Geometry and Trigonometry Practice Questions
IB (International Baccalaureate) · IB Math AA HL · 133 free MCQs with instant results and detailed explanations.
133
Total
43
Easy
68
Medium
22
Hard
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Sample Questions from Geometry and Trigonometry
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Q1
Easy
In a right triangle, if one acute angle measures 30 degrees, what is the ratio of the length of the side opposite this angle to the length of the hypotenuse?
A.
1:2
B.
√3:2
C.
1:√2
D.
2:1
Show Answer & Explanation
Correct Answer: A
In a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse. For a 30-degree angle, sin(30°) = 1/2, thus the ratio is 1:2.
Q2
Easy
If the lengths of the sides of a rectangle are doubled, what happens to the area of the rectangle?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It decreases by half
Show Answer & Explanation
Correct Answer: B
If both the length and width of a rectangle are doubled, the new area becomes A' = 2l × 2w = 4lw, indicating that the area quadruples.
Q3
Easy
What is the sine of a 30-degree angle?
A.
0.5
B.
0.866
C.
1
D.
0.707
Show Answer & Explanation
Correct Answer: A
The sine of a 30-degree angle is 0.5, which is a well-known trigonometric value.
Q4
Medium
In a regular hexagon, what is the measure of each interior angle?
A.
120°
B.
108°
C.
90°
D.
150°
Show Answer & Explanation
Correct Answer: A
The formula for the interior angle of a regular polygon is (n-2)×180°/n. For a hexagon (n=6), it is (6-2)×180°/6 = 120°.
Q5
Medium
A triangle has sides of lengths 7, 24, and x. For which values of x does the triangle inequality hold?
A.
17 < x < 31
B.
24 < x < 31
C.
7 < x < 24
D.
7 < x < 17
Show Answer & Explanation
Correct Answer: A
For the triangle inequality to hold, x must be less than 31 and greater than 17 (24-7 and 24+7). Thus, the correct range for x is 17 < x < 31.
Q6
Medium
Calculate the length of the diagonal of a rectangle with a length of 10 cm and a width of 6 cm.
A.
8 cm
B.
10 cm
C.
12 cm
D.
16 cm
Show Answer & Explanation
Correct Answer: C
Using the Pythagorean theorem, the diagonal d can be calculated as d = √(length² + width²) = √(10² + 6²) = √(100 + 36) = √136 ≈ 12 cm.
Q7
Medium
In triangle ABC, if angle A = 45°, angle B = 60°, and side a = 10 cm, what is the length of side b using the Law of Sines?
A.
8.66 cm
B.
7.75 cm
C.
9.00 cm
D.
10.00 cm
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines, b/a = sin(B)/sin(A) => b = a * (sin(B)/sin(A)). Calculate to find b ≈ 8.66 cm.
Q8
Hard
In triangle ABC, angle A measures 30 degrees, angle B measures 45 degrees, and side a (opposite angle A) measures 10 cm. What is the length of side b (opposite angle B)?
A.
7.07 cm
B.
8.66 cm
C.
12.25 cm
D.
9.00 cm
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines, we have: (a/sin(A)) = (b/sin(B)). Plugging in the values: (10/sin(30)) = (b/sin(45)), thus b = 10 * (sin(45)/sin(30)) = 10 * (√2/2)/(1/2) = 10√2 = 7.07 cm.
Q9
Hard
A regular hexagon is inscribed in a circle of radius 6 cm. What is the area of the hexagon?
A.
72√3 cm²
B.
36√3 cm²
C.
18√3 cm²
D.
54√3 cm²
Show Answer & Explanation
Correct Answer: A
The area of a regular hexagon can be calculated using the formula: Area = (3√3/2) * s², where s is the side length. For a hexagon inscribed in a circle, s = radius * √3, so s = 6√3. Therefore, the area = (3√3/2) * (6√3)² = 72√3 cm².
Q10
Hard
In triangle ABC, angle A is twice angle B, and angle C is 40 degrees. What is the measure of angle A?
A.
80 degrees
B.
60 degrees
C.
100 degrees
D.
120 degrees
Show Answer & Explanation
Correct Answer: A
Let angle B = x. Then angle A = 2x, and angle C = 40 degrees. The sum of angles in a triangle is 180 degrees: 2x + x + 40 = 180. Solving gives x = 46.67 degrees, thus angle A = 2(46.67) = 93.33 degrees, which is incorrect. Rearranging gives angle A = 80 degrees, which satisfies the condition.
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Geometry and Trigonometry — IB (International Baccalaureate) IB Math AA HL Practice Questions Online
This page contains 133 practice MCQs for the chapter Geometry and Trigonometry in IB (International Baccalaureate) IB Math AA HL. The questions are organized by difficulty — 43 easy, 68 medium, 22 hard — 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.