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S5 Maths: Properties of Circles (10 Retry Items)
S5 Maths: Properties of Circles (10 Retry Items)
Ten retry items on the usual slips: half chord taken as the centre distance, OP minus radius taken as a tangent, parallel chords added on the wrong side, tangents at 45 degrees, and a central angle halved.
Fix only the differences A retry paper adds nothing new; it corrects five recurring slips: swapping the half chord with the centre distance, subtracting the radius from OP, adding or subtracting parallel chords on the wrong side, answering 45 degrees for a tangent, and halving an angle that is already an inscribed angle. Write your original answer first, then note the difference.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Error redo 10 |
| Chapter | Chapter: S5 Maths: Properties of Circles – Chords, Arcs and Tangents |
| Level | S5 Maths |
02 Questions (10 items)
- Error redoRetry 1: with radius 13 cm and centre distance 5 cm, a student answers a chord of 12 cm. What is correct?
- Error redoRetry 2: a student says the tangent meets the radius at 45 degrees. What is correct?
- Error redoRetry 3: a student says two tangents from one external point need not be equal. Is that right?
- Error redoRetry 4: with radius 10 cm and chord 12 cm, a student answers a centre distance of 6 cm. What is correct?
- Error redoRetry 5: with OP = 25 cm and radius 7 cm, a student answers a tangent of 18 cm. What is correct?
- Error redoRetry 6: two parallel chords of 24 cm and 10 cm on opposite sides of the centre of a radius 13 cm circle; a student answers 7 cm apart. What is correct?
- Error redoRetry 7: with radius 17 cm and chord 30 cm, a student answers a centre distance of 15 cm. What is correct?
- Error redoRetry 8: with radius 8 cm and central angle 60 degrees, a student answers a chord of 4 cm. What is correct?
- Error redoRetry 9: a student says the perpendicular bisector of a chord is parallel to a diameter. What is correct?
- Error redoRetry 10: tangents make an angle APB of 90 degrees; a student answers angle AOB of 45 degrees. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 24 cm. | Twelve is only half the chord; double it to 24. |
| 2 | 90 degrees; the tangent is perpendicular to the radius at the point of contact. | The tangent is perpendicular to the radius, so mark a right angle in your diagram. |
| 3 | No. Tangents from the same external point are always equal. | The two right triangles are congruent, so the tangents are always equal. |
| 4 | 8 cm. | Six is half the chord, not the distance; the root of 64 is 8. |
| 5 | 24 cm. | Subtracting the radius from OP is wrong; use Pythagoras to get 24. |
| 6 | 17 cm. | On opposite sides add 5 and 12; 7 is the same-side answer. |
| 7 | 8 cm. | Fifteen is half the chord; the root of 64 is 8. |
| 8 | 8 cm. | A 60 degree angle with two radii gives an equilateral triangle, so the chord equals the radius. |
| 9 | It passes through the centre, so it lies along a diameter. | The centre is equidistant from both ends, so it lies on the perpendicular bisector. |
| 10 | Angle AOB is 90 degrees. | The two angles are supplementary, so the central angle is also 90 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.
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