Geometry and Trigonometry Practice Questions
IB (International Baccalaureate) · IB Math AI SL · 132 free MCQs with instant results and detailed explanations.
132
Total
43
Easy
68
Medium
21
Hard
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Sample Questions from Geometry and Trigonometry
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Q1
Easy
What is the sum of the interior angles of a hexagon?
A.
720 degrees
B.
180 degrees
C.
540 degrees
D.
360 degrees
Show Answer & Explanation
Correct Answer: A
The formula for the sum of interior angles of a polygon is (n-2) ร 180 degrees, where n is the number of sides. For a hexagon, n = 6, so (6-2) ร 180 = 720 degrees.
Q2
Easy
In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 units, what is the length of the side opposite the 30-degree angle?
A.
5 units
B.
10 units
C.
7.5 units
D.
8.66 units
Show Answer & Explanation
Correct Answer: A
In a right triangle, the side opposite a 30-degree angle is half the length of the hypotenuse. Thus, the length is 10 / 2 = 5 units.
Q3
Easy
If the radius of a circle is 4 units, what is the area of the circle?
A.
16ฯ square units
B.
8ฯ square units
C.
12ฯ square units
D.
20ฯ square units
Show Answer & Explanation
Correct Answer: A
The area A of a circle is calculated using the formula A = ฯrยฒ. For a radius (r) of 4 units, A = ฯ(4)ยฒ = ฯ(16) = 16ฯ square units.
Q4
Medium
In triangle ABC, angle A measures 30 degrees and angle B measures 60 degrees. What is the measure of angle C?
A.
90 degrees
B.
120 degrees
C.
150 degrees
D.
30 degrees
Show Answer & Explanation
Correct Answer: A
The sum of angles in a triangle is always 180 degrees. Here, angle C can be found by subtracting the sum of angles A and B from 180 degrees: C = 180 - (30 + 60) = 90 degrees.
Q5
Medium
A right triangle has one leg measuring 6 m and the hypotenuse measuring 10 m. What is the length of the other leg?
A.
8 m
B.
4 m
C.
5 m
D.
12 m
Show Answer & Explanation
Correct Answer: A
Using the Pythagorean theorem, aยฒ + bยฒ = cยฒ, where c is the hypotenuse. Here, 6ยฒ + bยฒ = 10ยฒ. This simplifies to 36 + bยฒ = 100, so bยฒ = 64, making b = 8 m.
Q6
Medium
In triangle ABC, if angle A measures 45 degrees and side a = 10 cm, what is the length of side b if angle B measures 60 degrees? (Use sine rule)
A.
12.25 cm
B.
8.66 cm
C.
7.50 cm
D.
9.97 cm
Show Answer & Explanation
Correct Answer: A
Using the sine rule, b/a = sin(B)/sin(A). Plugging in the values, we get b = 10 * (sin(60)/sin(45)) = 12.25 cm.
Q7
Medium
A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 120 degrees at the center of the circle?
A.
10.47 cm
B.
5.24 cm
C.
4.43 cm
D.
15.71 cm
Show Answer & Explanation
Correct Answer: A
Arc length L = r * ฮธ (in radians). Convert 120 degrees to radians (120ยฐ * ฯ/180 = 2ฯ/3). Then L = 5 * (2ฯ/3) = 10.47 cm.
Q8
Hard
In triangle ABC, angle A is 30 degrees, angle B is 60 degrees, and side a (opposite angle A) is 10 cm. What is the length of side b (opposite angle B)?
A.
8.66 cm
B.
5 cm
C.
7.5 cm
D.
10 cm
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines: b/a = sin(B)/sin(A). Substituting the values gives b/10 = sin(60ยฐ)/sin(30ยฐ). This simplifies to b = 10 * (โ3/2) / (1/2) = 10โ3/1 = 8.66 cm.
Q9
Hard
A circle is inscribed in an equilateral triangle with a side length of 12 cm. What is the radius of the inscribed circle?
A.
4 cm
B.
3โ3 cm
C.
2โ3 cm
D.
6 cm
Show Answer & Explanation
Correct Answer: C
For an equilateral triangle, the radius r of the inscribed circle is given by r = (side ร โ3)/6. Substituting the side length 12 cm gives r = (12 ร โ3)/6 = 2โ3 cm.
Q10
Hard
In a triangle ABC, the lengths of sides a, b, and c are 7, 8, and 9 units, respectively. What is the area of triangle ABC using Heron's formula?
A.
24.0 unitsยฒ
B.
26.8 unitsยฒ
C.
28.0 unitsยฒ
D.
30.5 unitsยฒ
Show Answer & Explanation
Correct Answer: B
The area of the triangle can be calculated using Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2. Here, s = (7+8+9)/2 = 12.5. Then, Area = sqrt(12.5(12.5-7)(12.5-8)(12.5-9)) = sqrt(12.5*5.5*4.5*3.5) = sqrt(24.1875) = 26.8 unitsยฒ.
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Geometry and Trigonometry โ IB (International Baccalaureate) IB Math AI SL Practice Questions Online
This page contains 132 practice MCQs for the chapter Geometry and Trigonometry in IB (International Baccalaureate) IB Math AI SL. The questions are organized by difficulty โ 43 easy, 68 medium, 21 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.