 UPSKILL MATH PLUS

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### Theory

 1 Introduction to circle 2 Circle through three points 3 Theorems on perpendicular from the centre to a chord 4 Theorems on angle subtended by the chord at the centre 5 Theorems on equal chords 6 Theorems on angle at the centre and the circumference 7 Special cases of angle at the centre and the circumference 8 Theorems on angles at the circumference to the same segment 9 Theorem on interior angles of a cyclic quadrilaterals 10 Theorem on exterior angles of a cyclic quadrilaterals 11 Construction of incircle of a triangle 12 Construction of centroid of a triangle

### Textbook Questions

 1 Multiple choice question I Difficulty: easy 2 2 Multiple choice question II Difficulty: easy 2 3 Multiple choice question III Difficulty: easy 2 4 Multiple choice question IV Difficulty: easy 2 5 Multiple choice question V Difficulty: easy 2 6 Two marks example problems I Difficulty: medium 2 7 Two marks example problems II Difficulty: medium 4 8 Two marks example problems III Difficulty: medium 4 9 Two marks example problems IV Difficulty: medium 4 10 Two marks example problems V Difficulty: medium 5 11 Two marks exercise problems I Difficulty: medium 4 12 Two marks exercise problems II Difficulty: medium 4 13 Two marks exercise problems III Difficulty: medium 2 14 Five marks example problems I Difficulty: hard 0 15 Five marks example problems II Difficulty: hard 5 16 Five marks example problems III Difficulty: hard 0 17 Five marks example problems IV Difficulty: hard 0 18 Five marks example problems V Difficulty: hard 0 19 Five marks exercise problems I Difficulty: hard 10 20 Five marks exercise problems II Difficulty: hard 5 21 Five marks exercise problems III Difficulty: hard 5 22 Five marks exercise problems IV Difficulty: hard 5 23 Five marks exercise problems V Difficulty: hard 5 24 Five marks exercise problems VI Difficulty: hard 5 25 Five marks exercise problems VII Difficulty: hard 5 26 Five marks exercise problems VIII Difficulty: hard 5 27 Five marks exercise problems IX Difficulty: hard 0 28 Five marks exercise problems X Difficulty: hard 0 29 Five marks exercise problems XI Difficulty: hard 0 30 Five marks exercise problems XII Difficulty: hard 0 31 Five marks exercise problems XIII Difficulty: hard 0 32 Five marks exercise problems IX Difficulty: hard 0 33 Five marks exercise problems X Difficulty: hard 0

### Practice Questions

 1 Choose the correct answer Difficulty: easy 2 2 Knowing the parts Difficulty: easy 3 3 Find the unknown angle Difficulty: easy 1 4 Find the required angle Difficulty: medium 3 5 Find the degree measure of 'x' Difficulty: medium 2 6 Find the distance Difficulty: medium 4 7 Find the area of the shaded region Difficulty: medium 2 8 Find the angles from the figure Difficulty: medium 3 9 Find the unknown angle 'y' Difficulty: medium 2 10 Find the subtended angle Difficulty: medium 2 11 Identify the theorem and analyse Difficulty: hard 4 12 Find the chord length Difficulty: hard 4 13 Prove the problem Difficulty: hard 4 14 Explore the unknown angles Difficulty: hard 5

### Key Questions for School Exam Preparation

 1 Calculate the required angles of the cyclic quadrilateral Difficulty: hard 5 2 Find the angle OAC Difficulty: hard 5 3 Find the angle RPO Difficulty: hard 5

### Tests

 1 Training test I Difficulty: medium 16 2 Training test II Difficulty: medium 16 3 Training test IV Difficulty: medium 21 4 Training test V Difficulty: medium 8 5 Training test VII Difficulty: medium 11

### Teacher manual

 1 Methodical recommendation