Geometry of 2D and 3D Shapes: Master Shapes and Solids

Question 1

A triangle with two equal sides is called an:

Accepted Answer

Isosceles triangle

Answer

Equilateral triangle

Answer

Scalene triangle

Answer

Right-angled triangle

Question 2

A vector with zero magnitude is known as a:

Accepted Answer

Zero vector

Answer

Unit vector

Answer

Parallel vector

Answer

Perpendicular vector

Question 3

The angle between two vectors is calculated using:

Accepted Answer

The dot product of the vectors

Answer

The scalar product of the vectors

Answer

The vector product of the vectors

Answer

The cross product of the vectors

Question 4

Which solid has the largest surface area given the same volume?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 5

Find the sum of the interior angles of a regular pentagon. (Select the best answer)

Accepted Answer

540°

Answer

324°

Answer

720°

Answer

900°

Question 6

Which transformation preserves both the shape and size of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 7

Calculate the area of a sector of a circle with a radius of 10 cm and a central angle of 60 degrees. (Provide the answer in terms of π)

Accepted Answer

25π cm²

Answer

50π cm²

Answer

100π cm²

Answer

200π cm²

Question 8

Identify the vector parallel to the vector (2, -3).

Accepted Answer

(4, -6)

Answer

(6, -9)

Answer

(1, -1.5)

Answer

(3, 4.5)

Question 9

Which of the following is NOT a common theorem used in geometry?

Accepted Answer

Converse of Base Angles Theorem

Answer

Pythagoras Theorem

Answer

Sine Rule

Answer

Law of Cosines

Question 10

Find the volume of a cube with side lengths of 3 cm

Accepted Answer

27 cm³

Answer

9 cm³

Answer

81 cm³

Answer

243 cm³

Question 11

Determine the gradient of the line connecting points (2, 3) and (4, 7)

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 12

Write down the equation of a circle centered at the origin with a radius of 5

Accepted Answer

x² + y² = 25

Answer

x² + y² = 5

Answer

(x - 5)² + (y - 5)² = 25

Answer

x² + y² = 100

Question 13

Which of the following physical quantities is a vector quantity?

Accepted Answer

Speed

Answer

Temperature

Answer

Mass

Answer

Volume

Question 14

Which of the following matrices represents the identity matrix?

Accepted Answer

[1 0]
[0 1]

Answer

[0 1]
[1 0]

Answer

[1 2]
[3 4]

Answer

[0 0]
[0 0]

Question 15

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a² + c² = b²

Question 16

Identify the transformation that does NOT preserve the shape of an object:

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 17

Identify the solid that is not a polyhedron:

Accepted Answer

Sphere

Answer

Cube

Answer

Tetrahedron

Answer

Cylinder

Question 18

Determine a vector equation of a line passing through the point (2, 3) and parallel to the vector v = (4, -1):

Accepted Answer

r = (2, 3) + t(4, -1)

Answer

r = (2, 3) - t(4, -1)

Answer

r = (4, -1) + t(2, 3)

Answer

r = (4, -1) - t(2, 3)

Question 19

Which transformation preserves distance?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 20

Find the surface area of a cube with side length 5 cm.

Accepted Answer

100 square centimeters

Answer

25 square centimeters

Answer

50 square centimeters

Answer

150 square centimeters

Question 21

Which shape exhibits rotational symmetry of order 6?

Accepted Answer

Regular hexagon

Answer

Triangle

Answer

Square

Answer

Circle

Question 22

Which of the following is not considered a transformation in geometry?

Accepted Answer

Multiplication of dimensions

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 23

Find the gradient of the line passing through the points (1, 2) and (3, 6).

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 24

Which matrix represents a 90-degree clockwise rotation?

Accepted Answer

[[0, -1], [1, 0]]

Answer

[[0, 1], [-1, 0]]

Answer

[[1, 0], [0, 1]]

Answer

[[1, 0], [0, -1]]

Question 25

Calculate the area of a triangular shape given its base of 10 cm and height of 5 cm.

Accepted Answer

25 cm²

Answer

50 cm²

Answer

75 cm²

Answer

100 cm²

Question 26

Formulate the equation for a circle with center at (2, 3) and radius 5.

Accepted Answer

(x - 2)² + (y - 3)² = 25

Answer

(x - 3)² + (y - 2)² = 5

Answer

(x + 2)² + (y + 3)² = 25

Answer

(x + 3)² + (y + 2)² = 5

Question 27

Determine the equation of a circle with center (-2, 3) and radius 5.

Accepted Answer

(x + 2)^2 + (y - 3)^2 = 25

Answer

(x + 2)^2 + (y - 3)^2 = 5

Answer

(x - 3)^2 + (y + 2)^2 = 25

Answer

(x - 3)^2 + (y + 2)^2 = 5

Question 28

Which of the following is the correct formula for finding the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

2 * base * height

Answer

1/4 * base * height

Answer

base * height

Question 29

Which transformation will not map a figure onto itself?

Accepted Answer

Reflection in a line that is not an axis of symmetry

Answer

Rotation by 180°

Answer

Translation

Question 30

Identify the matrix that represents a rotation of 90° clockwise about the origin.

Accepted Answer

[0, -1; 1, 0]

Answer

[1, 0; 0, 1]

Answer

[-1, 0; 0, -1]

Answer

[0, 1; -1, 0]

Question 31

Which of the geometric transformations does not alter the orientation of a figure?

Accepted Answer

Translation

Answer

Dilation

Answer

Rotation

Answer

Reflection

Question 32

A matrix with 3 rows and 2 columns has what order?

Accepted Answer

3 x 2

Answer

6

Answer

2 x 3

Question 33

Identify the vector quantity.

Accepted Answer

Velocity

Answer

Mass

Answer

Temperature

Answer

Density

Question 34

Calculate the volume of a rectangular prism with a length of 4 centimeters, a width of 3 centimeters, and a height of 5 centimeters.

Accepted Answer

60 cubic centimeters

Answer

20 cubic centimeters

Answer

120 cubic centimeters

Answer

30 cubic centimeters

Question 35

Identify the correct order of rotational symmetry for a regular hexagon.

Accepted Answer

C6

Answer

C12

Answer

C2

Answer

C3

Question 36

Which of the following solids has the smallest surface area?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 37

Which of the following is a property of a circle?

Accepted Answer

Equal radii from the center to any point on the circumference

Answer

Parallel sides

Answer

Number of sides

Answer

Congruent angles

Question 38

Which of the following transformations will map a shape onto itself?

Accepted Answer

Rotation by an angle of 180 degrees

Answer

Translation

Answer

Reflection over a line

Answer

Dilation

Question 39

Given a right-angled triangle with sides a, b, and hypotenuse c, what is the formula for Pythagoras' theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

a² + b² - c² = 0

Question 40

A cuboid has a length of 3 centimeters, a width of 2 centimeters, and a height of 5 centimeters. Calculate its volume.

Accepted Answer

30 cubic centimeters

Answer

60 cubic centimeters

Answer

10 cubic centimeters

Answer

15 cubic centimeters

Question 41

Which of the following is the equation of a straight line with a gradient of 2 and a y-intercept of -1?

Accepted Answer

y = 2x - 1

Answer

y = -2x + 1

Answer

y = 1x - 2

Answer

y = -1x + 2

Question 42

A sphere has a radius of 5 cm. What is its surface area?

Accepted Answer

100π sq cm

Answer

50π sq cm

Answer

25π sq cm

Answer

125π sq cm

Question 43

Given the matrix A = [2 3; 4 5], what is the value of the element at the first row and second column (A[1,2])?

Accepted Answer

3

Answer

4

Answer

5

Answer

2

Question 44

A regular hexagon has a side length of 6 cm. What is its area?

Accepted Answer

54√3 cm²

Answer

36√3 cm²

Answer

108 cm²

Answer

108√3 cm²

Question 45

A cube has a volume of 64 cm³. What is the length of one side of the cube?

Accepted Answer

4 cm

Answer

16 cm

Answer

8 cm

Answer

32 cm

Question 46

A sphere has a radius of 5 cm. What is its surface area?

Accepted Answer

100π cm²

Answer

125π cm²

Answer

25π cm²

Answer

50π cm²

Question 47

A triangle has vertices at A(1,2), B(3,4), and C(5,2). What is its area?

Accepted Answer

2 square units

Answer

6 square units

Answer

8 square units

Answer

4 square units

Question 48

A circle has a diameter of 10 cm. What is its circumference?

Accepted Answer

10π cm

Answer

5π cm

Answer

20π cm

Answer

25π cm

Question 49

A vector is represented by the coordinates (3, -2). What is its magnitude?

Accepted Answer

√13

Answer

1

Answer

5

Question 50

A triangle is reflected in the y-axis. What happens to the coordinates of its vertices?

Accepted Answer

The x-coordinates change sign, the y-coordinates remain the same.

Answer

Both x and y coordinates change sign.

Answer

The y-coordinates change sign, the x-coordinates remain the same.

Question 51

A matrix is used to represent a rotation of 90 degrees clockwise about the origin. What is the matrix?

Accepted Answer

[[0, 1], [-1, 0]]

Answer

[[0, -1], [1, 0]]

Answer

[[1, 0], [0, 1]]

Question 52

A pyramid has a square base with side length 4 cm and a height of 6 cm. What is the volume of the pyramid?

Accepted Answer

32 cm³

Answer

48 cm³

Answer

16 cm³

Answer

64 cm³

Question 53

A cone has a radius of 3 cm and a height of 4 cm. What is the slant height of the cone?

Accepted Answer

5 cm

Answer

4 cm

Answer

3 cm

Answer

7 cm