UPSKILL MATH PLUS
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Theory
| Number | Name | Description |
|---|---|---|
| 1. | Introduction | To recall the concept of circles and tangents. |
| 2. | Tangent to a circle | To learn what is a tangent and its real life examples. |
| 3. | Theorem 1 on circles and tangents | To learn and understand the theorem based on the relation between the radius of the circles and the tangent. |
| 4. | Number of tangents from a point to a circle | To learn and understand how many tangents can be drawn to a circle from a point. |
| 5. | Theorem 2 on circles and tangents | To learn and understand the results on circles and tangents. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Find the radius of the circle | 2nd type - interpretation | easy | 2 m. | To find the radius of the circle using the results on tangent to the circle. |
| 2. | Find the value of 'x' | 2nd type - interpretation | easy | 2 m. | To find the value of 'x' from the given figure. |
| 3. | Find the length as directed | 1st type - receptive | easy | 2 m. | To find the length of the tangent from the measurements provided. |
| 4. | Find the length | 1st type - receptive | easy | 2 m. | To find the given length using the property of the tangent to the circle. |
| 5. | Find the angle between the radii | 2nd type - interpretation | easy | 2 m. | To find the angle between the radii using the given information. |
| 6. | Find the angle 'b' | 2nd type - interpretation | easy | 3 m. | To find the measure of the angle 'b' using the property of tangent. |
| 7. | Find the length of the segment | 2nd type - interpretation | easy | 2 m. | To find the length of the required segment using the property of tangents. |
| 8. | Find the angles '1' and '2' | 2nd type - interpretation | medium | 3 m. | To find the angles '1' and '2' from the given data. |
| 9. | Find the length of the tangent | 2nd type - interpretation | medium | 3 m. | To find the length of the tangent using the using result of the tangent on a circle. |
| 10. | Find the value of 'y' | 2nd type - interpretation | medium | 3 m. | To find the value of 'y' from the given figure. |
| 11. | Find the unknown angle | 2nd type - interpretation | medium | 3 m. | To find the unknown angle using the given information. |
| 12. | Find the length of the chord | 2nd type - interpretation | medium | 3 m. | To find the length of the chord using the using result of the tangent on a circle. |
| 13. | Find the radius of the larger circle | 2nd type - interpretation | medium | 3 m. | To find the radius of the larger circle using the result of the tangent on a circle. |
| 14. | Find the angle | 2nd type - interpretation | medium | 3 m. | To find the unknown angle from the data provided. |
| 15. | Find the required length | 2nd type - interpretation | medium | 3 m. | To find the required length using the trigonometric property. |
| 16. | Find the value of 'x', 'y' and 'z' | 3rd type - analysis | hard | 6 m. | To find the value of 'x', 'y' and 'z' from the measurements provided. |
| 17. | Find the length of the required tangent | 3rd type - analysis | hard | 4 m. | To find the length of the tangent using the using result of the tangent on a circle. |
| 18. | Prove that the angles in the alternate segments are equal | 3rd type - analysis | hard | 5 m. | To prove that the angles in the alternate segments are equal using the given figure. |
| 19. | Find the unknown angle 'y' | 3rd type - analysis | hard | 4 m. | To find the value of the unknown angle 'y' from the given figure using the property of tangent. |
| 20. | Understand the figure and answer the following | 3rd type - analysis | hard | 5 m. | To understand the figure and answer the given questions from the measurements provided. |
| 21. | Find the required angle | 3rd type - analysis | hard | 4 m. | To find the required angle in the figure using the given data. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Prove the common tangents are equal | Other | easy | 2 m. | To prove the common tangents shown in the figure are equal using the property of tangents. |
| 2. | Determine the length | Other | easy | 2 m. | To determine the required length using the trigonometric property. |
| 3. | Find the length of the chord | Other | medium | 3 m. | To find the length of the chord from the given figure using the property of tangents. |
| 4. | Sketch the figure and prove the statement | Other | medium | 3 m. | To prove the given statement using the tangent property of a circle. |
| 5. | Prove the statement | Other | hard | 4 m. | To prove the given statement using the tangent property of a circle. |
| 6. | Radius of the circle | Other | easy | 1 m. | To find the radius of the circle using the results on tangent to the circle. |
| 7. | Tangent to a circle | Other | easy | 2 m. | To find the value of 'x' from the given figure. |
Tests
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training test I | 00:20:00 | medium | 10 m. | |
| 2. | Training test II | 00:20:00 | medium | 10 m. | |
| 3. | Training test III | 00:15:00 | medium | 8 m. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Homework I | 00:25:00 | hard | 9 m. | |
| 2. | Homework II | 00:25:00 | hard | 14 m. | |
| 3. | Progress test I | 00:30:00 | hard | 14 m. | |
| 4. | Progress test II | 00:30:00 | hard | 16 m. | |
| 5. | Periodic Assessment | 00:15:00 | medium | 4 m. | PA 2 |
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