Why is error correction better than more new questions?

It targets one failed judgement: the same diagram type and the same clue with different numbers. Naming exactly which step went wrong builds a fixed routine of locating the centre or the circumference first, then deciding whether to double or halve.

What counts as a proper correction?

Two sentences: one naming the wrong rule that was used, and one giving the correct steps and answer. Copying only the right answer leaves the same error for the next question.

S3 Mathematics: Circle Properties, Angles in a Circle and Tangents (Error Correction, 10 Questions)

2026-11-07

Tutor Prep Guide · S3 Mathematics

Ten error-correction items on circle properties: reversing the relationship between the angle at the circumference and the central angle, forgetting that the angle in a semicircle is a right angle, using the radius as a diameter, treating opposite angles of a cyclic quadrilateral as equal, and assuming tangents from one external point have different lengths. Each item names what the wrong answer missed, then gives the correct steps and answer with a one-line explanation.

Quick answer Answers in order: 58 degrees, 50 degrees, 25.12 cm, 50 degrees, 75 degrees, 48 degrees, 1/3, 10 cm, 6 cm, 90 degrees. State what went wrong first.

01 Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	about 30 minutes
Difficulty mix	Error redo 10
Chapter	Chapter: S3 Mathematics: Circle Properties, Angles in a Circle and Tangents
Level	S3

02 Questions (10 items)

Error redoAB is a diameter, C lies on the circle and angle ABC is 32 degrees. A student answers angle BAC = 148 degrees. What is wrong, and what is the correct answer?
Error redoA central angle standing on an arc is 100 degrees. A student says the angle at the circumference on the same arc is 200 degrees. What is wrong, and what is the correct answer?
Error redoA circle has radius 4 cm. A student gives 3.14 x 4 = 12.56 cm as the circumference. What is wrong, and what is the correct circumference? (Take pi as 3.14)
Error redoAn angle at the circumference standing on an arc is 25 degrees. A student answers that the central angle is 12.5 degrees. What is wrong, and what is the correct answer?
Error redoABCD is a cyclic quadrilateral and angle A is 105 degrees. A student answers that angle C is 105 degrees. What is wrong, and what is the correct answer?
Error redoTwo angles at the circumference stand on the same arc. One is 48 degrees and the other is x. A student answers x = 42 degrees. What is wrong, and what should x be?
Error redoA central angle in a circle is 120 degrees. A student says the arc is 1/2 of the whole circumference. What is wrong, and what is the correct fraction?
Error redoA circle has circumference 62.8 cm. A student answers that the radius is 20 cm. What is wrong, and what is the correct radius? (Take pi as 3.14)
Error redoTwo tangents PA and PB are drawn from an external point P, touching the circle at A and B, and PA is 6 cm. A student answers PB = 12 cm. What is wrong, and what is PB?
Error redoPA is a tangent touching the circle at A and O is the centre. A student answers that angle OAP is 45 degrees. What is wrong, and what is the correct answer?

03 Answers and one-line notes

#	Answer	One-line note
1	58 degrees	The student only did 180 minus 32 and forgot that the angle in a semicircle, angle ACB, is 90 degrees: 180 – 90 – 32 = 58 degrees.
2	50 degrees	The relationship is reversed: the angle at the circumference is half the central angle, not double it, so 100 divided by 2 gives 50 degrees.
3	25.12 cm	The student used the radius as if it were the diameter: circumference is 2 x pi x r, that is 2 x 3.14 x 4 = 25.12 cm.
4	50 degrees	The halving was applied in the wrong direction: from the angle at the circumference to the central angle you double, so 25 x 2 = 50 degrees.
5	75 degrees	The student assumed opposite angles are equal, but opposite angles of a cyclic quadrilateral are supplementary: 180 – 105 = 75 degrees.
6	48 degrees	The student treated the two angles as supplementary, but angles at the circumference on the same arc are equal, so x is 48 degrees.
7	1/3	The student used 180 degrees as the whole turn, but a full turn is 360 degrees, so 120 out of 360 is 1/3.
8	10 cm	The student divided by pi only once: r equals circumference divided by 2 pi, that is 62.8 divided by 6.28, giving 10 cm.
9	6 cm	The student assumed the second tangent is double the first, but tangents from the same external point are equal in length, so PB equals PA, that is 6 cm.
10	90 degrees	The student treated the radius and tangent as meeting at a slant, but a radius is perpendicular to the tangent at the point of contact, so the angle is 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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