FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Amakhadi akuleli qoqo

1. Ikhadi 1

   Umbuzo

   SI base unit of length?

   Impendulo

   The metre, symbol $m$.

2. Ikhadi 2

   Umbuzo

   Slope between two points?

   Impendulo

   $$m=\frac{y_2-y_1}{x_2-x_1}$$

   This requires $x_2\ne x_1$; slope is the change in the dependent variable per unit change in the independent variable.

3. Ikhadi 3

   Umbuzo

   Net force relationship for constant mass in an inertial frame?

   Impendulo

   $$\sum\mathbf{F}=m\mathbf{a}$$

   Use a coherent unit system and include only external forces on the chosen body.

4. Ikhadi 4

   Umbuzo

   Cash-flow sign convention from the decision maker's viewpoint?

   Impendulo

   Receipts are positive and disbursements are negative. Choose one viewpoint and keep it consistent across the cash-flow diagram and equations.

5. Ikhadi 5

   Umbuzo

   Where should an FE candidate get the current reference handbook for practice?

   Impendulo

   From the candidate's MyNCEES account. Use the current supplied file rather than an old indexed copy or a third-party mirror.

6. Ikhadi 6

   Umbuzo

   Probability of the complement of event $A$?

   Impendulo

   $$P(A^c)=1-P(A)$$

7. Ikhadi 7

   Umbuzo

   An engineering judgment conflicts with pressure to protect schedule or cost. First duty?

   Impendulo

   Protect public health, safety, and welfare. Document the technical concern and escalate through appropriate channels.

8. Ikhadi 8

   Umbuzo

   SI base unit of mass?

   Impendulo

   The kilogram, symbol $kg$. It is a mass unit, not a force unit.

9. Ikhadi 9

   Umbuzo

   Linear equation from slope and intercept?

   Impendulo

   $$y=mx+b$$

   Here $m$ is slope and $b$ is the value of $y$ where $x=0$.

10. Ikhadi 10

    Umbuzo

    Velocity after time $t$ under constant acceleration?

    Impendulo

    $$v=v_0+at$$

    This one-dimensional form requires constant $a$ and a consistent positive direction.

11. Ikhadi 11

    Umbuzo

    Where is an end-of-period cash flow placed?

    Impendulo

    At the boundary marking the end of that period. Interest factors assume consistent period lengths and cash-flow timing.

12. Ikhadi 12

    Umbuzo

    How is the FE reference handbook available during the exam?

    Impendulo

    It is supplied onscreen as a searchable PDF. Practice locating information in the same current reference rather than relying on memory of a printed layout.

13. Ikhadi 13

    Umbuzo

    Probability of $A$ or $B$ for possibly overlapping events?

    Impendulo

    $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

14. Ikhadi 14

    Umbuzo

    SI base unit of time?

    Impendulo

    The second, symbol $s$.

15. Ikhadi 15

    Umbuzo

    Linear equation from one point and a slope?

    Impendulo

    $$y-y_1=m(x-x_1)$$

    Use it when the line passes through $(x_1,y_1)$ and has slope $m$.

16. Ikhadi 16

    Umbuzo

    Position after time $t$ under constant acceleration?

    Impendulo

    $$x=x_0+v_0t+\frac{1}{2}at^2$$

    The acceleration is constant and all signed components use one coordinate direction.

17. Ikhadi 17

    Umbuzo

    A project assignment lies outside your competence. Proper response?

    Impendulo

    Accept only the parts you are qualified to perform, or obtain qualified supervision or support. Do not present unfamiliar work as your own competent judgment.

18. Ikhadi 18

    Umbuzo

    SI base unit of electric current?

    Impendulo

    The ampere, symbol $A$.

19. Ikhadi 19

    Umbuzo

    Future amount under simple interest?

    Impendulo

    $$F=P(1+in)$$

    Here $P$ is principal, $i$ is interest per period, and $n$ is the number of periods; interest is earned only on principal.

20. Ikhadi 20

    Umbuzo

    Distance between two Cartesian points?

    Impendulo

    $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

    The coordinate components must use the same length unit.

21. Ikhadi 21

    Umbuzo

    Constant-acceleration relation without elapsed time?

    Impendulo

    $$v^2=v_0^2+2a(x-x_0)$$

    Use signed one-dimensional components and constant $a$.

22. Ikhadi 22

    Umbuzo

    Where do you search the supplied reference material in the exam interface?

    Impendulo

    Use the exam software's search box beside the supplied reference material.

23. Ikhadi 23

    Umbuzo

    Conditional probability of $A$ given $B$?

    Impendulo

    $$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

    This requires $P(B)>0$.

24. Ikhadi 24

    Umbuzo

    SI base unit of thermodynamic temperature?

    Impendulo

    The kelvin, symbol $K$. Kelvin is written without a degree sign.

25. Ikhadi 25

    Umbuzo

    A client asks you to remove an unfavorable test result from a report. Proper response?

    Impendulo

    Keep the material result and explain it accurately. Engineering statements should be objective, complete enough to avoid deception, and supported by evidence.

26. Ikhadi 26

    Umbuzo

    Midpoint of two Cartesian points?

    Impendulo

    $$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$

    Average corresponding coordinates.

27. Ikhadi 27

    Umbuzo

    Linear momentum of a particle?

    Impendulo

    $$\mathbf{p}=m\mathbf{v}$$

    For constant mass, SI units are $kg\cdot m/s$.

28. Ikhadi 28

    Umbuzo

    Future amount under compound interest?

    Impendulo

    $$F=P(1+i)^n$$

    The rate period must match the period used for $n$.

29. Ikhadi 29

    Umbuzo

    Should an FE search workflow depend on Ctrl+F?

    Impendulo

    No. The May 2026 NCEES Examinee Guide says Ctrl+F isn't available; practice with the exam interface's own search box.

30. Ikhadi 30

    Umbuzo

    SI base unit of amount of substance?

    Impendulo

    The mole, symbol $mol$.

31. Ikhadi 31

    Umbuzo

    Joint probability expressed with a conditional probability?

    Impendulo

    $$P(A\cap B)=P(A\mid B)P(B)$$

    This elementary formula requires $P(B)>0$.

32. Ikhadi 32

    Umbuzo

    Standard equation of a circle centered at $(h,k)$?

    Impendulo

    $$(x-h)^2+(y-k)^2=r^2$$

    The coordinate units and radius unit must match.

33. Ikhadi 33

    Umbuzo

    Impulse-momentum relationship?

    Impendulo

    $$\int_{t_1}^{t_2}\sum\mathbf{F}\,dt=\mathbf{p}_2-\mathbf{p}_1$$

    The force is the net external force on the chosen system.

34. Ikhadi 34

    Umbuzo

    You discover a financial interest that could affect your recommendation. Proper response?

    Impendulo

    Disclose the conflict promptly to affected parties and obtain appropriate consent or withdraw. Hidden personal interests undermine independent judgment.

35. Ikhadi 35

    Umbuzo

    SI base unit of luminous intensity?

    Impendulo

    The candela, symbol $cd$.

36. Ikhadi 36

    Umbuzo

    Present worth of one future amount?

    Impendulo

    $$P=\frac{F}{(1+i)^n}$$

    Use an effective rate $i$ per period consistent with $n$.

37. Ikhadi 37

    Umbuzo

    Roots of $ax^2+bx+c=0$?

    Impendulo

    $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

    This form requires $a\ne0$.

38. Ikhadi 38

    Umbuzo

    When is total linear momentum conserved?

    Impendulo

    When net external impulse on the system is zero. Internal forces can redistribute momentum but do not change the system total.

39. Ikhadi 39

    Umbuzo

    Why avoid memorizing FE handbook page numbers?

    Impendulo

    Pagination and layout can change. Remember section names, concepts, and strong search terms instead.

40. Ikhadi 40

    Umbuzo

    Probability condition that defines independence of $A$ and $B$?

    Impendulo

    $$P(A\cap B)=P(A)P(B)$$

    Independence is not the same as mutual exclusivity.

41. Ikhadi 41

    Umbuzo

    SI unit of frequency in base-unit form?

    Impendulo

    The hertz, $Hz=s^{-1}$, applies to periodic phenomena. One hertz is one cycle per second.

42. Ikhadi 42

    Umbuzo

    Present worth of an end-of-period uniform series $A$?

    Impendulo

    $$P=A\frac{(1+i)^n-1}{i(1+i)^n}$$

    This requires $i\ne0$; at $i=0$, $P=An$.

43. Ikhadi 43

    Umbuzo

    What does $b^2-4ac$ reveal for a real-coefficient quadratic?

    Impendulo

    It determines the root type: positive gives two distinct real roots, zero gives one repeated real root, and negative gives a complex-conjugate pair.

44. Ikhadi 44

    Umbuzo

    Work done by a constant force through displacement?

    Impendulo

    $$W=\mathbf{F}\cdot\mathbf{s}=Fs\cos\theta$$

    Use the angle between force and displacement; SI units are joules.

45. Ikhadi 45

    Umbuzo

    A vendor offers a valuable gift while you evaluate bids. Proper response?

    Impendulo

    Decline it and follow the organization's disclosure policy. Even an intended courtesy can create an actual or apparent conflict.

46. Ikhadi 46

    Umbuzo

    SI unit of force in base-unit form?

    Impendulo

    The newton, $N=kg\cdot m/s^2$.

47. Ikhadi 47

    Umbuzo

    First search cue for a named quantity such as coefficient of thermal expansion?

    Impendulo

    Search the exact technical noun phrase. Distinctive nouns usually narrow results better than a whole question sentence.

48. Ikhadi 48

    Umbuzo

    Bayes' rule for $P(A\mid B)$?

    Impendulo

    $$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$$

    This requires $P(B)>0$.

49. Ikhadi 49

    Umbuzo

    Product of powers with the same positive base and real exponents?

    Impendulo

    $$a^m a^n=a^{m+n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

50. Ikhadi 50

    Umbuzo

    Translational kinetic energy of a particle?

    Impendulo

    $$K=\frac{1}{2}mv^2$$

    Mass and speed must use a coherent unit system.

51. Ikhadi 51

    Umbuzo

    SI unit of pressure in force-area form?

    Impendulo

    The pascal, $Pa=N/m^2$. It is the SI derived unit for pressure and stress.

52. Ikhadi 52

    Umbuzo

    Equivalent annual amount for present worth $P$?

    Impendulo

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=P/n$. Payments occur at period ends and $i$ matches that period.

53. Ikhadi 53

    Umbuzo

    May confidential client information be shared for personal benefit?

    Impendulo

    No. Protect it unless the client authorizes disclosure or law, safety, or professional duty requires it.

54. Ikhadi 54

    Umbuzo

    A handbook search term returns too many results. Best refinement?

    Impendulo

    Add one meaningful qualifier, such as the phenomenon, geometry, distribution, or material property you need.

55. Ikhadi 55

    Umbuzo

    Quotient of powers with the same positive base and real exponents?

    Impendulo

    $$\frac{a^m}{a^n}=a^{m-n}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

56. Ikhadi 56

    Umbuzo

    Net work-energy relationship for a particle?

    Impendulo

    $$W_{net}=K_2-K_1$$

    The net work includes the work of all forces represented in the particle model.

57. Ikhadi 57

    Umbuzo

    Ordered selections of $r$ objects from $n$ distinct objects?

    Impendulo

    $$P(n,r)=\frac{n!}{(n-r)!}$$

    Use this when order matters and selection is without replacement.

58. Ikhadi 58

    Umbuzo

    Future worth of an end-of-period uniform series $A$?

    Impendulo

    $$F=A\frac{(1+i)^n-1}{i}$$

    This requires $i\ne0$; at $i=0$, $F=An$.

59. Ikhadi 59

    Umbuzo

    Power of a power for a positive base and real exponents?

    Impendulo

    $$(a^m)^n=a^{mn}$$

    This form assumes $a>0$ and real exponents $m$ and $n$.

60. Ikhadi 60

    Umbuzo

    SI unit of energy in force-distance form?

    Impendulo

    The joule, $J=N\cdot m$.

61. Ikhadi 61

    Umbuzo

    A problem gives only an unfamiliar symbol. Best search preparation?

    Impendulo

    Translate the symbol into its likely quantity name and discipline context before searching; symbol-only searches are often ambiguous.

62. Ikhadi 62

    Umbuzo

    Confidential information reveals an imminent public-safety risk. What comes first?

    Impendulo

    Take steps required to protect people, using appropriate legal and organizational channels. Share only what is necessary and document the basis for escalation.

63. Ikhadi 63

    Umbuzo

    Unordered selections of $r$ objects from $n$ distinct objects?

    Impendulo

    $$C(n,r)=\frac{n!}{r!(n-r)!}$$

    Use this when order does not matter and selection is without replacement.

64. Ikhadi 64

    Umbuzo

    Change in gravitational potential energy near Earth's surface?

    Impendulo

    $$\Delta U_g=mg\Delta h$$

    Use approximately constant $g$ and a clearly chosen height datum.

65. Ikhadi 65

    Umbuzo

    Negative-exponent rule for a positive base and real exponent?

    Impendulo

    $$a^{-n}=\frac{1}{a^n}$$

    This form assumes $a>0$ and real exponent $n$.

66. Ikhadi 66

    Umbuzo

    Uniform end-of-period deposit needed for future amount $F$?

    Impendulo

    $$A=F\frac{i}{(1+i)^n-1}$$

    For the displayed formula, $i\ne0$; at $i=0$, $A=F/n$. The first deposit is one period from now and the last occurs at period $n$.

67. Ikhadi 67

    Umbuzo

    A handbook search for an acronym fails. Next move?

    Impendulo

    Try the expanded term and a common alternate name. Acronyms vary by section and discipline.

68. Ikhadi 68

    Umbuzo

    SI unit of power in energy-time form?

    Impendulo

    The watt, $W=J/s$.

69. Ikhadi 69

    Umbuzo

    Logarithm of a product?

    Impendulo

    $$\log_b(xy)=\log_b x+\log_b y$$

    For real logarithms, $b>0$, $b\ne1$, and both arguments are positive.

70. Ikhadi 70

    Umbuzo

    Conditions for a binomial model?

    Impendulo

    A fixed number of independent trials, two outcomes per trial, and the same success probability on every trial.

71. Ikhadi 71

    Umbuzo

    Using another engineer's analysis in your deliverable?

    Impendulo

    Credit the source and verify the analysis before relying on it. Do not present someone else's work as your own.

72. Ikhadi 72

    Umbuzo

    SI unit of electric charge in current-time form?

    Impendulo

    The coulomb, $C=A\cdot s$.

73. Ikhadi 73

    Umbuzo

    Average power from work over elapsed time?

    Impendulo

    $$P_{avg}=\frac{W}{\Delta t}$$

    Use consistent energy and time units; watts are joules per second.

74. Ikhadi 74

    Umbuzo

    Annual equivalent of cost $P$ with salvage $S$ after $n$ periods?

    Impendulo

    $$A=P\frac{i(1+i)^n}{(1+i)^n-1}-S\frac{i}{(1+i)^n-1}$$

    The first factor converts present cost to an annual amount; the second converts future salvage. Use the same effective rate and period basis. At $i=0$, $A=(P-S)/n$.

75. Ikhadi 75

    Umbuzo

    Logarithm of a positive quantity raised to a power?

    Impendulo

    $$\log_b(x^p)=p\log_b x$$

    For real logarithms, $x>0$, $b>0$, and $b\ne1$.

76. Ikhadi 76

    Umbuzo

    SI unit of electric potential difference in energy-charge form?

    Impendulo

    The volt, $V=J/C$.

77. Ikhadi 77

    Umbuzo

    Instantaneous mechanical power delivered by a force?

    Impendulo

    $$P=\mathbf{F}\cdot\mathbf{v}$$

    Use the velocity of the force's point of application.

78. Ikhadi 78

    Umbuzo

    A precise handbook term gives no useful match. Next move?

    Impendulo

    Try a standard synonym or the broader parent concept, then narrow within the relevant section.

79. Ikhadi 79

    Umbuzo

    Mean of $X\sim\operatorname{Binomial}(n,p)$?

    Impendulo

    $$E[X]=np$$

80. Ikhadi 80

    Umbuzo

    SI unit of electrical resistance in voltage-current form?

    Impendulo

    The ohm, $\Omega=V/A$.

81. Ikhadi 81

    Umbuzo

    Moment of a force about a point?

    Impendulo

    $$\mathbf{M}=\mathbf{r}\times\mathbf{F}$$

    Vector $\mathbf{r}$ runs from the moment point to a point on the force's line of action.

82. Ikhadi 82

    Umbuzo

    Cash-flow pattern described by an arithmetic gradient $G$?

    Impendulo

    A series that changes by the same amount $G$ each period. In the usual convention, the first gradient increment appears after the first base payment.

83. Ikhadi 83

    Umbuzo

    Inverse relationship between the natural log and exponential?

    Impendulo

    $$\ln(e^x)=x,\qquad e^{\ln x}=x$$

    The second identity requires $x>0$.

84. Ikhadi 84

    Umbuzo

    SI prefix giga?

    Impendulo

    $G=10^9$.

85. Ikhadi 85

    Umbuzo

    Angular velocity after time $t$ under constant angular acceleration?

    Impendulo

    $$\omega=\omega_0+\alpha t$$

    Use consistent angular sign convention and radians for angular measures.

86. Ikhadi 86

    Umbuzo

    When should an engineer sign or seal technical work?

    Impendulo

    Only when authorized and when the work was prepared by the engineer or under the level of responsible charge required by the applicable jurisdiction.

87. Ikhadi 87

    Umbuzo

    Best memory target for returning to a handbook formula?

    Impendulo

    The section or concept name plus a distinctive search phrase. That survives layout changes better than a page number.

88. Ikhadi 88

    Umbuzo

    SI prefix mega?

    Impendulo

    $M=10^6$. Uppercase matters: lowercase $m$ means milli.

89. Ikhadi 89

    Umbuzo

    Convert degrees to radians?

    Impendulo

    $$\theta_{rad}=\theta_{deg}\frac{\pi}{180}$$

    Use radians in calculus formulas unless a formula explicitly says otherwise.

90. Ikhadi 90

    Umbuzo

    Variance of $X\sim\operatorname{Binomial}(n,p)$?

    Impendulo

    $$\operatorname{Var}(X)=np(1-p)$$

91. Ikhadi 91

    Umbuzo

    Cash-flow pattern described by a geometric gradient rate $g$?

    Impendulo

    A series in which each payment is the previous payment multiplied by $1+g$. Keep $g$ on the same period basis as the interest rate.

92. Ikhadi 92

    Umbuzo

    Where do licensure and sealing requirements come from?

    Impendulo

    The applicable jurisdiction's current laws and board rules. Confirm local requirements rather than assuming one state's rules apply everywhere.

93. Ikhadi 93

    Umbuzo

    Rotational kinetic energy about a fixed axis?

    Impendulo

    $$K_{rot}=\frac{1}{2}I\omega^2$$

    $I$ is the mass moment of inertia about that axis.

94. Ikhadi 94

    Umbuzo

    SI prefix kilo?

    Impendulo

    $k=10^3$.

95. Ikhadi 95

    Umbuzo

    Right-triangle definition of sine?

    Impendulo

    Sine is opposite over hypotenuse. This definition applies to an acute angle in a right triangle.

96. Ikhadi 96

    Umbuzo

    After search lands near a result, what should you scan first?

    Impendulo

    The section heading and nearby subheading. They establish whether the result belongs to the right model and subject.

97. Ikhadi 97

    Umbuzo

    Rotational analogue of Newton's second law about a fixed principal axis?

    Impendulo

    $$\sum M=I\alpha$$

    This scalar form assumes the stated fixed-axis model and a consistent sign convention.

98. Ikhadi 98

    Umbuzo

    SI prefix milli?

    Impendulo

    $m=10^{-3}$. Context distinguishes the prefix from the metre symbol.

99. Ikhadi 99

    Umbuzo

    Meaning of a nominal annual rate compounded $m$ times per year?

    Impendulo

    It is a quoted annual rate equal to $m$ times the periodic rate. It is not itself the effective annual rate unless compounding is annual.

100. Ikhadi 100

     Umbuzo

     Standardize an observation $x$ from a distribution with mean $\mu$ and standard deviation $\sigma$?

     Impendulo

     $$z=\frac{x-\mu}{\sigma}$$

     This requires $\sigma>0$; using a normal probability table also assumes an appropriate normal model.

101. Ikhadi 101

     Umbuzo

     Right-triangle definition of cosine?

     Impendulo

     Cosine is adjacent over hypotenuse. This definition applies to an acute angle in a right triangle.

102. Ikhadi 102

     Umbuzo

     Force-displacement relation for an ideal linear spring?

     Impendulo

     $$F=-kx$$

     The minus sign shows restoring direction; the model applies within the spring's linear range.

103. Ikhadi 103

     Umbuzo

     May qualifications or project responsibility be exaggerated in a proposal?

     Impendulo

     No. State education, licensure, experience, and responsibility accurately, including the actual roles of collaborators.

104. Ikhadi 104

     Umbuzo

     SI prefix micro?

     Impendulo

     $\mu=10^{-6}$.

105. Ikhadi 105

     Umbuzo

     A handbook symbol conflicts with your usual notation. What controls?

     Impendulo

     The definition beside the selected relationship. Symbols can represent different quantities in different sections.

106. Ikhadi 106

     Umbuzo

     Periodic rate from nominal annual rate $r$ compounded $m$ times per year?

     Impendulo

     $$i=\frac{r}{m}$$

     Use consistent decimal units, and pair this rate with the number of compounding periods.

107. Ikhadi 107

     Umbuzo

     Right-triangle definition of tangent?

     Impendulo

     Tangent is opposite over adjacent, or $\sin\theta/\cos\theta$ where $\cos\theta\ne0$.

108. Ikhadi 108

     Umbuzo

     Average normal stress under centered axial load?

     Impendulo

     $$\sigma=\frac{F}{A}$$

     $F$ is normal to area $A$; the average ignores local stress concentrations.

109. Ikhadi 109

     Umbuzo

     Mean, median, and mode of a symmetric normal distribution?

     Impendulo

     They are equal and located at $\mu$. The distribution is symmetric about that center.

110. Ikhadi 110

     Umbuzo

     SI prefix nano?

     Impendulo

     $n=10^{-9}$.

111. Ikhadi 111

     Umbuzo

     Fundamental Pythagorean trigonometric identity?

     Impendulo

     $$\sin^2\theta+\cos^2\theta=1$$

112. Ikhadi 112

     Umbuzo

     Engineering normal strain?

     Impendulo

     $$\varepsilon=\frac{\Delta L}{L_0}$$

     It is dimensionless and uses original gauge length $L_0$.

113. Ikhadi 113

     Umbuzo

     A candidate retrieves a formula from the handbook. What must be checked with it?

     Impendulo

     Its applicability assumptions and variable definitions. A familiar equation used under the wrong model is still wrong.

114. Ikhadi 114

     Umbuzo

     Technical duty to an employer or client?

     Impendulo

     Act as a faithful professional within lawful, ethical limits, communicate material risks, and preserve independent technical judgment.

115. Ikhadi 115

     Umbuzo

     How does a length conversion factor apply to area?

     Impendulo

     Square it. If $1\,u=a\,v$, then $1\,u^2=a^2\,v^2$.

116. Ikhadi 116

     Umbuzo

     Effective annual rate from nominal rate $r$ compounded $m$ times per year?

     Impendulo

     $$i_{eff}=\left(1+\frac{r}{m}\right)^m-1$$

117. Ikhadi 117

     Umbuzo

     When is a Poisson count model reasonable?

     Impendulo

     For counts in a fixed interval when events occur independently at an approximately constant average rate and simultaneous events are negligible.

118. Ikhadi 118

     Umbuzo

     Relationship for the third side of a non-right triangle?

     Impendulo

     $$c^2=a^2+b^2-2ab\cos C$$

     Angle $C$ lies between sides $a$ and $b$, opposite side $c$.

119. Ikhadi 119

     Umbuzo

     Linear elastic stress-strain relation in uniaxial loading?

     Impendulo

     $$\sigma=E\varepsilon$$

     Use it in the material's linear elastic range; $E$ has stress units.

120. Ikhadi 120

     Umbuzo

     How does a length conversion factor apply to volume?

     Impendulo

     Cube it. If $1\,u=a\,v$, then $1\,u^3=a^3\,v^3$.

121. Ikhadi 121

     Umbuzo

     What should you record for every variable in a retrieved equation?

     Impendulo

     Its meaning and expected unit or dimension. This catches swapped symbols and incompatible substitutions.

122. Ikhadi 122

     Umbuzo

     Effective annual rate for continuous compounding at nominal rate $r$?

     Impendulo

     $$i_{eff}=e^r-1$$

     Here $r$ is expressed as a decimal per year.

123. Ikhadi 123

     Umbuzo

     A supervisor directs an illegal engineering action. Proper response?

     Impendulo

     Refuse the illegal action, document the direction, and escalate through appropriate legal or organizational channels.

124. Ikhadi 124

     Umbuzo

     Magnitude of a three-component vector $\mathbf{v}$?

     Impendulo

     $$\lVert\mathbf{v}\rVert=\sqrt{v_x^2+v_y^2+v_z^2}$$

     All components must represent the same physical quantity in compatible units.

125. Ikhadi 125

     Umbuzo

     Mass density?

     Impendulo

     $$\rho=\frac{m}{V}$$

     Use mass, not weight, in the numerator.

126. Ikhadi 126

     Umbuzo

     Inches in one foot?

     Impendulo

     $12\,in=1\,ft$.

127. Ikhadi 127

     Umbuzo

     Mean and variance of $X\sim\operatorname{Poisson}(\lambda)$?

     Impendulo

     Both equal $\lambda$. The standard deviation is $\sqrt{\lambda}$.

128. Ikhadi 128

     Umbuzo

     How should subscripts be handled in a retrieved relationship?

     Impendulo

     Read what each subscript identifies—state, direction, phase, location, or reference—before substituting values.

129. Ikhadi 129

     Umbuzo

     Dot product from vector magnitudes and included angle?

     Impendulo

     $$\mathbf{a}\cdot\mathbf{b}=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\cos\theta$$

     The result is a scalar.

130. Ikhadi 130

     Umbuzo

     Average normal pressure on an area?

     Impendulo

     $$p=\frac{F_n}{A}$$

     $F_n$ is the normal force; pressure is scalar in a fluid at rest.

131. Ikhadi 131

     Umbuzo

     Feet in one yard?

     Impendulo

     $3\,ft=1\,yd$.

132. Ikhadi 132

     Umbuzo

     When are two interest rates equivalent?

     Impendulo

     When they produce the same accumulation over the same time interval. Convert both rates to a common effective period before comparing them.

133. Ikhadi 133

     Umbuzo

     You discover a material error in issued work. Proper response?

     Impendulo

     Notify responsible parties promptly, assess the safety impact, correct the record, and document the response. Do not hide the error.

134. Ikhadi 134

     Umbuzo

     Expected value of a discrete random variable?

     Impendulo

     $$E[X]=\sum_x xP(X=x)$$

     Sum over all possible values with a valid probability mass function.

135. Ikhadi 135

     Umbuzo

     Dot-product test for perpendicular nonzero vectors?

     Impendulo

     Their dot product is zero. The zero vector also has zero dot product with every vector, so require both vectors to be nonzero before concluding perpendicularity.

136. Ikhadi 136

     Umbuzo

     Hydrostatic pressure change with vertical depth in a constant-density fluid?

     Impendulo

     $$\Delta p=\rho g\Delta h$$

     Depth increases downward and the fluid is at rest.

137. Ikhadi 137

     Umbuzo

     Feet in one statute mile?

     Impendulo

     $5280\,ft=1\,mi$.

138. Ikhadi 138

     Umbuzo

     Present-worth acceptance rule for an independent investment at the minimum attractive rate of return?

     Impendulo

     Accept it when net present worth is nonnegative. All cash flows must be discounted to the same time using the chosen comparison rate.

     

     amakhadi angu-276

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Funda leli qoqo mahhala

     I-Nibomo iyavuleka ukuze uqale ukufunda.

139. Ikhadi 139

     Umbuzo

     A retrieved formula contains signed quantities. What should you confirm?

     Impendulo

     The stated sign convention and positive direction. Do not mix magnitudes with signed components silently.

140. Ikhadi 140

     Umbuzo

     Magnitude of a vector cross product?

     Impendulo

     $$\lVert\mathbf{a}\times\mathbf{b}\rVert=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\sin\theta$$

     The direction follows the right-hand rule.

141. Ikhadi 141

     Umbuzo

     Exact inch-to-metre relationship?

     Impendulo

     $1\,in=0.0254\,m$ exactly.

142. Ikhadi 142

     Umbuzo

     Volumetric flow rate through a cross-section?

     Impendulo

     $$Q=Av_{avg}$$

     Velocity is the area-average component normal to the section.

143. Ikhadi 143

     Umbuzo

     Variance from the mean $\mu$?

     Impendulo

     $$\operatorname{Var}(X)=E[(X-\mu)^2]$$

     Variance has squared units; standard deviation has the original units.

144. Ikhadi 144

     Umbuzo

     Future-worth acceptance rule for an independent investment?

     Impendulo

     Accept it when net future worth at the study horizon is nonnegative, using the minimum attractive rate of return consistently.

145. Ikhadi 145

     Umbuzo

     What coordinate detail should be checked before using a vector or mechanics formula?

     Impendulo

     Axis directions and the reference point or origin. Components and moments depend on those choices.

146. Ikhadi 146

     Umbuzo

     Exact foot-to-metre relationship?

     Impendulo

     $1\,ft=0.3048\,m$ exactly.

147. Ikhadi 147

     Umbuzo

     How should important uncertainty be communicated?

     Impendulo

     State the assumptions, limits, and plausible consequences clearly enough for the decision maker to understand the risk.

148. Ikhadi 148

     Umbuzo

     When is the matrix product $AB$ defined?

     Impendulo

     It is defined when the number of columns of $A$ equals the number of rows of $B$. If $A$ is $m\times n$ and $B$ is $n\times p$, then $AB$ is $m\times p$.

149. Ikhadi 149

     Umbuzo

     Steady one-inlet, one-outlet mass continuity?

     Impendulo

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     Here $v_1$ and $v_2$ are cross-sectional average velocity components normal to their sections, with density treated as uniform over each section. For incompressible flow with constant density, this reduces to $A_1v_1=A_2v_2$.

150. Ikhadi 150

     Umbuzo

     Sample mean of observations $x_1,\ldots,x_n$?

     Impendulo

     $$\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$$

151. Ikhadi 151

     Umbuzo

     Square feet in one acre?

     Impendulo

     $1\,acre=43{,}560\,ft^2$.

152. Ikhadi 152

     Umbuzo

     Determinant of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$?

     Impendulo

     $$ad-bc$$

153. Ikhadi 153

     Umbuzo

     Bernoulli relationship along a streamline for ideal steady flow?

     Impendulo

     $$\frac{p}{\rho g}+\frac{v^2}{2g}+z=\text{constant}$$

     This basic form assumes steady, incompressible, negligible-viscosity flow with no shaft work or heat effects between points.

154. Ikhadi 154

     Umbuzo

     May inconvenient measurements be discarded without a technical basis?

     Impendulo

     No. Use a documented, technically justified rule for excluding data and preserve the original record.

155. Ikhadi 155

     Umbuzo

     Annual-worth acceptance rule for an independent investment?

     Impendulo

     Accept it when equivalent annual worth is nonnegative. Compare alternatives over compatible service assumptions.

156. Ikhadi 156

     Umbuzo

     Before using a handbook equation, what unit-system check matters?

     Impendulo

     Confirm that every input and any embedded constant use one compatible unit system. Convert first when necessary.

157. Ikhadi 157

     Umbuzo

     Cubic metres in one litre?

     Impendulo

     $1\,L=10^{-3}\,m^3$.

158. Ikhadi 158

     Umbuzo

     What does a zero determinant mean for a square matrix?

     Impendulo

     The matrix is singular and has no inverse. A corresponding linear system cannot have one unique solution.

159. Ikhadi 159

     Umbuzo

     Reynolds number for internal flow using characteristic length $L$?

     Impendulo

     $$Re=\frac{\rho vL}{\mu}=\frac{vL}{\nu}$$

     It is dimensionless; use consistent properties and the geometry-appropriate characteristic length.

160. Ikhadi 160

     Umbuzo

     Unbiased sample variance for an independent sample from one population?

     Impendulo

     $$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$$

     This requires at least two observations, so $n\ge2$. The $n-1$ denominator estimates population variance after fitting the sample mean.

161. Ikhadi 161

     Umbuzo

     How should mutually exclusive alternatives be compared?

     Impendulo

     Use one consistent economic measure over a common study period and select the economically preferred feasible alternative; do not accept every alternative with a positive individual worth.

162. Ikhadi 162

     Umbuzo

     Cubic centimetres in one millilitre?

     Impendulo

     $1\,mL=1\,cm^3$.

163. Ikhadi 163

     Umbuzo

     Why keep contemporaneous engineering records?

     Impendulo

     They preserve assumptions, decisions, calculations, approvals, and changes so the work can be checked and responsibilities understood.

164. Ikhadi 164

     Umbuzo

     Fast check after substituting into a handbook formula?

     Impendulo

     Verify that the resulting dimensions match the requested quantity and that additive terms share dimensions.

165. Ikhadi 165

     Umbuzo

     Matrix solution of $A\mathbf{x}=\mathbf{b}$ when $A$ is invertible?

     Impendulo

     $$\mathbf{x}=A^{-1}\mathbf{b}$$

     In numerical work, direct factorization is usually preferable to explicitly forming the inverse.

166. Ikhadi 166

     Umbuzo

     Sensible heat for constant specific heat and no phase change?

     Impendulo

     $$Q=mc\Delta T$$

     $c$ must match the material, temperature range, mass unit, and temperature-difference unit.

167. Ikhadi 167

     Umbuzo

     Standard error of the mean for an i.i.d. sample with population standard deviation $\sigma$?

     Impendulo

     $$SE(\bar{x})=\frac{\sigma}{\sqrt{n}}$$

     The observations are independent and identically distributed with common variance $\sigma^2$. Use $s$ for unknown $\sigma$ only when the selected inference method allows it.

168. Ikhadi 168

     Umbuzo

     Safe setup for converting $25\,ft^2$ to square metres?

     Impendulo

     $$25\,ft^2\left(\frac{0.3048\,m}{1\,ft}\right)^2$$

     The squared length factor cancels $ft^2$ and leaves $m^2$.

169. Ikhadi 169

     Umbuzo

     Purpose of incremental analysis for mutually exclusive alternatives?

     Impendulo

     It tests whether the additional investment in the higher-cost option earns the required return compared with the lower-cost option.

170. Ikhadi 170

     Umbuzo

     Physical meaning of $dy/dx$?

     Impendulo

     It is the instantaneous rate of change of $y$ with respect to $x$, with units of the $y$ unit divided by the $x$ unit.

171. Ikhadi 171

     Umbuzo

     One-dimensional steady conduction through a plane wall?

     Impendulo

     $$\dot Q=-kA\frac{dT}{dx}$$

     The minus sign indicates heat flows toward lower temperature; $k$ is thermal conductivity.

172. Ikhadi 172

     Umbuzo

     When should you algebraically rearrange a handbook relationship?

     Impendulo

     After confirming the correct equation, definitions, assumptions, and sign convention. Then isolate the requested variable without changing its domain restrictions.

173. Ikhadi 173

     Umbuzo

     Safe setup for converting $2\,in^3$ to cubic metres?

     Impendulo

     $$2\,in^3\left(\frac{0.0254\,m}{1\,in}\right)^3$$

     Cube the exact length conversion because the original quantity is volume.

174. Ikhadi 174

     Umbuzo

     A client changes a safety-critical design requirement verbally. Proper response?

     Impendulo

     Confirm the change in writing, analyze its consequences, and obtain the required approvals before relying on it.

175. Ikhadi 175

     Umbuzo

     Derivative of $x^n$ for constant $n$?

     Impendulo

     $$\frac{d}{dx}x^n=nx^{n-1}$$

     Apply domain restrictions when $n$ is non-integer or negative.

176. Ikhadi 176

     Umbuzo

     Convective heat-transfer rate at a surface?

     Impendulo

     $$\dot Q=hA(T_s-T_\infty)$$

     $h$ depends on the flow and geometry; the sign follows the chosen temperature difference.

177. Ikhadi 177

     Umbuzo

     What does the central limit theorem say about a sample mean?

     Impendulo

     For sufficiently large independent, identically distributed samples with finite variance, the sampling distribution of the properly standardized mean approaches normality. It does not make the raw data normal.

178. Ikhadi 178

     Umbuzo

     Internal rate of return?

     Impendulo

     The discount rate that makes net present worth zero. Multiple sign changes in cash flow can produce multiple or no meaningful real rates.

179. Ikhadi 179

     Umbuzo

     Several similar handbook equations appear together. How do you choose?

     Impendulo

     Match each equation's stated geometry, boundary conditions, material model, and variable definitions to the problem.

180. Ikhadi 180

     Umbuzo

     Convert Celsius temperature to kelvin?

     Impendulo

     $$T_K=T_{^\circ C}+273.15$$

     This conversion is for absolute temperature, not temperature difference.

181. Ikhadi 181

     Umbuzo

     Derivative of a product $u(x)v(x)$?

     Impendulo

     $$(uv)'=u'v+uv'$$

182. Ikhadi 182

     Umbuzo

     Internal escalation does not resolve a serious public-safety threat. Next step?

     Impendulo

     Use the next appropriate authority or reporting channel, consistent with law and the urgency of the hazard. Keep a factual record.

183. Ikhadi 183

     Umbuzo

     Two-sided confidence interval for a population mean with known $\sigma$?

     Impendulo

     $$\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$

     Use the normal-model conditions and the critical value for confidence level $1-\alpha$.

184. Ikhadi 184

     Umbuzo

     Net thermal radiation from a small gray surface to large surroundings?

     Impendulo

     $$\dot Q=\varepsilon\sigma A(T_s^4-T_{sur}^4)$$

     Use absolute temperatures; the model assumes the stated gray-surface surroundings.

185. Ikhadi 185

     Umbuzo

     Basic benefit-cost acceptance rule for an independent public project?

     Impendulo

     Accept when the consistently defined benefit-cost ratio is at least one. For mutually exclusive choices, use an incremental comparison rather than ranking by individual ratios alone.

186. Ikhadi 186

     Umbuzo

     Derivative of a composite function $f(g(x))$?

     Impendulo

     $$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$$

187. Ikhadi 187

     Umbuzo

     Why inspect boundary or initial conditions near a formula?

     Impendulo

     They determine which solution form applies and can eliminate constants or terms. A formula without its conditions may be unusable.

188. Ikhadi 188

     Umbuzo

     Convert Celsius temperature to Fahrenheit?

     Impendulo

     $$T_{^\circ F}=\frac{9}{5}T_{^\circ C}+32$$

189. Ikhadi 189

     Umbuzo

     Ethical basis for expert technical testimony?

     Impendulo

     Offer opinions only within your competence, disclose important assumptions and limitations, and distinguish facts from professional judgment.

190. Ikhadi 190

     Umbuzo

     Meaning of a breakeven value?

     Impendulo

     The value of a selected variable that makes two alternatives economically equivalent or makes net worth zero. Other assumptions are held fixed.

191. Ikhadi 191

     Umbuzo

     Derivative of $e^x$?

     Impendulo

     $$\frac{d}{dx}e^x=e^x$$

192. Ikhadi 192

     Umbuzo

     First-law energy balance for a closed system with work positive out?

     Impendulo

     $$\Delta E=Q-W$$

     $Q$ is heat into the system and $W$ is work done by the system; state a different sign convention before using it.

193. Ikhadi 193

     Umbuzo

     Frequentist meaning of a 95% confidence procedure?

     Impendulo

     Across repeated samples, about 95% of intervals built by the procedure would contain the fixed population parameter. It is not a 95% probability assigned to this already-computed interval.

194. Ikhadi 194

     Umbuzo

     A needed value falls between handbook table entries. What is the cue?

     Impendulo

     Check whether interpolation is appropriate, keep both axes and units straight, and avoid extrapolating unless the source supports it.

195. Ikhadi 195

     Umbuzo

     Derivative of $\ln x$ over the real domain?

     Impendulo

     $$\frac{d}{dx}\ln x=\frac{1}{x}$$

     This real-valued form requires $x>0$.

196. Ikhadi 196

     Umbuzo

     Relationship between Celsius and kelvin temperature differences?

     Impendulo

     $1\,K$ of temperature difference equals $1\,^{\circ}C$ of temperature difference. Do not add $273.15$ to a difference.

197. Ikhadi 197

     Umbuzo

     How should credit for team engineering work be assigned?

     Impendulo

     Accurately recognize each contributor's work and responsibility. Do not claim sole credit for a collaborative result.

198. Ikhadi 198

     Umbuzo

     Main limitation of simple payback period?

     Impendulo

     It ignores the time value of money and usually ignores cash flows after payback. Discounted payback fixes the first issue, not the second.

199. Ikhadi 199

     Umbuzo

     Roles of the null and alternative hypotheses?

     Impendulo

     The null states the baseline parameter claim tested; the alternative states the competing direction or difference supported when evidence is strong enough.

200. Ikhadi 200

     Umbuzo

     Ideal-gas equation of state?

     Impendulo

     $$pV=nRT$$

     Use absolute temperature and a gas constant consistent with pressure, volume, amount, and energy units.

201. Ikhadi 201

     Umbuzo

     First check when reading a handbook table?

     Impendulo

     Read the title, column headings, units, notes, and basis conditions before selecting a value.

202. Ikhadi 202

     Umbuzo

     Candidates for absolute extrema of a continuous function on a closed interval?

     Impendulo

     The endpoints and every interior point where the first derivative is zero or does not exist. Evaluate the function at each candidate; the largest and smallest values are the absolute extrema.

203. Ikhadi 203

     Umbuzo

     How should a sunk cost affect a current engineering-economy decision?

     Impendulo

     It should not affect the choice because it cannot be changed by the decision. Use future incremental cash flows instead.

204. Ikhadi 204

     Umbuzo

     Convert Fahrenheit absolute temperature to Rankine?

     Impendulo

     $$T_{^\circ R}=T_{^\circ F}+459.67$$

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Ikhadi 205

     Umbuzo

     Ohm's law for an ideal resistor?

     Impendulo

     $$V=IR$$

     Use a consistent passive sign convention; $R$ is constant only over the assumed operating range.

206. Ikhadi 206

     Umbuzo

     You have confidential details about a competitor's bid. Proper response?

     Impendulo

     Do not use or disclose improperly obtained information. Notify the appropriate procurement or ethics contact.

207. Ikhadi 207

     Umbuzo

     Physical meaning of a definite integral $\int_a^b f(x)\,dx$?

     Impendulo

     It is signed accumulation of $f$ from $a$ to $b$. Its units are the units of $f$ multiplied by the units of $x$.

208. Ikhadi 208

     Umbuzo

     Is a radian dimensionless?

     Impendulo

     Yes. It is the ratio of arc length to radius, so the length units cancel; keep $rad$ when it clarifies angular meaning.

209. Ikhadi 209

     Umbuzo

     Electrical power absorbed under the passive sign convention?

     Impendulo

     $$P=VI$$

     For a resistor, this also gives $P=I^2R=V^2/R$ when Ohm's law applies.

210. Ikhadi 210

     Umbuzo

     Meaning of a p-value?

     Impendulo

     Assuming the null hypothesis and model are correct, it is the probability of a result at least as extreme as the observed result. It is not the probability that the null is true.

211. Ikhadi 211

     Umbuzo

     First check when reading a handbook graph?

     Impendulo

     Identify both axes, scales, units, curve labels, and any log scale before estimating a value.

212. Ikhadi 212

     Umbuzo

     Difference between mass and weight?

     Impendulo

     Mass measures inertia; weight is gravitational force on that mass. Their dimensions and units are different.

213. Ikhadi 213

     Umbuzo

     Kirchhoff's current law at a node?

     Impendulo

     The algebraic sum of currents at a node is zero. Choose one sign convention, such as currents entering positive, and apply it consistently.

214. Ikhadi 214

     Umbuzo

     Evaluate $\int_a^b f(x)\,dx$ from an antiderivative $F$?

     Impendulo

     $$\int_a^b f(x)\,dx=F(b)-F(a)$$

     This applies when $F'=f$ on the interval under the usual continuity conditions.

215. Ikhadi 215

     Umbuzo

     Opportunity cost?

     Impendulo

     The value of the best forgone alternative. Include it when choosing one use of a scarce resource prevents another valuable use.

216. Ikhadi 216

     Umbuzo

     Weight from mass in a gravitational field?

     Impendulo

     $$W=mg$$

     Use compatible units; $g$ is local gravitational acceleration, not a universal constant for every location.

217. Ikhadi 217

     Umbuzo

     Kirchhoff's voltage law around a closed loop?

     Impendulo

     The algebraic sum of voltage rises and drops around the loop is zero. Traverse the loop once with a consistent polarity convention.

218. Ikhadi 218

     Umbuzo

     Decision rule using significance level $\alpha$?

     Impendulo

     Reject the null when the p-value is at most $\alpha$; otherwise fail to reject it. Failing to reject does not prove the null.

219. Ikhadi 219

     Umbuzo

     Can proprietary methods from a former employer be reused freely?

     Impendulo

     Only if you have the legal right or permission to use them. General skill and experience may transfer; confidential proprietary material does not.

220. Ikhadi 220

     Umbuzo

     Pound-force to newtons?

     Impendulo

     $1\,lbf\approx4.44822\,N$. Use more digits only when the required precision justifies them.

221. Ikhadi 221

     Umbuzo

     When does a definite integral equal ordinary geometric area?

     Impendulo

     When the integrand is nonnegative over the interval. If it changes sign, the integral is signed area; integrate the absolute value or split the interval for total area.

222. Ikhadi 222

     Umbuzo

     Charge-voltage relation for an ideal capacitor?

     Impendulo

     $$q=CV$$

     $C$ is capacitance in farads; $V$ is the voltage across the capacitor under the chosen polarity.

223. Ikhadi 223

     Umbuzo

     Searching for a material or fluid property: what qualifiers often matter?

     Impendulo

     Material identity, phase, temperature, pressure, and composition. Use only the qualifiers relevant to that property source.

224. Ikhadi 224

     Umbuzo

     Force produced when one slug accelerates at $1\,ft/s^2$?

     Impendulo

     $1\,lbf$. Equivalently, $1\,lbf=1\,slug\cdot ft/s^2$.

225. Ikhadi 225

     Umbuzo

     Relationship among nominal rate $i$, real rate $r$, and inflation $f$?

     Impendulo

     $$1+i=(1+r)(1+f)$$

     Keep cash-flow dollars and discount rates on the same real-or-nominal basis.

226. Ikhadi 226

     Umbuzo

     Antiderivative of $x^n$ for $n\ne-1$?

     Impendulo

     $$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C$$

227. Ikhadi 227

     Umbuzo

     Time constant of a first-order resistor-capacitor circuit?

     Impendulo

     $$\tau=RC$$

     Use the resistance seen by the capacitor in the applicable first-order linear circuit.

228. Ikhadi 228

     Umbuzo

     What physical quantity does pound-mass measure?

     Impendulo

     Mass. Do not substitute $lbm$ directly where a force unit such as $lbf$ is required.

229. Ikhadi 229

     Umbuzo

     Type I error?

     Impendulo

     Rejecting a true null hypothesis. Its probability is controlled by the chosen significance level under the test assumptions.

230. Ikhadi 230

     Umbuzo

     A search hit contains the right words. Is that enough?

     Impendulo

     No. Read the surrounding definition, equation label, units, and notes to confirm the hit answers the actual question.

231. Ikhadi 231

     Umbuzo

     Annual straight-line depreciation from basis $B$ to salvage $S$ over $n$ years?

     Impendulo

     $$D=\frac{B-S}{n}$$

     This is an accounting allocation, not a market-value forecast.

232. Ikhadi 232

     Umbuzo

     Purpose of $g_c$ in some US customary force-mass equations?

     Impendulo

     It reconciles chosen $lbm$, $lbf$, foot, and second units. Include it only when the equation and unit convention require it; coherent SI equations do not use it.

233. Ikhadi 233

     Umbuzo

     Recognizable form of a separable first-order differential equation?

     Impendulo

     $$\frac{dy}{dx}=g(x)h(y)$$

     Rearrange to place the $y$ terms with $dy$ and the $x$ terms with $dx$, while checking for solutions lost by division.

234. Ikhadi 234

     Umbuzo

     Using unverified software output in a safety-relevant calculation?

     Impendulo

     Check inputs, assumptions, units, and results with an independent method appropriate to the risk. The engineer remains responsible for professional judgment.

235. Ikhadi 235

     Umbuzo

     Equivalent resistance of ideal resistors in series?

     Impendulo

     $$R_{eq}=\sum_i R_i$$

     Series elements carry the same current with no branching node between them.

236. Ikhadi 236

     Umbuzo

     Pressure conversion from psi to pascals?

     Impendulo

     $1\,psi\approx6894.76\,Pa$. Keep enough significant figures for the problem's data.

237. Ikhadi 237

     Umbuzo

     Type II error?

     Impendulo

     Failing to reject a false null hypothesis. Its probability is $\beta$ for a specified alternative.

238. Ikhadi 238

     Umbuzo

     Useful flashcard to make after a failed handbook search?

     Impendulo

     A short scenario-to-search-cue card recording the section name and terms that eventually worked—not a copied problem or page number.

239. Ikhadi 239

     Umbuzo

     Standard form of a first-order linear differential equation?

     Impendulo

     $$\frac{dy}{dx}+P(x)y=Q(x)$$

     An integrating factor is $e^{\int P(x)\,dx}$.

240. Ikhadi 240

     Umbuzo

     Equivalent resistance of ideal resistors in parallel?

     Impendulo

     $$\frac{1}{R_{eq}}=\sum_i\frac{1}{R_i}$$

     Parallel elements share the same two nodes and therefore the same voltage.

241. Ikhadi 241

     Umbuzo

     Book value after $k$ years of straight-line depreciation?

     Impendulo

     $$BV_k=B-kD$$

     Apply it within the depreciable life and do not depreciate below the assumed salvage value.

242. Ikhadi 242

     Umbuzo

     Standard atmosphere in pascals?

     Impendulo

     $1\,atm=101{,}325\,Pa$ exactly.

243. Ikhadi 243

     Umbuzo

     Using AI-generated technical content in engineering work?

     Impendulo

     Treat it as unverified input: protect confidential data, check sources and calculations, disclose use when required, and keep accountable human review.

244. Ikhadi 244

     Umbuzo

     Trial form for a homogeneous linear ODE with constant coefficients?

     Impendulo

     Use $y=e^{rx}$ to obtain the characteristic polynomial in $r$. Repeated or complex roots require the corresponding standard solution forms.

245. Ikhadi 245

     Umbuzo

     Wave-speed relationship among frequency and wavelength?

     Impendulo

     $$v=f\lambda$$

     Use frequency in cycles per second and wavelength in compatible length units.

246. Ikhadi 246

     Umbuzo

     Statistical power?

     Impendulo

     The probability of rejecting the null when a specified alternative is true: $1-\beta$. Larger effects, larger samples, or lower variability commonly increase power.

247. Ikhadi 247

     Umbuzo

     Bar in pascals?

     Impendulo

     $1\,bar=100{,}000\,Pa$ exactly.

248. Ikhadi 248

     Umbuzo

     How should handbook navigation be practiced before the FE exam?

     Impendulo

     Use the current handbook from MyNCEES while solving original or properly licensed practice problems, and rehearse the exact search terms that find definitions and assumptions.

249. Ikhadi 249

     Umbuzo

     Is depreciation itself a cash outflow?

     Impendulo

     No. It is a noncash accounting expense, though it can affect taxes and therefore after-tax cash flow.

250. Ikhadi 250

     Umbuzo

     First-order linear approximation of $f(x)$ near $x=a$?

     Impendulo

     $$f(x)\approx f(a)+f'(a)(x-a)$$

     It is most accurate for $x$ close to $a$ when higher derivatives stay bounded.

251. Ikhadi 251

     Umbuzo

     Relationship between period and frequency?

     Impendulo

     $$T=\frac{1}{f}$$

     This requires $f>0$; $T$ has time units.

252. Ikhadi 252

     Umbuzo

     How should foreseeable environmental harm enter an engineering decision?

     Impendulo

     Identify and communicate it, follow applicable requirements, and consider practicable ways to reduce harm without compromising public safety.

253. Ikhadi 253

     Umbuzo

     Foot-pound-force in joules?

     Impendulo

     $1\,ft\cdot lbf\approx1.35582\,J$. This is a work or energy conversion; keep torque labeled as force times distance even though its dimensions match energy.

254. Ikhadi 254

     Umbuzo

     Allowed range and sign meaning of Pearson correlation $r$?

     Impendulo

     $-1\le r\le1$. The sign gives the direction of linear association, and magnitude measures its linear strength.

255. Ikhadi 255

     Umbuzo

     When should you search instead of relying on recall?

     Impendulo

     Search when a constant, coefficient, convention, specialized relationship, or applicability detail could change the result. Recall can start the route; the reference should confirm details.

256. Ikhadi 256

     Umbuzo

     After-tax effect of a deductible expense $E$ at marginal tax rate $t$?

     Impendulo

     The net cost is $E(1-t)$ under the simplified assumption that the deduction can be used fully in that period.

257. Ikhadi 257

     Umbuzo

     Centered finite-difference approximation to $f'(x)$?

     Impendulo

     $$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$$

     For smooth $f$, truncation error is proportional to $h^2$ before roundoff dominates.

258. Ikhadi 258

     Umbuzo

     General material balance on a control volume?

     Impendulo

     $$\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}$$

     At steady state, accumulation is zero; generation and consumption depend on reactions or sources.

259. Ikhadi 259

     Umbuzo

     Approximate joules in one International Table Btu?

     Impendulo

     $1\,Btu_{IT}\approx1055.06\,J$. Identify the Btu convention when precision matters.

260. Ikhadi 260

     Umbuzo

     What is the defender in a replacement analysis?

     Impendulo

     The currently owned asset being compared with a proposed replacement. Its current market value is an opportunity cost; its original purchase price is sunk.

261. Ikhadi 261

     Umbuzo

     Speaking publicly about a technical matter outside your expertise?

     Impendulo

     Limit claims to what you can support, identify the boundary of your expertise, and avoid implying qualifications you do not have.

262. Ikhadi 262

     Umbuzo

     Single-interval trapezoidal approximation to an integral?

     Impendulo

     $$\int_a^b f(x)\,dx\approx\frac{b-a}{2}[f(a)+f(b)]$$

     It is exact for linear $f$.

263. Ikhadi 263

     Umbuzo

     Energy efficiency of a device?

     Impendulo

     $$\eta=\frac{\text{useful output energy}}{\text{input energy}}$$

     Use the same energy basis in numerator and denominator; a real passive device has $0\le\eta\le1$.

264. Ikhadi 264

     Umbuzo

     Purpose of sensitivity analysis in engineering economics?

     Impendulo

     It shows how the decision changes when an uncertain input changes. Vary inputs over plausible ranges while preserving units and model relationships.

265. Ikhadi 265

     Umbuzo

     Can a strong correlation establish causation?

     Impendulo

     No. Correlation alone cannot rule out confounding, reverse direction, selection effects, or coincidence.

266. Ikhadi 266

     Umbuzo

     Where should you confirm the tested topics for your FE discipline?

     Impendulo

     Use the discipline specification linked from the official NCEES FE exam hub. This common deck does not replace that discipline-specific boundary.

267. Ikhadi 267

     Umbuzo

     Mechanical horsepower in watts?

     Impendulo

     $1\,hp\approx745.7\,W$, based on $550\,ft\cdot lbf/s$. Distinguish it from metric horsepower.

268. Ikhadi 268

     Umbuzo

     Combine independent standard uncertainties $u_1,\ldots,u_n$ in a sum or difference?

     Impendulo

     $$u_c=\sqrt{u_1^2+u_2^2+\cdots+u_n^2}$$

     This root-sum-square form assumes uncorrelated inputs and coefficients of magnitude one; otherwise include sensitivities and covariance.

269. Ikhadi 269

     Umbuzo

     Newton iteration for a root of $f(x)=0$?

     Impendulo

     $$x_{k+1}=x_k-\frac{f(x_k)}{f'(x_k)}$$

     It requires $f'(x_k)\ne0$ and a suitable starting value; convergence is not guaranteed.

270. Ikhadi 270

     Umbuzo

     Meaning of slope in simple linear regression of $y$ on $x$?

     Impendulo

     It is the estimated change in mean response $y$ for a one-unit increase in $x$, under the fitted linear model. Its units are $y$ units per $x$ unit.

271. Ikhadi 271

     Umbuzo

     Kilowatt-hour in joules?

     Impendulo

     $1\,kW\cdot h=3.6\times10^6\,J$. It is energy, not power.

272. Ikhadi 272

     Umbuzo

     Percent error relative to an accepted nonzero value?

     Impendulo

     $$\%\,error=\left|\frac{x_{measured}-x_{accepted}}{x_{accepted}}\right|100\%$$

     The accepted value must be nonzero and both values must use compatible units.

273. Ikhadi 273

     Umbuzo

     Does legal compliance alone settle an engineering ethics question?

     Impendulo

     No. Law sets mandatory boundaries, while professional duties can require stronger action, especially when safety, honesty, or conflicts are involved.

274. Ikhadi 274

     Umbuzo

     Does handbook fluency replace discipline-specific problem practice?

     Impendulo

     No. Pair navigation and common recall with the current discipline specification and timed, rights-safe problems that match your selected FE discipline.

275. Ikhadi 275

     Umbuzo

     Linear interpolation between $(x_1,y_1)$ and $(x_2,y_2)$?

     Impendulo

     $$y\approx y_1+(y_2-y_1)\frac{x-x_1}{x_2-x_1}$$

     Use it between distinct $x$ values when local linear behavior is reasonable.

276. Ikhadi 276

     Umbuzo

     Dimensional requirement for a physically meaningful additive equation?

     Impendulo

     Every term being added or equated must have the same dimensions. A dimensionally consistent equation can still be physically wrong, but an inconsistent one is wrong.