Form 3 Properties of Circles Practice
Form 3 · 20 practice questions with instant marking and worked solutions.
Properties of Circles is an important part of the Form 3 mathematics curriculum. This topic develops radius, diameter, circumference, area and angle properties. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.
A reliable approach to Properties of Circles has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.
The twenty original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Properties of Circles; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample.
Effective revision is more than recording a score. After completing the Properties of Circles set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.
Properties of Circles should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.
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0 / 20 answered
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1 BasicAn angle at the circumference subtended by an arc is 25°. Find the angle at the centre. Choose the correct answer.
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2 BasicAn angle at the circumference subtended by an arc is 30°. Find the angle at the centre. Give the numerical value only.
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3 BasicAn angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Show the essential working and give the numerical value.
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4 BasicIn Properties of Circles, the value of $2\times 20^\circ$ is 41. Is this statement true?
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5 StandardAn angle at the circumference subtended by an arc is 30°. Find the angle at the centre. Choose the correct answer.
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6 StandardAn angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Give the numerical value only.
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7 StandardAn angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Show the essential working and give the numerical value.
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8 StandardIn Properties of Circles, the value of $2\times 25^\circ$ is 50. Is this statement true?
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9 AdvancedAn angle at the circumference subtended by an arc is 35°. Find the angle at the centre. Choose the correct answer.
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10 AdvancedAn angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Give the numerical value only.
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11 AdvancedAn angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Show the essential working and give the numerical value.
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12 AdvancedIn Properties of Circles, the value of $2\times 30^\circ$ is 61. Is this statement true?
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13 ChallengingAn angle at the circumference subtended by an arc is 40°. Find the angle at the centre. Choose the correct answer.
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14 ChallengingAn angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Give the numerical value only.
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15 ChallengingAn angle at the circumference subtended by an arc is 50°. Find the angle at the centre. Show the essential working and give the numerical value.
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16 ChallengingIn Properties of Circles, the value of $2\times 35^\circ$ is 70. Is this statement true?
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17 EliteAn angle at the circumference subtended by an arc is 45°. Find the angle at the centre. Choose the correct answer.
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18 EliteAn angle at the circumference subtended by an arc is 50°. Find the angle at the centre. Give the numerical value only.
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19 EliteAn angle at the circumference subtended by an arc is 55°. Find the angle at the centre. Show the essential working and give the numerical value.
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20 EliteIn Properties of Circles, the value of $2\times 40^\circ$ is 81. Is this statement true?
The report lists what you got wrong and why. Only you can see it.
Common mistakes
Common mistakes in Properties of Circles
This topic needs particular care with radius, diameter, circumference, area and angle properties. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.
Keep missing the same type?
Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.