EIT Mathematics & Engineering Fundamentals

Question 1

What is the value of the derivative of x^2 at x = 3?

Accepted Answer

6

Answer

To find the value of the derivative of x^2 at x = 3, first, we apply the power rule for differentiation, which states that the derivative of x^n is nx^(n-1). For x^2, the derivative is 2x^(2-1) = 2x. Next, we substitute x = 3 into the derivative, yielding 2 * 3 = 6.

Question 2

Which of the following is a unit of force?

Accepted Answer

Newton

Answer

The Newton (N) is the standard SI (International System of Units) unit of force. It is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg·m/s²). Other options like Joule (energy), Watt (power), and Pascal (pressure) are units for different physical quantities.

Question 3

What is the integral of 2x dx?

Accepted Answer

x^2 + C

Answer

To find the integral of 2x dx, we use the power rule for integration, which states that the integral of x^n is (x^(n+1))/(n+1) + C. Applying this to 2x^1, we get 2 * (x^(1+1))/(1+1) + C, which simplifies to 2 * (x^2)/2 + C. Therefore, the integral is x^2 + C, where 'C' represents the constant of integration.

Question 4

What is Ohm’s Law?

Accepted Answer

V = IR

Answer

Ohm's Law describes the fundamental relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It states that the voltage across a conductor is directly proportional to the current flowing through it, provided temperature and other physical conditions remain constant. The mathematical expression for this relationship is V = IR.

Question 5

Which is an example of a scalar quantity?

Accepted Answer

Temperature

Answer

A scalar quantity is defined solely by its magnitude and does not have an associated direction. Temperature is an example of a scalar quantity because it only indicates how hot or cold something is (e.g., 25°C) without any directional component. In contrast, velocity, force, and displacement are vector quantities, possessing both magnitude and direction.

(EIT) Engineer In Training Certification Practice Test

(EIT) Engineer In Training Certification Practice Test

EIT Mathematics & Engineering Fundamentals