FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Šio rinkinio kortelės

1. 1 kortelė

   Klausimas

   SI base unit of length?

   Atsakymas

   The metre, symbol $m$.

2. 2 kortelė

   Klausimas

   Slope between two points?

   Atsakymas

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

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

3. 3 kortelė

   Klausimas

   Net force relationship for constant mass in an inertial frame?

   Atsakymas

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

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

4. 4 kortelė

   Klausimas

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

   Atsakymas

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

5. 5 kortelė

   Klausimas

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

   Atsakymas

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

6. 6 kortelė

   Klausimas

   Probability of the complement of event $A$?

   Atsakymas

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

7. 7 kortelė

   Klausimas

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

   Atsakymas

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

8. 8 kortelė

   Klausimas

   SI base unit of mass?

   Atsakymas

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

9. 9 kortelė

   Klausimas

   Linear equation from slope and intercept?

   Atsakymas

   $$y=mx+b$$

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

10. 10 kortelė

    Klausimas

    Velocity after time $t$ under constant acceleration?

    Atsakymas

    $$v=v_0+at$$

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

11. 11 kortelė

    Klausimas

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

    Atsakymas

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

12. 12 kortelė

    Klausimas

    How is the FE reference handbook available during the exam?

    Atsakymas

    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. 13 kortelė

    Klausimas

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

    Atsakymas

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

14. 14 kortelė

    Klausimas

    SI base unit of time?

    Atsakymas

    The second, symbol $s$.

15. 15 kortelė

    Klausimas

    Linear equation from one point and a slope?

    Atsakymas

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

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

16. 16 kortelė

    Klausimas

    Position after time $t$ under constant acceleration?

    Atsakymas

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

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

17. 17 kortelė

    Klausimas

    A project assignment lies outside your competence. Proper response?

    Atsakymas

    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. 18 kortelė

    Klausimas

    SI base unit of electric current?

    Atsakymas

    The ampere, symbol $A$.

19. 19 kortelė

    Klausimas

    Future amount under simple interest?

    Atsakymas

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

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

20. 20 kortelė

    Klausimas

    Distance between two Cartesian points?

    Atsakymas

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

    The coordinate components must use the same length unit.

21. 21 kortelė

    Klausimas

    Constant-acceleration relation without elapsed time?

    Atsakymas

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

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

22. 22 kortelė

    Klausimas

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

    Atsakymas

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

23. 23 kortelė

    Klausimas

    Conditional probability of $A$ given $B$?

    Atsakymas

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

    This requires $P(B)>0$.

24. 24 kortelė

    Klausimas

    SI base unit of thermodynamic temperature?

    Atsakymas

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

25. 25 kortelė

    Klausimas

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

    Atsakymas

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

26. 26 kortelė

    Klausimas

    Midpoint of two Cartesian points?

    Atsakymas

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

    Average corresponding coordinates.

27. 27 kortelė

    Klausimas

    Linear momentum of a particle?

    Atsakymas

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

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

28. 28 kortelė

    Klausimas

    Future amount under compound interest?

    Atsakymas

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

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

29. 29 kortelė

    Klausimas

    Should an FE search workflow depend on Ctrl+F?

    Atsakymas

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

30. 30 kortelė

    Klausimas

    SI base unit of amount of substance?

    Atsakymas

    The mole, symbol $mol$.

31. 31 kortelė

    Klausimas

    Joint probability expressed with a conditional probability?

    Atsakymas

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

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

32. 32 kortelė

    Klausimas

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

    Atsakymas

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

    The coordinate units and radius unit must match.

33. 33 kortelė

    Klausimas

    Impulse-momentum relationship?

    Atsakymas

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

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

34. 34 kortelė

    Klausimas

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

    Atsakymas

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

35. 35 kortelė

    Klausimas

    SI base unit of luminous intensity?

    Atsakymas

    The candela, symbol $cd$.

36. 36 kortelė

    Klausimas

    Present worth of one future amount?

    Atsakymas

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

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

37. 37 kortelė

    Klausimas

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

    Atsakymas

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

    This form requires $a\ne0$.

38. 38 kortelė

    Klausimas

    When is total linear momentum conserved?

    Atsakymas

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

39. 39 kortelė

    Klausimas

    Why avoid memorizing FE handbook page numbers?

    Atsakymas

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

40. 40 kortelė

    Klausimas

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

    Atsakymas

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

    Independence is not the same as mutual exclusivity.

41. 41 kortelė

    Klausimas

    SI unit of frequency in base-unit form?

    Atsakymas

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

42. 42 kortelė

    Klausimas

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

    Atsakymas

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

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

43. 43 kortelė

    Klausimas

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

    Atsakymas

    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. 44 kortelė

    Klausimas

    Work done by a constant force through displacement?

    Atsakymas

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

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

45. 45 kortelė

    Klausimas

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

    Atsakymas

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

46. 46 kortelė

    Klausimas

    SI unit of force in base-unit form?

    Atsakymas

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

47. 47 kortelė

    Klausimas

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

    Atsakymas

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

48. 48 kortelė

    Klausimas

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

    Atsakymas

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

    This requires $P(B)>0$.

49. 49 kortelė

    Klausimas

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

    Atsakymas

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

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

50. 50 kortelė

    Klausimas

    Translational kinetic energy of a particle?

    Atsakymas

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

    Mass and speed must use a coherent unit system.

51. 51 kortelė

    Klausimas

    SI unit of pressure in force-area form?

    Atsakymas

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

52. 52 kortelė

    Klausimas

    Equivalent annual amount for present worth $P$?

    Atsakymas

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

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

53. 53 kortelė

    Klausimas

    May confidential client information be shared for personal benefit?

    Atsakymas

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

54. 54 kortelė

    Klausimas

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

    Atsakymas

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

55. 55 kortelė

    Klausimas

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

    Atsakymas

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

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

56. 56 kortelė

    Klausimas

    Net work-energy relationship for a particle?

    Atsakymas

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

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

57. 57 kortelė

    Klausimas

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

    Atsakymas

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

    Use this when order matters and selection is without replacement.

58. 58 kortelė

    Klausimas

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

    Atsakymas

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

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

59. 59 kortelė

    Klausimas

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

    Atsakymas

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

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

60. 60 kortelė

    Klausimas

    SI unit of energy in force-distance form?

    Atsakymas

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

61. 61 kortelė

    Klausimas

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

    Atsakymas

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

62. 62 kortelė

    Klausimas

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

    Atsakymas

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

63. 63 kortelė

    Klausimas

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

    Atsakymas

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

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

64. 64 kortelė

    Klausimas

    Change in gravitational potential energy near Earth's surface?

    Atsakymas

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

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

65. 65 kortelė

    Klausimas

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

    Atsakymas

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

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

66. 66 kortelė

    Klausimas

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

    Atsakymas

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

    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. 67 kortelė

    Klausimas

    A handbook search for an acronym fails. Next move?

    Atsakymas

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

68. 68 kortelė

    Klausimas

    SI unit of power in energy-time form?

    Atsakymas

    The watt, $W=J/s$.

69. 69 kortelė

    Klausimas

    Logarithm of a product?

    Atsakymas

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

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

70. 70 kortelė

    Klausimas

    Conditions for a binomial model?

    Atsakymas

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

71. 71 kortelė

    Klausimas

    Using another engineer's analysis in your deliverable?

    Atsakymas

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

72. 72 kortelė

    Klausimas

    SI unit of electric charge in current-time form?

    Atsakymas

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

73. 73 kortelė

    Klausimas

    Average power from work over elapsed time?

    Atsakymas

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

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

74. 74 kortelė

    Klausimas

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

    Atsakymas

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

    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. 75 kortelė

    Klausimas

    Logarithm of a positive quantity raised to a power?

    Atsakymas

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

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

76. 76 kortelė

    Klausimas

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

    Atsakymas

    The volt, $V=J/C$.

77. 77 kortelė

    Klausimas

    Instantaneous mechanical power delivered by a force?

    Atsakymas

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

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

78. 78 kortelė

    Klausimas

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

    Atsakymas

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

79. 79 kortelė

    Klausimas

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

    Atsakymas

    $$E[X]=np$$

80. 80 kortelė

    Klausimas

    SI unit of electrical resistance in voltage-current form?

    Atsakymas

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

81. 81 kortelė

    Klausimas

    Moment of a force about a point?

    Atsakymas

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

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

82. 82 kortelė

    Klausimas

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

    Atsakymas

    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. 83 kortelė

    Klausimas

    Inverse relationship between the natural log and exponential?

    Atsakymas

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

    The second identity requires $x>0$.

84. 84 kortelė

    Klausimas

    SI prefix giga?

    Atsakymas

    $G=10^9$.

85. 85 kortelė

    Klausimas

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

    Atsakymas

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

    Use consistent angular sign convention and radians for angular measures.

86. 86 kortelė

    Klausimas

    When should an engineer sign or seal technical work?

    Atsakymas

    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. 87 kortelė

    Klausimas

    Best memory target for returning to a handbook formula?

    Atsakymas

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

88. 88 kortelė

    Klausimas

    SI prefix mega?

    Atsakymas

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

89. 89 kortelė

    Klausimas

    Convert degrees to radians?

    Atsakymas

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

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

90. 90 kortelė

    Klausimas

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

    Atsakymas

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

91. 91 kortelė

    Klausimas

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

    Atsakymas

    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. 92 kortelė

    Klausimas

    Where do licensure and sealing requirements come from?

    Atsakymas

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

93. 93 kortelė

    Klausimas

    Rotational kinetic energy about a fixed axis?

    Atsakymas

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

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

94. 94 kortelė

    Klausimas

    SI prefix kilo?

    Atsakymas

    $k=10^3$.

95. 95 kortelė

    Klausimas

    Right-triangle definition of sine?

    Atsakymas

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

96. 96 kortelė

    Klausimas

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

    Atsakymas

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

97. 97 kortelė

    Klausimas

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

    Atsakymas

    $$\sum M=I\alpha$$

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

98. 98 kortelė

    Klausimas

    SI prefix milli?

    Atsakymas

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

99. 99 kortelė

    Klausimas

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

    Atsakymas

    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. 100 kortelė

     Klausimas

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

     Atsakymas

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

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

101. 101 kortelė

     Klausimas

     Right-triangle definition of cosine?

     Atsakymas

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

102. 102 kortelė

     Klausimas

     Force-displacement relation for an ideal linear spring?

     Atsakymas

     $$F=-kx$$

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

103. 103 kortelė

     Klausimas

     May qualifications or project responsibility be exaggerated in a proposal?

     Atsakymas

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

104. 104 kortelė

     Klausimas

     SI prefix micro?

     Atsakymas

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

105. 105 kortelė

     Klausimas

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

     Atsakymas

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

106. 106 kortelė

     Klausimas

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

     Atsakymas

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

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

107. 107 kortelė

     Klausimas

     Right-triangle definition of tangent?

     Atsakymas

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

108. 108 kortelė

     Klausimas

     Average normal stress under centered axial load?

     Atsakymas

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

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

109. 109 kortelė

     Klausimas

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

     Atsakymas

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

110. 110 kortelė

     Klausimas

     SI prefix nano?

     Atsakymas

     $n=10^{-9}$.

111. 111 kortelė

     Klausimas

     Fundamental Pythagorean trigonometric identity?

     Atsakymas

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

112. 112 kortelė

     Klausimas

     Engineering normal strain?

     Atsakymas

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

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

113. 113 kortelė

     Klausimas

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

     Atsakymas

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

114. 114 kortelė

     Klausimas

     Technical duty to an employer or client?

     Atsakymas

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

115. 115 kortelė

     Klausimas

     How does a length conversion factor apply to area?

     Atsakymas

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

116. 116 kortelė

     Klausimas

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

     Atsakymas

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

117. 117 kortelė

     Klausimas

     When is a Poisson count model reasonable?

     Atsakymas

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

118. 118 kortelė

     Klausimas

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

     Atsakymas

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

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

119. 119 kortelė

     Klausimas

     Linear elastic stress-strain relation in uniaxial loading?

     Atsakymas

     $$\sigma=E\varepsilon$$

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

120. 120 kortelė

     Klausimas

     How does a length conversion factor apply to volume?

     Atsakymas

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

121. 121 kortelė

     Klausimas

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

     Atsakymas

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

122. 122 kortelė

     Klausimas

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

     Atsakymas

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

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

123. 123 kortelė

     Klausimas

     A supervisor directs an illegal engineering action. Proper response?

     Atsakymas

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

124. 124 kortelė

     Klausimas

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

     Atsakymas

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

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

125. 125 kortelė

     Klausimas

     Mass density?

     Atsakymas

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

     Use mass, not weight, in the numerator.

126. 126 kortelė

     Klausimas

     Inches in one foot?

     Atsakymas

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

127. 127 kortelė

     Klausimas

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

     Atsakymas

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

128. 128 kortelė

     Klausimas

     How should subscripts be handled in a retrieved relationship?

     Atsakymas

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

129. 129 kortelė

     Klausimas

     Dot product from vector magnitudes and included angle?

     Atsakymas

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

     The result is a scalar.

130. 130 kortelė

     Klausimas

     Average normal pressure on an area?

     Atsakymas

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

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

131. 131 kortelė

     Klausimas

     Feet in one yard?

     Atsakymas

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

132. 132 kortelė

     Klausimas

     When are two interest rates equivalent?

     Atsakymas

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

133. 133 kortelė

     Klausimas

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

     Atsakymas

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

134. 134 kortelė

     Klausimas

     Expected value of a discrete random variable?

     Atsakymas

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

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

135. 135 kortelė

     Klausimas

     Dot-product test for perpendicular nonzero vectors?

     Atsakymas

     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. 136 kortelė

     Klausimas

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

     Atsakymas

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

     Depth increases downward and the fluid is at rest.

137. 137 kortelė

     Klausimas

     Feet in one statute mile?

     Atsakymas

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

138. 138 kortelė

     Klausimas

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

     Atsakymas

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

     

     276 kortelės

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Mokytis iš šio rinkinio nemokamai

     Atsidarys Nibomo ir galėsite pradėti mokytis.

139. 139 kortelė

     Klausimas

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

     Atsakymas

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

140. 140 kortelė

     Klausimas

     Magnitude of a vector cross product?

     Atsakymas

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

     The direction follows the right-hand rule.

141. 141 kortelė

     Klausimas

     Exact inch-to-metre relationship?

     Atsakymas

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

142. 142 kortelė

     Klausimas

     Volumetric flow rate through a cross-section?

     Atsakymas

     $$Q=Av_{avg}$$

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

143. 143 kortelė

     Klausimas

     Variance from the mean $\mu$?

     Atsakymas

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

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

144. 144 kortelė

     Klausimas

     Future-worth acceptance rule for an independent investment?

     Atsakymas

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

145. 145 kortelė

     Klausimas

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

     Atsakymas

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

146. 146 kortelė

     Klausimas

     Exact foot-to-metre relationship?

     Atsakymas

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

147. 147 kortelė

     Klausimas

     How should important uncertainty be communicated?

     Atsakymas

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

148. 148 kortelė

     Klausimas

     When is the matrix product $AB$ defined?

     Atsakymas

     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. 149 kortelė

     Klausimas

     Steady one-inlet, one-outlet mass continuity?

     Atsakymas

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. 150 kortelė

     Klausimas

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

     Atsakymas

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

151. 151 kortelė

     Klausimas

     Square feet in one acre?

     Atsakymas

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

152. 152 kortelė

     Klausimas

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

     Atsakymas

     $$ad-bc$$

153. 153 kortelė

     Klausimas

     Bernoulli relationship along a streamline for ideal steady flow?

     Atsakymas

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

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

154. 154 kortelė

     Klausimas

     May inconvenient measurements be discarded without a technical basis?

     Atsakymas

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

155. 155 kortelė

     Klausimas

     Annual-worth acceptance rule for an independent investment?

     Atsakymas

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

156. 156 kortelė

     Klausimas

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

     Atsakymas

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

157. 157 kortelė

     Klausimas

     Cubic metres in one litre?

     Atsakymas

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

158. 158 kortelė

     Klausimas

     What does a zero determinant mean for a square matrix?

     Atsakymas

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

159. 159 kortelė

     Klausimas

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

     Atsakymas

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

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

160. 160 kortelė

     Klausimas

     Unbiased sample variance for an independent sample from one population?

     Atsakymas

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

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

161. 161 kortelė

     Klausimas

     How should mutually exclusive alternatives be compared?

     Atsakymas

     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. 162 kortelė

     Klausimas

     Cubic centimetres in one millilitre?

     Atsakymas

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

163. 163 kortelė

     Klausimas

     Why keep contemporaneous engineering records?

     Atsakymas

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

164. 164 kortelė

     Klausimas

     Fast check after substituting into a handbook formula?

     Atsakymas

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

165. 165 kortelė

     Klausimas

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

     Atsakymas

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

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

166. 166 kortelė

     Klausimas

     Sensible heat for constant specific heat and no phase change?

     Atsakymas

     $$Q=mc\Delta T$$

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

167. 167 kortelė

     Klausimas

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

     Atsakymas

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

     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. 168 kortelė

     Klausimas

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

     Atsakymas

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

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

169. 169 kortelė

     Klausimas

     Purpose of incremental analysis for mutually exclusive alternatives?

     Atsakymas

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

170. 170 kortelė

     Klausimas

     Physical meaning of $dy/dx$?

     Atsakymas

     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. 171 kortelė

     Klausimas

     One-dimensional steady conduction through a plane wall?

     Atsakymas

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

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

172. 172 kortelė

     Klausimas

     When should you algebraically rearrange a handbook relationship?

     Atsakymas

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

173. 173 kortelė

     Klausimas

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

     Atsakymas

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

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

174. 174 kortelė

     Klausimas

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

     Atsakymas

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

175. 175 kortelė

     Klausimas

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

     Atsakymas

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

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

176. 176 kortelė

     Klausimas

     Convective heat-transfer rate at a surface?

     Atsakymas

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

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

177. 177 kortelė

     Klausimas

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

     Atsakymas

     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. 178 kortelė

     Klausimas

     Internal rate of return?

     Atsakymas

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

179. 179 kortelė

     Klausimas

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

     Atsakymas

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

180. 180 kortelė

     Klausimas

     Convert Celsius temperature to kelvin?

     Atsakymas

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

     This conversion is for absolute temperature, not temperature difference.

181. 181 kortelė

     Klausimas

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

     Atsakymas

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

182. 182 kortelė

     Klausimas

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

     Atsakymas

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

183. 183 kortelė

     Klausimas

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

     Atsakymas

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

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

184. 184 kortelė

     Klausimas

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

     Atsakymas

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

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

185. 185 kortelė

     Klausimas

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

     Atsakymas

     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. 186 kortelė

     Klausimas

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

     Atsakymas

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

187. 187 kortelė

     Klausimas

     Why inspect boundary or initial conditions near a formula?

     Atsakymas

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

188. 188 kortelė

     Klausimas

     Convert Celsius temperature to Fahrenheit?

     Atsakymas

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

189. 189 kortelė

     Klausimas

     Ethical basis for expert technical testimony?

     Atsakymas

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

190. 190 kortelė

     Klausimas

     Meaning of a breakeven value?

     Atsakymas

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

191. 191 kortelė

     Klausimas

     Derivative of $e^x$?

     Atsakymas

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

192. 192 kortelė

     Klausimas

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

     Atsakymas

     $$\Delta E=Q-W$$

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

193. 193 kortelė

     Klausimas

     Frequentist meaning of a 95% confidence procedure?

     Atsakymas

     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. 194 kortelė

     Klausimas

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

     Atsakymas

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

195. 195 kortelė

     Klausimas

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

     Atsakymas

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

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

196. 196 kortelė

     Klausimas

     Relationship between Celsius and kelvin temperature differences?

     Atsakymas

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

197. 197 kortelė

     Klausimas

     How should credit for team engineering work be assigned?

     Atsakymas

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

198. 198 kortelė

     Klausimas

     Main limitation of simple payback period?

     Atsakymas

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

199. 199 kortelė

     Klausimas

     Roles of the null and alternative hypotheses?

     Atsakymas

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

200. 200 kortelė

     Klausimas

     Ideal-gas equation of state?

     Atsakymas

     $$pV=nRT$$

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

201. 201 kortelė

     Klausimas

     First check when reading a handbook table?

     Atsakymas

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

202. 202 kortelė

     Klausimas

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

     Atsakymas

     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. 203 kortelė

     Klausimas

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

     Atsakymas

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

204. 204 kortelė

     Klausimas

     Convert Fahrenheit absolute temperature to Rankine?

     Atsakymas

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. 205 kortelė

     Klausimas

     Ohm's law for an ideal resistor?

     Atsakymas

     $$V=IR$$

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

206. 206 kortelė

     Klausimas

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

     Atsakymas

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

207. 207 kortelė

     Klausimas

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

     Atsakymas

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

208. 208 kortelė

     Klausimas

     Is a radian dimensionless?

     Atsakymas

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

209. 209 kortelė

     Klausimas

     Electrical power absorbed under the passive sign convention?

     Atsakymas

     $$P=VI$$

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

210. 210 kortelė

     Klausimas

     Meaning of a p-value?

     Atsakymas

     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. 211 kortelė

     Klausimas

     First check when reading a handbook graph?

     Atsakymas

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

212. 212 kortelė

     Klausimas

     Difference between mass and weight?

     Atsakymas

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

213. 213 kortelė

     Klausimas

     Kirchhoff's current law at a node?

     Atsakymas

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

214. 214 kortelė

     Klausimas

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

     Atsakymas

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

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

215. 215 kortelė

     Klausimas

     Opportunity cost?

     Atsakymas

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

216. 216 kortelė

     Klausimas

     Weight from mass in a gravitational field?

     Atsakymas

     $$W=mg$$

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

217. 217 kortelė

     Klausimas

     Kirchhoff's voltage law around a closed loop?

     Atsakymas

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

218. 218 kortelė

     Klausimas

     Decision rule using significance level $\alpha$?

     Atsakymas

     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. 219 kortelė

     Klausimas

     Can proprietary methods from a former employer be reused freely?

     Atsakymas

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

220. 220 kortelė

     Klausimas

     Pound-force to newtons?

     Atsakymas

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

221. 221 kortelė

     Klausimas

     When does a definite integral equal ordinary geometric area?

     Atsakymas

     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. 222 kortelė

     Klausimas

     Charge-voltage relation for an ideal capacitor?

     Atsakymas

     $$q=CV$$

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

223. 223 kortelė

     Klausimas

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

     Atsakymas

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

224. 224 kortelė

     Klausimas

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

     Atsakymas

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

225. 225 kortelė

     Klausimas

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

     Atsakymas

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

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

226. 226 kortelė

     Klausimas

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

     Atsakymas

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

227. 227 kortelė

     Klausimas

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

     Atsakymas

     $$\tau=RC$$

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

228. 228 kortelė

     Klausimas

     What physical quantity does pound-mass measure?

     Atsakymas

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

229. 229 kortelė

     Klausimas

     Type I error?

     Atsakymas

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

230. 230 kortelė

     Klausimas

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

     Atsakymas

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

231. 231 kortelė

     Klausimas

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

     Atsakymas

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

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

232. 232 kortelė

     Klausimas

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

     Atsakymas

     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. 233 kortelė

     Klausimas

     Recognizable form of a separable first-order differential equation?

     Atsakymas

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

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

234. 234 kortelė

     Klausimas

     Using unverified software output in a safety-relevant calculation?

     Atsakymas

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

235. 235 kortelė

     Klausimas

     Equivalent resistance of ideal resistors in series?

     Atsakymas

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

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

236. 236 kortelė

     Klausimas

     Pressure conversion from psi to pascals?

     Atsakymas

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

237. 237 kortelė

     Klausimas

     Type II error?

     Atsakymas

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

238. 238 kortelė

     Klausimas

     Useful flashcard to make after a failed handbook search?

     Atsakymas

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

239. 239 kortelė

     Klausimas

     Standard form of a first-order linear differential equation?

     Atsakymas

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

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

240. 240 kortelė

     Klausimas

     Equivalent resistance of ideal resistors in parallel?

     Atsakymas

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

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

241. 241 kortelė

     Klausimas

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

     Atsakymas

     $$BV_k=B-kD$$

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

242. 242 kortelė

     Klausimas

     Standard atmosphere in pascals?

     Atsakymas

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

243. 243 kortelė

     Klausimas

     Using AI-generated technical content in engineering work?

     Atsakymas

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

244. 244 kortelė

     Klausimas

     Trial form for a homogeneous linear ODE with constant coefficients?

     Atsakymas

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

245. 245 kortelė

     Klausimas

     Wave-speed relationship among frequency and wavelength?

     Atsakymas

     $$v=f\lambda$$

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

246. 246 kortelė

     Klausimas

     Statistical power?

     Atsakymas

     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. 247 kortelė

     Klausimas

     Bar in pascals?

     Atsakymas

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

248. 248 kortelė

     Klausimas

     How should handbook navigation be practiced before the FE exam?

     Atsakymas

     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. 249 kortelė

     Klausimas

     Is depreciation itself a cash outflow?

     Atsakymas

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

250. 250 kortelė

     Klausimas

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

     Atsakymas

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

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

251. 251 kortelė

     Klausimas

     Relationship between period and frequency?

     Atsakymas

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

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

252. 252 kortelė

     Klausimas

     How should foreseeable environmental harm enter an engineering decision?

     Atsakymas

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

253. 253 kortelė

     Klausimas

     Foot-pound-force in joules?

     Atsakymas

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

254. 254 kortelė

     Klausimas

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

     Atsakymas

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

255. 255 kortelė

     Klausimas

     When should you search instead of relying on recall?

     Atsakymas

     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. 256 kortelė

     Klausimas

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

     Atsakymas

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

257. 257 kortelė

     Klausimas

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

     Atsakymas

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

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

258. 258 kortelė

     Klausimas

     General material balance on a control volume?

     Atsakymas

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

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

259. 259 kortelė

     Klausimas

     Approximate joules in one International Table Btu?

     Atsakymas

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

260. 260 kortelė

     Klausimas

     What is the defender in a replacement analysis?

     Atsakymas

     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. 261 kortelė

     Klausimas

     Speaking publicly about a technical matter outside your expertise?

     Atsakymas

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

262. 262 kortelė

     Klausimas

     Single-interval trapezoidal approximation to an integral?

     Atsakymas

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

     It is exact for linear $f$.

263. 263 kortelė

     Klausimas

     Energy efficiency of a device?

     Atsakymas

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

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

264. 264 kortelė

     Klausimas

     Purpose of sensitivity analysis in engineering economics?

     Atsakymas

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

265. 265 kortelė

     Klausimas

     Can a strong correlation establish causation?

     Atsakymas

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

266. 266 kortelė

     Klausimas

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

     Atsakymas

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

267. 267 kortelė

     Klausimas

     Mechanical horsepower in watts?

     Atsakymas

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

268. 268 kortelė

     Klausimas

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

     Atsakymas

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

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

269. 269 kortelė

     Klausimas

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

     Atsakymas

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

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

270. 270 kortelė

     Klausimas

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

     Atsakymas

     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. 271 kortelė

     Klausimas

     Kilowatt-hour in joules?

     Atsakymas

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

272. 272 kortelė

     Klausimas

     Percent error relative to an accepted nonzero value?

     Atsakymas

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

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

273. 273 kortelė

     Klausimas

     Does legal compliance alone settle an engineering ethics question?

     Atsakymas

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

274. 274 kortelė

     Klausimas

     Does handbook fluency replace discipline-specific problem practice?

     Atsakymas

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

275. 275 kortelė

     Klausimas

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

     Atsakymas

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

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

276. 276 kortelė

     Klausimas

     Dimensional requirement for a physically meaningful additive equation?

     Atsakymas

     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.