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Methodical recommendation:

Theory

Number Name Description
Number 1. Name A monomial and its standard form Description Monomer, monomer simplification, monomer normal form, monomer quotient, monomer degree, similar monomers.
Number 2. Name Similar monomials Description Similar, same, opposite monomers.
Number 3. Name Addition and subtraction of monomials Description Addition and subtraction of monomers
Number 4. Name Multiplication or division of a monomial by a number Description Multiplication and division by monomers. Multiplication of monomers.
Number 5. Name Multiplication of monomials Description Multiplication and division by monomers. Multiplication of monomers.
Number 6. Name Division of monomials Description Theory and examples of monomer division.
Number 7. Name Operations with monomials as fractions Description Operations with monomers in the form of parts.
Number 8. Name Raising a monomial to a power Description Monomer Raising Grade

Practice Questions

Number Name Type Difficulty Marks Description
Number 1. Name A monomial coefficient and degree Type 2nd type - interpretation Difficulty medium Marks 6 m. Description Fill in the table, determine the coefficients and grades of the monomer!
Number 2. Name The value of the algebraic expression. Multiplication Type 2nd type - interpretation Difficulty easy Marks 3 m. Description Calculation of the value of an algebraic expression, product.
Number 3. Name A coefficient and a degree of a monomial Type 2nd type - interpretation Difficulty easy Marks 2 m. Description Determination of the degree and coefficient of the monomial.
Number 4. Name Sum of monomials Type 1st type - receptive Difficulty easy Marks 3 m. Description Adding the monomers
Number 5. Name A coefficient and a degree of a monomial (fill in the table) Type 2nd type - interpretation Difficulty easy Marks 3 m. Description Determining the degree and coefficient of the monomial, the results are recorded in the table.
Number 6. Name A numerical value of a monomial Type 2nd type - interpretation Difficulty medium Marks 4 m. Description Insert two integers.
Number 7. Name Determine the coefficient and degree of the monomial Type 1st type - receptive Difficulty medium Marks 4 m. Description Determine the degree and coefficient of the given monomer
Number 8. Name Addition and subtraction of monomials Type 2nd type - interpretation Difficulty medium Marks 4 m. Description Simplification of expression.
Number 9. Name Standard form of the monomial Type 2nd type - interpretation Difficulty medium Marks 4 m. Description Bringing the monomial to standard form.
Number 10. Name Equation solution Type 2nd type - interpretation Difficulty medium Marks 4 m. Description To solve the equation, its left side to the monomial of the standard form is first simplified.
Number 11. Name The numerical value of the monomial Type 2nd type - interpretation Difficulty medium Marks 4 m. Description The calculation of the numerical value of the monomial.
Number 12. Name Defining rectangle sides Type 3rd type - analysis Difficulty hard Marks 8 m. Description 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.
Number 13. Name Calculation of dimensions of a rectangular box Type 3rd type - analysis Difficulty hard Marks 8 m. Description 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.
Number 14. Name Monomials with the same variable factors Type 3rd type - analysis Difficulty hard Marks 8 m. Description 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
Number 1. Name Monomial definition Type Other Difficulty easy Marks 3 m. Description Using the definition of a monomial, we conclude whether this expression will be a monomial or not.
Number 2. Name The numerical value of the monomial Type Other Difficulty easy Marks 3 m. Description The value of the monomial is determined for a certain value of the variables included in it.
Number 3. Name Standard form of the monomial Type Other Difficulty medium Marks 5 m. Description The monomial is converted to the standard form, and then its coefficient is called.
Number 4. Name Dimensions of a rectangular box Type Other Difficulty hard Marks 8 m. Description 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
Number 1. Name Training on the concept of a monomial Recomended time: 00:20:00 Difficulty easy Marks 5.5 m. Description Concept of a monomial

Periodic assessments

Number Name Recomended time: Difficulty Marks Description
Number 1. Name Verification work on the topic Standard view of the monomial Recomended time: 00:20:00 Difficulty medium Marks 10 m. Description Standard view of the monomial
Number 2. Name Progressive test for standard form of monomer Recomended time: 00:20:00 Difficulty medium Marks 6 m. Description Monomer standard form