Geometry and Trigonometry Quizzes - Test Your Skills

Question 1

A ladder is leaning against a wall. The base of the ladder is 5 meters from the wall, and the top of the ladder reaches a height of 3 meters. Calculate the length of the ladder using trigonometry.

Accepted Answer

√34 meters

Answer

4 meters

Answer

5 meters

Answer

3 meters

Question 2

Given the vector $\overrightarrow{AB} = \langle 3, -4 \rangle$, find its magnitude and the angle it makes with the positive x-axis.

Accepted Answer

Magnitude: $5$, Angle: $\arctan{(-4/3)}$

Answer

Magnitude: $5$, Angle: $\arctan{(3/4)}$

Answer

Magnitude: $7$, Angle: $\arctan{(4/3)}$

Answer

Magnitude: $7$, Angle: $\arctan{(-3/4)}$

Question 3

Given two similar triangles, ΔABC and ΔDEF, where the ratio of the lengths of their corresponding sides is 3:5, what is the ratio of their areas?

Accepted Answer

9:25

Answer

3:5

Answer

5:3

Answer

Cannot be determined

Question 4

In a right-angled triangle, which formula is used to calculate the area?

Accepted Answer

1/2 * base * height

Answer

π * radius^2

Answer

length * width

Answer

4 * side length^2

Question 5

Which of the following best describes the purpose of the cosine rule?

Accepted Answer

Finding the length of a side in a triangle

Answer

Calculating the area of a triangle

Answer

Determining the angle between two sides of a triangle

Answer

Calculating the volume of a sphere

Question 6

Which of the given options is NOT a trigonometric function?

Accepted Answer

Exponents

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 7

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

1

Question 8

Among the given options, which shape has the highest number of sides?

Accepted Answer

Hexagon

Answer

Triangle

Answer

Quadrilateral

Answer

Pentagon

Question 9

Calculate the sum of the interior angles of a triangle.

Accepted Answer

180 degrees

Answer

90 degrees

Answer

270 degrees

Answer

360 degrees

Question 10

Determine the formula for the volume of a cylinder.

Accepted Answer

V = π * radius^2 * height

Answer

V = 4/3 * π * radius^3

Answer

V = 2 * π * radius * height

Answer

V = π * radius * height

Question 11

The area of a circle with radius r is given by:

Accepted Answer

πr²

Answer

πr

Answer

2πr

Answer

2πr²

Question 12

The sine of an angle in a right-angled triangle is defined as the ratio of:

Accepted Answer

Opposite side to hypotenuse

Answer

Adjacent side to opposite side

Answer

Hypotenuse to adjacent side

Answer

Opposite side to adjacent side

Question 13

The tangent of an angle in a right-angled triangle is defined as the ratio of:

Accepted Answer

Opposite side to adjacent side

Answer

Opposite side to hypotenuse

Answer

Adjacent side to opposite side

Answer

Hypotenuse to adjacent side

Question 14

Which of the following is the period of the function f(x) = cos(2x)?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 15

Which of the following is not a rigid transformation?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 16

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

Accepted Answer

(x - 2)² + (y + 3)² = 25

Answer

(x + 2)² + (y - 3)² = 25

Answer

5x - 3y = 2

Answer

(2x + 3y)² = 5

Question 17

What is the value of cos 45°?

Accepted Answer

√2 / 2

Answer

0

Answer

1 / √2

Answer

1

Question 18

Which transformation does not alter the shape or size of a figure?

Accepted Answer

Translation

Answer

Rotation

Answer

Reflection

Answer

Dilation

Question 19

Write the equation of the straight line with gradient -2 and y-intercept 3.

Accepted Answer

y = -2x + 3

Answer

y = 2x + 3

Answer

y = 3x - 2

Answer

y = 3x + 2

Question 20

Find the sine of an angle measuring 30 degrees.

Accepted Answer

0.5

Answer

0.25

Answer

0.75

Answer

1

Question 21

In a triangle, the angle opposite the longest side is known as the:

Accepted Answer

largest angle

Answer

smallest angle

Answer

obtuse angle

Answer

acute angle

Question 22

The sine of an angle is defined as the ratio of the length of the:

Accepted Answer

opposite side to the length of the hypotenuse

Answer

adjacent side to the length of the hypotenuse

Answer

hypotenuse to the length of the opposite side

Answer

adjacent side to the length of the opposite side

Question 23

The volume of a sphere with radius 'r' is given by the formula:

Accepted Answer

(4/3)πr³

Answer

πr²h

Answer

πd²/4

Answer

(1/3)πr²h

Question 24

What is the equation of a straight line passing through the points (2, 3) and (4, 7)?

Accepted Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -x + 5

Question 25

The cosine rule is primarily used to find the:

Accepted Answer

length of a side in a triangle

Answer

size of an angle in a triangle

Answer

area of a triangle

Answer

volume of a cone

Question 26

The sum of the interior angles of a quadrilateral is:

Accepted Answer

360°

Answer

180°

Answer

540°

Answer

720°

Question 27

Find the equation of the line passing through the points (2, -1) and (4, 3).

Accepted Answer

y = 2x - 5

Answer

y = x + 1

Answer

y = -x + 3

Answer

y = x - 3

Question 28

Which trigonometric function represents the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 29

Find the volume of a sphere with a radius of 5 cm:

Accepted Answer

250π cm³

Answer

125π cm³

Answer

500π cm³

Answer

1000π cm³

Question 30

Find the measure of an angle that is supplementary to a 120° angle:

Accepted Answer

90°

Answer

30°

Answer

45°

Answer

60°

Question 31

Identify the Pythagorean triple from the following options:

Accepted Answer

(3, 4, 5)

Answer

(5, 10, 13)

Answer

(7, 15, 20)

Answer

(9, 16, 18)

Question 32

What is the area (in square centimeters) of a triangle with base length 6 cm and height 4 cm?

Accepted Answer

12

Answer

6

Answer

8

Answer

24

Question 33

In a right-angled triangle, which trigonometric function represents the ratio of the length of the adjacent side to the length of the hypotenuse?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 34

What is the value of sin(60°)?

Accepted Answer

√3/2

Answer

1/2

Answer

√2/2

Answer

1

Question 35

Which equation represents a straight line with a gradient of 2 and a y-intercept of 3?

Accepted Answer

y = 2x + 3

Answer

y = 3x + 2

Answer

x = 2y + 3

Answer

x = 3y + 2

Question 36

What is the volume (in cubic centimeters) of a cube with side length 5 cm?

Accepted Answer

125

Answer

25

Answer

50

Answer

250

Question 37

Which of the following is NOT a congruence theorem?

Accepted Answer

Angle-Angle-Angle (AAA)

Answer

Side-Side-Side (SSS)

Answer

Angle-Side-Angle (ASA)

Answer

Side-Angle-Side (SAS)

Question 38

What does the Pythagorean theorem state about right triangles?

Accepted Answer

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer

The sum of the squares of the two shorter sides is equal to the square of the longest side.

Answer

The square of the base is equal to the sum of the squares of the other two sides.

Answer

The sum of the interior angles is equal to 180 degrees.

Question 39

What is the formula for calculating the area of a sector of a circle with radius r and central angle θ?

Accepted Answer

1/2 * r^2 * θ

Answer

r^2 * θ

Answer

1/2 * θ / r^2

Answer

r * θ / 2

Question 40

What formula calculates the volume of a cone with radius r and height h?

Accepted Answer

1/3 * π * r^2 * h

Answer

π * r^2 * h

Answer

1/3 * π * h / r^2

Answer

π * h / r^2

Question 41

Which condition is NOT required for the similarity of triangles?

Accepted Answer

Areas are proportional.

Answer

Corresponding angles are congruent.

Answer

Corresponding sides are proportional.

Answer

Ratios of corresponding sides are equal.

Question 42

What inverse trigonometric function finds the angle given its cosine?

Accepted Answer

cos^-1

Answer

sin^-1

Answer

tan^-1

Answer

cot^-1

Question 43

What is the formula for calculating the area of a triangle?

Accepted Answer

A = (1/2) * base * height

Answer

A = π * radius^2

Answer

A = length * width

Answer

A = 4 * π * radius^2

Question 44

State the Pythagorean theorem.

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

c² - a² = b²

Answer

a/b = c/d

Question 45

Which shape is considered a regular polygon?

Accepted Answer

Square

Answer

Rectangle

Answer

Rhombus

Answer

Trapezium

Question 46

Calculate the measure of an interior angle of a regular hexagon.

Accepted Answer

120 degrees

Answer

60 degrees

Answer

180 degrees

Answer

240 degrees

Question 47

Which trigonometric function represents the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 48

In a square with a side length of 5 cm, what is the length of its diagonal?

Accepted Answer

7.07 cm

Answer

5 cm

Answer

10 cm

Answer

14.14 cm

Question 49

Which of the following sets of numbers form a Pythagorean triple?

Accepted Answer

3, 4, 5

Answer

4, 5, 6

Answer

5, 7, 9

Answer

6, 8, 10

Question 50

Which transformation preserves the original shape but changes its size?

Accepted Answer

Dilation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 51

Given that sin θ = 0.5, determine the value of cos θ.

Accepted Answer

0.866

Answer

0.5

Answer

1

Answer

Cannot be determined

Question 52

What is the inverse trigonometric function that corresponds to sin x?

Accepted Answer

arcsin x

Answer

cos x

Answer

tan x

Answer

arccos x

Question 53

The volume of a cone is given by V = (1/3)πr²h. If the radius of the cone is doubled, by what factor does the volume increase?

Accepted Answer

8

Answer

2

Answer

4

Answer

16

Question 54

Find the equation of the line that passes through the points (2, 3) and (4, 7).

Accepted Answer

y = 2x + 1

Answer

y = x + 1

Answer

y = x - 1

Answer

y = -2x + 7

Question 55

Which of the following is **NOT** a property of parallelograms?

Accepted Answer

All sides are congruent.

Answer

Opposite sides are parallel.

Answer

Opposite angles are congruent.

Answer

Diagonals intersect at their midpoint.

Question 56

Which trigonometric ratio is used to find the side adjacent to the given angle in a right triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cotangent

Question 57

Which of the following represents the angle of elevation?

Accepted Answer

Angle between the horizontal and the line of sight to an object above.

Answer

Angle between the horizontal and the line of sight to an object below.

Answer

Angle between two intersecting lines.

Answer

Angle between a line and a plane.

Question 58

What is the sine of a 45° angle?

Accepted Answer

0.707

Answer

0.5

Answer

1

Answer

2

Question 59

Which transformation will NOT maintain the original shape of a figure?

Accepted Answer

Shear transformation

Answer

Translation

Answer

Rotation

Answer

Reflection

Question 60

What is the value of sin(π/3)?

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 61

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

Accepted Answer

It has four right angles

Answer

It is a closed curve

Answer

It has a constant radius

Answer

It can be inscribed in a square

Question 62

What is the area of a triangle with a base of 8 cm and a height of 6 cm?

Accepted Answer

24 cm²

Answer

48 cm²

Answer

16 cm²

Answer

12 cm²

Question 63

What is the value of cos(π/3)?

Accepted Answer

1/2

Answer

0

Answer

1

Answer

√3/2

Question 64

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

Accepted Answer

y = 2x - 3

Answer

y = -2x - 3

Answer

y = -2x + 3

Answer

y = 2x + 3