FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

הכרטיסים בחפיסה הזו

1. כרטיס 1

   שאלה

   SI base unit of length?

   תשובה

   The metre, symbol $m$.

2. כרטיס 2

   שאלה

   Slope between two points?

   תשובה

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

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

3. כרטיס 3

   שאלה

   Net force relationship for constant mass in an inertial frame?

   תשובה

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

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

4. כרטיס 4

   שאלה

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

   תשובה

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

5. כרטיס 5

   שאלה

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

   תשובה

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

6. כרטיס 6

   שאלה

   Probability of the complement of event $A$?

   תשובה

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

7. כרטיס 7

   שאלה

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

   תשובה

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

8. כרטיס 8

   שאלה

   SI base unit of mass?

   תשובה

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

9. כרטיס 9

   שאלה

   Linear equation from slope and intercept?

   תשובה

   $$y=mx+b$$

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

10. כרטיס 10

    שאלה

    Velocity after time $t$ under constant acceleration?

    תשובה

    $$v=v_0+at$$

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

11. כרטיס 11

    שאלה

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

    תשובה

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

12. כרטיס 12

    שאלה

    How is the FE reference handbook available during the exam?

    תשובה

    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. כרטיס 13

    שאלה

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

    תשובה

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

14. כרטיס 14

    שאלה

    SI base unit of time?

    תשובה

    The second, symbol $s$.

15. כרטיס 15

    שאלה

    Linear equation from one point and a slope?

    תשובה

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

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

16. כרטיס 16

    שאלה

    Position after time $t$ under constant acceleration?

    תשובה

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

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

17. כרטיס 17

    שאלה

    A project assignment lies outside your competence. Proper response?

    תשובה

    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. כרטיס 18

    שאלה

    SI base unit of electric current?

    תשובה

    The ampere, symbol $A$.

19. כרטיס 19

    שאלה

    Future amount under simple interest?

    תשובה

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

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

20. כרטיס 20

    שאלה

    Distance between two Cartesian points?

    תשובה

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

    The coordinate components must use the same length unit.

21. כרטיס 21

    שאלה

    Constant-acceleration relation without elapsed time?

    תשובה

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

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

22. כרטיס 22

    שאלה

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

    תשובה

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

23. כרטיס 23

    שאלה

    Conditional probability of $A$ given $B$?

    תשובה

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

    This requires $P(B)>0$.

24. כרטיס 24

    שאלה

    SI base unit of thermodynamic temperature?

    תשובה

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

25. כרטיס 25

    שאלה

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

    תשובה

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

26. כרטיס 26

    שאלה

    Midpoint of two Cartesian points?

    תשובה

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

    Average corresponding coordinates.

27. כרטיס 27

    שאלה

    Linear momentum of a particle?

    תשובה

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

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

28. כרטיס 28

    שאלה

    Future amount under compound interest?

    תשובה

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

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

29. כרטיס 29

    שאלה

    Should an FE search workflow depend on Ctrl+F?

    תשובה

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

30. כרטיס 30

    שאלה

    SI base unit of amount of substance?

    תשובה

    The mole, symbol $mol$.

31. כרטיס 31

    שאלה

    Joint probability expressed with a conditional probability?

    תשובה

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

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

32. כרטיס 32

    שאלה

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

    תשובה

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

    The coordinate units and radius unit must match.

33. כרטיס 33

    שאלה

    Impulse-momentum relationship?

    תשובה

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

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

34. כרטיס 34

    שאלה

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

    תשובה

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

35. כרטיס 35

    שאלה

    SI base unit of luminous intensity?

    תשובה

    The candela, symbol $cd$.

36. כרטיס 36

    שאלה

    Present worth of one future amount?

    תשובה

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

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

37. כרטיס 37

    שאלה

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

    תשובה

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

    This form requires $a\ne0$.

38. כרטיס 38

    שאלה

    When is total linear momentum conserved?

    תשובה

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

39. כרטיס 39

    שאלה

    Why avoid memorizing FE handbook page numbers?

    תשובה

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

40. כרטיס 40

    שאלה

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

    תשובה

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

    Independence is not the same as mutual exclusivity.

41. כרטיס 41

    שאלה

    SI unit of frequency in base-unit form?

    תשובה

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

42. כרטיס 42

    שאלה

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

    תשובה

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

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

43. כרטיס 43

    שאלה

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

    תשובה

    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. כרטיס 44

    שאלה

    Work done by a constant force through displacement?

    תשובה

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

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

45. כרטיס 45

    שאלה

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

    תשובה

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

46. כרטיס 46

    שאלה

    SI unit of force in base-unit form?

    תשובה

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

47. כרטיס 47

    שאלה

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

    תשובה

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

48. כרטיס 48

    שאלה

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

    תשובה

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

    This requires $P(B)>0$.

49. כרטיס 49

    שאלה

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

    תשובה

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

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

50. כרטיס 50

    שאלה

    Translational kinetic energy of a particle?

    תשובה

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

    Mass and speed must use a coherent unit system.

51. כרטיס 51

    שאלה

    SI unit of pressure in force-area form?

    תשובה

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

52. כרטיס 52

    שאלה

    Equivalent annual amount for present worth $P$?

    תשובה

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

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

53. כרטיס 53

    שאלה

    May confidential client information be shared for personal benefit?

    תשובה

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

54. כרטיס 54

    שאלה

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

    תשובה

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

55. כרטיס 55

    שאלה

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

    תשובה

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

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

56. כרטיס 56

    שאלה

    Net work-energy relationship for a particle?

    תשובה

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

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

57. כרטיס 57

    שאלה

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

    תשובה

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

    Use this when order matters and selection is without replacement.

58. כרטיס 58

    שאלה

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

    תשובה

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

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

59. כרטיס 59

    שאלה

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

    תשובה

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

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

60. כרטיס 60

    שאלה

    SI unit of energy in force-distance form?

    תשובה

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

61. כרטיס 61

    שאלה

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

    תשובה

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

62. כרטיס 62

    שאלה

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

    תשובה

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

63. כרטיס 63

    שאלה

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

    תשובה

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

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

64. כרטיס 64

    שאלה

    Change in gravitational potential energy near Earth's surface?

    תשובה

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

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

65. כרטיס 65

    שאלה

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

    תשובה

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

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

66. כרטיס 66

    שאלה

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

    תשובה

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

    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. כרטיס 67

    שאלה

    A handbook search for an acronym fails. Next move?

    תשובה

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

68. כרטיס 68

    שאלה

    SI unit of power in energy-time form?

    תשובה

    The watt, $W=J/s$.

69. כרטיס 69

    שאלה

    Logarithm of a product?

    תשובה

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

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

70. כרטיס 70

    שאלה

    Conditions for a binomial model?

    תשובה

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

71. כרטיס 71

    שאלה

    Using another engineer's analysis in your deliverable?

    תשובה

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

72. כרטיס 72

    שאלה

    SI unit of electric charge in current-time form?

    תשובה

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

73. כרטיס 73

    שאלה

    Average power from work over elapsed time?

    תשובה

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

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

74. כרטיס 74

    שאלה

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

    תשובה

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

    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. כרטיס 75

    שאלה

    Logarithm of a positive quantity raised to a power?

    תשובה

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

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

76. כרטיס 76

    שאלה

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

    תשובה

    The volt, $V=J/C$.

77. כרטיס 77

    שאלה

    Instantaneous mechanical power delivered by a force?

    תשובה

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

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

78. כרטיס 78

    שאלה

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

    תשובה

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

79. כרטיס 79

    שאלה

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

    תשובה

    $$E[X]=np$$

80. כרטיס 80

    שאלה

    SI unit of electrical resistance in voltage-current form?

    תשובה

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

81. כרטיס 81

    שאלה

    Moment of a force about a point?

    תשובה

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

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

82. כרטיס 82

    שאלה

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

    תשובה

    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. כרטיס 83

    שאלה

    Inverse relationship between the natural log and exponential?

    תשובה

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

    The second identity requires $x>0$.

84. כרטיס 84

    שאלה

    SI prefix giga?

    תשובה

    $G=10^9$.

85. כרטיס 85

    שאלה

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

    תשובה

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

    Use consistent angular sign convention and radians for angular measures.

86. כרטיס 86

    שאלה

    When should an engineer sign or seal technical work?

    תשובה

    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. כרטיס 87

    שאלה

    Best memory target for returning to a handbook formula?

    תשובה

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

88. כרטיס 88

    שאלה

    SI prefix mega?

    תשובה

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

89. כרטיס 89

    שאלה

    Convert degrees to radians?

    תשובה

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

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

90. כרטיס 90

    שאלה

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

    תשובה

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

91. כרטיס 91

    שאלה

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

    תשובה

    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. כרטיס 92

    שאלה

    Where do licensure and sealing requirements come from?

    תשובה

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

93. כרטיס 93

    שאלה

    Rotational kinetic energy about a fixed axis?

    תשובה

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

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

94. כרטיס 94

    שאלה

    SI prefix kilo?

    תשובה

    $k=10^3$.

95. כרטיס 95

    שאלה

    Right-triangle definition of sine?

    תשובה

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

96. כרטיס 96

    שאלה

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

    תשובה

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

97. כרטיס 97

    שאלה

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

    תשובה

    $$\sum M=I\alpha$$

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

98. כרטיס 98

    שאלה

    SI prefix milli?

    תשובה

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

99. כרטיס 99

    שאלה

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

    תשובה

    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. כרטיס 100

     שאלה

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

     תשובה

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

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

101. כרטיס 101

     שאלה

     Right-triangle definition of cosine?

     תשובה

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

102. כרטיס 102

     שאלה

     Force-displacement relation for an ideal linear spring?

     תשובה

     $$F=-kx$$

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

103. כרטיס 103

     שאלה

     May qualifications or project responsibility be exaggerated in a proposal?

     תשובה

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

104. כרטיס 104

     שאלה

     SI prefix micro?

     תשובה

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

105. כרטיס 105

     שאלה

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

     תשובה

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

106. כרטיס 106

     שאלה

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

     תשובה

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

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

107. כרטיס 107

     שאלה

     Right-triangle definition of tangent?

     תשובה

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

108. כרטיס 108

     שאלה

     Average normal stress under centered axial load?

     תשובה

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

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

109. כרטיס 109

     שאלה

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

     תשובה

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

110. כרטיס 110

     שאלה

     SI prefix nano?

     תשובה

     $n=10^{-9}$.

111. כרטיס 111

     שאלה

     Fundamental Pythagorean trigonometric identity?

     תשובה

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

112. כרטיס 112

     שאלה

     Engineering normal strain?

     תשובה

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

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

113. כרטיס 113

     שאלה

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

     תשובה

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

114. כרטיס 114

     שאלה

     Technical duty to an employer or client?

     תשובה

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

115. כרטיס 115

     שאלה

     How does a length conversion factor apply to area?

     תשובה

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

116. כרטיס 116

     שאלה

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

     תשובה

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

117. כרטיס 117

     שאלה

     When is a Poisson count model reasonable?

     תשובה

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

118. כרטיס 118

     שאלה

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

     תשובה

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

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

119. כרטיס 119

     שאלה

     Linear elastic stress-strain relation in uniaxial loading?

     תשובה

     $$\sigma=E\varepsilon$$

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

120. כרטיס 120

     שאלה

     How does a length conversion factor apply to volume?

     תשובה

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

121. כרטיס 121

     שאלה

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

     תשובה

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

122. כרטיס 122

     שאלה

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

     תשובה

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

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

123. כרטיס 123

     שאלה

     A supervisor directs an illegal engineering action. Proper response?

     תשובה

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

124. כרטיס 124

     שאלה

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

     תשובה

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

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

125. כרטיס 125

     שאלה

     Mass density?

     תשובה

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

     Use mass, not weight, in the numerator.

126. כרטיס 126

     שאלה

     Inches in one foot?

     תשובה

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

127. כרטיס 127

     שאלה

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

     תשובה

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

128. כרטיס 128

     שאלה

     How should subscripts be handled in a retrieved relationship?

     תשובה

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

129. כרטיס 129

     שאלה

     Dot product from vector magnitudes and included angle?

     תשובה

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

     The result is a scalar.

130. כרטיס 130

     שאלה

     Average normal pressure on an area?

     תשובה

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

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

131. כרטיס 131

     שאלה

     Feet in one yard?

     תשובה

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

132. כרטיס 132

     שאלה

     When are two interest rates equivalent?

     תשובה

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

133. כרטיס 133

     שאלה

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

     תשובה

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

134. כרטיס 134

     שאלה

     Expected value of a discrete random variable?

     תשובה

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

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

135. כרטיס 135

     שאלה

     Dot-product test for perpendicular nonzero vectors?

     תשובה

     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. כרטיס 136

     שאלה

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

     תשובה

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

     Depth increases downward and the fluid is at rest.

137. כרטיס 137

     שאלה

     Feet in one statute mile?

     תשובה

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

138. כרטיס 138

     שאלה

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

     תשובה

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

     

     276 כרטיסים

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     ללמוד את החפיסה הזו בחינם

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139. כרטיס 139

     שאלה

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

     תשובה

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

140. כרטיס 140

     שאלה

     Magnitude of a vector cross product?

     תשובה

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

     The direction follows the right-hand rule.

141. כרטיס 141

     שאלה

     Exact inch-to-metre relationship?

     תשובה

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

142. כרטיס 142

     שאלה

     Volumetric flow rate through a cross-section?

     תשובה

     $$Q=Av_{avg}$$

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

143. כרטיס 143

     שאלה

     Variance from the mean $\mu$?

     תשובה

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

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

144. כרטיס 144

     שאלה

     Future-worth acceptance rule for an independent investment?

     תשובה

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

145. כרטיס 145

     שאלה

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

     תשובה

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

146. כרטיס 146

     שאלה

     Exact foot-to-metre relationship?

     תשובה

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

147. כרטיס 147

     שאלה

     How should important uncertainty be communicated?

     תשובה

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

148. כרטיס 148

     שאלה

     When is the matrix product $AB$ defined?

     תשובה

     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. כרטיס 149

     שאלה

     Steady one-inlet, one-outlet mass continuity?

     תשובה

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. כרטיס 150

     שאלה

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

     תשובה

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

151. כרטיס 151

     שאלה

     Square feet in one acre?

     תשובה

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

152. כרטיס 152

     שאלה

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

     תשובה

     $$ad-bc$$

153. כרטיס 153

     שאלה

     Bernoulli relationship along a streamline for ideal steady flow?

     תשובה

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

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

154. כרטיס 154

     שאלה

     May inconvenient measurements be discarded without a technical basis?

     תשובה

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

155. כרטיס 155

     שאלה

     Annual-worth acceptance rule for an independent investment?

     תשובה

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

156. כרטיס 156

     שאלה

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

     תשובה

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

157. כרטיס 157

     שאלה

     Cubic metres in one litre?

     תשובה

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

158. כרטיס 158

     שאלה

     What does a zero determinant mean for a square matrix?

     תשובה

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

159. כרטיס 159

     שאלה

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

     תשובה

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

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

160. כרטיס 160

     שאלה

     Unbiased sample variance for an independent sample from one population?

     תשובה

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

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

161. כרטיס 161

     שאלה

     How should mutually exclusive alternatives be compared?

     תשובה

     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. כרטיס 162

     שאלה

     Cubic centimetres in one millilitre?

     תשובה

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

163. כרטיס 163

     שאלה

     Why keep contemporaneous engineering records?

     תשובה

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

164. כרטיס 164

     שאלה

     Fast check after substituting into a handbook formula?

     תשובה

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

165. כרטיס 165

     שאלה

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

     תשובה

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

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

166. כרטיס 166

     שאלה

     Sensible heat for constant specific heat and no phase change?

     תשובה

     $$Q=mc\Delta T$$

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

167. כרטיס 167

     שאלה

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

     תשובה

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

     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. כרטיס 168

     שאלה

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

     תשובה

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

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

169. כרטיס 169

     שאלה

     Purpose of incremental analysis for mutually exclusive alternatives?

     תשובה

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

170. כרטיס 170

     שאלה

     Physical meaning of $dy/dx$?

     תשובה

     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. כרטיס 171

     שאלה

     One-dimensional steady conduction through a plane wall?

     תשובה

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

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

172. כרטיס 172

     שאלה

     When should you algebraically rearrange a handbook relationship?

     תשובה

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

173. כרטיס 173

     שאלה

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

     תשובה

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

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

174. כרטיס 174

     שאלה

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

     תשובה

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

175. כרטיס 175

     שאלה

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

     תשובה

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

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

176. כרטיס 176

     שאלה

     Convective heat-transfer rate at a surface?

     תשובה

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

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

177. כרטיס 177

     שאלה

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

     תשובה

     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. כרטיס 178

     שאלה

     Internal rate of return?

     תשובה

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

179. כרטיס 179

     שאלה

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

     תשובה

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

180. כרטיס 180

     שאלה

     Convert Celsius temperature to kelvin?

     תשובה

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

     This conversion is for absolute temperature, not temperature difference.

181. כרטיס 181

     שאלה

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

     תשובה

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

182. כרטיס 182

     שאלה

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

     תשובה

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

183. כרטיס 183

     שאלה

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

     תשובה

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

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

184. כרטיס 184

     שאלה

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

     תשובה

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

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

185. כרטיס 185

     שאלה

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

     תשובה

     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. כרטיס 186

     שאלה

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

     תשובה

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

187. כרטיס 187

     שאלה

     Why inspect boundary or initial conditions near a formula?

     תשובה

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

188. כרטיס 188

     שאלה

     Convert Celsius temperature to Fahrenheit?

     תשובה

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

189. כרטיס 189

     שאלה

     Ethical basis for expert technical testimony?

     תשובה

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

190. כרטיס 190

     שאלה

     Meaning of a breakeven value?

     תשובה

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

191. כרטיס 191

     שאלה

     Derivative of $e^x$?

     תשובה

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

192. כרטיס 192

     שאלה

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

     תשובה

     $$\Delta E=Q-W$$

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

193. כרטיס 193

     שאלה

     Frequentist meaning of a 95% confidence procedure?

     תשובה

     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. כרטיס 194

     שאלה

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

     תשובה

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

195. כרטיס 195

     שאלה

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

     תשובה

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

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

196. כרטיס 196

     שאלה

     Relationship between Celsius and kelvin temperature differences?

     תשובה

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

197. כרטיס 197

     שאלה

     How should credit for team engineering work be assigned?

     תשובה

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

198. כרטיס 198

     שאלה

     Main limitation of simple payback period?

     תשובה

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

199. כרטיס 199

     שאלה

     Roles of the null and alternative hypotheses?

     תשובה

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

200. כרטיס 200

     שאלה

     Ideal-gas equation of state?

     תשובה

     $$pV=nRT$$

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

201. כרטיס 201

     שאלה

     First check when reading a handbook table?

     תשובה

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

202. כרטיס 202

     שאלה

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

     תשובה

     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. כרטיס 203

     שאלה

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

     תשובה

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

204. כרטיס 204

     שאלה

     Convert Fahrenheit absolute temperature to Rankine?

     תשובה

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. כרטיס 205

     שאלה

     Ohm's law for an ideal resistor?

     תשובה

     $$V=IR$$

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

206. כרטיס 206

     שאלה

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

     תשובה

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

207. כרטיס 207

     שאלה

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

     תשובה

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

208. כרטיס 208

     שאלה

     Is a radian dimensionless?

     תשובה

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

209. כרטיס 209

     שאלה

     Electrical power absorbed under the passive sign convention?

     תשובה

     $$P=VI$$

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

210. כרטיס 210

     שאלה

     Meaning of a p-value?

     תשובה

     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. כרטיס 211

     שאלה

     First check when reading a handbook graph?

     תשובה

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

212. כרטיס 212

     שאלה

     Difference between mass and weight?

     תשובה

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

213. כרטיס 213

     שאלה

     Kirchhoff's current law at a node?

     תשובה

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

214. כרטיס 214

     שאלה

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

     תשובה

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

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

215. כרטיס 215

     שאלה

     Opportunity cost?

     תשובה

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

216. כרטיס 216

     שאלה

     Weight from mass in a gravitational field?

     תשובה

     $$W=mg$$

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

217. כרטיס 217

     שאלה

     Kirchhoff's voltage law around a closed loop?

     תשובה

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

218. כרטיס 218

     שאלה

     Decision rule using significance level $\alpha$?

     תשובה

     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. כרטיס 219

     שאלה

     Can proprietary methods from a former employer be reused freely?

     תשובה

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

220. כרטיס 220

     שאלה

     Pound-force to newtons?

     תשובה

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

221. כרטיס 221

     שאלה

     When does a definite integral equal ordinary geometric area?

     תשובה

     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. כרטיס 222

     שאלה

     Charge-voltage relation for an ideal capacitor?

     תשובה

     $$q=CV$$

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

223. כרטיס 223

     שאלה

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

     תשובה

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

224. כרטיס 224

     שאלה

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

     תשובה

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

225. כרטיס 225

     שאלה

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

     תשובה

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

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

226. כרטיס 226

     שאלה

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

     תשובה

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

227. כרטיס 227

     שאלה

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

     תשובה

     $$\tau=RC$$

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

228. כרטיס 228

     שאלה

     What physical quantity does pound-mass measure?

     תשובה

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

229. כרטיס 229

     שאלה

     Type I error?

     תשובה

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

230. כרטיס 230

     שאלה

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

     תשובה

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

231. כרטיס 231

     שאלה

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

     תשובה

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

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

232. כרטיס 232

     שאלה

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

     תשובה

     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. כרטיס 233

     שאלה

     Recognizable form of a separable first-order differential equation?

     תשובה

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

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

234. כרטיס 234

     שאלה

     Using unverified software output in a safety-relevant calculation?

     תשובה

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

235. כרטיס 235

     שאלה

     Equivalent resistance of ideal resistors in series?

     תשובה

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

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

236. כרטיס 236

     שאלה

     Pressure conversion from psi to pascals?

     תשובה

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

237. כרטיס 237

     שאלה

     Type II error?

     תשובה

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

238. כרטיס 238

     שאלה

     Useful flashcard to make after a failed handbook search?

     תשובה

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

239. כרטיס 239

     שאלה

     Standard form of a first-order linear differential equation?

     תשובה

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

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

240. כרטיס 240

     שאלה

     Equivalent resistance of ideal resistors in parallel?

     תשובה

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

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

241. כרטיס 241

     שאלה

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

     תשובה

     $$BV_k=B-kD$$

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

242. כרטיס 242

     שאלה

     Standard atmosphere in pascals?

     תשובה

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

243. כרטיס 243

     שאלה

     Using AI-generated technical content in engineering work?

     תשובה

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

244. כרטיס 244

     שאלה

     Trial form for a homogeneous linear ODE with constant coefficients?

     תשובה

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

245. כרטיס 245

     שאלה

     Wave-speed relationship among frequency and wavelength?

     תשובה

     $$v=f\lambda$$

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

246. כרטיס 246

     שאלה

     Statistical power?

     תשובה

     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. כרטיס 247

     שאלה

     Bar in pascals?

     תשובה

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

248. כרטיס 248

     שאלה

     How should handbook navigation be practiced before the FE exam?

     תשובה

     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. כרטיס 249

     שאלה

     Is depreciation itself a cash outflow?

     תשובה

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

250. כרטיס 250

     שאלה

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

     תשובה

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

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

251. כרטיס 251

     שאלה

     Relationship between period and frequency?

     תשובה

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

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

252. כרטיס 252

     שאלה

     How should foreseeable environmental harm enter an engineering decision?

     תשובה

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

253. כרטיס 253

     שאלה

     Foot-pound-force in joules?

     תשובה

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

254. כרטיס 254

     שאלה

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

     תשובה

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

255. כרטיס 255

     שאלה

     When should you search instead of relying on recall?

     תשובה

     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. כרטיס 256

     שאלה

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

     תשובה

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

257. כרטיס 257

     שאלה

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

     תשובה

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

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

258. כרטיס 258

     שאלה

     General material balance on a control volume?

     תשובה

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

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

259. כרטיס 259

     שאלה

     Approximate joules in one International Table Btu?

     תשובה

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

260. כרטיס 260

     שאלה

     What is the defender in a replacement analysis?

     תשובה

     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. כרטיס 261

     שאלה

     Speaking publicly about a technical matter outside your expertise?

     תשובה

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

262. כרטיס 262

     שאלה

     Single-interval trapezoidal approximation to an integral?

     תשובה

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

     It is exact for linear $f$.

263. כרטיס 263

     שאלה

     Energy efficiency of a device?

     תשובה

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

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

264. כרטיס 264

     שאלה

     Purpose of sensitivity analysis in engineering economics?

     תשובה

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

265. כרטיס 265

     שאלה

     Can a strong correlation establish causation?

     תשובה

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

266. כרטיס 266

     שאלה

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

     תשובה

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

267. כרטיס 267

     שאלה

     Mechanical horsepower in watts?

     תשובה

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

268. כרטיס 268

     שאלה

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

     תשובה

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

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

269. כרטיס 269

     שאלה

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

     תשובה

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

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

270. כרטיס 270

     שאלה

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

     תשובה

     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. כרטיס 271

     שאלה

     Kilowatt-hour in joules?

     תשובה

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

272. כרטיס 272

     שאלה

     Percent error relative to an accepted nonzero value?

     תשובה

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

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

273. כרטיס 273

     שאלה

     Does legal compliance alone settle an engineering ethics question?

     תשובה

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

274. כרטיס 274

     שאלה

     Does handbook fluency replace discipline-specific problem practice?

     תשובה

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

275. כרטיס 275

     שאלה

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

     תשובה

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

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

276. כרטיס 276

     שאלה

     Dimensional requirement for a physically meaningful additive equation?

     תשובה

     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.