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Methodical recommendation:
Theory
| Number | Name | Description |
|---|---|---|
| 1. | Introduction to powers and exponents | Introduction about powers and exponents |
| 2. | What is an exponent? | Example on exponents |
| 3. | Powers with positive and negative exponents | Laws of negative exponents |
| 4. | Power1 or 0 | Rules and laws with power 0 and 1 |
| 5. | Grades of exponents | Rules and examples on squaring and cubing of powers |
| 6. | Negative power | Finding the value of negative exponents |
| 7. | Law of exponents | Laws involving powers and exponents |
| 8. | The normal form of a number | Normal number form, number 10 degree, positive and negative multipliers. |
| 9. | Degrees of single prime numbers | The degrees of single digit prime numbers often used |
| 10. | Division of degrees with identical bases | Dividing degrees with same bases. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Area of square | 1st type - receptive | easy | 3 m. | Calculate the area of square using exponents. |
| 2. | Area of circle | 1st type - receptive | easy | 3 m. | Calculate the area of circle. |
| 3. | Product of degrees | 1st type - receptive | easy | 2 m. | Using degree properties. |
| 4. | Product in the form of a degree | 1st type - receptive | easy | 3.5 m. | Record a work as a degree by definition. |
| 5. | Base and exponent | 1st type - receptive | easy | 3 m. | Determination of base and exponent. |
| 6. | Squaring of decimals | 1st type - receptive | easy | 2 m. | Exponentiation. |
| 7. | Product of degrees with identical bases | 1st type - receptive | easy | 3 m. | Representation of an expression as a product of two degrees with the same bases |
| 8. | The equation | 2nd type - interpretation | medium | 5 m. | The solution of the equation. |
| 9. | Power of a fraction | 2nd type - interpretation | medium | 3 m. | Calculation of the value of an expression. |
| 10. | Value comparison | 2nd type - interpretation | medium | 1 m. | Compare function values. |
| 11. | Raising a fraction in a degree (negative denominator) | 2nd type - interpretation | medium | 5 m. | The raising to a power of a fraction. |
| 12. | Decreasing (increasing) degrees | 2nd type - interpretation | medium | 4 m. | The arrangement of numbers in descending (ascending) order. |
| 13. | Numerical value of fraction | 2nd type - interpretation | medium | 6 m. | Calculation of expression value. |
| 14. | The normal form of an integer | 2nd type - interpretation | medium | 1 m. | Choose 10 steps. |
| 15. | The normal form of a number | 2nd type - interpretation | medium | 2 m. | Write a normal number form. |
| 16. | The product of three fractions with the same exponents | 3rd type - analysis | hard | 6 m. | Calculation of the value of an expression. |
| 17. | Degree properties | 3rd type - analysis | hard | 6 m. | The solution of the equation. |
| 18. | Common fraction | 3rd type - analysis | hard | 6 m. | The solution of the equation. |
| 19. | To find the unknown exponent(product) | 3rd type - analysis | hard | 4 m. | Finding an unknown exponent. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Comparison of numerical inequalities | Other | easy | 1 m. | Comparison of inequalities which contains power. |
| 2. | Base and power | Other | easy | 0 m. | Find the base and power of the given number. |
| 3. | Finding unknown base squared | Other | medium | 4 m. | Finding a monomial in parentheses (equal degrees and the product of an ordinary fraction by a degree). |
| 4. | Fraction value calculation | Other | medium | 4 m. | The calculation of the fraction value. |
| 5. | Equation reducible to linear | Other | hard | 5 m. | Finding an unknown exponent. |
| 6. | Finding the unknown exponent(quotient) | Other | hard | 4 m. | Finding an unknown exponent. |
Tests
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training test | 00:15:00 | medium | 13 m. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Homework | 00:20:00 | medium | 17.5 m. | |
| 2. | Homework | 00:20:00 | hard | 19 m. | |
| 3. | Progress test | 00:20:00 | hard | 14 m. | |
| 4. | Progress test | 00:20:00 | hard | 25 m. |
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