Geometry for Business: Master Shapes and Angles for Success

Question 1

Which of these shapes has the greatest number of sides?

Accepted Answer

Hexagon

Answer

Triangle

Answer

Quadrilateral

Answer

Pentagon

Question 2

In a triangle, what is the total measure of its interior angles?

Accepted Answer

180 degrees

Answer

120 degrees

Answer

360 degrees

Answer

540 degrees

Question 3

What formula is used to calculate the area of a circle?

Accepted Answer

A = πr²

Answer

A = πr

Answer

A = 2πr

Answer

A = 4πr

Question 4

When two straight lines intersect and form a right angle, what is the measure of that angle?

Accepted Answer

90 degrees

Answer

30 degrees

Answer

45 degrees

Answer

120 degrees

Question 5

Among the following transformations, which one does not alter the size or shape of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 6

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

b² - a² = c²

Answer

c² - a² = b²

Question 7

Which of the following is a three-dimensional shape?

Accepted Answer

Sphere

Answer

Triangle

Answer

Square

Answer

Rectangle

Question 8

Which of the following is not a two-dimensional geometric shape?

Accepted Answer

Prism

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 9

What is the area of a circle with a radius of 4 centimeters?

Accepted Answer

16π cm²

Answer

8π cm²

Answer

2π cm²

Answer

4π cm²

Question 10

Which of the following is the correct formula for the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c

Answer

c² - a² = b

Answer

c - a² = b²

Question 11

What is the formula for the perimeter of a rectangle?

Accepted Answer

2(a + b)

Answer

(a + b) / 2

Answer

a + b + c + d

Answer

(a + b + c) / 2

Question 12

Which of the following is a three-dimensional shape with a circular base and a single vertex?

Accepted Answer

Cone

Answer

Cylinder

Answer

Sphere

Answer

Pyramid

Question 13

Which of the following is NOT a valid unit for measuring angles?

Accepted Answer

Centimeters

Answer

Degrees

Answer

Radians

Question 14

Which of the following is NOT a property of a parallelogram?

Accepted Answer

Adjacent angles are supplementary.

Answer

Opposite sides are parallel.

Answer

Opposite angles are equal.

Answer

Diagonals bisect each other.

Question 15

Which of the following shapes has 4 equal sides and 4 right angles?

Accepted Answer

Square

Answer

Rectangle

Answer

Kite

Answer

Trapezoid

Question 16

The Pythagorean theorem can be used to find the:

Accepted Answer

Length of the hypotenuse of a right-angled triangle.

Answer

Area of a right-angled triangle.

Answer

Perimeter of a right-angled triangle.

Answer

Height of a right-angled triangle.

Question 17

A circle's diameter measures 8 centimeters. What's the length of its radius?

Accepted Answer

4 cm

Answer

2 cm

Answer

8 cm

Answer

16 cm

Question 18

Which property is NOT characteristic of a circle?

Accepted Answer

A finite number of straight sides

Answer

Constant radius from the center to any point on the circumference

Answer

Unchanging area for a given radius

Answer

Closed and non-intersecting path

Question 19

The angles in an equilateral triangle measure:

Accepted Answer

60°, 60°, 60°

Answer

30°, 60°, 90°

Answer

45°, 45°, 90°

Answer

90°, 90°, 90°

Question 20

Calculate the area of a rectangle with a length of 5 cm and a width of 3 cm.

Accepted Answer

15 cm²

Answer

8 cm²

Answer

25 cm²

Answer

30 cm²

Question 21

Which of the following solids is a regular polyhedron?

Accepted Answer

Cube

Answer

Cylinder

Answer

Pyramid

Answer

Sphere

Question 22

Which of the following shapes has all sides and angles equal?

Accepted Answer

A square

Answer

A circle

Answer

A triangle

Answer

A trapezoid

Question 23

In a regular hexagon, what is the measure of each interior angle?

Accepted Answer

120°

Answer

150°

Answer

90°

Answer

60°

Question 24

Which formula calculates the area of a circle?

Accepted Answer

πr²

Answer

4πr

Answer

2πr

Answer

πr

Question 25

What is the volume of a cube with a side length of 5 cm?

Accepted Answer

125 cm³

Answer

25 cm³

Answer

15 cm³

Answer

65 cm³

Question 26

Which of the following is NOT a property of a parallelogram?

Accepted Answer

It has four equal sides

Answer

It has two pairs of parallel sides

Answer

Its diagonals bisect each other

Answer

Its opposite angles are congruent

Question 27

Which of the following represents the graph of a quadratic function with a positive leading coefficient?

Accepted Answer

A parabola that opens upward

Answer

A straight line

Answer

A parabola that opens downward

Question 28

Find the derivative of the function f(x) = x³ - 2x² + 1.

Accepted Answer

f'(x) = 3x² - 4x

Answer

f'(x) = x² - 4x + 1

Answer

f'(x) = 3x - 4

Answer

f'(x) = x³ - 2x + 1

Question 29

Which of the following is the formula for the area of a trapezium?

Accepted Answer

1/2 * (a + b) * h

Answer

a = b + c

Answer

V = 4/3πr^3

Answer

a^2 + b^2 = c^2

Question 30

What is the surface area of a sphere with radius 3 cm?

Accepted Answer

113.1 cm^2

Answer

282.6 cm^2

Answer

94.2 cm^2

Answer

37.7 cm^2

Question 31

In a right-angled triangle, the side opposite the right angle is called the:

Accepted Answer

Hypotenuse

Answer

Altitude

Answer

Opposite

Answer

Adjacent

Question 32

Which of the following is NOT a property of a circle?

Accepted Answer

It has four sides

Answer

It is symmetrical

Answer

It can be inscribed in a square

Answer

It has a constant radius

Question 33

What is the formula for the area of a triangle?

Accepted Answer

(1/2) * base * height

Answer

(1/4) * base * height

Answer

base * height

Question 34

What is the volume of a cube with a side length of 5 units?

Accepted Answer

125 cubic units

Answer

100 cubic units

Answer

25 cubic units

Answer

50 cubic units

Question 35

Which of the following is the equation of a straight line with a gradient of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = x + 3

Answer

y = 2x + 3

Question 36

What is the probability of rolling a 6 on a standard six-sided die?

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 37

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Temperature

Answer

Mass

Answer

Energy

Question 38

What is the area of a sector of a circle with a radius of 10 cm and an angle of 60 degrees?

Accepted Answer

(10/3)π cm²

Answer

(5/3)π cm²

Answer

(15/3)π cm²

Answer

(20/3)π cm²

Question 39

Which quadrilateral has four equal sides?

Accepted Answer

Rhombus

Answer

Rectangle

Answer

Parallelogram

Answer

Kite

Question 40

What is the formula to calculate the area of a triangle?

Accepted Answer

1/2 * base * height

Answer

1/4 * base * height

Answer

base * height

Answer

length * width

Question 41

A cube has a side length of 5 cm. What is its volume?

Accepted Answer

125 cm³

Answer

25 cm³

Answer

625 cm³

Answer

150 cm³

Question 42

The surface area of a rectangular prism is found by adding the areas of its:

Accepted Answer

Faces

Answer

Diagonals

Answer

Edges

Answer

Vertices

Question 43

A pyramid has a square base with sides of 6 cm. If the height of the pyramid is 10 cm, what is its volume?

Accepted Answer

120 cm³

Answer

180 cm³

Answer

240 cm³

Answer

60 cm³

Question 44

Which of the following is NOT a property of a circle?

Accepted Answer

The sum of its interior angles is 180 degrees.

Answer

It has a constant radius from the center to any point on the circle.

Answer

Its circumference is proportional to its diameter.

Answer

It can be inscribed in a square.

Question 45

A square has sides of 5 cm each. What is its area?

Accepted Answer

25 square cm

Answer

50 square cm

Answer

12.5 square cm

Answer

10 square cm

Question 46

The Pythagorean theorem states the relationship between the sides of a right-angled triangle. Which equation represents this theorem?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

a x b = c

Answer

a² - b² = c

Question 47

What is the equation of a straight line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = x + 2

Answer

y = 3x - 2

Answer

y = -2x - 3

Question 48

Which of these is NOT a property of a parallelogram?

Accepted Answer

All sides are equal

Answer

Opposite angles are equal

Answer

Diagonals bisect each other

Answer

Opposite sides are parallel

Question 49

What is the measure of each exterior angle of a regular hexagon?

Accepted Answer

60 degrees

Answer

90 degrees

Answer

180 degrees

Answer

120 degrees

Question 50

Which formula calculates the area of a circle?

Accepted Answer

πr²

Answer

4/3πr³

Answer

2πr

Answer

πd

Question 51

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). Which equation represents this theorem?

Accepted Answer

a² + b² = c²

Answer

c² + a² = b²

Answer

a² - b² = c²

Answer

c² - a² = b²

Question 52

What is the equation of a line with a slope of 3 and a y-intercept of -2?

Accepted Answer

y = 3x - 2

Answer

y = -3x + 2

Answer

y = 2x - 3

Answer

y = -2x + 3

Question 53

A rectangle has a length of 10 cm and a width of 5 cm. What is its perimeter?

Accepted Answer

30 cm

Answer

40 cm

Answer

50 cm

Answer

20 cm

Question 54

Which of the following solids is a prism?

Accepted Answer

Cube

Answer

Sphere

Answer

Cone

Answer

Cylinder

Question 55

What is the surface area of a rectangular prism with a length of 5 cm, a width of 3 cm, and a height of 2 cm?

Accepted Answer

56 cm^2

Answer

30 cm^2

Answer

90 cm^2

Answer

72 cm^2

Question 56

What is the volume of a sphere with a radius of 5 cm?

Accepted Answer

523.6 cm^3

Answer

654.5 cm^3

Answer

339.2 cm^3

Answer

1,047.2 cm^3