Circles Practice Questions
SPM (Malaysia) · SPM Mathematics · 144 free MCQs with instant results and detailed explanations.
144
Total
51
Easy
70
Medium
23
Hard
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Sample Questions from Circles
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
What is the radius of a circle if its diameter is 10 cm?
A.
5 cm
B.
10 cm
C.
20 cm
D.
15 cm
Show Answer & Explanation
Correct Answer: A
The radius is half of the diameter. Therefore, if the diameter is 10 cm, the radius is 10 cm / 2 = 5 cm.
Q2
Easy
What is the circumference of a circle with a radius of 7 cm? (Use ฯ โ 3.14)
A.
43.96 cm
B.
21.98 cm
C.
15.7 cm
D.
49.32 cm
Show Answer & Explanation
Correct Answer: A
The circumference of a circle is calculated using the formula C = 2ฯr. For a radius (r) of 7 cm, C = 2 ร 3.14 ร 7 = 43.96 cm.
Q3
Easy
If the diameter of a circle is 10 cm, what is its area? (Use ฯ โ 3.14)
A.
78.5 cmยฒ
B.
31.4 cmยฒ
C.
50 cmยฒ
D.
25 cmยฒ
Show Answer & Explanation
Correct Answer: A
The area of a circle is found using the formula A = ฯrยฒ. The diameter is 10 cm, so the radius (r) is 5 cm. Area = 3.14 ร (5)ยฒ = 3.14 ร 25 = 78.5 cmยฒ.
Q4
Medium
A circle has a radius of 7 cm. What is the circumference of the circle? (Use ฯ = 22/7)
A.
44 cm
B.
14 cm
C.
49 cm
D.
28 cm
Show Answer & Explanation
Correct Answer: A
The circumference of a circle is calculated using the formula C = 2ฯr. Here, C = 2 ร (22/7) ร 7 = 44 cm.
Q5
Medium
In a circle, the lengths of two chords are 12 cm and 16 cm. If they are equidistant from the center, what is the distance from the center to the chords?
A.
5 cm
B.
6 cm
C.
8 cm
D.
7 cm
Show Answer & Explanation
Correct Answer: B
For two chords equally distant from the center, the distance can be found using the perpendicular distance from the center to a chord formula. Here, the distance is 6 cm.
Q6
Medium
If the diameter of a circle is increased by 50%, what is the percentage increase in the area of the circle?
A.
75%
B.
100%
C.
125%
D.
150%
Show Answer & Explanation
Correct Answer: B
The area of a circle is proportional to the square of the radius. If the diameter increases by 50%, the radius increases by 25%, resulting in a 100% increase in area.
Q7
Medium
A tangent to a circle makes an angle of 30ยฐ with a line drawn from the center to the point of tangency. What is the measure of the angle between the tangent and the chord through the point of tangency?
A.
30ยฐ
B.
60ยฐ
C.
90ยฐ
D.
120ยฐ
Show Answer & Explanation
Correct Answer: B
The angle between the tangent and the chord is equal to the angle in the alternate segment. Here, it is 60ยฐ since the right angle is complementary to the 30ยฐ angle.
Q8
Hard
In a circle, an angle subtended at the center is twice the angle subtended at any point on the remaining part of the circle. If angle AOB is 60 degrees, what is the measure of angle APB where P is any point on the circumference of the circle?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
45 degrees
Show Answer & Explanation
Correct Answer: A
According to the theorem of angles subtended by the same arc, the angle at the circumference (angle APB) is half of the angle at the center (angle AOB). Therefore, angle APB = 60 degrees / 2 = 30 degrees.
Q9
Hard
A chord AB of a circle with radius 10 cm is 12 cm long. What is the distance from the center of the circle to the chord AB?
A.
6 cm
B.
8 cm
C.
5 cm
D.
7 cm
Show Answer & Explanation
Correct Answer: B
To find the distance from the center to the chord, we can use the Pythagorean theorem. The half-length of the chord is 6 cm, and the radius is 10 cm. The distance from the center to the chord is the square root of (radius^2 - half chord^2), which gives us โ(10^2 - 6^2) = โ(100 - 36) = โ64 = 8 cm.
Q10
Hard
A tangent to a circle intersects a line through the center of the circle at an angle of 60 degrees. If the radius of the circle is 10 cm, what is the length of the tangent segment from the point of tangency to the intersection with the line?
A.
5 cm
B.
10 cm
C.
5โ3 cm
D.
10โ3 cm
Show Answer & Explanation
Correct Answer: C
The length of the tangent segment can be calculated using the relationship between the angle and the radius. The tangent forms a right triangle with the radius and the angle; therefore, using trigonometry, tangent length = radius * tan(60ยฐ) = 10 cm * โ3 = 10โ3 cm. However, the question asks for the length from the point of tangency to the intersection, which is opposite the 60-degree angle, giving us 10 * sqrt(3)/2 = 5โ3 cm.
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Circles โ SPM (Malaysia) SPM Mathematics Practice Questions Online
This page contains 144 practice MCQs for the chapter Circles in SPM (Malaysia) SPM Mathematics. The questions are organized by difficulty โ 51 easy, 70 medium, 23 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.