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S5 Maths: Angles in Circles: Paper 4 (error replay)
S5 Maths: Angles in Circles: Paper 4 (error replay)
Ten items on the usual slips: doubling and halving mixed up, opposite angles treated as equal, and semicircle or arc ratio errors.
Direct answers Items 1-3: 37, 56, 46 degrees. Items 4-6: 62 degrees, x = 10 with 50 degrees, 40 degrees. Items 7-9: x = 20 with 132 degrees, x = 10 with 50 degrees, 100 degrees. Item 10: 180 degrees is wrong; the answer is 45 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 | Error replay |
02 Questions (10 items)
- FoundationThe central angle AOB = 74 degrees. Find the inscribed angle on the same arc.
- FoundationAn inscribed angle is 28 degrees. Find the central angle on the same arc.
- FoundationAB is a diameter and the angle ABC = 44 degrees. Find the angle BAC.
- IntermediateIn the cyclic quadrilateral ABCD the angle at D is 118 degrees. Find the angle at B.
- IntermediateIn the same segment the angle ACB = 5x and the angle ADB = 3x + 20. Find x and the angle.
- IntermediateThe arcs AB and BC are in the ratio 2 : 7 and the angle BOC = 140 degrees. Find the angle AOB.
- ChallengeThe central angle AOB = 6x + 12 and the inscribed angle ACB = 2x + 26 on the same arc. Find x and the central angle.
- ChallengeAB is a diameter, the angle ABC = 4x and the angle BAC = 5x. Find x and the angle BAC.
- ChallengeIn the cyclic quadrilateral ABCD the angles at A, B and C are in the ratio 3 : 4 : 6. Find the angle at D.
- Error redoA student sees a central angle of 90 degrees and writes the inscribed angle on the same arc as 180 degrees. What is wrong, and what is the correct value?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 37 degrees | Divide the central angle by 2 to get 37 degrees. |
| 2 | 56 degrees | Multiply the inscribed angle by 2 to get 56 degrees. |
| 3 | 46 degrees | The angle ACB is 90 degrees, so the angle BAC is 90 – 44 = 46 degrees. |
| 4 | 62 degrees | Opposite angles add to 180 degrees, so 180 – 118 = 62 degrees. |
| 5 | x = 10 and the angle is 50 degrees | Equal angles in the same segment give 5x = 3x + 20, so x = 10 and the angle is 50 degrees. |
| 6 | 40 degrees | One part is 140 / 7 = 20 degrees, so the arc AB gives 2 parts, that is 40 degrees. |
| 7 | x = 20 and the central angle is 132 degrees | From 6x + 12 = 2(2x + 26) we get x = 20 and the central angle is 132 degrees. |
| 8 | x = 10 and the angle BAC is 50 degrees | Since the angle ACB is 90 degrees, 9x = 90 gives x = 10 and the angle BAC is 50 degrees. |
| 9 | 100 degrees | The angles at A and C total 9 parts or 180 degrees, so one part is 20 degrees; the three known angles are 60, 80 and 120 degrees, so D is 360 – 260 = 100 degrees. |
| 10 | 180 degrees is wrong; it should be 45 degrees | The inscribed angle is half the central angle, so 90 / 2 = 45 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 one line for each slip, such as doubling the inscribed angle by mistake.Tutor Registration →
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