FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

بطاقات هذه الرزمة

1. البطاقة ١

   السؤال

   SI base unit of length?

   الإجابة

   The metre, symbol $m$.

2. البطاقة ٢

   السؤال

   Slope between two points?

   الإجابة

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

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

3. البطاقة ٣

   السؤال

   Net force relationship for constant mass in an inertial frame?

   الإجابة

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

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

4. البطاقة ٤

   السؤال

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

   الإجابة

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

5. البطاقة ٥

   السؤال

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

   الإجابة

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

6. البطاقة ٦

   السؤال

   Probability of the complement of event $A$?

   الإجابة

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

7. البطاقة ٧

   السؤال

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

   الإجابة

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

8. البطاقة ٨

   السؤال

   SI base unit of mass?

   الإجابة

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

9. البطاقة ٩

   السؤال

   Linear equation from slope and intercept?

   الإجابة

   $$y=mx+b$$

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

10. البطاقة ١٠

    السؤال

    Velocity after time $t$ under constant acceleration?

    الإجابة

    $$v=v_0+at$$

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

11. البطاقة ١١

    السؤال

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

    الإجابة

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

12. البطاقة ١٢

    السؤال

    How is the FE reference handbook available during the exam?

    الإجابة

    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. البطاقة ١٣

    السؤال

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

    الإجابة

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

14. البطاقة ١٤

    السؤال

    SI base unit of time?

    الإجابة

    The second, symbol $s$.

15. البطاقة ١٥

    السؤال

    Linear equation from one point and a slope?

    الإجابة

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

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

16. البطاقة ١٦

    السؤال

    Position after time $t$ under constant acceleration?

    الإجابة

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

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

17. البطاقة ١٧

    السؤال

    A project assignment lies outside your competence. Proper response?

    الإجابة

    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. البطاقة ١٨

    السؤال

    SI base unit of electric current?

    الإجابة

    The ampere, symbol $A$.

19. البطاقة ١٩

    السؤال

    Future amount under simple interest?

    الإجابة

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

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

20. البطاقة ٢٠

    السؤال

    Distance between two Cartesian points?

    الإجابة

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

    The coordinate components must use the same length unit.

21. البطاقة ٢١

    السؤال

    Constant-acceleration relation without elapsed time?

    الإجابة

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

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

22. البطاقة ٢٢

    السؤال

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

    الإجابة

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

23. البطاقة ٢٣

    السؤال

    Conditional probability of $A$ given $B$?

    الإجابة

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

    This requires $P(B)>0$.

24. البطاقة ٢٤

    السؤال

    SI base unit of thermodynamic temperature?

    الإجابة

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

25. البطاقة ٢٥

    السؤال

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

    الإجابة

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

26. البطاقة ٢٦

    السؤال

    Midpoint of two Cartesian points?

    الإجابة

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

    Average corresponding coordinates.

27. البطاقة ٢٧

    السؤال

    Linear momentum of a particle?

    الإجابة

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

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

28. البطاقة ٢٨

    السؤال

    Future amount under compound interest?

    الإجابة

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

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

29. البطاقة ٢٩

    السؤال

    Should an FE search workflow depend on Ctrl+F?

    الإجابة

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

30. البطاقة ٣٠

    السؤال

    SI base unit of amount of substance?

    الإجابة

    The mole, symbol $mol$.

31. البطاقة ٣١

    السؤال

    Joint probability expressed with a conditional probability?

    الإجابة

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

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

32. البطاقة ٣٢

    السؤال

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

    الإجابة

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

    The coordinate units and radius unit must match.

33. البطاقة ٣٣

    السؤال

    Impulse-momentum relationship?

    الإجابة

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

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

34. البطاقة ٣٤

    السؤال

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

    الإجابة

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

35. البطاقة ٣٥

    السؤال

    SI base unit of luminous intensity?

    الإجابة

    The candela, symbol $cd$.

36. البطاقة ٣٦

    السؤال

    Present worth of one future amount?

    الإجابة

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

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

37. البطاقة ٣٧

    السؤال

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

    الإجابة

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

    This form requires $a\ne0$.

38. البطاقة ٣٨

    السؤال

    When is total linear momentum conserved?

    الإجابة

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

39. البطاقة ٣٩

    السؤال

    Why avoid memorizing FE handbook page numbers?

    الإجابة

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

40. البطاقة ٤٠

    السؤال

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

    الإجابة

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

    Independence is not the same as mutual exclusivity.

41. البطاقة ٤١

    السؤال

    SI unit of frequency in base-unit form?

    الإجابة

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

42. البطاقة ٤٢

    السؤال

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

    الإجابة

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

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

43. البطاقة ٤٣

    السؤال

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

    الإجابة

    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. البطاقة ٤٤

    السؤال

    Work done by a constant force through displacement?

    الإجابة

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

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

45. البطاقة ٤٥

    السؤال

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

    الإجابة

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

46. البطاقة ٤٦

    السؤال

    SI unit of force in base-unit form?

    الإجابة

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

47. البطاقة ٤٧

    السؤال

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

    الإجابة

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

48. البطاقة ٤٨

    السؤال

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

    الإجابة

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

    This requires $P(B)>0$.

49. البطاقة ٤٩

    السؤال

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

    الإجابة

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

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

50. البطاقة ٥٠

    السؤال

    Translational kinetic energy of a particle?

    الإجابة

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

    Mass and speed must use a coherent unit system.

51. البطاقة ٥١

    السؤال

    SI unit of pressure in force-area form?

    الإجابة

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

52. البطاقة ٥٢

    السؤال

    Equivalent annual amount for present worth $P$?

    الإجابة

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

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

53. البطاقة ٥٣

    السؤال

    May confidential client information be shared for personal benefit?

    الإجابة

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

54. البطاقة ٥٤

    السؤال

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

    الإجابة

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

55. البطاقة ٥٥

    السؤال

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

    الإجابة

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

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

56. البطاقة ٥٦

    السؤال

    Net work-energy relationship for a particle?

    الإجابة

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

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

57. البطاقة ٥٧

    السؤال

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

    الإجابة

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

    Use this when order matters and selection is without replacement.

58. البطاقة ٥٨

    السؤال

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

    الإجابة

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

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

59. البطاقة ٥٩

    السؤال

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

    الإجابة

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

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

60. البطاقة ٦٠

    السؤال

    SI unit of energy in force-distance form?

    الإجابة

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

61. البطاقة ٦١

    السؤال

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

    الإجابة

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

62. البطاقة ٦٢

    السؤال

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

    الإجابة

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

63. البطاقة ٦٣

    السؤال

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

    الإجابة

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

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

64. البطاقة ٦٤

    السؤال

    Change in gravitational potential energy near Earth's surface?

    الإجابة

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

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

65. البطاقة ٦٥

    السؤال

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

    الإجابة

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

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

66. البطاقة ٦٦

    السؤال

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

    الإجابة

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

    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. البطاقة ٦٧

    السؤال

    A handbook search for an acronym fails. Next move?

    الإجابة

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

68. البطاقة ٦٨

    السؤال

    SI unit of power in energy-time form?

    الإجابة

    The watt, $W=J/s$.

69. البطاقة ٦٩

    السؤال

    Logarithm of a product?

    الإجابة

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

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

70. البطاقة ٧٠

    السؤال

    Conditions for a binomial model?

    الإجابة

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

71. البطاقة ٧١

    السؤال

    Using another engineer's analysis in your deliverable?

    الإجابة

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

72. البطاقة ٧٢

    السؤال

    SI unit of electric charge in current-time form?

    الإجابة

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

73. البطاقة ٧٣

    السؤال

    Average power from work over elapsed time?

    الإجابة

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

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

74. البطاقة ٧٤

    السؤال

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

    الإجابة

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

    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. البطاقة ٧٥

    السؤال

    Logarithm of a positive quantity raised to a power?

    الإجابة

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

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

76. البطاقة ٧٦

    السؤال

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

    الإجابة

    The volt, $V=J/C$.

77. البطاقة ٧٧

    السؤال

    Instantaneous mechanical power delivered by a force?

    الإجابة

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

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

78. البطاقة ٧٨

    السؤال

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

    الإجابة

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

79. البطاقة ٧٩

    السؤال

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

    الإجابة

    $$E[X]=np$$

80. البطاقة ٨٠

    السؤال

    SI unit of electrical resistance in voltage-current form?

    الإجابة

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

81. البطاقة ٨١

    السؤال

    Moment of a force about a point?

    الإجابة

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

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

82. البطاقة ٨٢

    السؤال

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

    الإجابة

    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. البطاقة ٨٣

    السؤال

    Inverse relationship between the natural log and exponential?

    الإجابة

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

    The second identity requires $x>0$.

84. البطاقة ٨٤

    السؤال

    SI prefix giga?

    الإجابة

    $G=10^9$.

85. البطاقة ٨٥

    السؤال

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

    الإجابة

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

    Use consistent angular sign convention and radians for angular measures.

86. البطاقة ٨٦

    السؤال

    When should an engineer sign or seal technical work?

    الإجابة

    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. البطاقة ٨٧

    السؤال

    Best memory target for returning to a handbook formula?

    الإجابة

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

88. البطاقة ٨٨

    السؤال

    SI prefix mega?

    الإجابة

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

89. البطاقة ٨٩

    السؤال

    Convert degrees to radians?

    الإجابة

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

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

90. البطاقة ٩٠

    السؤال

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

    الإجابة

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

91. البطاقة ٩١

    السؤال

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

    الإجابة

    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. البطاقة ٩٢

    السؤال

    Where do licensure and sealing requirements come from?

    الإجابة

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

93. البطاقة ٩٣

    السؤال

    Rotational kinetic energy about a fixed axis?

    الإجابة

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

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

94. البطاقة ٩٤

    السؤال

    SI prefix kilo?

    الإجابة

    $k=10^3$.

95. البطاقة ٩٥

    السؤال

    Right-triangle definition of sine?

    الإجابة

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

96. البطاقة ٩٦

    السؤال

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

    الإجابة

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

97. البطاقة ٩٧

    السؤال

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

    الإجابة

    $$\sum M=I\alpha$$

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

98. البطاقة ٩٨

    السؤال

    SI prefix milli?

    الإجابة

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

99. البطاقة ٩٩

    السؤال

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

    الإجابة

    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. البطاقة ١٠٠

     السؤال

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

     الإجابة

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

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

101. البطاقة ١٠١

     السؤال

     Right-triangle definition of cosine?

     الإجابة

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

102. البطاقة ١٠٢

     السؤال

     Force-displacement relation for an ideal linear spring?

     الإجابة

     $$F=-kx$$

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

103. البطاقة ١٠٣

     السؤال

     May qualifications or project responsibility be exaggerated in a proposal?

     الإجابة

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

104. البطاقة ١٠٤

     السؤال

     SI prefix micro?

     الإجابة

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

105. البطاقة ١٠٥

     السؤال

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

     الإجابة

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

106. البطاقة ١٠٦

     السؤال

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

     الإجابة

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

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

107. البطاقة ١٠٧

     السؤال

     Right-triangle definition of tangent?

     الإجابة

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

108. البطاقة ١٠٨

     السؤال

     Average normal stress under centered axial load?

     الإجابة

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

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

109. البطاقة ١٠٩

     السؤال

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

     الإجابة

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

110. البطاقة ١١٠

     السؤال

     SI prefix nano?

     الإجابة

     $n=10^{-9}$.

111. البطاقة ١١١

     السؤال

     Fundamental Pythagorean trigonometric identity?

     الإجابة

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

112. البطاقة ١١٢

     السؤال

     Engineering normal strain?

     الإجابة

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

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

113. البطاقة ١١٣

     السؤال

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

     الإجابة

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

114. البطاقة ١١٤

     السؤال

     Technical duty to an employer or client?

     الإجابة

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

115. البطاقة ١١٥

     السؤال

     How does a length conversion factor apply to area?

     الإجابة

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

116. البطاقة ١١٦

     السؤال

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

     الإجابة

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

117. البطاقة ١١٧

     السؤال

     When is a Poisson count model reasonable?

     الإجابة

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

118. البطاقة ١١٨

     السؤال

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

     الإجابة

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

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

119. البطاقة ١١٩

     السؤال

     Linear elastic stress-strain relation in uniaxial loading?

     الإجابة

     $$\sigma=E\varepsilon$$

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

120. البطاقة ١٢٠

     السؤال

     How does a length conversion factor apply to volume?

     الإجابة

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

121. البطاقة ١٢١

     السؤال

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

     الإجابة

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

122. البطاقة ١٢٢

     السؤال

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

     الإجابة

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

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

123. البطاقة ١٢٣

     السؤال

     A supervisor directs an illegal engineering action. Proper response?

     الإجابة

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

124. البطاقة ١٢٤

     السؤال

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

     الإجابة

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

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

125. البطاقة ١٢٥

     السؤال

     Mass density?

     الإجابة

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

     Use mass, not weight, in the numerator.

126. البطاقة ١٢٦

     السؤال

     Inches in one foot?

     الإجابة

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

127. البطاقة ١٢٧

     السؤال

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

     الإجابة

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

128. البطاقة ١٢٨

     السؤال

     How should subscripts be handled in a retrieved relationship?

     الإجابة

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

129. البطاقة ١٢٩

     السؤال

     Dot product from vector magnitudes and included angle?

     الإجابة

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

     The result is a scalar.

130. البطاقة ١٣٠

     السؤال

     Average normal pressure on an area?

     الإجابة

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

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

131. البطاقة ١٣١

     السؤال

     Feet in one yard?

     الإجابة

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

132. البطاقة ١٣٢

     السؤال

     When are two interest rates equivalent?

     الإجابة

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

133. البطاقة ١٣٣

     السؤال

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

     الإجابة

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

134. البطاقة ١٣٤

     السؤال

     Expected value of a discrete random variable?

     الإجابة

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

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

135. البطاقة ١٣٥

     السؤال

     Dot-product test for perpendicular nonzero vectors?

     الإجابة

     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. البطاقة ١٣٦

     السؤال

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

     الإجابة

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

     Depth increases downward and the fluid is at rest.

137. البطاقة ١٣٧

     السؤال

     Feet in one statute mile?

     الإجابة

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

138. البطاقة ١٣٨

     السؤال

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

     الإجابة

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

     

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     ادرس هذه الرزمة مجانًا

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139. البطاقة ١٣٩

     السؤال

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

     الإجابة

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

140. البطاقة ١٤٠

     السؤال

     Magnitude of a vector cross product?

     الإجابة

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

     The direction follows the right-hand rule.

141. البطاقة ١٤١

     السؤال

     Exact inch-to-metre relationship?

     الإجابة

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

142. البطاقة ١٤٢

     السؤال

     Volumetric flow rate through a cross-section?

     الإجابة

     $$Q=Av_{avg}$$

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

143. البطاقة ١٤٣

     السؤال

     Variance from the mean $\mu$?

     الإجابة

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

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

144. البطاقة ١٤٤

     السؤال

     Future-worth acceptance rule for an independent investment?

     الإجابة

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

145. البطاقة ١٤٥

     السؤال

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

     الإجابة

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

146. البطاقة ١٤٦

     السؤال

     Exact foot-to-metre relationship?

     الإجابة

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

147. البطاقة ١٤٧

     السؤال

     How should important uncertainty be communicated?

     الإجابة

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

148. البطاقة ١٤٨

     السؤال

     When is the matrix product $AB$ defined?

     الإجابة

     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. البطاقة ١٤٩

     السؤال

     Steady one-inlet, one-outlet mass continuity?

     الإجابة

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. البطاقة ١٥٠

     السؤال

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

     الإجابة

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

151. البطاقة ١٥١

     السؤال

     Square feet in one acre?

     الإجابة

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

152. البطاقة ١٥٢

     السؤال

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

     الإجابة

     $$ad-bc$$

153. البطاقة ١٥٣

     السؤال

     Bernoulli relationship along a streamline for ideal steady flow?

     الإجابة

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

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

154. البطاقة ١٥٤

     السؤال

     May inconvenient measurements be discarded without a technical basis?

     الإجابة

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

155. البطاقة ١٥٥

     السؤال

     Annual-worth acceptance rule for an independent investment?

     الإجابة

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

156. البطاقة ١٥٦

     السؤال

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

     الإجابة

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

157. البطاقة ١٥٧

     السؤال

     Cubic metres in one litre?

     الإجابة

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

158. البطاقة ١٥٨

     السؤال

     What does a zero determinant mean for a square matrix?

     الإجابة

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

159. البطاقة ١٥٩

     السؤال

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

     الإجابة

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

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

160. البطاقة ١٦٠

     السؤال

     Unbiased sample variance for an independent sample from one population?

     الإجابة

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

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

161. البطاقة ١٦١

     السؤال

     How should mutually exclusive alternatives be compared?

     الإجابة

     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. البطاقة ١٦٢

     السؤال

     Cubic centimetres in one millilitre?

     الإجابة

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

163. البطاقة ١٦٣

     السؤال

     Why keep contemporaneous engineering records?

     الإجابة

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

164. البطاقة ١٦٤

     السؤال

     Fast check after substituting into a handbook formula?

     الإجابة

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

165. البطاقة ١٦٥

     السؤال

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

     الإجابة

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

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

166. البطاقة ١٦٦

     السؤال

     Sensible heat for constant specific heat and no phase change?

     الإجابة

     $$Q=mc\Delta T$$

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

167. البطاقة ١٦٧

     السؤال

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

     الإجابة

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

     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. البطاقة ١٦٨

     السؤال

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

     الإجابة

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

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

169. البطاقة ١٦٩

     السؤال

     Purpose of incremental analysis for mutually exclusive alternatives?

     الإجابة

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

170. البطاقة ١٧٠

     السؤال

     Physical meaning of $dy/dx$?

     الإجابة

     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. البطاقة ١٧١

     السؤال

     One-dimensional steady conduction through a plane wall?

     الإجابة

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

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

172. البطاقة ١٧٢

     السؤال

     When should you algebraically rearrange a handbook relationship?

     الإجابة

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

173. البطاقة ١٧٣

     السؤال

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

     الإجابة

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

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

174. البطاقة ١٧٤

     السؤال

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

     الإجابة

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

175. البطاقة ١٧٥

     السؤال

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

     الإجابة

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

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

176. البطاقة ١٧٦

     السؤال

     Convective heat-transfer rate at a surface?

     الإجابة

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

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

177. البطاقة ١٧٧

     السؤال

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

     الإجابة

     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. البطاقة ١٧٨

     السؤال

     Internal rate of return?

     الإجابة

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

179. البطاقة ١٧٩

     السؤال

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

     الإجابة

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

180. البطاقة ١٨٠

     السؤال

     Convert Celsius temperature to kelvin?

     الإجابة

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

     This conversion is for absolute temperature, not temperature difference.

181. البطاقة ١٨١

     السؤال

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

     الإجابة

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

182. البطاقة ١٨٢

     السؤال

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

     الإجابة

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

183. البطاقة ١٨٣

     السؤال

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

     الإجابة

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

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

184. البطاقة ١٨٤

     السؤال

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

     الإجابة

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

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

185. البطاقة ١٨٥

     السؤال

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

     الإجابة

     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. البطاقة ١٨٦

     السؤال

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

     الإجابة

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

187. البطاقة ١٨٧

     السؤال

     Why inspect boundary or initial conditions near a formula?

     الإجابة

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

188. البطاقة ١٨٨

     السؤال

     Convert Celsius temperature to Fahrenheit?

     الإجابة

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

189. البطاقة ١٨٩

     السؤال

     Ethical basis for expert technical testimony?

     الإجابة

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

190. البطاقة ١٩٠

     السؤال

     Meaning of a breakeven value?

     الإجابة

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

191. البطاقة ١٩١

     السؤال

     Derivative of $e^x$?

     الإجابة

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

192. البطاقة ١٩٢

     السؤال

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

     الإجابة

     $$\Delta E=Q-W$$

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

193. البطاقة ١٩٣

     السؤال

     Frequentist meaning of a 95% confidence procedure?

     الإجابة

     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. البطاقة ١٩٤

     السؤال

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

     الإجابة

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

195. البطاقة ١٩٥

     السؤال

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

     الإجابة

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

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

196. البطاقة ١٩٦

     السؤال

     Relationship between Celsius and kelvin temperature differences?

     الإجابة

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

197. البطاقة ١٩٧

     السؤال

     How should credit for team engineering work be assigned?

     الإجابة

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

198. البطاقة ١٩٨

     السؤال

     Main limitation of simple payback period?

     الإجابة

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

199. البطاقة ١٩٩

     السؤال

     Roles of the null and alternative hypotheses?

     الإجابة

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

200. البطاقة ٢٠٠

     السؤال

     Ideal-gas equation of state?

     الإجابة

     $$pV=nRT$$

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

201. البطاقة ٢٠١

     السؤال

     First check when reading a handbook table?

     الإجابة

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

202. البطاقة ٢٠٢

     السؤال

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

     الإجابة

     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. البطاقة ٢٠٣

     السؤال

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

     الإجابة

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

204. البطاقة ٢٠٤

     السؤال

     Convert Fahrenheit absolute temperature to Rankine?

     الإجابة

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. البطاقة ٢٠٥

     السؤال

     Ohm's law for an ideal resistor?

     الإجابة

     $$V=IR$$

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

206. البطاقة ٢٠٦

     السؤال

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

     الإجابة

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

207. البطاقة ٢٠٧

     السؤال

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

     الإجابة

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

208. البطاقة ٢٠٨

     السؤال

     Is a radian dimensionless?

     الإجابة

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

209. البطاقة ٢٠٩

     السؤال

     Electrical power absorbed under the passive sign convention?

     الإجابة

     $$P=VI$$

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

210. البطاقة ٢١٠

     السؤال

     Meaning of a p-value?

     الإجابة

     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. البطاقة ٢١١

     السؤال

     First check when reading a handbook graph?

     الإجابة

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

212. البطاقة ٢١٢

     السؤال

     Difference between mass and weight?

     الإجابة

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

213. البطاقة ٢١٣

     السؤال

     Kirchhoff's current law at a node?

     الإجابة

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

214. البطاقة ٢١٤

     السؤال

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

     الإجابة

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

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

215. البطاقة ٢١٥

     السؤال

     Opportunity cost?

     الإجابة

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

216. البطاقة ٢١٦

     السؤال

     Weight from mass in a gravitational field?

     الإجابة

     $$W=mg$$

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

217. البطاقة ٢١٧

     السؤال

     Kirchhoff's voltage law around a closed loop?

     الإجابة

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

218. البطاقة ٢١٨

     السؤال

     Decision rule using significance level $\alpha$?

     الإجابة

     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. البطاقة ٢١٩

     السؤال

     Can proprietary methods from a former employer be reused freely?

     الإجابة

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

220. البطاقة ٢٢٠

     السؤال

     Pound-force to newtons?

     الإجابة

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

221. البطاقة ٢٢١

     السؤال

     When does a definite integral equal ordinary geometric area?

     الإجابة

     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. البطاقة ٢٢٢

     السؤال

     Charge-voltage relation for an ideal capacitor?

     الإجابة

     $$q=CV$$

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

223. البطاقة ٢٢٣

     السؤال

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

     الإجابة

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

224. البطاقة ٢٢٤

     السؤال

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

     الإجابة

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

225. البطاقة ٢٢٥

     السؤال

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

     الإجابة

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

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

226. البطاقة ٢٢٦

     السؤال

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

     الإجابة

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

227. البطاقة ٢٢٧

     السؤال

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

     الإجابة

     $$\tau=RC$$

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

228. البطاقة ٢٢٨

     السؤال

     What physical quantity does pound-mass measure?

     الإجابة

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

229. البطاقة ٢٢٩

     السؤال

     Type I error?

     الإجابة

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

230. البطاقة ٢٣٠

     السؤال

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

     الإجابة

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

231. البطاقة ٢٣١

     السؤال

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

     الإجابة

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

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

232. البطاقة ٢٣٢

     السؤال

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

     الإجابة

     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. البطاقة ٢٣٣

     السؤال

     Recognizable form of a separable first-order differential equation?

     الإجابة

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

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

234. البطاقة ٢٣٤

     السؤال

     Using unverified software output in a safety-relevant calculation?

     الإجابة

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

235. البطاقة ٢٣٥

     السؤال

     Equivalent resistance of ideal resistors in series?

     الإجابة

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

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

236. البطاقة ٢٣٦

     السؤال

     Pressure conversion from psi to pascals?

     الإجابة

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

237. البطاقة ٢٣٧

     السؤال

     Type II error?

     الإجابة

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

238. البطاقة ٢٣٨

     السؤال

     Useful flashcard to make after a failed handbook search?

     الإجابة

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

239. البطاقة ٢٣٩

     السؤال

     Standard form of a first-order linear differential equation?

     الإجابة

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

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

240. البطاقة ٢٤٠

     السؤال

     Equivalent resistance of ideal resistors in parallel?

     الإجابة

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

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

241. البطاقة ٢٤١

     السؤال

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

     الإجابة

     $$BV_k=B-kD$$

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

242. البطاقة ٢٤٢

     السؤال

     Standard atmosphere in pascals?

     الإجابة

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

243. البطاقة ٢٤٣

     السؤال

     Using AI-generated technical content in engineering work?

     الإجابة

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

244. البطاقة ٢٤٤

     السؤال

     Trial form for a homogeneous linear ODE with constant coefficients?

     الإجابة

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

245. البطاقة ٢٤٥

     السؤال

     Wave-speed relationship among frequency and wavelength?

     الإجابة

     $$v=f\lambda$$

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

246. البطاقة ٢٤٦

     السؤال

     Statistical power?

     الإجابة

     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. البطاقة ٢٤٧

     السؤال

     Bar in pascals?

     الإجابة

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

248. البطاقة ٢٤٨

     السؤال

     How should handbook navigation be practiced before the FE exam?

     الإجابة

     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. البطاقة ٢٤٩

     السؤال

     Is depreciation itself a cash outflow?

     الإجابة

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

250. البطاقة ٢٥٠

     السؤال

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

     الإجابة

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

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

251. البطاقة ٢٥١

     السؤال

     Relationship between period and frequency?

     الإجابة

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

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

252. البطاقة ٢٥٢

     السؤال

     How should foreseeable environmental harm enter an engineering decision?

     الإجابة

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

253. البطاقة ٢٥٣

     السؤال

     Foot-pound-force in joules?

     الإجابة

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

254. البطاقة ٢٥٤

     السؤال

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

     الإجابة

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

255. البطاقة ٢٥٥

     السؤال

     When should you search instead of relying on recall?

     الإجابة

     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. البطاقة ٢٥٦

     السؤال

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

     الإجابة

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

257. البطاقة ٢٥٧

     السؤال

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

     الإجابة

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

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

258. البطاقة ٢٥٨

     السؤال

     General material balance on a control volume?

     الإجابة

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

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

259. البطاقة ٢٥٩

     السؤال

     Approximate joules in one International Table Btu?

     الإجابة

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

260. البطاقة ٢٦٠

     السؤال

     What is the defender in a replacement analysis?

     الإجابة

     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. البطاقة ٢٦١

     السؤال

     Speaking publicly about a technical matter outside your expertise?

     الإجابة

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

262. البطاقة ٢٦٢

     السؤال

     Single-interval trapezoidal approximation to an integral?

     الإجابة

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

     It is exact for linear $f$.

263. البطاقة ٢٦٣

     السؤال

     Energy efficiency of a device?

     الإجابة

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

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

264. البطاقة ٢٦٤

     السؤال

     Purpose of sensitivity analysis in engineering economics?

     الإجابة

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

265. البطاقة ٢٦٥

     السؤال

     Can a strong correlation establish causation?

     الإجابة

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

266. البطاقة ٢٦٦

     السؤال

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

     الإجابة

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

267. البطاقة ٢٦٧

     السؤال

     Mechanical horsepower in watts?

     الإجابة

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

268. البطاقة ٢٦٨

     السؤال

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

     الإجابة

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

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

269. البطاقة ٢٦٩

     السؤال

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

     الإجابة

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

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

270. البطاقة ٢٧٠

     السؤال

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

     الإجابة

     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. البطاقة ٢٧١

     السؤال

     Kilowatt-hour in joules?

     الإجابة

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

272. البطاقة ٢٧٢

     السؤال

     Percent error relative to an accepted nonzero value?

     الإجابة

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

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

273. البطاقة ٢٧٣

     السؤال

     Does legal compliance alone settle an engineering ethics question?

     الإجابة

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

274. البطاقة ٢٧٤

     السؤال

     Does handbook fluency replace discipline-specific problem practice?

     الإجابة

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

275. البطاقة ٢٧٥

     السؤال

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

     الإجابة

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

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

276. البطاقة ٢٧٦

     السؤال

     Dimensional requirement for a physically meaningful additive equation?

     الإجابة

     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.