PRC Electronics Engineering Licensure Examination

In the ECE board exam Mathematics subject, what is the value of the imaginary unit j raised to the fourth power (j^4)?

• A-1
• Bj
• C1
• D-j

What is the derivative of f(x) = sin(2x) with respect to x?

• Acos(2x)
• B-2cos(2x)
• C2cos(2x)
• D2sin(2x)

The Laplace transform of the unit step function u(t) is which of the following?

• A1
• B1/s^2
• C1/s
• Ds

A 3x3 matrix has a determinant of zero. What does this indicate about the matrix?

• AIt is orthogonal
• BIt is symmetric
• CIt is singular and has no inverse
• DIts eigenvalues are all positive

Two dice are rolled. What is the probability that the sum of the two faces equals 7?

• A1/9
• B1/12
• C1/6
• D5/36

In a designed experiment, what is the variable deliberately changed by the investigator called?

• AResponse variable
• BUncontrolled confounding variable
• CFactor or independent variable
• DRandom experimental error

What is the general solution form for the first-order linear differential equation dy/dx + Py = Q, where P and Q are functions of x?

• Ay = Q/P
• By = e^(Px)
• Cy multiplied by the integrating factor equals the integral of Q times the integrating fac…
• Dy = integral of (Q - P) dx

For the vector field F = 2x ax + 3y ay + 4z az, what is the divergence of F?

• A5
• B7
• C9
• D12

What is the magnitude of the complex number 3 + 4j?

• A7
• B12
• C5
• D1

The integral of 1/x dx is equal to which of the following?

• Ax^2/2 + C
• B-1/x^2 + C
• Cln|x| + C
• D1/(x^2) + C

In a Fourier series representation of a periodic signal, the DC component corresponds to which coefficient?

• AThe fundamental frequency amplitude
• BThe highest harmonic
• CThe zero-frequency coefficient, often represented by a0/2
• DThe phase angle

What is the slope of the line tangent to y = x^2 at the point x = 3?

• A3
• B9
• C6
• D12

A control-system transfer function has a pole in the right half of the s-plane. What does this imply about system stability?

• AThe system is stable
• BThe system is marginally stable
• CThe system is unstable
• DStability cannot be determined

For a forward path G(s) with unity negative feedback, what is the closed-loop transfer function?

• AG(s)/(1 - G(s))
• B1/G(s)
• CG(s)/(1 + G(s))
• D1 + G(s)

The dot product of two perpendicular (orthogonal) vectors is equal to which value?

• AThe product of their magnitudes
• BOne
• CZero
• DThe cross product

For a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?

• A50%
• B95%
• C68%
• D99.7%

What is the period of the function f(t) = sin(100*pi*t)?

• A0.01 s
• B0.05 s
• C0.02 s
• D0.1 s

For which condition on p does the improper integral from 1 to infinity of 1/x^p converge?

• Ap < 0
• Bp = 1
• Cp > 1
• DEvery real value of p

The Z-transform is the discrete-time analog of which continuous-time transform, commonly used in ECE signals and spectra topics?

• AFourier transform
• BHilbert transform
• CLaplace transform
• DWavelet transform

What is the value of the double integral of 1 over the rectangle 0 <= x <= 2 and 0 <= y <= 3?

• A2
• B3
• C5
• D6

Under Republic Act No. 9292, which body is responsible for administering the licensure examination for Electronics Engineers in the Philippines?

• AThe Institute of Electronics Engineers of the Philippines (IECEP)
• BThe Department of Information and Communications Technology
• CThe Professional Regulatory Board of Electronics Engineering under the PRC
• DThe National Telecommunications Commission

A machine purchased for 100,000 pesos depreciates by straight-line method over 10 years with no salvage value. What is the annual depreciation charge?

• A5,000 pesos
• B15,000 pesos
• C10,000 pesos
• D20,000 pesos

In materials science, a semiconductor such as silicon has how many valence electrons in its outermost shell?

• A2
• B6
• C4
• D8