FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

کارت‌های این دسته

1. کارت ۱

   پرسش

   SI base unit of length?

   پاسخ

   The metre, symbol $m$.

2. کارت ۲

   پرسش

   Slope between two points?

   پاسخ

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

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

3. کارت ۳

   پرسش

   Net force relationship for constant mass in an inertial frame?

   پاسخ

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

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

4. کارت ۴

   پرسش

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

   پاسخ

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

5. کارت ۵

   پرسش

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

   پاسخ

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

6. کارت ۶

   پرسش

   Probability of the complement of event $A$?

   پاسخ

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

7. کارت ۷

   پرسش

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

   پاسخ

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

8. کارت ۸

   پرسش

   SI base unit of mass?

   پاسخ

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

9. کارت ۹

   پرسش

   Linear equation from slope and intercept?

   پاسخ

   $$y=mx+b$$

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

10. کارت ۱۰

    پرسش

    Velocity after time $t$ under constant acceleration?

    پاسخ

    $$v=v_0+at$$

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

11. کارت ۱۱

    پرسش

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

    پاسخ

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

12. کارت ۱۲

    پرسش

    How is the FE reference handbook available during the exam?

    پاسخ

    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. کارت ۱۳

    پرسش

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

    پاسخ

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

14. کارت ۱۴

    پرسش

    SI base unit of time?

    پاسخ

    The second, symbol $s$.

15. کارت ۱۵

    پرسش

    Linear equation from one point and a slope?

    پاسخ

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

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

16. کارت ۱۶

    پرسش

    Position after time $t$ under constant acceleration?

    پاسخ

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

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

17. کارت ۱۷

    پرسش

    A project assignment lies outside your competence. Proper response?

    پاسخ

    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. کارت ۱۸

    پرسش

    SI base unit of electric current?

    پاسخ

    The ampere, symbol $A$.

19. کارت ۱۹

    پرسش

    Future amount under simple interest?

    پاسخ

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

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

20. کارت ۲۰

    پرسش

    Distance between two Cartesian points?

    پاسخ

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

    The coordinate components must use the same length unit.

21. کارت ۲۱

    پرسش

    Constant-acceleration relation without elapsed time?

    پاسخ

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

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

22. کارت ۲۲

    پرسش

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

    پاسخ

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

23. کارت ۲۳

    پرسش

    Conditional probability of $A$ given $B$?

    پاسخ

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

    This requires $P(B)>0$.

24. کارت ۲۴

    پرسش

    SI base unit of thermodynamic temperature?

    پاسخ

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

25. کارت ۲۵

    پرسش

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

    پاسخ

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

26. کارت ۲۶

    پرسش

    Midpoint of two Cartesian points?

    پاسخ

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

    Average corresponding coordinates.

27. کارت ۲۷

    پرسش

    Linear momentum of a particle?

    پاسخ

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

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

28. کارت ۲۸

    پرسش

    Future amount under compound interest?

    پاسخ

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

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

29. کارت ۲۹

    پرسش

    Should an FE search workflow depend on Ctrl+F?

    پاسخ

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

30. کارت ۳۰

    پرسش

    SI base unit of amount of substance?

    پاسخ

    The mole, symbol $mol$.

31. کارت ۳۱

    پرسش

    Joint probability expressed with a conditional probability?

    پاسخ

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

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

32. کارت ۳۲

    پرسش

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

    پاسخ

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

    The coordinate units and radius unit must match.

33. کارت ۳۳

    پرسش

    Impulse-momentum relationship?

    پاسخ

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

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

34. کارت ۳۴

    پرسش

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

    پاسخ

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

35. کارت ۳۵

    پرسش

    SI base unit of luminous intensity?

    پاسخ

    The candela, symbol $cd$.

36. کارت ۳۶

    پرسش

    Present worth of one future amount?

    پاسخ

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

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

37. کارت ۳۷

    پرسش

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

    پاسخ

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

    This form requires $a\ne0$.

38. کارت ۳۸

    پرسش

    When is total linear momentum conserved?

    پاسخ

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

39. کارت ۳۹

    پرسش

    Why avoid memorizing FE handbook page numbers?

    پاسخ

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

40. کارت ۴۰

    پرسش

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

    پاسخ

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

    Independence is not the same as mutual exclusivity.

41. کارت ۴۱

    پرسش

    SI unit of frequency in base-unit form?

    پاسخ

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

42. کارت ۴۲

    پرسش

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

    پاسخ

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

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

43. کارت ۴۳

    پرسش

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

    پاسخ

    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. کارت ۴۴

    پرسش

    Work done by a constant force through displacement?

    پاسخ

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

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

45. کارت ۴۵

    پرسش

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

    پاسخ

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

46. کارت ۴۶

    پرسش

    SI unit of force in base-unit form?

    پاسخ

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

47. کارت ۴۷

    پرسش

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

    پاسخ

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

48. کارت ۴۸

    پرسش

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

    پاسخ

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

    This requires $P(B)>0$.

49. کارت ۴۹

    پرسش

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

    پاسخ

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

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

50. کارت ۵۰

    پرسش

    Translational kinetic energy of a particle?

    پاسخ

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

    Mass and speed must use a coherent unit system.

51. کارت ۵۱

    پرسش

    SI unit of pressure in force-area form?

    پاسخ

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

52. کارت ۵۲

    پرسش

    Equivalent annual amount for present worth $P$?

    پاسخ

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

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

53. کارت ۵۳

    پرسش

    May confidential client information be shared for personal benefit?

    پاسخ

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

54. کارت ۵۴

    پرسش

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

    پاسخ

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

55. کارت ۵۵

    پرسش

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

    پاسخ

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

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

56. کارت ۵۶

    پرسش

    Net work-energy relationship for a particle?

    پاسخ

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

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

57. کارت ۵۷

    پرسش

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

    پاسخ

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

    Use this when order matters and selection is without replacement.

58. کارت ۵۸

    پرسش

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

    پاسخ

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

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

59. کارت ۵۹

    پرسش

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

    پاسخ

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

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

60. کارت ۶۰

    پرسش

    SI unit of energy in force-distance form?

    پاسخ

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

61. کارت ۶۱

    پرسش

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

    پاسخ

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

62. کارت ۶۲

    پرسش

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

    پاسخ

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

63. کارت ۶۳

    پرسش

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

    پاسخ

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

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

64. کارت ۶۴

    پرسش

    Change in gravitational potential energy near Earth's surface?

    پاسخ

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

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

65. کارت ۶۵

    پرسش

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

    پاسخ

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

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

66. کارت ۶۶

    پرسش

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

    پاسخ

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

    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. کارت ۶۷

    پرسش

    A handbook search for an acronym fails. Next move?

    پاسخ

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

68. کارت ۶۸

    پرسش

    SI unit of power in energy-time form?

    پاسخ

    The watt, $W=J/s$.

69. کارت ۶۹

    پرسش

    Logarithm of a product?

    پاسخ

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

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

70. کارت ۷۰

    پرسش

    Conditions for a binomial model?

    پاسخ

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

71. کارت ۷۱

    پرسش

    Using another engineer's analysis in your deliverable?

    پاسخ

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

72. کارت ۷۲

    پرسش

    SI unit of electric charge in current-time form?

    پاسخ

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

73. کارت ۷۳

    پرسش

    Average power from work over elapsed time?

    پاسخ

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

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

74. کارت ۷۴

    پرسش

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

    پاسخ

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

    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. کارت ۷۵

    پرسش

    Logarithm of a positive quantity raised to a power?

    پاسخ

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

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

76. کارت ۷۶

    پرسش

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

    پاسخ

    The volt, $V=J/C$.

77. کارت ۷۷

    پرسش

    Instantaneous mechanical power delivered by a force?

    پاسخ

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

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

78. کارت ۷۸

    پرسش

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

    پاسخ

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

79. کارت ۷۹

    پرسش

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

    پاسخ

    $$E[X]=np$$

80. کارت ۸۰

    پرسش

    SI unit of electrical resistance in voltage-current form?

    پاسخ

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

81. کارت ۸۱

    پرسش

    Moment of a force about a point?

    پاسخ

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

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

82. کارت ۸۲

    پرسش

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

    پاسخ

    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. کارت ۸۳

    پرسش

    Inverse relationship between the natural log and exponential?

    پاسخ

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

    The second identity requires $x>0$.

84. کارت ۸۴

    پرسش

    SI prefix giga?

    پاسخ

    $G=10^9$.

85. کارت ۸۵

    پرسش

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

    پاسخ

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

    Use consistent angular sign convention and radians for angular measures.

86. کارت ۸۶

    پرسش

    When should an engineer sign or seal technical work?

    پاسخ

    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. کارت ۸۷

    پرسش

    Best memory target for returning to a handbook formula?

    پاسخ

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

88. کارت ۸۸

    پرسش

    SI prefix mega?

    پاسخ

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

89. کارت ۸۹

    پرسش

    Convert degrees to radians?

    پاسخ

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

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

90. کارت ۹۰

    پرسش

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

    پاسخ

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

91. کارت ۹۱

    پرسش

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

    پاسخ

    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. کارت ۹۲

    پرسش

    Where do licensure and sealing requirements come from?

    پاسخ

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

93. کارت ۹۳

    پرسش

    Rotational kinetic energy about a fixed axis?

    پاسخ

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

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

94. کارت ۹۴

    پرسش

    SI prefix kilo?

    پاسخ

    $k=10^3$.

95. کارت ۹۵

    پرسش

    Right-triangle definition of sine?

    پاسخ

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

96. کارت ۹۶

    پرسش

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

    پاسخ

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

97. کارت ۹۷

    پرسش

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

    پاسخ

    $$\sum M=I\alpha$$

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

98. کارت ۹۸

    پرسش

    SI prefix milli?

    پاسخ

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

99. کارت ۹۹

    پرسش

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

    پاسخ

    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. کارت ۱۰۰

     پرسش

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

     پاسخ

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

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

101. کارت ۱۰۱

     پرسش

     Right-triangle definition of cosine?

     پاسخ

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

102. کارت ۱۰۲

     پرسش

     Force-displacement relation for an ideal linear spring?

     پاسخ

     $$F=-kx$$

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

103. کارت ۱۰۳

     پرسش

     May qualifications or project responsibility be exaggerated in a proposal?

     پاسخ

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

104. کارت ۱۰۴

     پرسش

     SI prefix micro?

     پاسخ

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

105. کارت ۱۰۵

     پرسش

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

     پاسخ

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

106. کارت ۱۰۶

     پرسش

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

     پاسخ

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

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

107. کارت ۱۰۷

     پرسش

     Right-triangle definition of tangent?

     پاسخ

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

108. کارت ۱۰۸

     پرسش

     Average normal stress under centered axial load?

     پاسخ

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

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

109. کارت ۱۰۹

     پرسش

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

     پاسخ

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

110. کارت ۱۱۰

     پرسش

     SI prefix nano?

     پاسخ

     $n=10^{-9}$.

111. کارت ۱۱۱

     پرسش

     Fundamental Pythagorean trigonometric identity?

     پاسخ

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

112. کارت ۱۱۲

     پرسش

     Engineering normal strain?

     پاسخ

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

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

113. کارت ۱۱۳

     پرسش

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

     پاسخ

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

114. کارت ۱۱۴

     پرسش

     Technical duty to an employer or client?

     پاسخ

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

115. کارت ۱۱۵

     پرسش

     How does a length conversion factor apply to area?

     پاسخ

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

116. کارت ۱۱۶

     پرسش

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

     پاسخ

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

117. کارت ۱۱۷

     پرسش

     When is a Poisson count model reasonable?

     پاسخ

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

118. کارت ۱۱۸

     پرسش

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

     پاسخ

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

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

119. کارت ۱۱۹

     پرسش

     Linear elastic stress-strain relation in uniaxial loading?

     پاسخ

     $$\sigma=E\varepsilon$$

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

120. کارت ۱۲۰

     پرسش

     How does a length conversion factor apply to volume?

     پاسخ

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

121. کارت ۱۲۱

     پرسش

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

     پاسخ

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

122. کارت ۱۲۲

     پرسش

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

     پاسخ

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

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

123. کارت ۱۲۳

     پرسش

     A supervisor directs an illegal engineering action. Proper response?

     پاسخ

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

124. کارت ۱۲۴

     پرسش

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

     پاسخ

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

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

125. کارت ۱۲۵

     پرسش

     Mass density?

     پاسخ

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

     Use mass, not weight, in the numerator.

126. کارت ۱۲۶

     پرسش

     Inches in one foot?

     پاسخ

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

127. کارت ۱۲۷

     پرسش

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

     پاسخ

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

128. کارت ۱۲۸

     پرسش

     How should subscripts be handled in a retrieved relationship?

     پاسخ

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

129. کارت ۱۲۹

     پرسش

     Dot product from vector magnitudes and included angle?

     پاسخ

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

     The result is a scalar.

130. کارت ۱۳۰

     پرسش

     Average normal pressure on an area?

     پاسخ

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

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

131. کارت ۱۳۱

     پرسش

     Feet in one yard?

     پاسخ

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

132. کارت ۱۳۲

     پرسش

     When are two interest rates equivalent?

     پاسخ

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

133. کارت ۱۳۳

     پرسش

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

     پاسخ

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

134. کارت ۱۳۴

     پرسش

     Expected value of a discrete random variable?

     پاسخ

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

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

135. کارت ۱۳۵

     پرسش

     Dot-product test for perpendicular nonzero vectors?

     پاسخ

     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. کارت ۱۳۶

     پرسش

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

     پاسخ

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

     Depth increases downward and the fluid is at rest.

137. کارت ۱۳۷

     پرسش

     Feet in one statute mile?

     پاسخ

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

138. کارت ۱۳۸

     پرسش

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

     پاسخ

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

     

     ۲۷۶ کارت

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     این دسته را رایگان مطالعه کنید

     Nibomo باز می‌شود تا بتوانید مطالعه را شروع کنید.

139. کارت ۱۳۹

     پرسش

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

     پاسخ

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

140. کارت ۱۴۰

     پرسش

     Magnitude of a vector cross product?

     پاسخ

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

     The direction follows the right-hand rule.

141. کارت ۱۴۱

     پرسش

     Exact inch-to-metre relationship?

     پاسخ

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

142. کارت ۱۴۲

     پرسش

     Volumetric flow rate through a cross-section?

     پاسخ

     $$Q=Av_{avg}$$

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

143. کارت ۱۴۳

     پرسش

     Variance from the mean $\mu$?

     پاسخ

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

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

144. کارت ۱۴۴

     پرسش

     Future-worth acceptance rule for an independent investment?

     پاسخ

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

145. کارت ۱۴۵

     پرسش

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

     پاسخ

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

146. کارت ۱۴۶

     پرسش

     Exact foot-to-metre relationship?

     پاسخ

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

147. کارت ۱۴۷

     پرسش

     How should important uncertainty be communicated?

     پاسخ

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

148. کارت ۱۴۸

     پرسش

     When is the matrix product $AB$ defined?

     پاسخ

     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. کارت ۱۴۹

     پرسش

     Steady one-inlet, one-outlet mass continuity?

     پاسخ

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. کارت ۱۵۰

     پرسش

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

     پاسخ

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

151. کارت ۱۵۱

     پرسش

     Square feet in one acre?

     پاسخ

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

152. کارت ۱۵۲

     پرسش

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

     پاسخ

     $$ad-bc$$

153. کارت ۱۵۳

     پرسش

     Bernoulli relationship along a streamline for ideal steady flow?

     پاسخ

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

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

154. کارت ۱۵۴

     پرسش

     May inconvenient measurements be discarded without a technical basis?

     پاسخ

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

155. کارت ۱۵۵

     پرسش

     Annual-worth acceptance rule for an independent investment?

     پاسخ

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

156. کارت ۱۵۶

     پرسش

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

     پاسخ

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

157. کارت ۱۵۷

     پرسش

     Cubic metres in one litre?

     پاسخ

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

158. کارت ۱۵۸

     پرسش

     What does a zero determinant mean for a square matrix?

     پاسخ

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

159. کارت ۱۵۹

     پرسش

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

     پاسخ

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

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

160. کارت ۱۶۰

     پرسش

     Unbiased sample variance for an independent sample from one population?

     پاسخ

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

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

161. کارت ۱۶۱

     پرسش

     How should mutually exclusive alternatives be compared?

     پاسخ

     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. کارت ۱۶۲

     پرسش

     Cubic centimetres in one millilitre?

     پاسخ

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

163. کارت ۱۶۳

     پرسش

     Why keep contemporaneous engineering records?

     پاسخ

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

164. کارت ۱۶۴

     پرسش

     Fast check after substituting into a handbook formula?

     پاسخ

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

165. کارت ۱۶۵

     پرسش

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

     پاسخ

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

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

166. کارت ۱۶۶

     پرسش

     Sensible heat for constant specific heat and no phase change?

     پاسخ

     $$Q=mc\Delta T$$

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

167. کارت ۱۶۷

     پرسش

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

     پاسخ

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

     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. کارت ۱۶۸

     پرسش

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

     پاسخ

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

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

169. کارت ۱۶۹

     پرسش

     Purpose of incremental analysis for mutually exclusive alternatives?

     پاسخ

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

170. کارت ۱۷۰

     پرسش

     Physical meaning of $dy/dx$?

     پاسخ

     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. کارت ۱۷۱

     پرسش

     One-dimensional steady conduction through a plane wall?

     پاسخ

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

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

172. کارت ۱۷۲

     پرسش

     When should you algebraically rearrange a handbook relationship?

     پاسخ

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

173. کارت ۱۷۳

     پرسش

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

     پاسخ

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

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

174. کارت ۱۷۴

     پرسش

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

     پاسخ

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

175. کارت ۱۷۵

     پرسش

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

     پاسخ

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

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

176. کارت ۱۷۶

     پرسش

     Convective heat-transfer rate at a surface?

     پاسخ

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

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

177. کارت ۱۷۷

     پرسش

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

     پاسخ

     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. کارت ۱۷۸

     پرسش

     Internal rate of return?

     پاسخ

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

179. کارت ۱۷۹

     پرسش

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

     پاسخ

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

180. کارت ۱۸۰

     پرسش

     Convert Celsius temperature to kelvin?

     پاسخ

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

     This conversion is for absolute temperature, not temperature difference.

181. کارت ۱۸۱

     پرسش

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

     پاسخ

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

182. کارت ۱۸۲

     پرسش

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

     پاسخ

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

183. کارت ۱۸۳

     پرسش

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

     پاسخ

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

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

184. کارت ۱۸۴

     پرسش

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

     پاسخ

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

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

185. کارت ۱۸۵

     پرسش

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

     پاسخ

     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. کارت ۱۸۶

     پرسش

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

     پاسخ

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

187. کارت ۱۸۷

     پرسش

     Why inspect boundary or initial conditions near a formula?

     پاسخ

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

188. کارت ۱۸۸

     پرسش

     Convert Celsius temperature to Fahrenheit?

     پاسخ

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

189. کارت ۱۸۹

     پرسش

     Ethical basis for expert technical testimony?

     پاسخ

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

190. کارت ۱۹۰

     پرسش

     Meaning of a breakeven value?

     پاسخ

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

191. کارت ۱۹۱

     پرسش

     Derivative of $e^x$?

     پاسخ

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

192. کارت ۱۹۲

     پرسش

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

     پاسخ

     $$\Delta E=Q-W$$

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

193. کارت ۱۹۳

     پرسش

     Frequentist meaning of a 95% confidence procedure?

     پاسخ

     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. کارت ۱۹۴

     پرسش

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

     پاسخ

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

195. کارت ۱۹۵

     پرسش

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

     پاسخ

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

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

196. کارت ۱۹۶

     پرسش

     Relationship between Celsius and kelvin temperature differences?

     پاسخ

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

197. کارت ۱۹۷

     پرسش

     How should credit for team engineering work be assigned?

     پاسخ

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

198. کارت ۱۹۸

     پرسش

     Main limitation of simple payback period?

     پاسخ

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

199. کارت ۱۹۹

     پرسش

     Roles of the null and alternative hypotheses?

     پاسخ

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

200. کارت ۲۰۰

     پرسش

     Ideal-gas equation of state?

     پاسخ

     $$pV=nRT$$

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

201. کارت ۲۰۱

     پرسش

     First check when reading a handbook table?

     پاسخ

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

202. کارت ۲۰۲

     پرسش

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

     پاسخ

     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. کارت ۲۰۳

     پرسش

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

     پاسخ

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

204. کارت ۲۰۴

     پرسش

     Convert Fahrenheit absolute temperature to Rankine?

     پاسخ

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. کارت ۲۰۵

     پرسش

     Ohm's law for an ideal resistor?

     پاسخ

     $$V=IR$$

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

206. کارت ۲۰۶

     پرسش

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

     پاسخ

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

207. کارت ۲۰۷

     پرسش

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

     پاسخ

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

208. کارت ۲۰۸

     پرسش

     Is a radian dimensionless?

     پاسخ

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

209. کارت ۲۰۹

     پرسش

     Electrical power absorbed under the passive sign convention?

     پاسخ

     $$P=VI$$

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

210. کارت ۲۱۰

     پرسش

     Meaning of a p-value?

     پاسخ

     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. کارت ۲۱۱

     پرسش

     First check when reading a handbook graph?

     پاسخ

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

212. کارت ۲۱۲

     پرسش

     Difference between mass and weight?

     پاسخ

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

213. کارت ۲۱۳

     پرسش

     Kirchhoff's current law at a node?

     پاسخ

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

214. کارت ۲۱۴

     پرسش

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

     پاسخ

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

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

215. کارت ۲۱۵

     پرسش

     Opportunity cost?

     پاسخ

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

216. کارت ۲۱۶

     پرسش

     Weight from mass in a gravitational field?

     پاسخ

     $$W=mg$$

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

217. کارت ۲۱۷

     پرسش

     Kirchhoff's voltage law around a closed loop?

     پاسخ

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

218. کارت ۲۱۸

     پرسش

     Decision rule using significance level $\alpha$?

     پاسخ

     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. کارت ۲۱۹

     پرسش

     Can proprietary methods from a former employer be reused freely?

     پاسخ

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

220. کارت ۲۲۰

     پرسش

     Pound-force to newtons?

     پاسخ

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

221. کارت ۲۲۱

     پرسش

     When does a definite integral equal ordinary geometric area?

     پاسخ

     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. کارت ۲۲۲

     پرسش

     Charge-voltage relation for an ideal capacitor?

     پاسخ

     $$q=CV$$

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

223. کارت ۲۲۳

     پرسش

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

     پاسخ

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

224. کارت ۲۲۴

     پرسش

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

     پاسخ

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

225. کارت ۲۲۵

     پرسش

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

     پاسخ

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

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

226. کارت ۲۲۶

     پرسش

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

     پاسخ

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

227. کارت ۲۲۷

     پرسش

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

     پاسخ

     $$\tau=RC$$

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

228. کارت ۲۲۸

     پرسش

     What physical quantity does pound-mass measure?

     پاسخ

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

229. کارت ۲۲۹

     پرسش

     Type I error?

     پاسخ

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

230. کارت ۲۳۰

     پرسش

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

     پاسخ

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

231. کارت ۲۳۱

     پرسش

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

     پاسخ

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

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

232. کارت ۲۳۲

     پرسش

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

     پاسخ

     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. کارت ۲۳۳

     پرسش

     Recognizable form of a separable first-order differential equation?

     پاسخ

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

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

234. کارت ۲۳۴

     پرسش

     Using unverified software output in a safety-relevant calculation?

     پاسخ

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

235. کارت ۲۳۵

     پرسش

     Equivalent resistance of ideal resistors in series?

     پاسخ

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

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

236. کارت ۲۳۶

     پرسش

     Pressure conversion from psi to pascals?

     پاسخ

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

237. کارت ۲۳۷

     پرسش

     Type II error?

     پاسخ

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

238. کارت ۲۳۸

     پرسش

     Useful flashcard to make after a failed handbook search?

     پاسخ

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

239. کارت ۲۳۹

     پرسش

     Standard form of a first-order linear differential equation?

     پاسخ

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

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

240. کارت ۲۴۰

     پرسش

     Equivalent resistance of ideal resistors in parallel?

     پاسخ

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

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

241. کارت ۲۴۱

     پرسش

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

     پاسخ

     $$BV_k=B-kD$$

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

242. کارت ۲۴۲

     پرسش

     Standard atmosphere in pascals?

     پاسخ

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

243. کارت ۲۴۳

     پرسش

     Using AI-generated technical content in engineering work?

     پاسخ

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

244. کارت ۲۴۴

     پرسش

     Trial form for a homogeneous linear ODE with constant coefficients?

     پاسخ

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

245. کارت ۲۴۵

     پرسش

     Wave-speed relationship among frequency and wavelength?

     پاسخ

     $$v=f\lambda$$

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

246. کارت ۲۴۶

     پرسش

     Statistical power?

     پاسخ

     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. کارت ۲۴۷

     پرسش

     Bar in pascals?

     پاسخ

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

248. کارت ۲۴۸

     پرسش

     How should handbook navigation be practiced before the FE exam?

     پاسخ

     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. کارت ۲۴۹

     پرسش

     Is depreciation itself a cash outflow?

     پاسخ

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

250. کارت ۲۵۰

     پرسش

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

     پاسخ

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

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

251. کارت ۲۵۱

     پرسش

     Relationship between period and frequency?

     پاسخ

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

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

252. کارت ۲۵۲

     پرسش

     How should foreseeable environmental harm enter an engineering decision?

     پاسخ

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

253. کارت ۲۵۳

     پرسش

     Foot-pound-force in joules?

     پاسخ

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

254. کارت ۲۵۴

     پرسش

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

     پاسخ

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

255. کارت ۲۵۵

     پرسش

     When should you search instead of relying on recall?

     پاسخ

     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. کارت ۲۵۶

     پرسش

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

     پاسخ

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

257. کارت ۲۵۷

     پرسش

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

     پاسخ

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

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

258. کارت ۲۵۸

     پرسش

     General material balance on a control volume?

     پاسخ

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

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

259. کارت ۲۵۹

     پرسش

     Approximate joules in one International Table Btu?

     پاسخ

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

260. کارت ۲۶۰

     پرسش

     What is the defender in a replacement analysis?

     پاسخ

     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. کارت ۲۶۱

     پرسش

     Speaking publicly about a technical matter outside your expertise?

     پاسخ

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

262. کارت ۲۶۲

     پرسش

     Single-interval trapezoidal approximation to an integral?

     پاسخ

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

     It is exact for linear $f$.

263. کارت ۲۶۳

     پرسش

     Energy efficiency of a device?

     پاسخ

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

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

264. کارت ۲۶۴

     پرسش

     Purpose of sensitivity analysis in engineering economics?

     پاسخ

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

265. کارت ۲۶۵

     پرسش

     Can a strong correlation establish causation?

     پاسخ

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

266. کارت ۲۶۶

     پرسش

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

     پاسخ

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

267. کارت ۲۶۷

     پرسش

     Mechanical horsepower in watts?

     پاسخ

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

268. کارت ۲۶۸

     پرسش

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

     پاسخ

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

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

269. کارت ۲۶۹

     پرسش

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

     پاسخ

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

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

270. کارت ۲۷۰

     پرسش

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

     پاسخ

     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. کارت ۲۷۱

     پرسش

     Kilowatt-hour in joules?

     پاسخ

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

272. کارت ۲۷۲

     پرسش

     Percent error relative to an accepted nonzero value?

     پاسخ

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

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

273. کارت ۲۷۳

     پرسش

     Does legal compliance alone settle an engineering ethics question?

     پاسخ

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

274. کارت ۲۷۴

     پرسش

     Does handbook fluency replace discipline-specific problem practice?

     پاسخ

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

275. کارت ۲۷۵

     پرسش

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

     پاسخ

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

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

276. کارت ۲۷۶

     پرسش

     Dimensional requirement for a physically meaningful additive equation?

     پاسخ

     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.