FE ETHICS CORE EXAMS SET QUESTIONS AND ANSWERS
2025/2026 ALL RATED A+
✔✔All equations for a straight line - ✔✔Y = Mx+b
Ax+By+C=0
Y-y1 = x-x1m
✔✔Angles between two slope lines - ✔✔Arctan (m2-m1)/(1+m1m2)
✔✔Distance between two points - ✔✔d = √(x₁-x₂)² + (y₁-y₂)²
✔✔Quadratic surface (sphere) - ✔✔(X-h)^2 + (y-k)^2 +(z-m)^2 = r^2
✔✔log base notation - ✔✔Log (base b) (x) = c
Where b^c=x
✔✔Change from one base to another in log form - ✔✔Log (base a)(x) = log(base b) (x)
/log(base b)(a)
✔✔Polar form of complex numbers - ✔✔Z=c<theta
Where c is the magnitude
Theta is inverse tangent of imaginary over real
✔✔Euler identity for cos and sin - ✔✔Cos = e^ix +e^-ix /2
Sin = e^ix -e^-ix /2
✔✔Law of sines - ✔✔a/SinA = b/SinB =c/sinC
✔✔Law of cosines - ✔✔a²=b²+c²-2bcCosA
✔✔Perimeter of an ellipse - ✔✔2pi sqrt(a^2 + b^2 /2)
✔✔equation for hyperbola - ✔✔x^2/a^2 - y^2/b^2 = 1
✔✔Test for maximum and minimum and inflection - ✔✔f'(a) = 0 and f''(a) < 0 (MAX)
f'(a) = 0 and f''(a) > 0 (MIN)
f''(a) = 0 (INFLECTION)
✔✔radius of curvature - ✔✔Y'' / (1 + y'^2)^3/2
✔✔Integration by parts - ✔✔∫ u dv = uv - ∫ v du
✔✔arithmetic progression - ✔✔a sequence of numbers in which the difference of two
consecutive numbers is the same
, ✔✔geometric progression - ✔✔A sequence of numbers in which the ratio of one
number to its predecessor is always the same
✔✔Fourier Series - ✔✔ao + sigma (an cos(nwt) + bn sin(nwt))
✔✔Taylor Series Formula - ✔✔Sigma f'n(c) / n! * (x-c)^n
✔✔Gradient divergence and curl and laplacian - ✔✔Del = partial of all components
Del • = divergence
Del x = curl
Del ^2 = scalar with second partials
✔✔variance of a population formula - ✔✔1/N Sigma (x-u)^2
Stdv is the sqrt of this
✔✔Number of Permutations - ✔✔P= n! / x!⋅(n-x)!
✔✔The number of combinations of n objects taken r at a time - ✔✔nCr = n!/(n-r)!r!
✔✔Bayes' Rule - ✔✔P(A|B) = P(B|A)P(A)/P(B)
✔✔Avogadro's number - ✔✔number of representative particles in a mole, 6.02 X 10^23
✔✔Coordinates of foci of ellipse - ✔✔Y = X sqrt(1-e^2)
Where y and x and the intercepts.
Solve for e.
Then multiply by larger intercept value since other will be zero.
✔✔angles between vectors - ✔✔A•B/mag(A)mag(B) = cos(theta)
✔✔diffusion coefficient - ✔✔D = Do e^ (-Q/RT)
Where Do is proportionality constant
Q is activation energy
R is gas constant (8.314)
T is absolute temperature
✔✔cold working/strain hardening - ✔✔Plastically deforming at a temp below
recrystallization. Increases strength and reduces ductility.
✔✔hot working - ✔✔Any metal-forming operation performed above a metal's
recrystallization temperature. Includes stress relief, recrystallization and grain growth.
2025/2026 ALL RATED A+
✔✔All equations for a straight line - ✔✔Y = Mx+b
Ax+By+C=0
Y-y1 = x-x1m
✔✔Angles between two slope lines - ✔✔Arctan (m2-m1)/(1+m1m2)
✔✔Distance between two points - ✔✔d = √(x₁-x₂)² + (y₁-y₂)²
✔✔Quadratic surface (sphere) - ✔✔(X-h)^2 + (y-k)^2 +(z-m)^2 = r^2
✔✔log base notation - ✔✔Log (base b) (x) = c
Where b^c=x
✔✔Change from one base to another in log form - ✔✔Log (base a)(x) = log(base b) (x)
/log(base b)(a)
✔✔Polar form of complex numbers - ✔✔Z=c<theta
Where c is the magnitude
Theta is inverse tangent of imaginary over real
✔✔Euler identity for cos and sin - ✔✔Cos = e^ix +e^-ix /2
Sin = e^ix -e^-ix /2
✔✔Law of sines - ✔✔a/SinA = b/SinB =c/sinC
✔✔Law of cosines - ✔✔a²=b²+c²-2bcCosA
✔✔Perimeter of an ellipse - ✔✔2pi sqrt(a^2 + b^2 /2)
✔✔equation for hyperbola - ✔✔x^2/a^2 - y^2/b^2 = 1
✔✔Test for maximum and minimum and inflection - ✔✔f'(a) = 0 and f''(a) < 0 (MAX)
f'(a) = 0 and f''(a) > 0 (MIN)
f''(a) = 0 (INFLECTION)
✔✔radius of curvature - ✔✔Y'' / (1 + y'^2)^3/2
✔✔Integration by parts - ✔✔∫ u dv = uv - ∫ v du
✔✔arithmetic progression - ✔✔a sequence of numbers in which the difference of two
consecutive numbers is the same
, ✔✔geometric progression - ✔✔A sequence of numbers in which the ratio of one
number to its predecessor is always the same
✔✔Fourier Series - ✔✔ao + sigma (an cos(nwt) + bn sin(nwt))
✔✔Taylor Series Formula - ✔✔Sigma f'n(c) / n! * (x-c)^n
✔✔Gradient divergence and curl and laplacian - ✔✔Del = partial of all components
Del • = divergence
Del x = curl
Del ^2 = scalar with second partials
✔✔variance of a population formula - ✔✔1/N Sigma (x-u)^2
Stdv is the sqrt of this
✔✔Number of Permutations - ✔✔P= n! / x!⋅(n-x)!
✔✔The number of combinations of n objects taken r at a time - ✔✔nCr = n!/(n-r)!r!
✔✔Bayes' Rule - ✔✔P(A|B) = P(B|A)P(A)/P(B)
✔✔Avogadro's number - ✔✔number of representative particles in a mole, 6.02 X 10^23
✔✔Coordinates of foci of ellipse - ✔✔Y = X sqrt(1-e^2)
Where y and x and the intercepts.
Solve for e.
Then multiply by larger intercept value since other will be zero.
✔✔angles between vectors - ✔✔A•B/mag(A)mag(B) = cos(theta)
✔✔diffusion coefficient - ✔✔D = Do e^ (-Q/RT)
Where Do is proportionality constant
Q is activation energy
R is gas constant (8.314)
T is absolute temperature
✔✔cold working/strain hardening - ✔✔Plastically deforming at a temp below
recrystallization. Increases strength and reduces ductility.
✔✔hot working - ✔✔Any metal-forming operation performed above a metal's
recrystallization temperature. Includes stress relief, recrystallization and grain growth.
