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Methodical recommendation:
Theory
| Number | Name | Description |
|---|---|---|
| 1. | A monomial and its standard form | Monomer, monomer simplification, monomer normal form, monomer quotient, monomer degree, similar monomers. |
| 2. | Similar monomials | Similar, same, opposite monomers. |
| 3. | Addition and subtraction of monomials | Addition and subtraction of monomers |
| 4. | Multiplication or division of a monomial by a number | Multiplication and division by monomers. Multiplication of monomers. |
| 5. | Multiplication of monomials | Multiplication and division by monomers. Multiplication of monomers. |
| 6. | Division of monomials | Theory and examples of monomer division. |
| 7. | Operations with monomials as fractions | Operations with monomers in the form of parts. |
| 8. | Raising a monomial to a power | Monomer Raising Grade |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | A monomial coefficient and degree | 2nd type - interpretation | medium | 6 m. | Fill in the table, determine the coefficients and grades of the monomer! |
| 2. | The value of the algebraic expression. Multiplication | 2nd type - interpretation | easy | 3 m. | Calculation of the value of an algebraic expression, product. |
| 3. | A coefficient and a degree of a monomial | 2nd type - interpretation | easy | 2 m. | Determination of the degree and coefficient of the monomial. |
| 4. | Sum of monomials | 1st type - receptive | easy | 3 m. | Adding the monomers |
| 5. | A coefficient and a degree of a monomial (fill in the table) | 2nd type - interpretation | easy | 3 m. | Determining the degree and coefficient of the monomial, the results are recorded in the table. |
| 6. | A numerical value of a monomial | 2nd type - interpretation | medium | 4 m. | Insert two integers. |
| 7. | Determine the coefficient and degree of the monomial | 1st type - receptive | medium | 4 m. | Determine the degree and coefficient of the given monomer |
| 8. | Addition and subtraction of monomials | 2nd type - interpretation | medium | 4 m. | Simplification of expression. |
| 9. | Standard form of the monomial | 2nd type - interpretation | medium | 4 m. | Bringing the monomial to standard form. |
| 10. | Equation solution | 2nd type - interpretation | medium | 4 m. | To solve the equation, its left side to the monomial of the standard form is first simplified. |
| 11. | The numerical value of the monomial | 2nd type - interpretation | medium | 4 m. | The calculation of the numerical value of the monomial. |
| 12. | Defining rectangle sides | 3rd type - analysis | hard | 8 m. | We make the equation, having the aspect ratio of the rectangle. The left side of the equation is converted to a monomial of the standard form. Having solved the equation, we find the sides of the rectangle. |
| 13. | Calculation of dimensions of a rectangular box | 3rd type - analysis | hard | 8 m. | We draw up the equation, having a relationship between the dimensions of a rectangular box. The left side of the equation is converted to a monomial of the standard form. Having solved the equation, we find the dimensions of the rectangular parallel piped. |
| 14. | Monomials with the same variable factors | 3rd type - analysis | hard | 8 m. | It is proposed to bring monomials to a standard form and define monomials with the same letter part. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Monomial definition | Other | easy | 3 m. | Using the definition of a monomial, we conclude whether this expression will be a monomial or not. |
| 2. | The numerical value of the monomial | Other | easy | 3 m. | The value of the monomial is determined for a certain value of the variables included in it. |
| 3. | Standard form of the monomial | Other | medium | 5 m. | The monomial is converted to the standard form, and then its coefficient is called. |
| 4. | Dimensions of a rectangular box | Other | hard | 8 m. | We compose the equation, having the ratio of the dimensions of a rectangular box. The left side of the equation is converted to a monomial of the standard form. Having solved the equation, we find the dimensions of the rectangular parallelepiped. |
Tests
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training on the concept of a monomial | 00:20:00 | easy | 5.5 m. | Concept of a monomial |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Verification work on the topic Standard view of the monomial | 00:20:00 | medium | 10 m. | Standard view of the monomial |
| 2. | Progressive test for standard form of monomer | 00:20:00 | medium | 6 m. | Monomer standard form |
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