Engineering Mathematics: Master the Math Behind Engineering

Question 1

Identify the trigonometric identity that is incorrect:

Accepted Answer

sin(x + y) = sin(x) + sin(y)

Answer

sin^2(x) + cos^2(x) = 1

Answer

tan(x) = sin(x) / cos(x)

Question 2

Which of the following mathematical operations is NOT considered fundamental in algebra?

Accepted Answer

Integration

Answer

Addition

Answer

Subtraction

Answer

Multiplication

Question 3

Determine the sine value of a 30-degree angle.

Accepted Answer

0.5

Answer

1

Answer

0

Answer

0.75

Question 4

State the Pythagorean theorem, which describes the relationship between the sides of a right-angled triangle.

Accepted Answer

Square of hypotenuse equals sum of squares of shorter sides

Answer

Sum of squares of shorter sides equals square of hypotenuse

Answer

Sum of longer sides equals square of shortest side

Answer

Product of shorter sides equals square of hypotenuse

Question 5

Calculate the volume of a sphere with radius r.

Accepted Answer

(4/3)πr^3

Answer

4πr^2

Answer

πr^2h

Answer

(1/3)πr^3

Question 6

Which of the following functions is NOT a trigonometric function?

Accepted Answer

Exponential

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 7

Find the derivative of the function f(x) = x^2 + 3x - 5.

Accepted Answer

2x + 3

Answer

x^2 + 3

Answer

2x

Answer

3x - 5

Question 8

Which formula calculates the area of a circle?

Accepted Answer

πr^2

Answer

2πr^2

Answer

πd^2

Answer

2πd^2

Question 9

Calculate the integral of the function ∫(x^2 + 2x - 1) dx.

Accepted Answer

x^3/3 + x^2 - x + C

Answer

x^2/3 + 2x - 1 + C

Answer

3x^2 + 2x - x + C

Answer

2x^3 + x^2 - x + C

Question 10

Which quantity is a vector?

Accepted Answer

Acceleration

Answer

Speed

Answer

Mass

Answer

Temperature

Question 11

Identify the SI unit of force.

Accepted Answer

Newton

Answer

Joule

Answer

Watt

Answer

Pascal

Question 12

Which of the following numbers is a complex number?

Accepted Answer

3+4i

Answer

3-4

Answer

4i

Answer

3

Question 13

What is the sine of an angle of 60 degrees?

Accepted Answer

0.707

Answer

0.5

Answer

1

Answer

1.414

Question 14

Which of the following is the derivative of sin(x)?

Accepted Answer

cos(x)

Answer

sin(x)

Answer

x*cos(x)

Answer

-sin(x)

Question 15

What is the area of a triangle with a base of 10 cm and a height of 8 cm?

Accepted Answer

40 cm^2

Answer

20 cm^2

Answer

80 cm^2

Answer

160 cm^2

Question 16

Which of the following is the correct unit for force?

Accepted Answer

Newtons (N)

Answer

Kilograms (kg)

Answer

Joules (J)

Answer

Watts (W)

Question 17

What is the Pythagorean theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

c^2 + a^2 = b^2

Question 18

Which of the following is the correct equation for Ohm's law?

Accepted Answer

V = IR

Answer

I = VR

Answer

R = IV

Answer

V = RI

Question 19

What is the purpose of a fuse?

Accepted Answer

To protect electrical circuits from overcurrent

Answer

To store electrical energy

Answer

To amplify electrical signals

Answer

To generate electrical current

Question 20

Which of the following is NOT a fundamental mathematical concept used in engineering?

Accepted Answer

Statistics

Answer

Algebra

Answer

Trigonometry

Answer

Geometry

Question 21

What is the derivative of the function f(x) = x^2?

Accepted Answer

2x

Answer

x

Answer

x^3

Answer

2

Question 22

Which trigonometric function is used to find the perpendicular height of a right-angled triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Secant

Question 23

What is the value of the integral ∫(x^3 + 1) dx?

Accepted Answer

x^4/4 + x + C

Answer

x^3 + x + C

Answer

x^4 + x^2 + C

Answer

x^2 + C

Question 24

Which of the following is a vector quantity?

Accepted Answer

Force

Answer

Volume

Answer

Temperature

Answer

Mass

Question 25

What is the formula to determine the area of a circle?

Accepted Answer

A = πr^2

Answer

A = 2πr

Answer

A = πr^3

Answer

A = 4πr^2

Question 26

Which of the following is a type of graphical representation of trigonometric functions?

Accepted Answer

Unit circle

Answer

Bar chart

Answer

Line chart

Answer

Pie chart

Question 27

What is the equation of a straight line passing through the points (1, 2) and (3, 4)?

Accepted Answer

y = 2x - 1

Answer

y = x + 1

Answer

y = 2x

Answer

y = x - 1

Question 28

In a right-angled triangle with sides a, b, and c, and angle C = 90 degrees, what trigonometric ratio represents the relationship between the opposite side and the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 29

Find the derivative of the function f(x) = x^3.

Accepted Answer

3x^2

Answer

3x

Answer

x^2

Answer

x

Question 30

Which of the following is NOT a type of conic section?

Accepted Answer

Triangle

Answer

Circle

Answer

Ellipse

Answer

Hyperbola

Question 31

Identify the valid trigonometric identity:

Accepted Answer

sin^2(x) + cos^2(x) = 1

Answer

tan(x) = cos(x) / sin(x)

Answer

cos(x + y) = cos(x) + cos(y)

Answer

sin(x - y) = sin(x) - sin(y)

Question 32

Find the integral of x^2 with respect to x.

Accepted Answer

x^3/3 + C

Answer

2x + C

Answer

x + C

Answer

x^2 + C

Question 33

Which quantity is a vector?

Accepted Answer

Displacement

Answer

Speed

Answer

Mass

Answer

Temperature

Question 34

What is the value of the trigonometric expression sin(π/3) + cos(π/6)?

Accepted Answer

√3/2

Answer

0

Answer

1

Answer

√2/2

Question 35

What is the complex conjugate of the number 3 + 4i?

Accepted Answer

3 - 4i

Answer

-3 - 4i

Answer

4 + 3i

Answer

-3 + 4i

Question 36

What is the order of the differential equation y''' + 2y'' - 5y' + 6y = 0?

Accepted Answer

3

Answer

4

Answer

2

Answer

5

Question 37

Which mathematical expression accurately represents the area of a triangle?

Accepted Answer

0.5 * base * height

Answer

base + height

Answer

base * height

Answer

base / height

Question 38

Find the derivative of the function f(x) = x³.

Accepted Answer

3x²

Answer

x²

Answer

2x

Answer

3

Question 39

A complex number is expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit. Determine the complex conjugate of the number 3 + 4i.

Accepted Answer

3 - 4i

Answer

3 + 4i

Answer

-3 + 4i

Answer

-3 - 4i

Question 40

What mathematical expression represents Ohm's law?

Accepted Answer

V = IR

Answer

R = I/V

Answer

I = VR

Answer

R = VI