FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Kaarten in dit deck

1. Kaart 1

   Vraag

   SI base unit of length?

   Antwoord

   The metre, symbol $m$.

2. Kaart 2

   Vraag

   Slope between two points?

   Antwoord

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

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

3. Kaart 3

   Vraag

   Net force relationship for constant mass in an inertial frame?

   Antwoord

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

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

4. Kaart 4

   Vraag

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

   Antwoord

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

5. Kaart 5

   Vraag

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

   Antwoord

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

6. Kaart 6

   Vraag

   Probability of the complement of event $A$?

   Antwoord

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

7. Kaart 7

   Vraag

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

   Antwoord

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

8. Kaart 8

   Vraag

   SI base unit of mass?

   Antwoord

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

9. Kaart 9

   Vraag

   Linear equation from slope and intercept?

   Antwoord

   $$y=mx+b$$

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

10. Kaart 10

    Vraag

    Velocity after time $t$ under constant acceleration?

    Antwoord

    $$v=v_0+at$$

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

11. Kaart 11

    Vraag

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

    Antwoord

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

12. Kaart 12

    Vraag

    How is the FE reference handbook available during the exam?

    Antwoord

    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. Kaart 13

    Vraag

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

    Antwoord

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

14. Kaart 14

    Vraag

    SI base unit of time?

    Antwoord

    The second, symbol $s$.

15. Kaart 15

    Vraag

    Linear equation from one point and a slope?

    Antwoord

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

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

16. Kaart 16

    Vraag

    Position after time $t$ under constant acceleration?

    Antwoord

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

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

17. Kaart 17

    Vraag

    A project assignment lies outside your competence. Proper response?

    Antwoord

    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. Kaart 18

    Vraag

    SI base unit of electric current?

    Antwoord

    The ampere, symbol $A$.

19. Kaart 19

    Vraag

    Future amount under simple interest?

    Antwoord

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

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

20. Kaart 20

    Vraag

    Distance between two Cartesian points?

    Antwoord

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

    The coordinate components must use the same length unit.

21. Kaart 21

    Vraag

    Constant-acceleration relation without elapsed time?

    Antwoord

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

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

22. Kaart 22

    Vraag

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

    Antwoord

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

23. Kaart 23

    Vraag

    Conditional probability of $A$ given $B$?

    Antwoord

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

    This requires $P(B)>0$.

24. Kaart 24

    Vraag

    SI base unit of thermodynamic temperature?

    Antwoord

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

25. Kaart 25

    Vraag

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

    Antwoord

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

26. Kaart 26

    Vraag

    Midpoint of two Cartesian points?

    Antwoord

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

    Average corresponding coordinates.

27. Kaart 27

    Vraag

    Linear momentum of a particle?

    Antwoord

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

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

28. Kaart 28

    Vraag

    Future amount under compound interest?

    Antwoord

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

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

29. Kaart 29

    Vraag

    Should an FE search workflow depend on Ctrl+F?

    Antwoord

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

30. Kaart 30

    Vraag

    SI base unit of amount of substance?

    Antwoord

    The mole, symbol $mol$.

31. Kaart 31

    Vraag

    Joint probability expressed with a conditional probability?

    Antwoord

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

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

32. Kaart 32

    Vraag

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

    Antwoord

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

    The coordinate units and radius unit must match.

33. Kaart 33

    Vraag

    Impulse-momentum relationship?

    Antwoord

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

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

34. Kaart 34

    Vraag

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

    Antwoord

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

35. Kaart 35

    Vraag

    SI base unit of luminous intensity?

    Antwoord

    The candela, symbol $cd$.

36. Kaart 36

    Vraag

    Present worth of one future amount?

    Antwoord

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

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

37. Kaart 37

    Vraag

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

    Antwoord

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

    This form requires $a\ne0$.

38. Kaart 38

    Vraag

    When is total linear momentum conserved?

    Antwoord

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

39. Kaart 39

    Vraag

    Why avoid memorizing FE handbook page numbers?

    Antwoord

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

40. Kaart 40

    Vraag

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

    Antwoord

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

    Independence is not the same as mutual exclusivity.

41. Kaart 41

    Vraag

    SI unit of frequency in base-unit form?

    Antwoord

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

42. Kaart 42

    Vraag

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

    Antwoord

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

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

43. Kaart 43

    Vraag

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

    Antwoord

    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. Kaart 44

    Vraag

    Work done by a constant force through displacement?

    Antwoord

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

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

45. Kaart 45

    Vraag

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

    Antwoord

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

46. Kaart 46

    Vraag

    SI unit of force in base-unit form?

    Antwoord

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

47. Kaart 47

    Vraag

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

    Antwoord

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

48. Kaart 48

    Vraag

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

    Antwoord

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

    This requires $P(B)>0$.

49. Kaart 49

    Vraag

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

    Antwoord

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

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

50. Kaart 50

    Vraag

    Translational kinetic energy of a particle?

    Antwoord

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

    Mass and speed must use a coherent unit system.

51. Kaart 51

    Vraag

    SI unit of pressure in force-area form?

    Antwoord

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

52. Kaart 52

    Vraag

    Equivalent annual amount for present worth $P$?

    Antwoord

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

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

53. Kaart 53

    Vraag

    May confidential client information be shared for personal benefit?

    Antwoord

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

54. Kaart 54

    Vraag

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

    Antwoord

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

55. Kaart 55

    Vraag

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

    Antwoord

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

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

56. Kaart 56

    Vraag

    Net work-energy relationship for a particle?

    Antwoord

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

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

57. Kaart 57

    Vraag

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

    Antwoord

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

    Use this when order matters and selection is without replacement.

58. Kaart 58

    Vraag

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

    Antwoord

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

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

59. Kaart 59

    Vraag

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

    Antwoord

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

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

60. Kaart 60

    Vraag

    SI unit of energy in force-distance form?

    Antwoord

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

61. Kaart 61

    Vraag

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

    Antwoord

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

62. Kaart 62

    Vraag

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

    Antwoord

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

63. Kaart 63

    Vraag

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

    Antwoord

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

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

64. Kaart 64

    Vraag

    Change in gravitational potential energy near Earth's surface?

    Antwoord

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

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

65. Kaart 65

    Vraag

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

    Antwoord

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

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

66. Kaart 66

    Vraag

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

    Antwoord

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

    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. Kaart 67

    Vraag

    A handbook search for an acronym fails. Next move?

    Antwoord

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

68. Kaart 68

    Vraag

    SI unit of power in energy-time form?

    Antwoord

    The watt, $W=J/s$.

69. Kaart 69

    Vraag

    Logarithm of a product?

    Antwoord

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

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

70. Kaart 70

    Vraag

    Conditions for a binomial model?

    Antwoord

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

71. Kaart 71

    Vraag

    Using another engineer's analysis in your deliverable?

    Antwoord

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

72. Kaart 72

    Vraag

    SI unit of electric charge in current-time form?

    Antwoord

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

73. Kaart 73

    Vraag

    Average power from work over elapsed time?

    Antwoord

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

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

74. Kaart 74

    Vraag

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

    Antwoord

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

    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. Kaart 75

    Vraag

    Logarithm of a positive quantity raised to a power?

    Antwoord

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

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

76. Kaart 76

    Vraag

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

    Antwoord

    The volt, $V=J/C$.

77. Kaart 77

    Vraag

    Instantaneous mechanical power delivered by a force?

    Antwoord

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

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

78. Kaart 78

    Vraag

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

    Antwoord

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

79. Kaart 79

    Vraag

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

    Antwoord

    $$E[X]=np$$

80. Kaart 80

    Vraag

    SI unit of electrical resistance in voltage-current form?

    Antwoord

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

81. Kaart 81

    Vraag

    Moment of a force about a point?

    Antwoord

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

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

82. Kaart 82

    Vraag

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

    Antwoord

    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. Kaart 83

    Vraag

    Inverse relationship between the natural log and exponential?

    Antwoord

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

    The second identity requires $x>0$.

84. Kaart 84

    Vraag

    SI prefix giga?

    Antwoord

    $G=10^9$.

85. Kaart 85

    Vraag

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

    Antwoord

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

    Use consistent angular sign convention and radians for angular measures.

86. Kaart 86

    Vraag

    When should an engineer sign or seal technical work?

    Antwoord

    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. Kaart 87

    Vraag

    Best memory target for returning to a handbook formula?

    Antwoord

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

88. Kaart 88

    Vraag

    SI prefix mega?

    Antwoord

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

89. Kaart 89

    Vraag

    Convert degrees to radians?

    Antwoord

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

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

90. Kaart 90

    Vraag

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

    Antwoord

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

91. Kaart 91

    Vraag

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

    Antwoord

    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. Kaart 92

    Vraag

    Where do licensure and sealing requirements come from?

    Antwoord

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

93. Kaart 93

    Vraag

    Rotational kinetic energy about a fixed axis?

    Antwoord

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

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

94. Kaart 94

    Vraag

    SI prefix kilo?

    Antwoord

    $k=10^3$.

95. Kaart 95

    Vraag

    Right-triangle definition of sine?

    Antwoord

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

96. Kaart 96

    Vraag

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

    Antwoord

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

97. Kaart 97

    Vraag

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

    Antwoord

    $$\sum M=I\alpha$$

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

98. Kaart 98

    Vraag

    SI prefix milli?

    Antwoord

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

99. Kaart 99

    Vraag

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

    Antwoord

    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. Kaart 100

     Vraag

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

     Antwoord

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

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

101. Kaart 101

     Vraag

     Right-triangle definition of cosine?

     Antwoord

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

102. Kaart 102

     Vraag

     Force-displacement relation for an ideal linear spring?

     Antwoord

     $$F=-kx$$

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

103. Kaart 103

     Vraag

     May qualifications or project responsibility be exaggerated in a proposal?

     Antwoord

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

104. Kaart 104

     Vraag

     SI prefix micro?

     Antwoord

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

105. Kaart 105

     Vraag

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

     Antwoord

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

106. Kaart 106

     Vraag

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

     Antwoord

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

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

107. Kaart 107

     Vraag

     Right-triangle definition of tangent?

     Antwoord

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

108. Kaart 108

     Vraag

     Average normal stress under centered axial load?

     Antwoord

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

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

109. Kaart 109

     Vraag

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

     Antwoord

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

110. Kaart 110

     Vraag

     SI prefix nano?

     Antwoord

     $n=10^{-9}$.

111. Kaart 111

     Vraag

     Fundamental Pythagorean trigonometric identity?

     Antwoord

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

112. Kaart 112

     Vraag

     Engineering normal strain?

     Antwoord

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

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

113. Kaart 113

     Vraag

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

     Antwoord

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

114. Kaart 114

     Vraag

     Technical duty to an employer or client?

     Antwoord

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

115. Kaart 115

     Vraag

     How does a length conversion factor apply to area?

     Antwoord

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

116. Kaart 116

     Vraag

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

     Antwoord

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

117. Kaart 117

     Vraag

     When is a Poisson count model reasonable?

     Antwoord

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

118. Kaart 118

     Vraag

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

     Antwoord

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

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

119. Kaart 119

     Vraag

     Linear elastic stress-strain relation in uniaxial loading?

     Antwoord

     $$\sigma=E\varepsilon$$

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

120. Kaart 120

     Vraag

     How does a length conversion factor apply to volume?

     Antwoord

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

121. Kaart 121

     Vraag

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

     Antwoord

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

122. Kaart 122

     Vraag

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

     Antwoord

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

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

123. Kaart 123

     Vraag

     A supervisor directs an illegal engineering action. Proper response?

     Antwoord

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

124. Kaart 124

     Vraag

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

     Antwoord

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

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

125. Kaart 125

     Vraag

     Mass density?

     Antwoord

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

     Use mass, not weight, in the numerator.

126. Kaart 126

     Vraag

     Inches in one foot?

     Antwoord

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

127. Kaart 127

     Vraag

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

     Antwoord

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

128. Kaart 128

     Vraag

     How should subscripts be handled in a retrieved relationship?

     Antwoord

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

129. Kaart 129

     Vraag

     Dot product from vector magnitudes and included angle?

     Antwoord

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

     The result is a scalar.

130. Kaart 130

     Vraag

     Average normal pressure on an area?

     Antwoord

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

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

131. Kaart 131

     Vraag

     Feet in one yard?

     Antwoord

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

132. Kaart 132

     Vraag

     When are two interest rates equivalent?

     Antwoord

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

133. Kaart 133

     Vraag

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

     Antwoord

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

134. Kaart 134

     Vraag

     Expected value of a discrete random variable?

     Antwoord

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

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

135. Kaart 135

     Vraag

     Dot-product test for perpendicular nonzero vectors?

     Antwoord

     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. Kaart 136

     Vraag

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

     Antwoord

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

     Depth increases downward and the fluid is at rest.

137. Kaart 137

     Vraag

     Feet in one statute mile?

     Antwoord

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

138. Kaart 138

     Vraag

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

     Antwoord

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

     

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     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

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139. Kaart 139

     Vraag

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

     Antwoord

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

140. Kaart 140

     Vraag

     Magnitude of a vector cross product?

     Antwoord

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

     The direction follows the right-hand rule.

141. Kaart 141

     Vraag

     Exact inch-to-metre relationship?

     Antwoord

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

142. Kaart 142

     Vraag

     Volumetric flow rate through a cross-section?

     Antwoord

     $$Q=Av_{avg}$$

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

143. Kaart 143

     Vraag

     Variance from the mean $\mu$?

     Antwoord

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

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

144. Kaart 144

     Vraag

     Future-worth acceptance rule for an independent investment?

     Antwoord

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

145. Kaart 145

     Vraag

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

     Antwoord

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

146. Kaart 146

     Vraag

     Exact foot-to-metre relationship?

     Antwoord

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

147. Kaart 147

     Vraag

     How should important uncertainty be communicated?

     Antwoord

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

148. Kaart 148

     Vraag

     When is the matrix product $AB$ defined?

     Antwoord

     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. Kaart 149

     Vraag

     Steady one-inlet, one-outlet mass continuity?

     Antwoord

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Kaart 150

     Vraag

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

     Antwoord

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

151. Kaart 151

     Vraag

     Square feet in one acre?

     Antwoord

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

152. Kaart 152

     Vraag

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

     Antwoord

     $$ad-bc$$

153. Kaart 153

     Vraag

     Bernoulli relationship along a streamline for ideal steady flow?

     Antwoord

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

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

154. Kaart 154

     Vraag

     May inconvenient measurements be discarded without a technical basis?

     Antwoord

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

155. Kaart 155

     Vraag

     Annual-worth acceptance rule for an independent investment?

     Antwoord

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

156. Kaart 156

     Vraag

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

     Antwoord

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

157. Kaart 157

     Vraag

     Cubic metres in one litre?

     Antwoord

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

158. Kaart 158

     Vraag

     What does a zero determinant mean for a square matrix?

     Antwoord

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

159. Kaart 159

     Vraag

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

     Antwoord

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

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

160. Kaart 160

     Vraag

     Unbiased sample variance for an independent sample from one population?

     Antwoord

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

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

161. Kaart 161

     Vraag

     How should mutually exclusive alternatives be compared?

     Antwoord

     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. Kaart 162

     Vraag

     Cubic centimetres in one millilitre?

     Antwoord

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

163. Kaart 163

     Vraag

     Why keep contemporaneous engineering records?

     Antwoord

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

164. Kaart 164

     Vraag

     Fast check after substituting into a handbook formula?

     Antwoord

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

165. Kaart 165

     Vraag

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

     Antwoord

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

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

166. Kaart 166

     Vraag

     Sensible heat for constant specific heat and no phase change?

     Antwoord

     $$Q=mc\Delta T$$

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

167. Kaart 167

     Vraag

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

     Antwoord

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

     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. Kaart 168

     Vraag

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

     Antwoord

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

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

169. Kaart 169

     Vraag

     Purpose of incremental analysis for mutually exclusive alternatives?

     Antwoord

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

170. Kaart 170

     Vraag

     Physical meaning of $dy/dx$?

     Antwoord

     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. Kaart 171

     Vraag

     One-dimensional steady conduction through a plane wall?

     Antwoord

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

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

172. Kaart 172

     Vraag

     When should you algebraically rearrange a handbook relationship?

     Antwoord

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

173. Kaart 173

     Vraag

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

     Antwoord

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

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

174. Kaart 174

     Vraag

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

     Antwoord

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

175. Kaart 175

     Vraag

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

     Antwoord

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

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

176. Kaart 176

     Vraag

     Convective heat-transfer rate at a surface?

     Antwoord

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

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

177. Kaart 177

     Vraag

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

     Antwoord

     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. Kaart 178

     Vraag

     Internal rate of return?

     Antwoord

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

179. Kaart 179

     Vraag

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

     Antwoord

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

180. Kaart 180

     Vraag

     Convert Celsius temperature to kelvin?

     Antwoord

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

     This conversion is for absolute temperature, not temperature difference.

181. Kaart 181

     Vraag

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

     Antwoord

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

182. Kaart 182

     Vraag

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

     Antwoord

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

183. Kaart 183

     Vraag

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

     Antwoord

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

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

184. Kaart 184

     Vraag

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

     Antwoord

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

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

185. Kaart 185

     Vraag

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

     Antwoord

     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. Kaart 186

     Vraag

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

     Antwoord

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

187. Kaart 187

     Vraag

     Why inspect boundary or initial conditions near a formula?

     Antwoord

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

188. Kaart 188

     Vraag

     Convert Celsius temperature to Fahrenheit?

     Antwoord

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

189. Kaart 189

     Vraag

     Ethical basis for expert technical testimony?

     Antwoord

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

190. Kaart 190

     Vraag

     Meaning of a breakeven value?

     Antwoord

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

191. Kaart 191

     Vraag

     Derivative of $e^x$?

     Antwoord

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

192. Kaart 192

     Vraag

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

     Antwoord

     $$\Delta E=Q-W$$

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

193. Kaart 193

     Vraag

     Frequentist meaning of a 95% confidence procedure?

     Antwoord

     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. Kaart 194

     Vraag

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

     Antwoord

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

195. Kaart 195

     Vraag

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

     Antwoord

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

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

196. Kaart 196

     Vraag

     Relationship between Celsius and kelvin temperature differences?

     Antwoord

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

197. Kaart 197

     Vraag

     How should credit for team engineering work be assigned?

     Antwoord

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

198. Kaart 198

     Vraag

     Main limitation of simple payback period?

     Antwoord

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

199. Kaart 199

     Vraag

     Roles of the null and alternative hypotheses?

     Antwoord

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

200. Kaart 200

     Vraag

     Ideal-gas equation of state?

     Antwoord

     $$pV=nRT$$

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

201. Kaart 201

     Vraag

     First check when reading a handbook table?

     Antwoord

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

202. Kaart 202

     Vraag

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

     Antwoord

     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. Kaart 203

     Vraag

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

     Antwoord

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

204. Kaart 204

     Vraag

     Convert Fahrenheit absolute temperature to Rankine?

     Antwoord

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Kaart 205

     Vraag

     Ohm's law for an ideal resistor?

     Antwoord

     $$V=IR$$

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

206. Kaart 206

     Vraag

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

     Antwoord

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

207. Kaart 207

     Vraag

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

     Antwoord

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

208. Kaart 208

     Vraag

     Is a radian dimensionless?

     Antwoord

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

209. Kaart 209

     Vraag

     Electrical power absorbed under the passive sign convention?

     Antwoord

     $$P=VI$$

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

210. Kaart 210

     Vraag

     Meaning of a p-value?

     Antwoord

     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. Kaart 211

     Vraag

     First check when reading a handbook graph?

     Antwoord

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

212. Kaart 212

     Vraag

     Difference between mass and weight?

     Antwoord

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

213. Kaart 213

     Vraag

     Kirchhoff's current law at a node?

     Antwoord

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

214. Kaart 214

     Vraag

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

     Antwoord

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

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

215. Kaart 215

     Vraag

     Opportunity cost?

     Antwoord

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

216. Kaart 216

     Vraag

     Weight from mass in a gravitational field?

     Antwoord

     $$W=mg$$

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

217. Kaart 217

     Vraag

     Kirchhoff's voltage law around a closed loop?

     Antwoord

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

218. Kaart 218

     Vraag

     Decision rule using significance level $\alpha$?

     Antwoord

     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. Kaart 219

     Vraag

     Can proprietary methods from a former employer be reused freely?

     Antwoord

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

220. Kaart 220

     Vraag

     Pound-force to newtons?

     Antwoord

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

221. Kaart 221

     Vraag

     When does a definite integral equal ordinary geometric area?

     Antwoord

     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. Kaart 222

     Vraag

     Charge-voltage relation for an ideal capacitor?

     Antwoord

     $$q=CV$$

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

223. Kaart 223

     Vraag

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

     Antwoord

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

224. Kaart 224

     Vraag

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

     Antwoord

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

225. Kaart 225

     Vraag

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

     Antwoord

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

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

226. Kaart 226

     Vraag

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

     Antwoord

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

227. Kaart 227

     Vraag

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

     Antwoord

     $$\tau=RC$$

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

228. Kaart 228

     Vraag

     What physical quantity does pound-mass measure?

     Antwoord

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

229. Kaart 229

     Vraag

     Type I error?

     Antwoord

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

230. Kaart 230

     Vraag

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

     Antwoord

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

231. Kaart 231

     Vraag

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

     Antwoord

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

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

232. Kaart 232

     Vraag

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

     Antwoord

     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. Kaart 233

     Vraag

     Recognizable form of a separable first-order differential equation?

     Antwoord

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

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

234. Kaart 234

     Vraag

     Using unverified software output in a safety-relevant calculation?

     Antwoord

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

235. Kaart 235

     Vraag

     Equivalent resistance of ideal resistors in series?

     Antwoord

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

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

236. Kaart 236

     Vraag

     Pressure conversion from psi to pascals?

     Antwoord

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

237. Kaart 237

     Vraag

     Type II error?

     Antwoord

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

238. Kaart 238

     Vraag

     Useful flashcard to make after a failed handbook search?

     Antwoord

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

239. Kaart 239

     Vraag

     Standard form of a first-order linear differential equation?

     Antwoord

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

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

240. Kaart 240

     Vraag

     Equivalent resistance of ideal resistors in parallel?

     Antwoord

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

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

241. Kaart 241

     Vraag

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

     Antwoord

     $$BV_k=B-kD$$

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

242. Kaart 242

     Vraag

     Standard atmosphere in pascals?

     Antwoord

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

243. Kaart 243

     Vraag

     Using AI-generated technical content in engineering work?

     Antwoord

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

244. Kaart 244

     Vraag

     Trial form for a homogeneous linear ODE with constant coefficients?

     Antwoord

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

245. Kaart 245

     Vraag

     Wave-speed relationship among frequency and wavelength?

     Antwoord

     $$v=f\lambda$$

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

246. Kaart 246

     Vraag

     Statistical power?

     Antwoord

     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. Kaart 247

     Vraag

     Bar in pascals?

     Antwoord

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

248. Kaart 248

     Vraag

     How should handbook navigation be practiced before the FE exam?

     Antwoord

     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. Kaart 249

     Vraag

     Is depreciation itself a cash outflow?

     Antwoord

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

250. Kaart 250

     Vraag

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

     Antwoord

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

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

251. Kaart 251

     Vraag

     Relationship between period and frequency?

     Antwoord

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

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

252. Kaart 252

     Vraag

     How should foreseeable environmental harm enter an engineering decision?

     Antwoord

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

253. Kaart 253

     Vraag

     Foot-pound-force in joules?

     Antwoord

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

254. Kaart 254

     Vraag

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

     Antwoord

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

255. Kaart 255

     Vraag

     When should you search instead of relying on recall?

     Antwoord

     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. Kaart 256

     Vraag

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

     Antwoord

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

257. Kaart 257

     Vraag

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

     Antwoord

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

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

258. Kaart 258

     Vraag

     General material balance on a control volume?

     Antwoord

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

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

259. Kaart 259

     Vraag

     Approximate joules in one International Table Btu?

     Antwoord

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

260. Kaart 260

     Vraag

     What is the defender in a replacement analysis?

     Antwoord

     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. Kaart 261

     Vraag

     Speaking publicly about a technical matter outside your expertise?

     Antwoord

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

262. Kaart 262

     Vraag

     Single-interval trapezoidal approximation to an integral?

     Antwoord

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

     It is exact for linear $f$.

263. Kaart 263

     Vraag

     Energy efficiency of a device?

     Antwoord

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

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

264. Kaart 264

     Vraag

     Purpose of sensitivity analysis in engineering economics?

     Antwoord

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

265. Kaart 265

     Vraag

     Can a strong correlation establish causation?

     Antwoord

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

266. Kaart 266

     Vraag

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

     Antwoord

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

267. Kaart 267

     Vraag

     Mechanical horsepower in watts?

     Antwoord

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

268. Kaart 268

     Vraag

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

     Antwoord

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

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

269. Kaart 269

     Vraag

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

     Antwoord

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

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

270. Kaart 270

     Vraag

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

     Antwoord

     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. Kaart 271

     Vraag

     Kilowatt-hour in joules?

     Antwoord

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

272. Kaart 272

     Vraag

     Percent error relative to an accepted nonzero value?

     Antwoord

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

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

273. Kaart 273

     Vraag

     Does legal compliance alone settle an engineering ethics question?

     Antwoord

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

274. Kaart 274

     Vraag

     Does handbook fluency replace discipline-specific problem practice?

     Antwoord

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

275. Kaart 275

     Vraag

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

     Antwoord

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

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

276. Kaart 276

     Vraag

     Dimensional requirement for a physically meaningful additive equation?

     Antwoord

     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.