
    6. Fractions. Actions and expressions with fractions.
    7. Tasks for movement.
    8. The concept of average values. Average.
    9. The concept of relationship. Scale. The concept of proportion and the main property of proportion. Actions with proportions and their transformation.
    10. Dependencies between quantities. Direct and inverse proportionality and their graphs. Solving problems using proportions.
    11. Concept of interest. Percentage growth. Interest problems.
    12. Coefficient. Similar terms. Expression transformations.
    13. Linear equations. Graphs of dependence of quantities.
    14. Solving problems with applied content by the method of equations.
    15. Logical following and equivalence. Denial of following. Reverse statements.
    16. Images and definitions of geometric concepts.
    17. Properties of geometric shapes.
    18. Measurement of geometric values. Length, area, volume.

    7th grade

    1. Fractions. Actions with fractions 2. Modulus of number. The geometric meaning of the module.
    3. A lot. Elements of the set. Subset.
    4. Determination of the degree with a natural indicator. Multiplication and division of degrees.
    5. Monomial. Actions with monomials. Identities.
    6. Polynomial. Calculating the values \u200b\u200bof a polynomial and its standard form. Actions with polynomials.
    7. Equations. Roots of linear equations in one variable. Solving problems using equations.
    8. Factorization. Proof of identities. Solving equations.
    9. Function. Formula. Calculating the values \u200b\u200bof a function using a formula. Function graph. Mutual arrangement of graphs of functions.
    10. Linear equations with two variables and their graphs.
    11. Systems of equations. Methods for solving systems of equations. Graphical way. Solving problems using systems of equations.
    12. Initial geometric concepts. Line, point, ray, segment. Corners. Measurement of angles.
    13. Signs of parallelism of two lines. Axiom of parallel lines.
    14. Vector. Types and equality of vectors. Actions with vectors. The projection of the vector onto the coordinate axis.
    15. Triangles. Signs of equality of triangles.
    16. Relationship between sides and angles of a triangle. Right triangle.
    17. Circumference. The length and area of \u200b\u200bthe circle. Ball.
    18. Elements of combinatorics. Counting the number of options. Combinations with repetitions. Statistical characteristics.
    19. The probability of occurrence of events. The classical scheme for determining the probability.

    8th grade

    1. Monomials. Polynomials. Actions with polynomials. Abbreviated multiplication formulas. Expression transformations.
    Degree with a natural indicator.
    2. Function. Formula. Calculating the values \u200b\u200bof a function using a formula. Function graph.
    3. Square roots. Approximate extraction of arithmetic square roots. Exact and approximate values.
    Function y \u003d x1 / 2 and its graph.
    4. Transformations of expressions containing a root.
    5. Function y \u003d 1 / x and its graph. Quadratic function and its graph.
    6. Quadratic equations. Full square selection method.
    7. Module number.
    8. Linear function. Linear function graph. Plot of the modulus of a linear function.
    9. Parameters in equations.
    Logical enumeration in problems with a parameter.
    10. Elements of number theory.
    11. Severability. Divisibility criteria. Prime and composite numbers. The main theorem of arithmetic.
    12. Decomposition into prime factors. Greatest common divisor (GCD). Least Common Multiple (LCM).
    14. Triangles. The problem of dividing a segment.
    15. Figures on a plane. Areal considerations.

    Grade 9

    1. Rational equations. Selection of roots. Range of permissible values \u200b\u200b(ODZ). Equivalent transitions. Quadratic equations.
    Biquadratic equations. Cubic equations.
    2. Parameters in rational equations. Logical enumeration in problems with a parameter. Parameters in quadratic equations.
    3. Right-angled triangle. Medians, bisectors, and heights in a triangle. Triangle area formulas.
    4. Rational inequalities. The method of intervals.
    5. Parameters in rational equations and inequalities.
    6. Trapezium.
    7. Systems of nonlinear equations.
    8. Solving problems using systems of equations.
    9. Irrational equations. ODZ in irrational equations. Equivalent transitions.
    10. Equations with modulus.
    11. Irrational inequalities. Inequalities with the module.
    11. Quadrangles.
    12. Parameters in irrational equations and inequalities.
    13. Problems of segment division
    14. Sets. Statements. Theorems.
    15. Sets on the plane.
    16. Areal considerations when solving planimetric problems.
    17. Numerical sequence. Arithmetic and geometric progressions.
    18. Circles.
    19. Different tasks for planimetry.

    Grade 10

    1. Decomposition of a polynomial into sets. Cubic equations. Rational equations. Rational inequalities.
    The method of intervals. Irrational equations. Equations with modulus.
    2. Method of rationalization for irrational inequalities and inequalities with modulus.
    3. Cube. Prism. Parallelepiped. Pyramid. Sections in stereometry.
    4. Geometric ideas for solving problems with parameters.
    5. Functions and their properties. Inverse function. Parity, periodicity.
    6. Perpendicularity of lines and planes. Three perpendicular theorem.
    7. Trigonometric functions. Trigonometric circle. Basic trigonometric formulas.
    8. Trigonometric equations.
    9. Selection of roots in trigonometric equations.
    10. Planimetry. Sine and cosine theorems.
    11. Various stereometric problems on the topic: sections, perpendicularity of lines and planes.
    12. Systems of trigonometric equations.
    13. Trigonometric inequalities.
    14. Inverse trigonometric functions.
    15. Areal considerations in solving geometric problems on a plane.
    16. Angle between crossed lines. The angle between a straight line and a plane.
    17. Numerical sequence. Sequence limit.
    18. Derivative.
    19. Vectors.

    Grade 11

    1. Indicative functions. Exponential equations.
    2. Logarithms. Logarithmic equations.
    3. The angle between crossing lines. The angle between a straight line and a plane.
    The distance between crossing lines.
    4. Solution of cubic rational equations. Rational inequalities. The method of intervals.
    Rationalization method in modulus inequalities, with a root, as well as in exponential and logarithmic inequalities.
    6. Vectors and coordinates in space. Solution of stereometric problems by the coordinate method.
    Vector method for solving stereometric problems.
    7. Sphere. Ball. Cylinder. Cone.
    9. Inscribed and described spheres.
    10. Systems of equations; rational and irrational inequalities (including problems with a parameter).
    11. Sections, perpendicularity of lines and planes.
    12. Repetition: trigonometric equations and inequalities, exponential and logarithmic equations and inequalities
    (including tasks with a parameter).
    13. Solving planimetric problems using algebraic and trigonometric methods.
    14. Elements of number theory. Divisibility. Divisibility criteria. Prime and composite numbers. The main theorem of arithmetic.
    Prime factorization.
    15. Elements of financial mathematics.

    Olympiad physics

    Olympiad mathematics

    Informatics

    Theoretical


    1) Mathematical theory of information. The amount of information.

    2) The theory of information coding. Coding algorithms.

    3) Representation of numerical information. Number systems. Types of number systems. Algorithms for translating numbers.

    4) Representation of numerical information in a computer. Computer arithmetic.

    5) Presentation of text information. Code tables.

    6) Presentation of graphic and sound information.

    7) Fundamentals of the device of computer networks. Network addressing.

    8) Strategy for solving problems "Dynamic programming"

    9) Algebra of logic. Logical operations. The laws of the algebra of logic.

    10) Logical expressions. Simplification of logical expressions.

    11) Analysis of logical expressions.

    12) Systems of logical equations. Solution methods.

    13) Fundamentals of game theory. Search for a winning strategy on the game tree.


    Programming


    1) Formal description of the programming language: syntax diagrams, Backus-Naur notation forms.

    2) Language base: variables, types, assignment. Program structure, language operators.

    3) Features of input and output.

    4) Branching operators. Case analysis strategies.

    5) Operators of the cycle.

    6) Processing of sequences of elements. Standard templates. Typical tasks and methods for their solution.
    Types of correct initialization.

    7) Processing character data.

    8) Working with strings.

    9) Arrays of data. Features of processing arrays.

    10) Algorithms for finding an element in an array and sorting an array.

    11) Processing of multidimensional arrays.

    12) Description of algorithms in the form of functions and procedures. Name localization principle.
    Methods for passing parameters by value and by reference.

    13) Recursion. Drawing up recursive algorithms. Tracing recursive algorithms.


    Unified State Exam


    1) Features of the conduct, verification and appeal of the Unified State Exam in Informatics.

    2) Registration of solutions to the tasks of the second part of the exam.

    3) Examples of tasks from previous years and methods of solving them.

    4) Conducting and analyzing trainings.


    In grades 10 and 11, the list of topics is almost the same, but different degrees of depth and pace of passage.
    Informatics. Teachers


    Merzlyakov Vasily Vladimirovich

    Head of the Department

    Graduated from the Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University and

    Faculty of Pedagogical Education, Moscow State University MV Lomonosov with honors.

    Has extensive experience working with gifted children.

    Unified State Exam Expert.

    Works with specialized groups in grades 10-11.

    Vladimir
    Vladimirovich Usatyuk

    Teacher of informatics at the boarding school. A. N. Kolmogorov (SSC MSU).

    Programmer researcher at Paragon Software.

    Physics teacherGOBU "Phystech- lyceum» nameP.L.Kapitsa.

    The total work experience is 36 years. Teaching experience - 33 years.

    Three times Soros teacher,

    Seven times laureate"All-Russian competition of teachers of physics and mathematics" in the nomination "Mentor of Future Scientists",

    Honorary Worker of General Education of the Russian Federation,

    Winner of the competition for the best teachers in Russia 2006,

    Awarded the medal "People's Recognition of Pedagogical Labor"

    Honored teacher of the Russian Federation.

    Russian language

    • Grade 9
    • Grade 10
    • Grade 11

    Robotics

    Purpose: Teach a child to solve technical and technological issues and give engineering knowledge in accordance with age.

    The robotics course is aimed at professional orientation and acquaintance of children in the field of prototyping, 3D modeling, electronics, soldering and programming of microcontrollers, as well as the basics of mechanics and mechartonics. After completing this course, the child will form the correct picture of the world and the correct direction in further education.
    The entire course is designed for lessons lasting 5 years and students up to the 7th grade.
    Classes are held once a week for 2 astronomical hours.
    For a better and more effective mastering of the material received in the classroom, children are organized into groups in accordance with the class of students at school. The conduct of the classes is adapted in accordance with the intellectual development and age of the child.
    Education is carried out from grade 2 to grade 6 inclusive.

    Programming

    2-3 class
    Basics of arithmetic in Python:

    • Arithmetic operations.
    • Fractions.
    • Measure.
    • Units.
    • Share of the number.
    Basics of layout in Python:
    • Concept of point, line, angle.
    • Simple shapes.
    • Perimeter.
    • Area.
    • Number beam.
    • Coordinate plane.
    4th grade
    Solving problems in Python:
    • Arithmetic operations: repetition and reinforcement.
    • Fractions and operations with fractions.
    • Simple equations.
    • The processes of motion of one body (speed, time, distance),
    • Work processes (labor productivity, time, workload)
    Advanced layout in Python:
    • Draw simple shapes with given dimensions
    • Regular polygons.
    • Spirals.
    • Circle and circle elements.
    • Objects of rotation: ball, cylinder, cone.
    • Rotation, translation, scaling
    Grade 5
    Basics of algebra and geometry in Python:
    • Fractions and decimals: repetition and reinforcement.
    • Equations and formulas.
    • Numbers and scales.
    • Area and volume of figures
    • Charts
    Python Programming Basics:
    • Logic elements and logical operations
    • Branching operators.
    • Loop operators.
    • Creation of scenes and objects.
    6th grade
    Modeling dynamic scenes in Python:
    • Graphic primitives
    • Relationships and proportions
    • Perpendicular and parallel lines
    • Creating simple objects
    • Movement of simple objects
    • Interaction of objects with each other
    Advanced Python Programming:
    • Variable types
    • Basic operators
    • Coordinate relationship methods
    • Creating your own functions
    • Touch, drag and drop
    7th grade
    The beginnings of probability theory in Python:
    • Combinatorial elements
    • Random phenomena
    • The probability of a random event
    • Formula for adding probabilities
    • The formula for multiplying probabilities
    The beginnings of statistics in Python:
    • Data collection
    • Data processing
    • Data exploration
    • Simple statistical analysis
    • Linear function and its graphs
    • Data visualization
    • UML Modeling Basics
    • Basic UML Elements
    • Linking UML Elements
    • Simple UML Models
    8th grade
    Modeling processes in Python:
    • Parameters
    • Power function
    • Equations and inequalities
    • Optimization basics
    • Software Engineering in UML
    • Objects and Classes
    • Object Oriented Programming Principles
    • Process models in UML

    Medical Biophysical Engineering

    Creation

    In our classes, children get acquainted with the wonderful world of ceramics.

    Ceramics is one of the oldest types of artistic creation. Plasticity of clay, its ubiquity, ability
    in combination with water, take any forms, as well as the property of hardening as a result of hardening in fire - they determined its important
    value in human life.

    The lesson program has a specific goal - to help children fall in love with the art of ceramics, to acquaint them with the features and properties
    its various types. In the course of the lesson, students get acquainted with the manufacture of products by hand - modeling a folk toy,
    rope technique for making ceramic products, making tiles and decorating, forming a product on a shuttle
    using a template, drying, decorating, firing.

    Children get acquainted with the basics of ceramics, with many techniques of working with clay, they begin to solve more complex problems in their work:
    emotionally - figurative expression of life impressions, associative perception of an artistic image.

    You can work with clay directly with your hands, without special tools, which significantly expands the horizons of self-expression.
    Clay is very plastic, pliable, but with its own character. Take the clay in your hands and feel the handshake of a friend.

    The classes are taught by a professional ceramic artist.

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