FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Kartītes šajā kavā

1. 1. kartīte

   Jautājums

   SI base unit of length?

   Atbilde

   The metre, symbol $m$.

2. 2. kartīte

   Jautājums

   Slope between two points?

   Atbilde

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

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

3. 3. kartīte

   Jautājums

   Net force relationship for constant mass in an inertial frame?

   Atbilde

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

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

4. 4. kartīte

   Jautājums

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

   Atbilde

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

5. 5. kartīte

   Jautājums

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

   Atbilde

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

6. 6. kartīte

   Jautājums

   Probability of the complement of event $A$?

   Atbilde

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

7. 7. kartīte

   Jautājums

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

   Atbilde

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

8. 8. kartīte

   Jautājums

   SI base unit of mass?

   Atbilde

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

9. 9. kartīte

   Jautājums

   Linear equation from slope and intercept?

   Atbilde

   $$y=mx+b$$

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

10. 10. kartīte

    Jautājums

    Velocity after time $t$ under constant acceleration?

    Atbilde

    $$v=v_0+at$$

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

11. 11. kartīte

    Jautājums

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

    Atbilde

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

12. 12. kartīte

    Jautājums

    How is the FE reference handbook available during the exam?

    Atbilde

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

13. 13. kartīte

    Jautājums

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

    Atbilde

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

14. 14. kartīte

    Jautājums

    SI base unit of time?

    Atbilde

    The second, symbol $s$.

15. 15. kartīte

    Jautājums

    Linear equation from one point and a slope?

    Atbilde

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

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

16. 16. kartīte

    Jautājums

    Position after time $t$ under constant acceleration?

    Atbilde

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

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

17. 17. kartīte

    Jautājums

    A project assignment lies outside your competence. Proper response?

    Atbilde

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

18. 18. kartīte

    Jautājums

    SI base unit of electric current?

    Atbilde

    The ampere, symbol $A$.

19. 19. kartīte

    Jautājums

    Future amount under simple interest?

    Atbilde

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

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

20. 20. kartīte

    Jautājums

    Distance between two Cartesian points?

    Atbilde

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

    The coordinate components must use the same length unit.

21. 21. kartīte

    Jautājums

    Constant-acceleration relation without elapsed time?

    Atbilde

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

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

22. 22. kartīte

    Jautājums

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

    Atbilde

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

23. 23. kartīte

    Jautājums

    Conditional probability of $A$ given $B$?

    Atbilde

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

    This requires $P(B)>0$.

24. 24. kartīte

    Jautājums

    SI base unit of thermodynamic temperature?

    Atbilde

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

25. 25. kartīte

    Jautājums

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

    Atbilde

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

26. 26. kartīte

    Jautājums

    Midpoint of two Cartesian points?

    Atbilde

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

    Average corresponding coordinates.

27. 27. kartīte

    Jautājums

    Linear momentum of a particle?

    Atbilde

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

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

28. 28. kartīte

    Jautājums

    Future amount under compound interest?

    Atbilde

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

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

29. 29. kartīte

    Jautājums

    Should an FE search workflow depend on Ctrl+F?

    Atbilde

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

30. 30. kartīte

    Jautājums

    SI base unit of amount of substance?

    Atbilde

    The mole, symbol $mol$.

31. 31. kartīte

    Jautājums

    Joint probability expressed with a conditional probability?

    Atbilde

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

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

32. 32. kartīte

    Jautājums

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

    Atbilde

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

    The coordinate units and radius unit must match.

33. 33. kartīte

    Jautājums

    Impulse-momentum relationship?

    Atbilde

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

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

34. 34. kartīte

    Jautājums

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

    Atbilde

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

35. 35. kartīte

    Jautājums

    SI base unit of luminous intensity?

    Atbilde

    The candela, symbol $cd$.

36. 36. kartīte

    Jautājums

    Present worth of one future amount?

    Atbilde

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

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

37. 37. kartīte

    Jautājums

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

    Atbilde

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

    This form requires $a\ne0$.

38. 38. kartīte

    Jautājums

    When is total linear momentum conserved?

    Atbilde

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

39. 39. kartīte

    Jautājums

    Why avoid memorizing FE handbook page numbers?

    Atbilde

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

40. 40. kartīte

    Jautājums

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

    Atbilde

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

    Independence is not the same as mutual exclusivity.

41. 41. kartīte

    Jautājums

    SI unit of frequency in base-unit form?

    Atbilde

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

42. 42. kartīte

    Jautājums

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

    Atbilde

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

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

43. 43. kartīte

    Jautājums

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

    Atbilde

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

44. 44. kartīte

    Jautājums

    Work done by a constant force through displacement?

    Atbilde

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

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

45. 45. kartīte

    Jautājums

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

    Atbilde

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

46. 46. kartīte

    Jautājums

    SI unit of force in base-unit form?

    Atbilde

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

47. 47. kartīte

    Jautājums

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

    Atbilde

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

48. 48. kartīte

    Jautājums

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

    Atbilde

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

    This requires $P(B)>0$.

49. 49. kartīte

    Jautājums

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

    Atbilde

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

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

50. 50. kartīte

    Jautājums

    Translational kinetic energy of a particle?

    Atbilde

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

    Mass and speed must use a coherent unit system.

51. 51. kartīte

    Jautājums

    SI unit of pressure in force-area form?

    Atbilde

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

52. 52. kartīte

    Jautājums

    Equivalent annual amount for present worth $P$?

    Atbilde

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

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

53. 53. kartīte

    Jautājums

    May confidential client information be shared for personal benefit?

    Atbilde

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

54. 54. kartīte

    Jautājums

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

    Atbilde

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

55. 55. kartīte

    Jautājums

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

    Atbilde

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

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

56. 56. kartīte

    Jautājums

    Net work-energy relationship for a particle?

    Atbilde

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

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

57. 57. kartīte

    Jautājums

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

    Atbilde

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

    Use this when order matters and selection is without replacement.

58. 58. kartīte

    Jautājums

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

    Atbilde

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

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

59. 59. kartīte

    Jautājums

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

    Atbilde

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

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

60. 60. kartīte

    Jautājums

    SI unit of energy in force-distance form?

    Atbilde

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

61. 61. kartīte

    Jautājums

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

    Atbilde

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

62. 62. kartīte

    Jautājums

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

    Atbilde

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

63. 63. kartīte

    Jautājums

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

    Atbilde

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

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

64. 64. kartīte

    Jautājums

    Change in gravitational potential energy near Earth's surface?

    Atbilde

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

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

65. 65. kartīte

    Jautājums

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

    Atbilde

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

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

66. 66. kartīte

    Jautājums

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

    Atbilde

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

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

67. 67. kartīte

    Jautājums

    A handbook search for an acronym fails. Next move?

    Atbilde

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

68. 68. kartīte

    Jautājums

    SI unit of power in energy-time form?

    Atbilde

    The watt, $W=J/s$.

69. 69. kartīte

    Jautājums

    Logarithm of a product?

    Atbilde

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

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

70. 70. kartīte

    Jautājums

    Conditions for a binomial model?

    Atbilde

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

71. 71. kartīte

    Jautājums

    Using another engineer's analysis in your deliverable?

    Atbilde

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

72. 72. kartīte

    Jautājums

    SI unit of electric charge in current-time form?

    Atbilde

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

73. 73. kartīte

    Jautājums

    Average power from work over elapsed time?

    Atbilde

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

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

74. 74. kartīte

    Jautājums

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

    Atbilde

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

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

75. 75. kartīte

    Jautājums

    Logarithm of a positive quantity raised to a power?

    Atbilde

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

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

76. 76. kartīte

    Jautājums

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

    Atbilde

    The volt, $V=J/C$.

77. 77. kartīte

    Jautājums

    Instantaneous mechanical power delivered by a force?

    Atbilde

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

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

78. 78. kartīte

    Jautājums

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

    Atbilde

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

79. 79. kartīte

    Jautājums

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

    Atbilde

    $$E[X]=np$$

80. 80. kartīte

    Jautājums

    SI unit of electrical resistance in voltage-current form?

    Atbilde

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

81. 81. kartīte

    Jautājums

    Moment of a force about a point?

    Atbilde

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

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

82. 82. kartīte

    Jautājums

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

    Atbilde

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

83. 83. kartīte

    Jautājums

    Inverse relationship between the natural log and exponential?

    Atbilde

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

    The second identity requires $x>0$.

84. 84. kartīte

    Jautājums

    SI prefix giga?

    Atbilde

    $G=10^9$.

85. 85. kartīte

    Jautājums

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

    Atbilde

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

    Use consistent angular sign convention and radians for angular measures.

86. 86. kartīte

    Jautājums

    When should an engineer sign or seal technical work?

    Atbilde

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

87. 87. kartīte

    Jautājums

    Best memory target for returning to a handbook formula?

    Atbilde

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

88. 88. kartīte

    Jautājums

    SI prefix mega?

    Atbilde

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

89. 89. kartīte

    Jautājums

    Convert degrees to radians?

    Atbilde

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

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

90. 90. kartīte

    Jautājums

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

    Atbilde

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

91. 91. kartīte

    Jautājums

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

    Atbilde

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

92. 92. kartīte

    Jautājums

    Where do licensure and sealing requirements come from?

    Atbilde

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

93. 93. kartīte

    Jautājums

    Rotational kinetic energy about a fixed axis?

    Atbilde

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

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

94. 94. kartīte

    Jautājums

    SI prefix kilo?

    Atbilde

    $k=10^3$.

95. 95. kartīte

    Jautājums

    Right-triangle definition of sine?

    Atbilde

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

96. 96. kartīte

    Jautājums

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

    Atbilde

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

97. 97. kartīte

    Jautājums

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

    Atbilde

    $$\sum M=I\alpha$$

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

98. 98. kartīte

    Jautājums

    SI prefix milli?

    Atbilde

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

99. 99. kartīte

    Jautājums

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

    Atbilde

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

100. 100. kartīte

     Jautājums

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

     Atbilde

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

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

101. 101. kartīte

     Jautājums

     Right-triangle definition of cosine?

     Atbilde

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

102. 102. kartīte

     Jautājums

     Force-displacement relation for an ideal linear spring?

     Atbilde

     $$F=-kx$$

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

103. 103. kartīte

     Jautājums

     May qualifications or project responsibility be exaggerated in a proposal?

     Atbilde

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

104. 104. kartīte

     Jautājums

     SI prefix micro?

     Atbilde

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

105. 105. kartīte

     Jautājums

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

     Atbilde

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

106. 106. kartīte

     Jautājums

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

     Atbilde

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

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

107. 107. kartīte

     Jautājums

     Right-triangle definition of tangent?

     Atbilde

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

108. 108. kartīte

     Jautājums

     Average normal stress under centered axial load?

     Atbilde

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

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

109. 109. kartīte

     Jautājums

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

     Atbilde

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

110. 110. kartīte

     Jautājums

     SI prefix nano?

     Atbilde

     $n=10^{-9}$.

111. 111. kartīte

     Jautājums

     Fundamental Pythagorean trigonometric identity?

     Atbilde

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

112. 112. kartīte

     Jautājums

     Engineering normal strain?

     Atbilde

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

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

113. 113. kartīte

     Jautājums

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

     Atbilde

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

114. 114. kartīte

     Jautājums

     Technical duty to an employer or client?

     Atbilde

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

115. 115. kartīte

     Jautājums

     How does a length conversion factor apply to area?

     Atbilde

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

116. 116. kartīte

     Jautājums

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

     Atbilde

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

117. 117. kartīte

     Jautājums

     When is a Poisson count model reasonable?

     Atbilde

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

118. 118. kartīte

     Jautājums

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

     Atbilde

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

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

119. 119. kartīte

     Jautājums

     Linear elastic stress-strain relation in uniaxial loading?

     Atbilde

     $$\sigma=E\varepsilon$$

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

120. 120. kartīte

     Jautājums

     How does a length conversion factor apply to volume?

     Atbilde

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

121. 121. kartīte

     Jautājums

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

     Atbilde

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

122. 122. kartīte

     Jautājums

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

     Atbilde

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

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

123. 123. kartīte

     Jautājums

     A supervisor directs an illegal engineering action. Proper response?

     Atbilde

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

124. 124. kartīte

     Jautājums

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

     Atbilde

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

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

125. 125. kartīte

     Jautājums

     Mass density?

     Atbilde

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

     Use mass, not weight, in the numerator.

126. 126. kartīte

     Jautājums

     Inches in one foot?

     Atbilde

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

127. 127. kartīte

     Jautājums

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

     Atbilde

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

128. 128. kartīte

     Jautājums

     How should subscripts be handled in a retrieved relationship?

     Atbilde

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

129. 129. kartīte

     Jautājums

     Dot product from vector magnitudes and included angle?

     Atbilde

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

     The result is a scalar.

130. 130. kartīte

     Jautājums

     Average normal pressure on an area?

     Atbilde

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

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

131. 131. kartīte

     Jautājums

     Feet in one yard?

     Atbilde

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

132. 132. kartīte

     Jautājums

     When are two interest rates equivalent?

     Atbilde

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

133. 133. kartīte

     Jautājums

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

     Atbilde

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

134. 134. kartīte

     Jautājums

     Expected value of a discrete random variable?

     Atbilde

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

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

135. 135. kartīte

     Jautājums

     Dot-product test for perpendicular nonzero vectors?

     Atbilde

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

136. 136. kartīte

     Jautājums

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

     Atbilde

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

     Depth increases downward and the fluid is at rest.

137. 137. kartīte

     Jautājums

     Feet in one statute mile?

     Atbilde

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

138. 138. kartīte

     Jautājums

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

     Atbilde

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

     

     276 kartītes

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Mācies šo kavu bez maksas

     Atvērsies Nibomo, lai vari sākt mācīties.

139. 139. kartīte

     Jautājums

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

     Atbilde

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

140. 140. kartīte

     Jautājums

     Magnitude of a vector cross product?

     Atbilde

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

     The direction follows the right-hand rule.

141. 141. kartīte

     Jautājums

     Exact inch-to-metre relationship?

     Atbilde

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

142. 142. kartīte

     Jautājums

     Volumetric flow rate through a cross-section?

     Atbilde

     $$Q=Av_{avg}$$

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

143. 143. kartīte

     Jautājums

     Variance from the mean $\mu$?

     Atbilde

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

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

144. 144. kartīte

     Jautājums

     Future-worth acceptance rule for an independent investment?

     Atbilde

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

145. 145. kartīte

     Jautājums

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

     Atbilde

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

146. 146. kartīte

     Jautājums

     Exact foot-to-metre relationship?

     Atbilde

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

147. 147. kartīte

     Jautājums

     How should important uncertainty be communicated?

     Atbilde

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

148. 148. kartīte

     Jautājums

     When is the matrix product $AB$ defined?

     Atbilde

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

149. 149. kartīte

     Jautājums

     Steady one-inlet, one-outlet mass continuity?

     Atbilde

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

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

150. 150. kartīte

     Jautājums

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

     Atbilde

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

151. 151. kartīte

     Jautājums

     Square feet in one acre?

     Atbilde

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

152. 152. kartīte

     Jautājums

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

     Atbilde

     $$ad-bc$$

153. 153. kartīte

     Jautājums

     Bernoulli relationship along a streamline for ideal steady flow?

     Atbilde

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

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

154. 154. kartīte

     Jautājums

     May inconvenient measurements be discarded without a technical basis?

     Atbilde

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

155. 155. kartīte

     Jautājums

     Annual-worth acceptance rule for an independent investment?

     Atbilde

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

156. 156. kartīte

     Jautājums

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

     Atbilde

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

157. 157. kartīte

     Jautājums

     Cubic metres in one litre?

     Atbilde

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

158. 158. kartīte

     Jautājums

     What does a zero determinant mean for a square matrix?

     Atbilde

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

159. 159. kartīte

     Jautājums

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

     Atbilde

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

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

160. 160. kartīte

     Jautājums

     Unbiased sample variance for an independent sample from one population?

     Atbilde

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

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

161. 161. kartīte

     Jautājums

     How should mutually exclusive alternatives be compared?

     Atbilde

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

162. 162. kartīte

     Jautājums

     Cubic centimetres in one millilitre?

     Atbilde

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

163. 163. kartīte

     Jautājums

     Why keep contemporaneous engineering records?

     Atbilde

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

164. 164. kartīte

     Jautājums

     Fast check after substituting into a handbook formula?

     Atbilde

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

165. 165. kartīte

     Jautājums

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

     Atbilde

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

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

166. 166. kartīte

     Jautājums

     Sensible heat for constant specific heat and no phase change?

     Atbilde

     $$Q=mc\Delta T$$

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

167. 167. kartīte

     Jautājums

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

     Atbilde

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

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

168. 168. kartīte

     Jautājums

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

     Atbilde

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

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

169. 169. kartīte

     Jautājums

     Purpose of incremental analysis for mutually exclusive alternatives?

     Atbilde

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

170. 170. kartīte

     Jautājums

     Physical meaning of $dy/dx$?

     Atbilde

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

171. 171. kartīte

     Jautājums

     One-dimensional steady conduction through a plane wall?

     Atbilde

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

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

172. 172. kartīte

     Jautājums

     When should you algebraically rearrange a handbook relationship?

     Atbilde

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

173. 173. kartīte

     Jautājums

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

     Atbilde

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

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

174. 174. kartīte

     Jautājums

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

     Atbilde

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

175. 175. kartīte

     Jautājums

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

     Atbilde

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

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

176. 176. kartīte

     Jautājums

     Convective heat-transfer rate at a surface?

     Atbilde

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

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

177. 177. kartīte

     Jautājums

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

     Atbilde

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

178. 178. kartīte

     Jautājums

     Internal rate of return?

     Atbilde

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

179. 179. kartīte

     Jautājums

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

     Atbilde

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

180. 180. kartīte

     Jautājums

     Convert Celsius temperature to kelvin?

     Atbilde

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

     This conversion is for absolute temperature, not temperature difference.

181. 181. kartīte

     Jautājums

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

     Atbilde

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

182. 182. kartīte

     Jautājums

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

     Atbilde

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

183. 183. kartīte

     Jautājums

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

     Atbilde

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

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

184. 184. kartīte

     Jautājums

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

     Atbilde

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

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

185. 185. kartīte

     Jautājums

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

     Atbilde

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

186. 186. kartīte

     Jautājums

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

     Atbilde

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

187. 187. kartīte

     Jautājums

     Why inspect boundary or initial conditions near a formula?

     Atbilde

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

188. 188. kartīte

     Jautājums

     Convert Celsius temperature to Fahrenheit?

     Atbilde

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

189. 189. kartīte

     Jautājums

     Ethical basis for expert technical testimony?

     Atbilde

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

190. 190. kartīte

     Jautājums

     Meaning of a breakeven value?

     Atbilde

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

191. 191. kartīte

     Jautājums

     Derivative of $e^x$?

     Atbilde

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

192. 192. kartīte

     Jautājums

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

     Atbilde

     $$\Delta E=Q-W$$

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

193. 193. kartīte

     Jautājums

     Frequentist meaning of a 95% confidence procedure?

     Atbilde

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

194. 194. kartīte

     Jautājums

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

     Atbilde

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

195. 195. kartīte

     Jautājums

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

     Atbilde

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

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

196. 196. kartīte

     Jautājums

     Relationship between Celsius and kelvin temperature differences?

     Atbilde

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

197. 197. kartīte

     Jautājums

     How should credit for team engineering work be assigned?

     Atbilde

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

198. 198. kartīte

     Jautājums

     Main limitation of simple payback period?

     Atbilde

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

199. 199. kartīte

     Jautājums

     Roles of the null and alternative hypotheses?

     Atbilde

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

200. 200. kartīte

     Jautājums

     Ideal-gas equation of state?

     Atbilde

     $$pV=nRT$$

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

201. 201. kartīte

     Jautājums

     First check when reading a handbook table?

     Atbilde

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

202. 202. kartīte

     Jautājums

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

     Atbilde

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

203. 203. kartīte

     Jautājums

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

     Atbilde

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

204. 204. kartīte

     Jautājums

     Convert Fahrenheit absolute temperature to Rankine?

     Atbilde

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. 205. kartīte

     Jautājums

     Ohm's law for an ideal resistor?

     Atbilde

     $$V=IR$$

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

206. 206. kartīte

     Jautājums

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

     Atbilde

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

207. 207. kartīte

     Jautājums

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

     Atbilde

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

208. 208. kartīte

     Jautājums

     Is a radian dimensionless?

     Atbilde

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

209. 209. kartīte

     Jautājums

     Electrical power absorbed under the passive sign convention?

     Atbilde

     $$P=VI$$

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

210. 210. kartīte

     Jautājums

     Meaning of a p-value?

     Atbilde

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

211. 211. kartīte

     Jautājums

     First check when reading a handbook graph?

     Atbilde

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

212. 212. kartīte

     Jautājums

     Difference between mass and weight?

     Atbilde

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

213. 213. kartīte

     Jautājums

     Kirchhoff's current law at a node?

     Atbilde

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

214. 214. kartīte

     Jautājums

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

     Atbilde

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

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

215. 215. kartīte

     Jautājums

     Opportunity cost?

     Atbilde

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

216. 216. kartīte

     Jautājums

     Weight from mass in a gravitational field?

     Atbilde

     $$W=mg$$

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

217. 217. kartīte

     Jautājums

     Kirchhoff's voltage law around a closed loop?

     Atbilde

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

218. 218. kartīte

     Jautājums

     Decision rule using significance level $\alpha$?

     Atbilde

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

219. 219. kartīte

     Jautājums

     Can proprietary methods from a former employer be reused freely?

     Atbilde

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

220. 220. kartīte

     Jautājums

     Pound-force to newtons?

     Atbilde

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

221. 221. kartīte

     Jautājums

     When does a definite integral equal ordinary geometric area?

     Atbilde

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

222. 222. kartīte

     Jautājums

     Charge-voltage relation for an ideal capacitor?

     Atbilde

     $$q=CV$$

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

223. 223. kartīte

     Jautājums

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

     Atbilde

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

224. 224. kartīte

     Jautājums

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

     Atbilde

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

225. 225. kartīte

     Jautājums

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

     Atbilde

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

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

226. 226. kartīte

     Jautājums

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

     Atbilde

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

227. 227. kartīte

     Jautājums

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

     Atbilde

     $$\tau=RC$$

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

228. 228. kartīte

     Jautājums

     What physical quantity does pound-mass measure?

     Atbilde

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

229. 229. kartīte

     Jautājums

     Type I error?

     Atbilde

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

230. 230. kartīte

     Jautājums

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

     Atbilde

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

231. 231. kartīte

     Jautājums

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

     Atbilde

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

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

232. 232. kartīte

     Jautājums

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

     Atbilde

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

233. 233. kartīte

     Jautājums

     Recognizable form of a separable first-order differential equation?

     Atbilde

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

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

234. 234. kartīte

     Jautājums

     Using unverified software output in a safety-relevant calculation?

     Atbilde

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

235. 235. kartīte

     Jautājums

     Equivalent resistance of ideal resistors in series?

     Atbilde

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

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

236. 236. kartīte

     Jautājums

     Pressure conversion from psi to pascals?

     Atbilde

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

237. 237. kartīte

     Jautājums

     Type II error?

     Atbilde

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

238. 238. kartīte

     Jautājums

     Useful flashcard to make after a failed handbook search?

     Atbilde

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

239. 239. kartīte

     Jautājums

     Standard form of a first-order linear differential equation?

     Atbilde

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

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

240. 240. kartīte

     Jautājums

     Equivalent resistance of ideal resistors in parallel?

     Atbilde

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

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

241. 241. kartīte

     Jautājums

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

     Atbilde

     $$BV_k=B-kD$$

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

242. 242. kartīte

     Jautājums

     Standard atmosphere in pascals?

     Atbilde

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

243. 243. kartīte

     Jautājums

     Using AI-generated technical content in engineering work?

     Atbilde

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

244. 244. kartīte

     Jautājums

     Trial form for a homogeneous linear ODE with constant coefficients?

     Atbilde

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

245. 245. kartīte

     Jautājums

     Wave-speed relationship among frequency and wavelength?

     Atbilde

     $$v=f\lambda$$

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

246. 246. kartīte

     Jautājums

     Statistical power?

     Atbilde

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

247. 247. kartīte

     Jautājums

     Bar in pascals?

     Atbilde

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

248. 248. kartīte

     Jautājums

     How should handbook navigation be practiced before the FE exam?

     Atbilde

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

249. 249. kartīte

     Jautājums

     Is depreciation itself a cash outflow?

     Atbilde

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

250. 250. kartīte

     Jautājums

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

     Atbilde

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

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

251. 251. kartīte

     Jautājums

     Relationship between period and frequency?

     Atbilde

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

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

252. 252. kartīte

     Jautājums

     How should foreseeable environmental harm enter an engineering decision?

     Atbilde

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

253. 253. kartīte

     Jautājums

     Foot-pound-force in joules?

     Atbilde

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

254. 254. kartīte

     Jautājums

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

     Atbilde

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

255. 255. kartīte

     Jautājums

     When should you search instead of relying on recall?

     Atbilde

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

256. 256. kartīte

     Jautājums

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

     Atbilde

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

257. 257. kartīte

     Jautājums

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

     Atbilde

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

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

258. 258. kartīte

     Jautājums

     General material balance on a control volume?

     Atbilde

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

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

259. 259. kartīte

     Jautājums

     Approximate joules in one International Table Btu?

     Atbilde

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

260. 260. kartīte

     Jautājums

     What is the defender in a replacement analysis?

     Atbilde

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

261. 261. kartīte

     Jautājums

     Speaking publicly about a technical matter outside your expertise?

     Atbilde

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

262. 262. kartīte

     Jautājums

     Single-interval trapezoidal approximation to an integral?

     Atbilde

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

     It is exact for linear $f$.

263. 263. kartīte

     Jautājums

     Energy efficiency of a device?

     Atbilde

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

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

264. 264. kartīte

     Jautājums

     Purpose of sensitivity analysis in engineering economics?

     Atbilde

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

265. 265. kartīte

     Jautājums

     Can a strong correlation establish causation?

     Atbilde

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

266. 266. kartīte

     Jautājums

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

     Atbilde

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

267. 267. kartīte

     Jautājums

     Mechanical horsepower in watts?

     Atbilde

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

268. 268. kartīte

     Jautājums

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

     Atbilde

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

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

269. 269. kartīte

     Jautājums

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

     Atbilde

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

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

270. 270. kartīte

     Jautājums

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

     Atbilde

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

271. 271. kartīte

     Jautājums

     Kilowatt-hour in joules?

     Atbilde

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

272. 272. kartīte

     Jautājums

     Percent error relative to an accepted nonzero value?

     Atbilde

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

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

273. 273. kartīte

     Jautājums

     Does legal compliance alone settle an engineering ethics question?

     Atbilde

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

274. 274. kartīte

     Jautājums

     Does handbook fluency replace discipline-specific problem practice?

     Atbilde

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

275. 275. kartīte

     Jautājums

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

     Atbilde

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

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

276. 276. kartīte

     Jautājums

     Dimensional requirement for a physically meaningful additive equation?

     Atbilde

     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.