IB Class 10 Mathematics Group 5 Geometry & Trigonometry by Pavan | Practice Test to Test Your Knowledge
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  3. IB Class 10 Mathematics Group 5 Geometry & Trigonometry
IB Class 10 Mathematics Group 5 Geometry & Trigonometry

IB Class 10 Mathematics Group 5 Geometry & Trigonometry

Comprehensive mock test on mathematical reasoning, problem-solving, and statistical analysis. Features both standard and extended level concepts with real-world mathematical applications.

2025-07-21
Pavan Pavan
IB Class 10 Mathematics Geometry Trigonometry Grade 10

Duration

30 min

Questions

30

Marking

Negative

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Questions Preview

Which of the following is an example of a scalene triangle?

A
A triangle with all sides equal
B
A triangle with two sides equal
C
A triangle with all sides unequal
D
A triangle with one 90° angle

What is the sum of the interior angles of any triangle?

A
90°
B
180°
C
270°
D
360°

In a right triangle, if the legs have lengths 3 and 4, what is the length of the hypotenuse?

A
5
B
6
C
7
D
8

Which of the following triangles is congruent by the SAS (Side-Angle-Side) criterion?

A
Two triangles with equal angles and sides
B
Two triangles with two sides equal and one included angle equal
C
Two triangles with all sides equal
D
Two triangles with no equal sides or angles

What is the formula to calculate the area of a triangle using base and height?

A
Area = 2 × base × height
B
Area = 1/2 × base × height
C
Area = base × height
D
Area = base × height × 2

In a triangle, the sum of the lengths of any two sides must be greater than which side?

A
The third side
B
The smallest side
C
The largest side
D
The average side

What is the median of the following data set: {4, 7, 1, 9, 5}?

A
4
B
5
C
6
D
7

Which of the following is true for the centroid of a triangle?

A
It is equidistant from all three vertices.
B
It divides each median into a 1:2 ratio.
C
It lies on the Euler line of the triangle.
D
It is located at the intersection of the altitudes.

In a triangle, the exterior angle is equal to the sum of which two interior angles?

A
The adjacent angle and the opposite angle.
B
The two opposite interior angles.
C
The two adjacent angles.
D
The opposite and adjacent angles.

If a triangle has sides of lengths 5, 12, and 13, what type of triangle is it?

A
Acute
B
Right-angled
C
Obtuse
D
Equilateral

Which of the following is the Law of Sines formula?

A
a/sin(A) = b/sin(B) = c/sin(C)
B
a² + b² = c²
C
sin(A) = opposite/hypotenuse
D
a/c = b/c

In a triangle with angles A, B, and C, what is the sum of all the interior angles?

A
90°
B
180°
C
360°
D
270°

What does the Law of Cosines allow you to find in a triangle?

A
It allows you to find an angle given two sides.
B
It allows you to find a side given two angles.
C
It allows you to find the perimeter of the triangle.
D
It allows you to find the area of the triangle.

What is the correct formula for the area of a triangle when given two sides and the included angle?

A
Area = (1/2)ab sin(C)
B
Area = ab + sin(C)
C
Area = (1/2)(a + b) × C
D
Area = (1/2)ab cos(C)

Which of the following statements is true about an isosceles triangle?

A
All three sides are equal.
B
It has two equal angles.
C
It has no equal angles.
D
It has no equal sides.

If a triangle has an area of 12 cm² and a base of 6 cm, what is the height of the triangle?

A
2 cm
B
4 cm
C
6 cm
D
8 cm

Which triangle is classified as 'obtuse'?

A
A triangle with one angle equal to 90°.
B
A triangle with all angles less than 90°.
C
A triangle with one angle greater than 90°.
D
A triangle with all angles equal to 60°.

Which property is true for all similar triangles?

A
They have the same shape and size.
B
Their corresponding angles are equal, and their sides are proportional.
C
Their corresponding sides are equal.
D
They are always congruent.

What does the angle sum property of a triangle state?

A
The sum of any two angles is 90°.
B
The sum of the three interior angles is 180°.
C
The sum of the exterior angle and an adjacent interior angle is 180°.
D
The sum of all angles in a triangle is 360°.

Which of the following triangles can be congruent by the SSS (Side-Side-Side) criterion?

A
Two triangles with three sides equal.
B
Two triangles with two angles and one side equal.
C
Two triangles with two sides and one angle equal.
D
Two triangles with all angles equal.

If the hypotenuse of a right triangle is 13 units and one leg is 5 units, what is the length of the other leg?

A
12 units
B
7 units
C
6 units
D
10 units

Which of the following is true for a right triangle?

A
The sum of the squares of the legs equals the square of the hypotenuse.
B
The sum of all three sides is always 180°.
C
The hypotenuse is the shortest side.
D
All three angles are less than 90°.

What is the formula for calculating the area of a triangle using Heron's formula?

A
Area = √[s(s – a)(s – b)(s – c)]
B
Area = (1/2) × base × height
C
Area = (1/2) × side × side
D
Area = base × height

Which of the following is the correct Law of Sines formula for a triangle?

A
a/sin(A) = b/sin(B) = c/sin(C)
B
a² + b² = c²
C
sin(A) = opposite/hypotenuse
D
a/c = b/c

Which of the following is the definition of the circumcenter of a triangle?

A
It is the intersection of the medians.
B
It is the intersection of the perpendicular bisectors.
C
It is the intersection of the altitudes.
D
It is the intersection of the angle bisectors.

What is the main difference between congruent and similar triangles?

A
Congruent triangles have equal sides and angles, while similar triangles have proportional sides and equal angles.
B
Congruent triangles have proportional sides and angles, while similar triangles have equal sides.
C
Congruent triangles have no equal angles, while similar triangles have equal angles.
D
Congruent triangles have proportional angles, while similar triangles have equal sides.

Which of the following is the Law of Cosines formula?

A
a² = b² + c² − 2bc cos(A)
B
a/sin(A) = b/sin(B) = c/sin(C)
C
sin(A) = opposite/hypotenuse
D
a + b + c = 180°

What does the Pythagorean Theorem relate?

A
It relates the angles of a triangle.
B
It relates the sides of a right triangle.
C
It relates the perimeter of a triangle.
D
It relates the area of a triangle.

In a triangle, the centroid is the intersection of which lines?

A
The altitudes
B
The perpendicular bisectors
C
The medians
D
The angle bisectors

Which of the following is the correct definition of an equilateral triangle?

A
A triangle with two equal sides.
B
A triangle with all three sides equal.
C
A triangle with one angle equal to 90°.
D
A triangle with one obtuse angle.