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S5 Maths: Angles in Circles: Paper 2 (intermediate)
S5 Maths: Angles in Circles: Paper 2 (intermediate)
Ten items mixing central and inscribed angles, arc ratios and cyclic quadrilaterals, with unknowns.
Direct answers Items 1-3: 64, 82, 62 degrees. Items 4-6: 72 degrees, x = 15 with 45 degrees, 160 degrees. Items 7-9: x = 20 with 90 degrees, x = 18 with 54 degrees, 72 and 108 degrees. Item 10: 80 degrees.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S5 Maths: Angles in Circles |
| Level | Intermediate |
02 Questions (10 items)
- FoundationThe central angle AOB = 128 degrees. Find the inscribed angle ACB on the same arc.
- FoundationThe inscribed angle ACB = 41 degrees. Find the central angle AOB on the same arc.
- FoundationAB is a diameter and the angle BAC = 28 degrees. Find the angle ABC.
- IntermediateIn the cyclic quadrilateral ABCD the angle at B is 108 degrees. Find the angle at D.
- IntermediateIn the same segment the angle ACB = 3x and the angle ADB = 2x + 15. Find x and the angle.
- IntermediateThe points A, B and C divide the circle so that the arcs AB, BC and CA are in the ratio 2 : 3 : 4. Find the largest central angle.
- ChallengeThe central angle AOB = 4x + 10 and the inscribed angle ACB = x + 25 on the same arc. Find x and the central angle.
- ChallengeAB is a diameter, the angle ABC = 3x and the angle BAC = 2x. Find x and the angle ABC.
- ChallengeIn the cyclic quadrilateral ABCD the angles at A and C are in the ratio 2 : 3. Find both angles.
- Error redoA student assumes opposite angles of a cyclic quadrilateral are equal and answers 100 degrees for C when A is 100 degrees. What is the correct value?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 64 degrees | Half of the central angle gives 128 / 2 = 64 degrees. |
| 2 | 82 degrees | Double the inscribed angle: 41 x 2 = 82 degrees. |
| 3 | 62 degrees | The angle ACB is 90 degrees, so the angle ABC is 180 – 90 – 28 = 62 degrees. |
| 4 | 72 degrees | Opposite angles are supplementary, so 180 – 108 = 72 degrees. |
| 5 | x = 15 and the angle is 45 degrees | Equal angles in the same segment give 3x = 2x + 15, so x = 15 and the angle is 45 degrees. |
| 6 | 160 degrees | The largest share is 4 of 9 parts, so 360 x 4 / 9 = 160 degrees. |
| 7 | x = 20 and the central angle is 90 degrees | From 4x + 10 = 2(x + 25) we get x = 20 and the central angle is 90 degrees. |
| 8 | x = 18 and the angle ABC is 54 degrees | Since the angle ACB is 90 degrees, 5x = 90 gives x = 18 and the angle ABC is 54 degrees. |
| 9 | A = 72 degrees and C = 108 degrees | The two angles add to 180 degrees, so one part is 36 degrees and the angles are 72 and 108 degrees. |
| 10 | 80 degrees | Opposite angles are supplementary rather than equal, so 180 – 100 = 80 degrees. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Write the relation as an equation first, solve for x, then substitute back to get the angle.Tutor Registration →
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