UPSKILL MATH PLUS
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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 perpendicular from the centre to a chord | Learn the theorems based on perpendicular from the centre to a chord |
| 4. | Theorems on angle subtended by the chord at the centre | Learn the theorems based on angle subtended by the chord at the centre. |
| 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. | 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. |
| 8. | Theorems on angles at the circumference to the same segment | Learn the theorems based on angles at the circumference to the same segment 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. |
| 10. | Theorem on exterior angles of a cyclic quadrilaterals | Learn the theorem based on the exterior angle property of a cyclic quadrilateral. |
| 11. | Construction of incircle of a triangle | Learn how to construct the incircle of a triangle. |
| 12. | Construction of centroid of a triangle | Learn how to construct the centroid of a triangle. |
Textbook Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Multiple choice question I | Other | easy | 2 m. | This exercise is to check your knowledge in the properties of circles. |
| 2. | Multiple choice question II | Other | easy | 2 m. | This exercise is to check your knowledge about cyclic quadrilateral. |
| 3. | Multiple choice question III | Other | easy | 2 m. | This exercise is to check your knowledge in the properties of circles. |
| 4. | Multiple choice question IV | Other | easy | 2 m. | This exercise is to check your knowledge about cyclic quadrilateral. |
| 5. | Multiple choice question V | Other | easy | 2 m. | This exercise is to check your knowledge in the properties of circles. |
| 6. | Two marks example problems I | Other | medium | 2 m. | Find the length of the chord using the properties of chords of circle. |
| 7. | Two marks example problems II | Other | medium | 4 m. | Determine the value of 'x' using the properties of cyclic quadrilateral. |
| 8. | Two marks example problems III | Other | medium | 4 m. | Determine the measure of the angle 'x' using the properties of cyclic quadrilateral. |
| 9. | Two marks example problems IV | Other | medium | 4 m. | Find the missing angles using the properties of circles. |
| 10. | Two marks example problems V | Other | medium | 5 m. | Find the missing angles using the properties of cyclic quadrilateral. |
| 11. | Two marks exercise problems I | Other | medium | 4 m. | Apply the properties of chords of a circle and find the length of the chord and the radius of the circle. |
| 12. | Two marks exercise problems II | Other | medium | 4 m. | Apply the properties of chords of a circle and find the length of the chord. |
| 13. | Two marks exercise problems III | Other | medium | 2 m. | Find the measure of the angle 'x' using the properties of cyclic quadrilateral. |
| 14. | Five marks example problems I | Other | hard | 0 m. | Prove the given statement using the properties of circles. |
| 15. | Five marks example problems II | Other | hard | 5 m. | Find the missing angles using the properties of circle. |
| 16. | Five marks example problems III | Other | hard | 0 m. | Construct the centroid of the triangle PQR. |
| 17. | Five marks example problems IV | Other | hard | 0 m. | Construct the incentre and incircle of the triangle ABC. |
| 18. | Five marks example problems V | Other | hard | 0 m. | Construct the incentre and incircle of an equilateral triangle. |
| 19. | Five marks exercise problems I | Other | hard | 10 m. | Find the length of the chord and the missing angles using the properties of circles. |
| 20. | Five marks exercise problems II | Other | hard | 5 m. | Determine all the angles of a cyclic quadrilateral. |
| 21. | Five marks exercise problems III | Other | hard | 5 m. | Find the missing angles of the cyclic quadrilateral. |
| 22. | Five marks exercise problems IV | Other | hard | 5 m. | Find the radius of the circle using the properties of chords of a circle. |
| 23. | Five marks exercise problems V | Other | hard | 5 m. | Find the radius of the circle using the properties of chords of a circle. |
| 24. | Five marks exercise problems VI | Other | hard | 5 m. | Determine the missing angle using the properties of cyclic quadrilateral. |
| 25. | Five marks exercise problems VII | Other | hard | 5 m. | This exercise is to check your knowledge in the properties of chords of circle. |
| 26. | Five marks exercise problems VIII | Other | hard | 5 m. | Find the length of the angle required using the properties of circles. |
| 27. | Five marks exercise problems IX | Other | hard | 0 m. | Construct the centroid of the triangle LMN. |
| 28. | Five marks exercise problems X | Other | hard | 0 m. | Draw the centroid of the right triangle ABC. |
| 29. | Five marks exercise problems XI | Other | hard | 0 m. | Construct the centroid of the triangle ABC. |
| 30. | Five marks exercise problems XII | Other | hard | 0 m. | Draw the centroid of the triangle PQR. |
| 31. | Five marks exercise problems XIII | Other | hard | 0 m. | Construct the incentre and incircle of the right triangle. |
| 32. | Five marks exercise problems IX | Other | hard | 0 m. | Construct the incentre and incircle of the triangle ABC. |
| 33. | Five marks exercise problems X | Other | hard | 0 m. | Construct the incentre and incircle of the triangle ABC. |
Practice Questions
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Choose the correct answer | Other | easy | 2 m. | Exercise on position of points on the circle and types of circles. |
| 2. | Knowing the parts | Other | easy | 3 m. | Exercise based on the parts of the circle. |
| 3. | Find the unknown angle | Other | easy | 1 m. | Exercise based on the theorem on cyclic quadrilateral. |
| 4. | Find the required angle | Other | medium | 3 m. | Exercise based on the theorems of the angle subtended by the parts of the circle. |
| 5. | Find the degree measure of 'x' | Other | medium | 2 m. | Exercise based on the theorem of angle at the centre and the circumference of a circle. |
| 6. | Find the distance | Other | medium | 4 m. | Application problem based on the the properties of the chord. |
| 7. | Find the area of the shaded region | Other | medium | 2 m. | Exercise based on the theorem of the angle subtended by the diameter. |
| 8. | Find the angles from the figure | Other | medium | 3 m. | Exercise based on the theorem subtended by the chords and the theorem on cyclic quadrilaterals. |
| 9. | Find the unknown angle 'y' | Other | medium | 2 m. | Exercise based on the theorem on angle subtended by the chord. |
| 10. | Find the subtended angle | Other | medium | 2 m. | Exercise based on the angle subtended by the chord and the interior angles of a cyclic quadrilateral. |
| 11. | Identify the theorem and analyse | Other | hard | 4 m. | Exercises based on the theorems of properties of a chord. |
| 12. | Find the chord length | Other | hard | 4 m. | Exercises based on perpendicular from the centre to a chord. |
| 13. | Prove the problem | Other | hard | 4 m. | Exercise based on the angle subtended by the chord at the centre. |
| 14. | Explore the unknown angles | Other | hard | 5 m. | To practice the theorems on circle and cyclic quadrilaterals. |
Key Questions for School Exam Preparation
| Number | Name | Type | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Calculate the required angles of the cyclic quadrilateral | Other | hard | 5 m. | Find the missing angles using the properties of circle. |
| 2. | Find the angle OAC | Other | hard | 5 m. | Determine the missing angle using the properties of cyclic quadrilateral. |
| 3. | Find the angle RPO | Other | hard | 5 m. | Find the length of the angle required using the properties of circles. |
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. | Think about it! | Other | medium | 3 m. | Creative exercise based on chord length and the distance of the chord from the centre. |
| 3. | Construct the incircle of a right triangle | Other | medium | 8 m. | To construct the incircle of a right triangle for the given measurements. |
| 4. | Construct the centroid of a right triangle | Other | medium | 8 m. | To construct the centroid of a right triangle for the given measurements. |
| 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 |
| 7. | Construct the incircle of an equilateral triangle | Other | hard | 10 m. | To construct the incircle of an equilateral triangle for the given measurements. |
| 8. | Construct the centroid of an equilateral triangle | Other | hard | 10 m. | To construct the centroid and incentre of an equilateral triangle for the given measurements. |
| 9. | Angle subtended by an arc of a circle | Other | medium | 1 m. | Determine the value of 'x' using the properties of cyclic quadrilateral. |
| 10. | Length of the chord | Other | medium | 2 m. | Apply the properties of chords of a circle and find the length of the chord. |
| 11. | Exterior angles of a cyclic quadrilaterals | Other | easy | 1 m. | Exercise based on the theorem on cyclic quadrilateral. |
| 12. | Angles of a cyclic quadrilateral | Other | easy | 1 m. | This exercise is to check your knowledge about cyclic quadrilateral. |
| 13. | Radius of the circle | Other | medium | 1 m. | Apply the properties of chords of a circle and find the length of the chord and the radius of the circle. |
| 14. | Calculate the angle subtended by the circle | Other | medium | 1 m. | Determine the value of 'x' using the properties of cyclic quadrilateral. |
| 15. | Determine the angle using chords | Other | easy | 1 m. | This exercise is to check your knowledge in the properties of circles. |
| 16. | Exterior angle of quadrilateral | Other | medium | 1 m. | Find the missing angles using the properties of cyclic quadrilateral. |
| 17. | The length of a chord | Other | medium | 1 m. | Find the length of the chord using the properties of chords of circle. |
Tests
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training test I | 00:15:00 | medium | 16 m. | |
| 2. | Training test II | 00:15:00 | medium | 16 m. | |
| 3. | Training test IV | 00:20:00 | medium | 21 m. | |
| 4. | Training test V | 00:15:00 | medium | 8 m. | |
| 5. | Training test VII | 00:15:00 | medium | 11 m. |
Periodic assessments
| Number | Name | Recomended time: | Difficulty | Marks | Description |
|---|---|---|---|---|---|
| 1. | Training test III | 00:20:00 | medium | 21 m. | |
| 2. | Training test VI | 00:20:00 | medium | 10 m. | |
| 3. | Homework I | 00:15:00 | medium | 14 m. | |
| 4. | Homework II | 00:15:00 | medium | 7 m. | |
| 5. | Homework III | 00:20:00 | medium | 10 m. | |
| 6. | Homework VI | 00:15:00 | medium | 16 m. | |
| 7. | Homework V | 00:15:00 | medium | 9 m. | |
| 8. | Homework VI | 00:15:00 | medium | 12 m. | |
| 9. | Homework VII | 00:15:00 | medium | 13 m. | |
| 10. | Homework VIII | 00:15:00 | medium | 24 m. | |
| 11. | Periodic Assessment | 00:10:00 | medium | 8 m. | PA 2 |
| 12. | Bridge Course Demo 2 | 00:10:00 | medium | 2 m. | |
| 13. | Periodic Assessment - Extended version | 00:10:00 | medium | 8 m. | PA 2 |
| 14. | Periodic Assessment 2.0 | 00:10:00 | medium | 20 m. | PA 2 |
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