Effective methods for teaching mathematics and preparing for exams

Mathematics and Russian are compulsory subjects in the Unified State Exam. They are taken even by those who do not intend to enter universities for technical or philological specialties. If future tests in their native language worry a few, then the upcoming assault on the fortress, which is defended by the queen of sciences, causes confusion among most eleventh graders. Therefore, it is not surprising that almost all graduates are looking for ways to prepare for the Unified State Exam in mathematics as effectively as possible.

The secret to successfully preparing for the exam is simple: it is thoughtful and systematic work. The sooner you get down to business, the greater the chances of getting good results. You need to understand the principles of solving mathematical problems, then during the exam itself you will be able to solve any tasks without being afraid of unusual wording or conditions.

Preparing for the lesson. Downloads

Useful materials for conducting extraordinary classes in primary and secondary schools.

1. Work programs in mathematics, algebra, geometry
2. Teaching aids on mathematics, algebra, geometry
3. Development of lessons in mathematics, algebra, geometry
4. Visual and handout materials on mathematics, algebra, geometry

To the begining

Work program of the mathematics curriculum “Preparation for the Unified State Exam at the profile level”

Private educational institution "Albion Plus" Ivanovo

Approved

"___" ___________ 201__

Head of the institution

__________________

WORKING PROGRAM OF THE MATHEMATICS COURSE

“PREPARATION FOR THE PROFILE LEVEL Unified State Exam”

The program is designed for group and individual lessons

with 11th grade students of secondary schools and students

graduate courses of secondary vocational education institutions.

Implementation period: 1 academic year (70 lessons)

G. Ivanovo

2015

EXPLANATORY NOTE

.

Work program of the mathematics curriculum “Preparation for the Unified State Exam at the profile level”

designed to:

· ensuring the constitutional right of citizens of the Russian Federation to receive high-quality general education, allowing them to continue their education at a higher level;

· ensuring that students achieve learning outcomes in accordance with federal state educational standards;

· providing graduates of educational institutions of secondary professional level with favorable conditions for passing a unified entrance exam to continue their education, i.e., increasing their general educational level in mathematics to match the level of graduates of secondary schools;

· organizing additional educational process in accordance with the requests of citizens.

When implementing the work program, the following goals and objectives are achieved:

o formation of a competent person who clearly understands his or her potential capabilities;

o development of a teenager’s personality by including him in various types of value-based human activities: study, cognition, communication, adaptation to new conditions;

o developing a broader understanding of the ideas and methods of mathematics;

o development of logical thinking, spatial imagination, algorithmic and graphic culture, critical thinking at the level necessary for future professional activity, as well as subsequent studies in higher education;

o education of personal culture through mathematics;

o mastery of advanced mathematical knowledge and the necessary terminology, their effective use and application of knowledge in non-standard and problematic situations;

o intellectual development of students, formation of logical skills of identifying the main thing, comparison, analysis, synthesis, generalization, systematization, abstraction;

o ensuring guaranteed quality of training of graduates for entering a university and continuing education, as well as for professional activities requiring a high mathematical culture.

INFORMATION ABOUT THE PROGRAM.

The work program is compiled on the basis of the requirements for the results of mastering the basic educational program of secondary general education, implemented in secondary educational institutions of the city of Ivanovo;

- an exemplary curriculum recommended by the Ministry of Education and Science of the Russian Federation (letter from the Ministry of Education and Science of the Russian Federation dated January 1, 2001 “On exemplary programs in academic subjects of the Federal Basic Curriculum”)

-Federal component of the state educational standard of the basic level of general education, approved by the order of the Ministry of Education and Science of the Russian Federation “On approval of the federal component of state standards of primary, general and secondary (complete) general education” (Order of the Ministry of Education of Russia)

The content of the program is developed on the basis of the mandatory minimum content of basic educational programs: secondary (complete) general education, in-depth study of mathematics, as well as specialized training programs. At the same time, a codifier and specification of demonstration versions of test and measurement materials were used for conducting the unified state exam in mathematics in 2020.

The mathematics curriculum program “Preparation for the profile-level Unified State Exam” is an addition to the school component of mathematics education for students both who have some gaps in knowledge in the main course and those who want to improve their basic knowledge in order to enter universities. A serious part of the course is devoted to repetition and generalization of basic knowledge necessary for successful final and entrance assessments. Much attention when studying the course is given to mastering methods for solving problems related to the study of functions (including when solving problems, equations and inequalities), their differentiation and integration, as well as mathematical modeling of applied processes, for example, the study of economic processes expressed in mathematical language . Particular attention is paid to solving non-standard problems of a combined nature.

When drawing up the program, topics were selected for repetition, generalization and in-depth study in preparation for the Unified State Exam. The course contributes not only to the systematization of school knowledge, but also to its significant expansion and the acquisition of additional experience in the application of non-standard methods of solving problems of an increased level of complexity, which undoubtedly serves the intellectual and general cultural development of adolescents, and also equips students with special and general educational skills that allow them independently navigate, analyze and find ways to resolve non-standard and unfamiliar situations.

A plan has been drawn up calculating the number of hours by topic.

SCOPE OF THE COURSE AND ORGANIZATION OF THE EDUCATIONAL PROCESS.

The course is designed to be implemented for 11th grade students or graduate college students during the academic year in the amount of 112 astronomical hours. The main form of organizing the educational process is weekly classes (2 times a week) lasting 1.5 astronomical hours. Classes are planned - lectures on studying new material (to study topics not included in the school course), classes on problem solving and workshops on practice testing, the duration of which can increase up to two hours.

TYPES AND FORMS OF CONTROL

Types and forms of control during training are: ongoing control in the form of oral and written questioning, as well as control in the form of independent work, home tests and tests on individual topics, final testing on tests, the structure of which corresponds to the demo version of the Unified State Exam in Mathematics 2016.

EXPECTED OUTCOMES OF STUDYING THE COURSE.

As a result of studying the course, the student gets the opportunity to know/understand/be able to:

× master basic mathematical knowledge;

× to master the standard apparatus for solving the simplest equations and inequalities and their use as the main means of mathematical modeling of applied problems;

× understand the system for solving basic planimetric and stereometric problems;

× be able to apply the basic theorems of planimetry and stereometry;

× systematize all types of trigonometry problems according to methods of solution;

× know the basic formulas of trigonometry and be able to solve the simplest trigonometric equations;

× know the necessary methods for solving trigonometric equations of an increased level of complexity;

× know methods for studying functions using differentiation;

× know the properties of logarithmic and exponential functions, and be able to use them to transform logarithmic and power expressions;

× know standard methods for solving equations;

× be able to solve algebraic, trigonometric, exponential and logarithmic equations and inequalities of an increased level of complexity;

× be able to solve systems of equations and inequalities;

× be able to depict in drawings and drawings geometric figures specified by the conditions of the tasks, including constructing sections;

× be able to reduce the conditions of applied economic problems to solving equations and inequalities.

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At the same time, the amount of knowledge must be sufficient to successfully pass the Unified State Exam at the profile level.

USED ​​BOOKS

[1] Student Preparation Toolkit. Unified State Exam 2020. Mathematics. . . . Moscow "Intellect-Center" 2020.

[2] Optimal bank of tasks for preparing for the Unified State Exam 2020. Mathematics. . . . Moscow Intellectcenter 2020.

[3] Unified State Exam 2020. Mathematics. Problem solving. We rent without any problems. , .

[4] Non-standard methods for solving equations and inequalities. Preparation for the Unified State Exam, edited by. Ed. "Legion" 2013.

[5] Solving inequalities with one variable. , . "Legion" 2015

[6] Mathematics. A problem with economic content. Profile level. Edited by , . Ed. "Legion" 2020.

[7] Mathematics. Preparation for the Unified State Exam. Solving problems of stereometry using the coordinate method. Ed. "Legion" 2020.

[8] Mathematics of the Unified State Examination. Typical test tasks 2020, edited by.

[9] Mathematics. Probability theory. Preparation for the Unified State Exam 2020. Ed. "Legion" 2020.

Internet resources

1. Mathematics. Open bank of tasks for the Unified State Exam 2020. https://www. mathege. ru

2. I will pass the Unified State Examination Gushchin Dmitry. https://sdamgia. ru/

CONTENT OF THE WORK PROGRAM

I.

Practice-oriented tasks. (6 hours).

Actions with rational numbers (decimal and ordinary fractions, positive and negative numbers), numerical expressions and their meanings, solving arithmetic problems of various contents: purchase cost, calculation by tariffs, problems involving percentages and directly and inversely proportional quantities, arithmetic mean, optimal choice of conditions , converting units from one system to another, using formulas in arithmetic problems.

II.

Solving rational and irrational equations (13.5 hours).

Rational expressions and their transformation. Solving integer and fractional rational equations. Methods for solving high degree equations. Dividing a polynomial by a polynomial. Solving systems of rational equations. Irrational expressions and their transformations, calculation of values. Irrational equations, equivalent transition method. Solving problems using equations and systems of equations.

III.

Trigonometric expressions and equations (15 hours).

Definition of trigonometric functions of a numeric argument. Degree and radian measure of angle. Basic trigonometric identities. Properties of trigonometric functions (parity, periodicity, constant sign). Trigonometric formulas and their applications. Convert trigonometric expressions using addition formulas, double angle formulas, reduction formulas, and reduction formulas. Solving simple trigonometric equations. Methods for solving trigonometric equations of an increased level of complexity (variable replacement method, factorization method, equations reducible to quadratic equations, homogeneous equations, use of formulas for reducing degrees and universal substitution). Solving trigonometric equations of an increased level of complexity (C1) from the Unified State Examination materials. Selection of roots of trigonometric equations from a given finite interval.

IV.

Derivative of a function and its application (7.5 hours).

Definition of the derivative of a function, table of derivatives, rules for differentiating functions, differentiating a complex function, meaning of the derivative. Geometric and physical meaning of derivative. Studying a function using its derivative. The largest and smallest values ​​of a function on a segment.

V.

Integration of functions (3 hours).

Definition of an antiderivative function, table of antiderivatives for individual functions, rules for integrating functions, integration of a complex function f(kx+b). Calculation of a definite integral using the Newton–Leibniz formula. Area of ​​a curved trapezoid geometric interpretation.

VI.

Exponential and logarithmic expressions and equations (7.5 hours).

Degree with natural, integer, rational and irrational exponent. Properties of degree. Converting expressions containing powers. Irrational expressions containing roots of the nth degree, and their transformation using the properties of roots and properties of degrees with a rational exponent.

Exponential functions and their properties. The concept of logarithm and logarithmic function. Properties of logarithms, basic logarithmic identity, transformation of logarithmic expressions. Solving simple logarithmic and exponential equations. Exponential and logarithmic equations of an increased level of complexity, methods for solving them. Solving combined equations with trigonometric, logarithmic and exponential functions (C1) from the Unified State Exam materials.

VII.

Logarithmic and exponential inequalities and systems of inequalities (10.5 hours).

Application of the properties of logarithmic and exponential functions to solve simple logarithmic and exponential inequalities. The role of ODZ of logarithmic inequalities. Variable replacement method. Solving logarithmic inequalities with a variable in the base. Solving inequalities of an increased level of complexity using the interval method. Rationalization method for solving inequalities. Solving inequalities and systems of inequalities of an increased level of complexity based on materials from the Unified State Exam (C3).

VIII.

Solving planimetric problems (6 hours).

Calculation of lengths in triangles (Pythagorean theorem, sine and cosine theorems), midline of a triangle and trapezoid, inscribed and circumscribed circle radii for polygons, properties of inscribed and circumscribed polygons. Angles on a plane: adjacent and vertical angles, angles with parallel lines and transversals, angles in triangles and polygons, angles in a circle. Areas of basic geometric figures, areas of geometric figures on a coordinate plane, areas of figures on a checkered basis. Elements of trigonometry in planimetry: determining trigonometric functions of an acute angle of a right triangle, solving right triangles, using trigonometry to find elements of arbitrary triangles.

IX.

Solving stereometric problems (24 hours).

The main types of polyhedra, finding their elements, areas of the full and lateral surfaces, finding the volume. Regular polyhedra and their properties. Construction of sections of polyhedra. Basic bodies of rotation, their elements, surface areas and volumes. The relative position of bodies of rotation and polyhedra, inscribed and circumscribed spheres. The angle between straight lines in space, the angle between planes in space, the angle between a straight line and a plane. The distance from a point to a line and a plane, the distance between intersecting lines. Sectional area of ​​a polyhedron. Coordinate system in space. A coordinate-vector method for solving problems of an increased level of complexity. Solving problems of an increased level of complexity (C2) from Unified State Examination materials.

X.

Elements of probability theory (4.5 hours).

Determination of the probability of an event, the probability of an opposite event, the probability of combining incompatible and joint events, the probability of the intersection of independent and dependent events, Bernoulli's formula.

XI.

Problems with economic content (7.5 hours).

Simple and compound percentages, shares, ratios. Tasks for banking operations: loans, deposits. Production and everyday tasks, economic tasks to find extreme points. Solving economic problems based on materials from the Unified State Exam 2020.

XII.

Solution and analysis of training test papers in the format of the demo version of the Unified State Exam 2016

( 7 o'clock).

CALENDAR - THEMATIC PLANNING

Webinars

How to make a lesson modern and memorable? Let's talk about the possibilities of the electronic form of the textbook and electronic educational resources. Let's talk about the role of the educational and methodological complex in organizing specialized education, and touch on the topic of individual trajectories of learning mathematics for children with different backgrounds. What should a mathematics teacher know and be able to do? Together with experts, we will analyze what competencies teachers need to master, and delve into the history of professional standards and labor functions of a school teacher.

• We prepare students in grades 5–6 to study geometry courses in grades 7–11
• Electronic educational resources for mathematics lessons
• Mathematics. Profile training
• Development of competencies of primary and secondary school mathematics teachers
• Organization of specialized training using teaching materials in mathematics

Other webinars on mathematics
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Preparation for the Unified State Exam in mathematics using new technologies

Prepared by a math teacher

Zabroda Galina Sergeevna

“Preparation for the Unified State Exam in Mathematics

using new technologies"

The main task facing every mathematics teacher is to prepare students as best as possible for passing the Unified State Exam. It's good if the child is motivated, but what if there are no motivated students in the class? Such preparation becomes possible with the use of information technology.

Now we cannot imagine our life without a computer. Neither teachers nor students can do without it. The computer is a huge indispensable assistant. In the context of informatization of education, the teacher is faced with the task of improving methods, teaching aids and ways of organizing practical and cognitive activities of students based on the use of ICT tools.

I have accumulated some experience in using ICT in mathematics lessons in order to improve the level of mathematical preparation of students.

One of the most effective methods of preparing for the Unified State Exam is the method of solving test tasks. Analyzing my experience, I come to the conclusion that the use of ICT in preparing for testing, conducting tests on a computer, leads to an increase in the percentage of training and quality of knowledge, sometimes they remain at the same level, but nowhere does it decrease. As they say, it is better to see once than to hear several times. And I agree with this. Computer simulators help develop practical skills. The use of ICT in preparation for the Unified State Exam gives a new quality in the transfer and assimilation of a knowledge system.

In classes devoted to preparing for the final certification in mathematics, first, using a computer, I display theoretical material on the projector screen, or on the computer screen at which the students are sitting. After reading this material and discussing the main points of this material, I display tasks similar to those presented in the demo Unified State Exam. The practical application of test technologies in preparation for the Unified State Exam has shown that students familiar with the techniques of working on tests are superior in their level of preparation to schoolchildren who prepared using regular textbooks and problem books, which, of course, cannot be excluded.

Forms of ICT use.

1. Use of ready-made electronic products.

They allow you to intensify the activities of the teacher and student, and improve the quality of teaching the subject. Electronic educational publications based on preparation for the Unified State Exam and trial testing allow you to:

1) create psychological conditions for including students in testing;

2) effectively solve the problem of more complete immersion in the specific features of test tasks;

3) to develop the ability to navigate educational material, the ability to quickly act and choose.

When preparing for the Unified State Exam, I use the disk “Interactive course for preparing for the Unified State Exam. Mathematics". This disk contains recommendations for carrying out work in the process of preparing for the exam, methodological and psychological recommendations, a codifier, etc. The principles of constructing methodological preparation for the Unified State Exam are determined. “Interactive preparation course for the Unified State Exam. Mathematics" contains theoretical material, tasks with analyzed solutions. The manual contains lesson notes with tasks for practicing solution skills and homework. This disc is interesting because it can be recommended to students for independent work. In this case, they have the opportunity to familiarize themselves with theoretical information on a topic of interest, with examples of solving mathematical problems, and also try their hand at answering test questions on a studied topic or solving individual problems, where the computer checks the correctness of their answers.

The next disk that I use in my work is “Mathematics Task Generator”. The mathematics assignment generator is capable of generating a test or independent work on any topic in a mathematics course within a few seconds, selecting the required completeness of the printed material.

Testing is one of the types of knowledge control, which has recently become increasingly part of the life of a modern school. The high effectiveness of control programs is determined by the fact that they strengthen feedback in the teacher-student system. Test programs allow you to quickly evaluate the result of your work and accurately identify topics in which there are gaps in knowledge.

"Unified State Exam Simulator in Mathematics." The proposed computer program allows me to monitor the correctness of students' completion of test tasks and assess the level of knowledge, which, if desired, can be increased by periodic training.

2. Use of Internet resources.

The Internet has enormous potential for educational services and is becoming an integral part of modern education. The use of Internet resources greatly facilitates the work of a mathematics teacher when organizing the educational process.

I widely use in my work the Internet portals of the Unified State Examination (Federal Institute of Pedagogical Measurements) www.fipi.ru

–
Testing and measuring materials, open segment of FBTZ, methodological letters, publications recommended in preparation for the Unified State Examination
Center for Assessment of the Quality of Education (www.centeroko.ru) – administrative and regulatory documents, information and reference materials, demo versions, Unified State Examination results

Educational resources on the Internet - mathematics ( www.alleng.ru) demo version of the Unified State Exam, standard versions of the Unified State Exam, standard thematic tasks of the Unified State Exam, educational (reference) manuals for preparing for the Unified State Exam.

The following pages of the website (https://www.alleng.ru) became assistants in our work: “For a mathematics lesson”, “Solving problems in mathematics”, “Exam in mathematics”, “Mathematics for applicants”, “Formula in mathematics”, “ Textbooks, reference books, manuals." Here you can find demo versions of previous years, materials and tests for preparing for the Unified State Examination in mathematics, options for final exams in mathematics of previous years with answers and solutions. Also, 11th grade students can download any study guides to prepare for the Unified State Exam.

Open bank of tasks in mathematics for the Unified State Exam (www.mathege.ru) - demo version, training work, tasks similar to exam ones.

There is a catalog by tasks, by content, by skills. On the pages of this site you can not only obtain this or that information on a topic of interest, but also perform training and diagnostic work on-line. My 11th grade students became regular participants in this project. The proposed system allows each student to complete tasks in the quantity required for him and at a pace accessible to him, regardless of the amount of work and the speed at which others complete it. (They either print the results or photograph them on their phone)

www.school-tests.ru – testarius. Computer program for preparing for the Unified State Examination and State Examination (GIA) (training and examination modes)

https://www.uztest.ru - Mathematics teacher's office The site is organized in the form of a virtual teacher's office, which contains information resources and interactive services for preparing and conducting mathematics classes.

https://uztest.ru/, where trial testing of students is carried out online using tasks similar to those that graduates will have at the Unified State Exam, followed by evaluation of their answers. Organize control of students' knowledge. There are more than 13,000 problems in all areas of school mathematics. The program on the site https://uztest.ru/ automatically generates individual assignments for each student, according to the conditions set by the teacher; there is no need to waste time checking assignments - the results of students’ work are visible on the computer. I organize skills training using a training system. Training is a group of simple, similar examples. If a student solves an example incorrectly, he is shown a detailed explanation and given the next, similar example.

In addition, I maintain an online journal of student evaluations: I post student grades in the journal on the Network City “Education” website - which means the information is always available to the student and his parents.

Working on a computer, the student has the opportunity to complete the solution of any educational task, since he is provided with the necessary assistance or the solution is fully explained. All this allows us to largely eliminate one of the important reasons for a negative attitude towards learning - failure due to a lack of understanding of the essence of the problem and significant gaps in knowledge.

I think that the obvious positive aspects of this work are that the children not only restore gaps in knowledge, but learn to extract the necessary information from educational and scientific texts, collect material on a given topic, create a database of tasks, and check the level of their preparation for the exam.

I pay great attention to diagnosing gaps in students’ knowledge. I monitor both the entire class and each student individually.

I organize differentiated training based on diagnostic data. Thus, when preparing for the Unified State Exam, I monitor how each key topic is mastered over time and plan my further work based on the information received.

Diagnosis of students' level of learning is carried out on the basis of testing students using test and measurement materials.

In order to increase the efficiency of preparation for the Unified State Exam, we carried out diagnostic and training work through the StatGrad system of the Moscow Institute of Open Education. After analyzing the results of the work, I identify gaps in students’ knowledge and organize repetition of the material, taking into account the mistakes made. At the same time, I implement an individual and differentiated approach to teaching, creating tasks depending on the individual abilities of each student. This opportunity is provided by a large number of tasks published on the sites listed above. I select tasks in such a way that the student can subsequently score the maximum possible number of points on the Unified State Exam.

For independent work, I suggest students complete the test tasks on-line on the portal www.ege.edu.ru.

K. F. Gauss said: “Mathematics is a science for the eyes, not for the ears.” I believe that mathematics is one of those subjects in which the use of ICT can enhance all types of learning activities. Based on the use of ICT, many methodological goals can be realized more effectively. The use of ICT in preparation for the Unified State Exam allows you to:

• to intensify the cognitive activity of students;
• ensure a high degree of individualization of training;
• increase the amount of work performed in the lesson;
• improve knowledge control;
• provide access to various reference systems, electronic libraries, and other information resources.

Methodological techniques for conducting classes using ICT

I divide all the educational material that a student must know when passing the state final certification (level of compulsory preparation) into twenty large topics based on the codifier of content elements for the level of preparation of graduates of general education institutions for the unified state exam in mathematics in 2012.

I consider the key point in preparing for the Unified State Exam to be keeping “Thematic Notebooks” on these topics. Thus, by the end of the first half of the year, eleventh graders have a complete set of materials on the main topics of the program. This technique allows you to have all the information in one place and at the same time makes it possible to quickly find the desired section. When conducting lessons on general repetition and workshops on preparing for the final certification in the form of the Unified State Exam, “Thematic notebooks” became indispensable assistants.

At the stage of preparation for the Unified State Exam in Mathematics, each student can find out the level of their knowledge by taking online testing. I try to choose the most competent sites myself.

Sometimes we conduct testing in the computer science classroom, then students can discuss the results with the teacher and see gaps in their knowledge, as well as plan work to eliminate them.

Thus, the effectiveness of passing the Unified State Exam is largely determined by how effectively the preparation process is organized at all levels of education, with all categories of students. And if we are able to instill in students independence, responsibility and readiness to continue learning throughout their entire lives, then we will not only fulfill the order of the state and society, but also increase our own self-esteem.

In conclusion, I would like to remind you of the eternal internal incentives for learning:

• success of training

  (the student must clearly understand what has been learned and independently complete educational tasks);

• awareness of the usefulness of training

  , that is, the applicability of what has been studied to solving practical problems.

Thank you for your attention!

Refresher courses

Video lectures and methodological recommendations from leading experts in the field of education provide an opportunity to develop your professional skills. After completing all verification work, you will receive a certificate of the established form. There is a license for educational activities.

• New technologies and tools in education
• Formation of professional competencies of a teacher in the context of the implementation of the Federal State Educational Standard when organizing training sessions using EFU
• Implementation of the requirements for mastering the basic educational program (mathematics, geometry)

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Preparation courses for the Unified State Exam

But what to do if time is lost and everything suggests that the existing stock of knowledge will not bring good results? What is the minimum period in which you can prepare for the exam? There are no specific deadlines; everything will depend on the initial level, performance, motivation and desire of the graduate to learn.

There are intensive preparation courses for the Unified State Exam. During classes you will be in conditions similar to the exam. You will have to get ready to work with full dedication and fulfill all homework requirements. Each group studies according to an individual program, which is built taking into account the speed of learning the material and is aimed at the final result. If necessary, additional lessons are held for repetition or trial testing so that students can evaluate their strengths.

Lesson with LECTA

• Classwork. Ready-made work programs and materials for conducting lessons, which can be edited by adding slides, hyperlinks, audio and video materials.
• Test. Ready-made test tasks of different difficulty levels with keys for the teacher, automatic checking and analysis of results.
• Preparing for the VPR. Training and testing materials for practicing and consolidating the necessary skills, designed to help in preparation for the All-Russian testing work.

Go to LECTA
To the beginning

Preparation for the Unified State Exam

Here are links to methods used in individual preparation for the Unified State Exam in mathematics. The pages are aimed primarily at teachers, although I do not exclude that some materials will be useful to parents too. If parents are not indifferent to which math tutor will teach their child, then they are interested in the teacher’s work system, the content of classes, and even the methods of explanation. And above all, in preparation for the Unified State Exam. As I have free time, I will publish pages on individual topics and sections of the school mathematics course. They will provide comments and advice on working with individual tasks of the Unified State Exam. Read and express your opinion about the materials. If you are an experienced mathematics tutor or a competent school teacher, send your ideas, descriptions and reflections on the topic of working with the Unified State Exam. I will be very happy to post materials on the site.

Cards - reminders for lessons with a math tutor . Takeaways from the basic theoretical set of reference information on geometry for preparing for the Unified State Exam, designed in the form of cheat sheets. Methodology of training with cards - reminders. About the work of a tutor with illustrations of mathematical formulas and theorems.

Preparation for the Unified State Exam in mathematics: planimetry - C4 . Peculiarities of a tutor's work with complex competitive tasks. Step-by-step preparation for task C4. Problems of quality preparation for the Unified State Exam. Advice for tutors and parents.

Mathematics tutor about the method of intervals . Techniques and rules for working as a tutor with algebraic inequalities of various types. A method for explaining the method of arranging signs without trial points. Features of the design of the drawing and a description of typical mistakes made by students.

What materials does a math tutor use to build work on the topic “angles between straight lines? ” Methods of visual tasks. The author's approach to organizing problem solving in the classroom. Features of working with inattentive and disorganized students when preparing for number C2 on the Unified State Exam. Tutor didactics, a collection of tasks.

Math tutor's work with vectors. Preparation for the Unified State Exam - task C2 Techniques for solving problems on the Unified State Exam using analytical geometry. Using the coordinate method to find angles. Advice for math tutors and students. Methodological analysis of problem areas in mastering the material. Techniques for learning formulas.

Learning to calculate the values ​​of trigonometric functions . A page describing the technique used by the tutor to replace an arbitrary angle with an angle lying in the first quadrant. Using the example of finding a number

Working with records of system solutions. How a tutor formalizes the integration of systems. Discussions about the effectiveness and accessibility for schoolchildren of strict mathematical formulation of systems of equations and inequalities. Typical mistakes caused by poor record keeping techniques. A math tutor technique used for most students when preparing for the Unified State Exam. Advice for beginning tutors.

How a math tutor solves systems of inequalities . Peculiarities of design, explanations and tasks when a tutor works on the topic “solving systems of inequalities”. Examples of mistakes that are often found among school teachers. Methods for optimal techniques for solving standard systems, taking into account the problems of weak students.

Math tutor in first lesson. Initial test for preparing for the Unified State Exam (without derivative) Standard material for diagnosing the level of knowledge in algebra for grades 9-10. Information about the content of assignments for a new student for the first lesson. Features of individual testing and tutor comments on some numbers. Student level: slightly above average or high

Trigonometry: preparation for the Unified State Exam. Task C1 Description of some methodological techniques and strategies for a tutor to work on task C1 under time pressure with a not-so-strong student. How to prepare for the Unified State Exam in mathematics with weak applicants who need a result in the range of 55-65 points.

Stereometry C2 Inequalities C3 Problems with parameters C5 Problem C6

Kolpakov Alexander Nikolaevich, mathematics tutor in Moscow. Professional tutor – Strogino .

Final control and certification. Preparation for the OGE and the Unified State Exam

VPR: analysis of tasks and advice to the teacher

Experts say that when preparing for a test in mathematics, it is imperative to practice solving examples with decimal fractions. It is also necessary to teach schoolchildren to carefully read long texts of assignments and devote time to analyzing non-standard problems.

• Preparation for VPR-2019 in mathematics in grades 5 and 6
• Guidelines for preparing for the CPR in mathematics in grades 5 and 6 (UMK A.G. Merzlyak)
• VPR-2019 in mathematics, grade 5: options, analysis and solution of tasks
• VPR-2019 in mathematics, grade 6: options, analysis and solution of tasks
• VPR-2019 in mathematics, grade 7: options, analysis and solution of tasks

Mathematics. A large collection of training versions of test papers to prepare for the VPR. 6th grade

The manual contains 15 training versions of test papers. The content of the test corresponds to the Federal State Educational Standard for basic general education. Each option is compiled in full accordance with the demonstration version presented on the information portal on the All-Russian testing works www.vpr.statgrad.org.

Buy
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Preparing for the OGE and the Unified State Exam

We solve and analyze demo tasks together with experts, pay attention to difficult moments, remember important topics and give advice on effective preparation for the final tests.

• Preparation for the Unified State Exam in mathematics: examples of solving economic problems
• Unified State Exam 2019 in mathematics. Analysis of the early option
• Unified State Exam. Mathematics. Solving problems of increased complexity
• Unified State Exam 2019 in mathematics: solving equations, inequalities and their systems
• Preparation for the Unified State Examination in mathematics at the profile level (Merzlyak, Polyakov teaching materials). Part 1
• Preparation for the Unified State Examination in mathematics at the profile level (Merzlyak, Polyakov teaching materials). Part 2
• Unified State Exam 2019. Mathematics. Profile level. Geometry

OGE-2020. Mathematics. 750 tasks with answers

The publication is intended to prepare students for the OGE in mathematics. The manual includes 750 tasks of different types, grouped by topic; reference theoretical material; answers to all tasks; detailed solutions to problems. All educational topics are presented, knowledge of which is tested by exam.

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Preparation program for the Unified State Exam in mathematics

Anna Malkova

The preparation program for the Unified State Exam in mathematics is designed for 11th grade students preparing for the Unified State Exam for one academic year, from September to May at Educational. Compiled in accordance with the requirements of FIPI. The author of the program is Anna Georgievna Malkova (author’s methodology).

Entry level – about 60 points.

The initial level is determined during entrance testing.

Level at the end of the course: 85-100 points.

Average score in mathematics for Education graduates: 83 points.

September. Text problems for the Unified State Exam in mathematics.

1. Problems on percentages for the Unified State Examination in mathematics. 2. Text problems on movement and work. 3. Problems on alloys, mixtures, solutions. 4. Problems on the motion of extended bodies, on average speed and motion in a circle. 5. Algebraic problems with physical content. 6. Probability theory on the Unified State Exam in mathematics

7. Problems with economic content (preparatory classes) 8. Introduction to non-standard problems on the Unified State Exam in mathematics (Task 19). Additionally: quick counting techniques without a calculator. Techniques for solving algebraic equations and systems of equations. Algebraic transformations.

October. Geometry and stereometry on the Unified State Examination in mathematics, part 1.

9. Planimetry, basic formulas. Calculating the areas of figures on checkered paper. Derivation of the formula for the area of ​​a rectangle, parallelogram, triangle, trapezoid. 10. Trigonometry on the Unified State Examination in mathematics. Definitions of sine, cosine, tangent of an angle in a right triangle. 11. External angle of a triangle - how to find its sine, cosine and tangent. The concept of adjacent angles. Height in a right triangle. 12. Definitions of median, bisector, height. Simple geometric constructions. Sum of angles of a triangle. 13. Short course in geometry: here. 14. Vectors on a plane. 15. Stereometry. Formulas for volume and surface area of ​​polyhedra and bodies of revolution. 16. All problems on stereometry from the First part of the Unified State Exam in mathematics

October November. Algebra on the Unified State Examination in mathematics, part 1.

17. Roots and degrees. 18. Concept of function. Study of the graph of a function. The concepts of increasing and decreasing functions, zeros of a function, intervals of constant sign, points of maximum and minimum of a function, evenness and oddness of a function. 19. Quadratic function and quadratic inequalities. 20. Fractional rational function and interval method. Solving fractional rational inequalities. 21. Number module. Equations and inequalities with modulus. 22. Exponential function. Exponential equations (part 1) 23. Logarithms. Converting logarithmic expressions. 24. Logarithmic function. The concept of an inverse function. 25. Problems with physical content on the topics covered.

Trigonometry on the Unified State Exam in mathematics 26. Definitions of sine, cosine, tangent for an arbitrary angle. 27. Trigonometric circle. Trigonometric functions. 28. Trigonometry formulas. 29. Trigonometric transformations. The simplest trigonometric equations. 30. Inverse trigonometric functions and their graphs. 31. Trigonometric equations (part 2) December. Derivative of a function. Geometric meaning of derivative.

32. Derivative of a function. Studying a function using its derivative. 33. Antiderivative of a function.

Stereometry on the Unified State Examination in mathematics.

34. Program on stereometry: here. 35. Classical method for solving problems in stereometry. 36. Vectors in space. Vector coordinate method. January. Continuation of the topic: Stereometry on the Unified State Examination in mathematics. Inequalities on the Unified State Examination in mathematics.

37. Exponential and logarithmic inequalities. (Part 2 of the Unified State Examination in mathematics). 38. Method of rationalization (replacing the factor). Evaluation method. February. Geometry on the Unified State Examination in mathematics. Task C4. Problems with economic content on the Unified State Examination in mathematics.

39. What is a mathematical proof. Proof problems. 40. Problems of part 2 of the Unified State Exam, Geometry. 41. Problems with economic content on the Unified State Examination in mathematics. 42. Arithmetic and geometric progressions. 43. Formulas for solving problems with economic content. March. Problems with parameters on the Unified State Exam in mathematics.

44. Elementary functions and their graphs. 45. Transformations of graphs of functions 46. Sets of points on a plane. "Basic" solution schemes. Circle, circle, semicircle, rhombus, sum of modules, half-plane, strip, segment. 47. Training problems with parameters 48. Quadratic equations and inequalities with parameters 49. Graphical method for solving problems with parameters 50. Symmetry method, parameter as a variable and other methods. April. Non-standard problems on the Unified State Exam in mathematics (C6)

51. Divisibility. Signs of divisibility. 52. Method “Evaluation plus example”. 53. Real non-standard problems on the Unified State Exam in mathematics.

May. Repetition of all topics and solution of Unified State Exam variants.

Materials for preparation:

1. Anna Malkova’s book “Mathematics. The author’s preparation course for the Unified State Exam.” 2. The program is synchronized with the Annual Preparation Course for the Unified State Exam in Mathematics. 3. Each topic ends with a test or test. 4. Materials and resources for preparation: 1) Video courses by Anna Malkova. 2) Materials for preparation are free. 3) Video channel on YouTube.

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