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Methodical recommendation:
Theory
| Number | Name | Description |
|---|---|---|
| 1. | Introduction to circle | Learn the definition and know the parts of the circle. |
| 2. | Circle through three points | Learn the number of circles that can pass through 1, 2 and 3 points. |
| 3. | Theorems on angle subtended by the chord at the centre | Learn the theorems based on angle subtended by the chord at the centre. |
| 4. | Theorems on perpendicular from the centre to a chord | Learn the theorems based on perpendicular from the centre to a chord |
| 5. | Theorems on equal chords | Learn the theorems based on the properties of equal chords. |
| 6. | Theorems on angle at the centre and the circumference | Learn the theorem based on the angle subtended by the arc of the circle. |
| 7. | Theorems on angles at the circumference on the same segment | Learn the theorems based on angles at the circumference to the same segment of the circle. |
| 8. | Special cases of angle at the centre and the circumference | Learn the conjecture based on the theorems on angle at the centre and the circumference of the circle. |
| 9. | Theorem on interior angles of a cyclic quadrilaterals | Learn what is cyclic quadrilateral and the theorem on property of the interior angles. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Knowing the parts | 1st type - receptive | easy | 3 m. | Exercise based on the parts of the circle. |
| 2. | Choose the correct answer | 1st type - receptive | easy | 1 m. | Exercise on position of points on the circle and types of circles. |
| 3. | Find the angle | 2nd type - interpretation | easy | 1 m. | Exercise based on the theorem subtended by the chords. |
| 4. | Find the measure of 'b' | 2nd type - interpretation | easy | 1 m. | To find the angle 'b' using the theorem on the interior angles of a cyclic quadrilateral. |
| 5. | Find the required angle | 2nd type - interpretation | medium | 1 m. | Exercise based on the theorems of the angle subtended by the parts of the circle. |
| 6. | Find the degree measure of 'x' | 2nd type - interpretation | medium | 2 m. | Exercise based on the theorem of angle at the centre and the circumference of a circle. |
| 7. | Find the subtended angle | 3rd type - analysis | medium | 2 m. | Exercise based on the angle subtended by the chord and the interior angles of a cyclic quadrilateral. |
| 8. | Find the distance | 2nd type - interpretation | medium | 1 m. | Application problem based on the the properties of the chord. |
| 9. | Find the area of the shaded region | 3rd type - analysis | medium | 5 m. | Exercise based on the theorem of the angle subtended by the diameter. |
| 10. | Find the angle from the figure | 2nd type - interpretation | medium | 1 m. | Exercise based on the theorem on cyclic quadrilaterals. |
| 11. | Find the unknown angle 'y' | 3rd type - analysis | medium | 2 m. | Exercise based on the theorem on angle subtended by the chord. |
| 12. | Find the distance between the chords | 3rd type - analysis | hard | 2 m. | Exercises based on the theorems of properties of a chord. |
| 13. | Find the chord length | 2nd type - interpretation | hard | 4 m. | Exercises based on perpendicular from the centre to a chord. |
| 14. | Prove the problem | 3rd type - analysis | hard | 3 m. | Exercise based on the angle subtended by the chord at the centre. |
| 15. | Explore the unknown angles | 3rd type - analysis | hard | 4 m. | To practise the theorems on circle and cyclic quadrilaterals. |
Questions for Teacher Use
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Learn it! | Other | easy | 1 m. | To understand that circle is not a polygon. |
| 2. | Find the unknown angle 'z' | Other | easy | 2 m. | Based on the theorem on interior angles of a cyclic quadrilateral. |
| 3. | Think about it! | Other | medium | 3 m. | Creative exercise based on chord length and the distance of the chord from the centre. |
| 4. | Find the measure of the angle | Other | medium | 1 m. | Bases on theorems on angle subtended by the chord and the theorem on cyclic quadrilateral. |
| 5. | Analyse the problem | Other | hard | 4 m. | Exercise based on the angle subtended by the chord. |
| 6. | Try it! | Other | hard | 4 m. | Exercise based on theorem on angle subtended by chord at the centre. |
Tests
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training test | 00:20:00 | medium | 10 m. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Homework | 00:25:00 | medium | 8 m. | |
| 2. | Homework | 00:20:00 | hard | 6 m. | |
| 3. | Progress test | 00:30:00 | hard | 11 m. | |
| 4. | Progress test | 00:30:00 | hard | 14 m. |
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