FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

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1. Kad 1

   Soalan

   SI base unit of length?

   Jawapan

   The metre, symbol $m$.

2. Kad 2

   Soalan

   Slope between two points?

   Jawapan

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

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

3. Kad 3

   Soalan

   Net force relationship for constant mass in an inertial frame?

   Jawapan

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

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

4. Kad 4

   Soalan

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

   Jawapan

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

5. Kad 5

   Soalan

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

   Jawapan

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

6. Kad 6

   Soalan

   Probability of the complement of event $A$?

   Jawapan

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

7. Kad 7

   Soalan

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

   Jawapan

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

8. Kad 8

   Soalan

   SI base unit of mass?

   Jawapan

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

9. Kad 9

   Soalan

   Linear equation from slope and intercept?

   Jawapan

   $$y=mx+b$$

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

10. Kad 10

    Soalan

    Velocity after time $t$ under constant acceleration?

    Jawapan

    $$v=v_0+at$$

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

11. Kad 11

    Soalan

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

    Jawapan

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

12. Kad 12

    Soalan

    How is the FE reference handbook available during the exam?

    Jawapan

    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. Kad 13

    Soalan

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

    Jawapan

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

14. Kad 14

    Soalan

    SI base unit of time?

    Jawapan

    The second, symbol $s$.

15. Kad 15

    Soalan

    Linear equation from one point and a slope?

    Jawapan

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

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

16. Kad 16

    Soalan

    Position after time $t$ under constant acceleration?

    Jawapan

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

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

17. Kad 17

    Soalan

    A project assignment lies outside your competence. Proper response?

    Jawapan

    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. Kad 18

    Soalan

    SI base unit of electric current?

    Jawapan

    The ampere, symbol $A$.

19. Kad 19

    Soalan

    Future amount under simple interest?

    Jawapan

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

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

20. Kad 20

    Soalan

    Distance between two Cartesian points?

    Jawapan

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

    The coordinate components must use the same length unit.

21. Kad 21

    Soalan

    Constant-acceleration relation without elapsed time?

    Jawapan

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

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

22. Kad 22

    Soalan

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

    Jawapan

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

23. Kad 23

    Soalan

    Conditional probability of $A$ given $B$?

    Jawapan

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

    This requires $P(B)>0$.

24. Kad 24

    Soalan

    SI base unit of thermodynamic temperature?

    Jawapan

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

25. Kad 25

    Soalan

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

    Jawapan

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

26. Kad 26

    Soalan

    Midpoint of two Cartesian points?

    Jawapan

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

    Average corresponding coordinates.

27. Kad 27

    Soalan

    Linear momentum of a particle?

    Jawapan

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

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

28. Kad 28

    Soalan

    Future amount under compound interest?

    Jawapan

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

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

29. Kad 29

    Soalan

    Should an FE search workflow depend on Ctrl+F?

    Jawapan

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

30. Kad 30

    Soalan

    SI base unit of amount of substance?

    Jawapan

    The mole, symbol $mol$.

31. Kad 31

    Soalan

    Joint probability expressed with a conditional probability?

    Jawapan

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

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

32. Kad 32

    Soalan

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

    Jawapan

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

    The coordinate units and radius unit must match.

33. Kad 33

    Soalan

    Impulse-momentum relationship?

    Jawapan

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

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

34. Kad 34

    Soalan

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

    Jawapan

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

35. Kad 35

    Soalan

    SI base unit of luminous intensity?

    Jawapan

    The candela, symbol $cd$.

36. Kad 36

    Soalan

    Present worth of one future amount?

    Jawapan

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

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

37. Kad 37

    Soalan

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

    Jawapan

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

    This form requires $a\ne0$.

38. Kad 38

    Soalan

    When is total linear momentum conserved?

    Jawapan

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

39. Kad 39

    Soalan

    Why avoid memorizing FE handbook page numbers?

    Jawapan

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

40. Kad 40

    Soalan

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

    Jawapan

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

    Independence is not the same as mutual exclusivity.

41. Kad 41

    Soalan

    SI unit of frequency in base-unit form?

    Jawapan

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

42. Kad 42

    Soalan

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

    Jawapan

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

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

43. Kad 43

    Soalan

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

    Jawapan

    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. Kad 44

    Soalan

    Work done by a constant force through displacement?

    Jawapan

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

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

45. Kad 45

    Soalan

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

    Jawapan

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

46. Kad 46

    Soalan

    SI unit of force in base-unit form?

    Jawapan

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

47. Kad 47

    Soalan

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

    Jawapan

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

48. Kad 48

    Soalan

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

    Jawapan

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

    This requires $P(B)>0$.

49. Kad 49

    Soalan

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

    Jawapan

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

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

50. Kad 50

    Soalan

    Translational kinetic energy of a particle?

    Jawapan

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

    Mass and speed must use a coherent unit system.

51. Kad 51

    Soalan

    SI unit of pressure in force-area form?

    Jawapan

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

52. Kad 52

    Soalan

    Equivalent annual amount for present worth $P$?

    Jawapan

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

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

53. Kad 53

    Soalan

    May confidential client information be shared for personal benefit?

    Jawapan

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

54. Kad 54

    Soalan

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

    Jawapan

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

55. Kad 55

    Soalan

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

    Jawapan

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

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

56. Kad 56

    Soalan

    Net work-energy relationship for a particle?

    Jawapan

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

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

57. Kad 57

    Soalan

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

    Jawapan

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

    Use this when order matters and selection is without replacement.

58. Kad 58

    Soalan

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

    Jawapan

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

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

59. Kad 59

    Soalan

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

    Jawapan

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

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

60. Kad 60

    Soalan

    SI unit of energy in force-distance form?

    Jawapan

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

61. Kad 61

    Soalan

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

    Jawapan

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

62. Kad 62

    Soalan

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

    Jawapan

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

63. Kad 63

    Soalan

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

    Jawapan

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

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

64. Kad 64

    Soalan

    Change in gravitational potential energy near Earth's surface?

    Jawapan

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

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

65. Kad 65

    Soalan

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

    Jawapan

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

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

66. Kad 66

    Soalan

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

    Jawapan

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

    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. Kad 67

    Soalan

    A handbook search for an acronym fails. Next move?

    Jawapan

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

68. Kad 68

    Soalan

    SI unit of power in energy-time form?

    Jawapan

    The watt, $W=J/s$.

69. Kad 69

    Soalan

    Logarithm of a product?

    Jawapan

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

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

70. Kad 70

    Soalan

    Conditions for a binomial model?

    Jawapan

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

71. Kad 71

    Soalan

    Using another engineer's analysis in your deliverable?

    Jawapan

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

72. Kad 72

    Soalan

    SI unit of electric charge in current-time form?

    Jawapan

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

73. Kad 73

    Soalan

    Average power from work over elapsed time?

    Jawapan

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

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

74. Kad 74

    Soalan

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

    Jawapan

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

    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. Kad 75

    Soalan

    Logarithm of a positive quantity raised to a power?

    Jawapan

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

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

76. Kad 76

    Soalan

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

    Jawapan

    The volt, $V=J/C$.

77. Kad 77

    Soalan

    Instantaneous mechanical power delivered by a force?

    Jawapan

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

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

78. Kad 78

    Soalan

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

    Jawapan

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

79. Kad 79

    Soalan

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

    Jawapan

    $$E[X]=np$$

80. Kad 80

    Soalan

    SI unit of electrical resistance in voltage-current form?

    Jawapan

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

81. Kad 81

    Soalan

    Moment of a force about a point?

    Jawapan

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

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

82. Kad 82

    Soalan

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

    Jawapan

    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. Kad 83

    Soalan

    Inverse relationship between the natural log and exponential?

    Jawapan

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

    The second identity requires $x>0$.

84. Kad 84

    Soalan

    SI prefix giga?

    Jawapan

    $G=10^9$.

85. Kad 85

    Soalan

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

    Jawapan

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

    Use consistent angular sign convention and radians for angular measures.

86. Kad 86

    Soalan

    When should an engineer sign or seal technical work?

    Jawapan

    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. Kad 87

    Soalan

    Best memory target for returning to a handbook formula?

    Jawapan

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

88. Kad 88

    Soalan

    SI prefix mega?

    Jawapan

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

89. Kad 89

    Soalan

    Convert degrees to radians?

    Jawapan

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

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

90. Kad 90

    Soalan

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

    Jawapan

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

91. Kad 91

    Soalan

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

    Jawapan

    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. Kad 92

    Soalan

    Where do licensure and sealing requirements come from?

    Jawapan

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

93. Kad 93

    Soalan

    Rotational kinetic energy about a fixed axis?

    Jawapan

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

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

94. Kad 94

    Soalan

    SI prefix kilo?

    Jawapan

    $k=10^3$.

95. Kad 95

    Soalan

    Right-triangle definition of sine?

    Jawapan

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

96. Kad 96

    Soalan

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

    Jawapan

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

97. Kad 97

    Soalan

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

    Jawapan

    $$\sum M=I\alpha$$

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

98. Kad 98

    Soalan

    SI prefix milli?

    Jawapan

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

99. Kad 99

    Soalan

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

    Jawapan

    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. Kad 100

     Soalan

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

     Jawapan

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

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

101. Kad 101

     Soalan

     Right-triangle definition of cosine?

     Jawapan

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

102. Kad 102

     Soalan

     Force-displacement relation for an ideal linear spring?

     Jawapan

     $$F=-kx$$

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

103. Kad 103

     Soalan

     May qualifications or project responsibility be exaggerated in a proposal?

     Jawapan

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

104. Kad 104

     Soalan

     SI prefix micro?

     Jawapan

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

105. Kad 105

     Soalan

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

     Jawapan

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

106. Kad 106

     Soalan

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

     Jawapan

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

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

107. Kad 107

     Soalan

     Right-triangle definition of tangent?

     Jawapan

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

108. Kad 108

     Soalan

     Average normal stress under centered axial load?

     Jawapan

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

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

109. Kad 109

     Soalan

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

     Jawapan

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

110. Kad 110

     Soalan

     SI prefix nano?

     Jawapan

     $n=10^{-9}$.

111. Kad 111

     Soalan

     Fundamental Pythagorean trigonometric identity?

     Jawapan

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

112. Kad 112

     Soalan

     Engineering normal strain?

     Jawapan

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

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

113. Kad 113

     Soalan

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

     Jawapan

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

114. Kad 114

     Soalan

     Technical duty to an employer or client?

     Jawapan

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

115. Kad 115

     Soalan

     How does a length conversion factor apply to area?

     Jawapan

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

116. Kad 116

     Soalan

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

     Jawapan

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

117. Kad 117

     Soalan

     When is a Poisson count model reasonable?

     Jawapan

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

118. Kad 118

     Soalan

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

     Jawapan

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

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

119. Kad 119

     Soalan

     Linear elastic stress-strain relation in uniaxial loading?

     Jawapan

     $$\sigma=E\varepsilon$$

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

120. Kad 120

     Soalan

     How does a length conversion factor apply to volume?

     Jawapan

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

121. Kad 121

     Soalan

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

     Jawapan

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

122. Kad 122

     Soalan

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

     Jawapan

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

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

123. Kad 123

     Soalan

     A supervisor directs an illegal engineering action. Proper response?

     Jawapan

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

124. Kad 124

     Soalan

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

     Jawapan

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

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

125. Kad 125

     Soalan

     Mass density?

     Jawapan

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

     Use mass, not weight, in the numerator.

126. Kad 126

     Soalan

     Inches in one foot?

     Jawapan

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

127. Kad 127

     Soalan

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

     Jawapan

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

128. Kad 128

     Soalan

     How should subscripts be handled in a retrieved relationship?

     Jawapan

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

129. Kad 129

     Soalan

     Dot product from vector magnitudes and included angle?

     Jawapan

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

     The result is a scalar.

130. Kad 130

     Soalan

     Average normal pressure on an area?

     Jawapan

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

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

131. Kad 131

     Soalan

     Feet in one yard?

     Jawapan

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

132. Kad 132

     Soalan

     When are two interest rates equivalent?

     Jawapan

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

133. Kad 133

     Soalan

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

     Jawapan

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

134. Kad 134

     Soalan

     Expected value of a discrete random variable?

     Jawapan

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

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

135. Kad 135

     Soalan

     Dot-product test for perpendicular nonzero vectors?

     Jawapan

     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. Kad 136

     Soalan

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

     Jawapan

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

     Depth increases downward and the fluid is at rest.

137. Kad 137

     Soalan

     Feet in one statute mile?

     Jawapan

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

138. Kad 138

     Soalan

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

     Jawapan

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

     

     276 kad

     FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

     Ulang kaji dek ini secara percuma

     Nibomo akan dibuka supaya anda boleh mula mengulang kaji.

139. Kad 139

     Soalan

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

     Jawapan

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

140. Kad 140

     Soalan

     Magnitude of a vector cross product?

     Jawapan

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

     The direction follows the right-hand rule.

141. Kad 141

     Soalan

     Exact inch-to-metre relationship?

     Jawapan

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

142. Kad 142

     Soalan

     Volumetric flow rate through a cross-section?

     Jawapan

     $$Q=Av_{avg}$$

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

143. Kad 143

     Soalan

     Variance from the mean $\mu$?

     Jawapan

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

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

144. Kad 144

     Soalan

     Future-worth acceptance rule for an independent investment?

     Jawapan

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

145. Kad 145

     Soalan

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

     Jawapan

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

146. Kad 146

     Soalan

     Exact foot-to-metre relationship?

     Jawapan

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

147. Kad 147

     Soalan

     How should important uncertainty be communicated?

     Jawapan

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

148. Kad 148

     Soalan

     When is the matrix product $AB$ defined?

     Jawapan

     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. Kad 149

     Soalan

     Steady one-inlet, one-outlet mass continuity?

     Jawapan

     $$\rho_1A_1v_1=\rho_2A_2v_2$$

     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. Kad 150

     Soalan

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

     Jawapan

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

151. Kad 151

     Soalan

     Square feet in one acre?

     Jawapan

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

152. Kad 152

     Soalan

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

     Jawapan

     $$ad-bc$$

153. Kad 153

     Soalan

     Bernoulli relationship along a streamline for ideal steady flow?

     Jawapan

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

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

154. Kad 154

     Soalan

     May inconvenient measurements be discarded without a technical basis?

     Jawapan

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

155. Kad 155

     Soalan

     Annual-worth acceptance rule for an independent investment?

     Jawapan

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

156. Kad 156

     Soalan

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

     Jawapan

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

157. Kad 157

     Soalan

     Cubic metres in one litre?

     Jawapan

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

158. Kad 158

     Soalan

     What does a zero determinant mean for a square matrix?

     Jawapan

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

159. Kad 159

     Soalan

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

     Jawapan

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

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

160. Kad 160

     Soalan

     Unbiased sample variance for an independent sample from one population?

     Jawapan

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

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

161. Kad 161

     Soalan

     How should mutually exclusive alternatives be compared?

     Jawapan

     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. Kad 162

     Soalan

     Cubic centimetres in one millilitre?

     Jawapan

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

163. Kad 163

     Soalan

     Why keep contemporaneous engineering records?

     Jawapan

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

164. Kad 164

     Soalan

     Fast check after substituting into a handbook formula?

     Jawapan

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

165. Kad 165

     Soalan

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

     Jawapan

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

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

166. Kad 166

     Soalan

     Sensible heat for constant specific heat and no phase change?

     Jawapan

     $$Q=mc\Delta T$$

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

167. Kad 167

     Soalan

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

     Jawapan

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

     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. Kad 168

     Soalan

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

     Jawapan

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

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

169. Kad 169

     Soalan

     Purpose of incremental analysis for mutually exclusive alternatives?

     Jawapan

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

170. Kad 170

     Soalan

     Physical meaning of $dy/dx$?

     Jawapan

     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. Kad 171

     Soalan

     One-dimensional steady conduction through a plane wall?

     Jawapan

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

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

172. Kad 172

     Soalan

     When should you algebraically rearrange a handbook relationship?

     Jawapan

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

173. Kad 173

     Soalan

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

     Jawapan

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

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

174. Kad 174

     Soalan

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

     Jawapan

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

175. Kad 175

     Soalan

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

     Jawapan

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

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

176. Kad 176

     Soalan

     Convective heat-transfer rate at a surface?

     Jawapan

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

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

177. Kad 177

     Soalan

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

     Jawapan

     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. Kad 178

     Soalan

     Internal rate of return?

     Jawapan

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

179. Kad 179

     Soalan

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

     Jawapan

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

180. Kad 180

     Soalan

     Convert Celsius temperature to kelvin?

     Jawapan

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

     This conversion is for absolute temperature, not temperature difference.

181. Kad 181

     Soalan

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

     Jawapan

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

182. Kad 182

     Soalan

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

     Jawapan

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

183. Kad 183

     Soalan

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

     Jawapan

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

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

184. Kad 184

     Soalan

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

     Jawapan

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

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

185. Kad 185

     Soalan

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

     Jawapan

     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. Kad 186

     Soalan

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

     Jawapan

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

187. Kad 187

     Soalan

     Why inspect boundary or initial conditions near a formula?

     Jawapan

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

188. Kad 188

     Soalan

     Convert Celsius temperature to Fahrenheit?

     Jawapan

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

189. Kad 189

     Soalan

     Ethical basis for expert technical testimony?

     Jawapan

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

190. Kad 190

     Soalan

     Meaning of a breakeven value?

     Jawapan

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

191. Kad 191

     Soalan

     Derivative of $e^x$?

     Jawapan

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

192. Kad 192

     Soalan

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

     Jawapan

     $$\Delta E=Q-W$$

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

193. Kad 193

     Soalan

     Frequentist meaning of a 95% confidence procedure?

     Jawapan

     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. Kad 194

     Soalan

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

     Jawapan

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

195. Kad 195

     Soalan

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

     Jawapan

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

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

196. Kad 196

     Soalan

     Relationship between Celsius and kelvin temperature differences?

     Jawapan

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

197. Kad 197

     Soalan

     How should credit for team engineering work be assigned?

     Jawapan

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

198. Kad 198

     Soalan

     Main limitation of simple payback period?

     Jawapan

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

199. Kad 199

     Soalan

     Roles of the null and alternative hypotheses?

     Jawapan

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

200. Kad 200

     Soalan

     Ideal-gas equation of state?

     Jawapan

     $$pV=nRT$$

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

201. Kad 201

     Soalan

     First check when reading a handbook table?

     Jawapan

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

202. Kad 202

     Soalan

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

     Jawapan

     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. Kad 203

     Soalan

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

     Jawapan

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

204. Kad 204

     Soalan

     Convert Fahrenheit absolute temperature to Rankine?

     Jawapan

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

     Rankine uses the Fahrenheit-sized degree from absolute zero.

205. Kad 205

     Soalan

     Ohm's law for an ideal resistor?

     Jawapan

     $$V=IR$$

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

206. Kad 206

     Soalan

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

     Jawapan

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

207. Kad 207

     Soalan

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

     Jawapan

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

208. Kad 208

     Soalan

     Is a radian dimensionless?

     Jawapan

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

209. Kad 209

     Soalan

     Electrical power absorbed under the passive sign convention?

     Jawapan

     $$P=VI$$

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

210. Kad 210

     Soalan

     Meaning of a p-value?

     Jawapan

     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. Kad 211

     Soalan

     First check when reading a handbook graph?

     Jawapan

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

212. Kad 212

     Soalan

     Difference between mass and weight?

     Jawapan

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

213. Kad 213

     Soalan

     Kirchhoff's current law at a node?

     Jawapan

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

214. Kad 214

     Soalan

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

     Jawapan

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

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

215. Kad 215

     Soalan

     Opportunity cost?

     Jawapan

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

216. Kad 216

     Soalan

     Weight from mass in a gravitational field?

     Jawapan

     $$W=mg$$

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

217. Kad 217

     Soalan

     Kirchhoff's voltage law around a closed loop?

     Jawapan

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

218. Kad 218

     Soalan

     Decision rule using significance level $\alpha$?

     Jawapan

     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. Kad 219

     Soalan

     Can proprietary methods from a former employer be reused freely?

     Jawapan

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

220. Kad 220

     Soalan

     Pound-force to newtons?

     Jawapan

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

221. Kad 221

     Soalan

     When does a definite integral equal ordinary geometric area?

     Jawapan

     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. Kad 222

     Soalan

     Charge-voltage relation for an ideal capacitor?

     Jawapan

     $$q=CV$$

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

223. Kad 223

     Soalan

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

     Jawapan

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

224. Kad 224

     Soalan

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

     Jawapan

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

225. Kad 225

     Soalan

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

     Jawapan

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

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

226. Kad 226

     Soalan

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

     Jawapan

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

227. Kad 227

     Soalan

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

     Jawapan

     $$\tau=RC$$

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

228. Kad 228

     Soalan

     What physical quantity does pound-mass measure?

     Jawapan

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

229. Kad 229

     Soalan

     Type I error?

     Jawapan

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

230. Kad 230

     Soalan

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

     Jawapan

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

231. Kad 231

     Soalan

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

     Jawapan

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

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

232. Kad 232

     Soalan

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

     Jawapan

     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. Kad 233

     Soalan

     Recognizable form of a separable first-order differential equation?

     Jawapan

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

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

234. Kad 234

     Soalan

     Using unverified software output in a safety-relevant calculation?

     Jawapan

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

235. Kad 235

     Soalan

     Equivalent resistance of ideal resistors in series?

     Jawapan

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

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

236. Kad 236

     Soalan

     Pressure conversion from psi to pascals?

     Jawapan

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

237. Kad 237

     Soalan

     Type II error?

     Jawapan

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

238. Kad 238

     Soalan

     Useful flashcard to make after a failed handbook search?

     Jawapan

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

239. Kad 239

     Soalan

     Standard form of a first-order linear differential equation?

     Jawapan

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

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

240. Kad 240

     Soalan

     Equivalent resistance of ideal resistors in parallel?

     Jawapan

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

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

241. Kad 241

     Soalan

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

     Jawapan

     $$BV_k=B-kD$$

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

242. Kad 242

     Soalan

     Standard atmosphere in pascals?

     Jawapan

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

243. Kad 243

     Soalan

     Using AI-generated technical content in engineering work?

     Jawapan

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

244. Kad 244

     Soalan

     Trial form for a homogeneous linear ODE with constant coefficients?

     Jawapan

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

245. Kad 245

     Soalan

     Wave-speed relationship among frequency and wavelength?

     Jawapan

     $$v=f\lambda$$

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

246. Kad 246

     Soalan

     Statistical power?

     Jawapan

     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. Kad 247

     Soalan

     Bar in pascals?

     Jawapan

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

248. Kad 248

     Soalan

     How should handbook navigation be practiced before the FE exam?

     Jawapan

     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. Kad 249

     Soalan

     Is depreciation itself a cash outflow?

     Jawapan

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

250. Kad 250

     Soalan

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

     Jawapan

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

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

251. Kad 251

     Soalan

     Relationship between period and frequency?

     Jawapan

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

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

252. Kad 252

     Soalan

     How should foreseeable environmental harm enter an engineering decision?

     Jawapan

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

253. Kad 253

     Soalan

     Foot-pound-force in joules?

     Jawapan

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

254. Kad 254

     Soalan

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

     Jawapan

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

255. Kad 255

     Soalan

     When should you search instead of relying on recall?

     Jawapan

     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. Kad 256

     Soalan

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

     Jawapan

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

257. Kad 257

     Soalan

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

     Jawapan

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

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

258. Kad 258

     Soalan

     General material balance on a control volume?

     Jawapan

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

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

259. Kad 259

     Soalan

     Approximate joules in one International Table Btu?

     Jawapan

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

260. Kad 260

     Soalan

     What is the defender in a replacement analysis?

     Jawapan

     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. Kad 261

     Soalan

     Speaking publicly about a technical matter outside your expertise?

     Jawapan

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

262. Kad 262

     Soalan

     Single-interval trapezoidal approximation to an integral?

     Jawapan

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

     It is exact for linear $f$.

263. Kad 263

     Soalan

     Energy efficiency of a device?

     Jawapan

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

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

264. Kad 264

     Soalan

     Purpose of sensitivity analysis in engineering economics?

     Jawapan

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

265. Kad 265

     Soalan

     Can a strong correlation establish causation?

     Jawapan

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

266. Kad 266

     Soalan

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

     Jawapan

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

267. Kad 267

     Soalan

     Mechanical horsepower in watts?

     Jawapan

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

268. Kad 268

     Soalan

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

     Jawapan

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

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

269. Kad 269

     Soalan

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

     Jawapan

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

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

270. Kad 270

     Soalan

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

     Jawapan

     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. Kad 271

     Soalan

     Kilowatt-hour in joules?

     Jawapan

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

272. Kad 272

     Soalan

     Percent error relative to an accepted nonzero value?

     Jawapan

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

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

273. Kad 273

     Soalan

     Does legal compliance alone settle an engineering ethics question?

     Jawapan

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

274. Kad 274

     Soalan

     Does handbook fluency replace discipline-specific problem practice?

     Jawapan

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

275. Kad 275

     Soalan

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

     Jawapan

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

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

276. Kad 276

     Soalan

     Dimensional requirement for a physically meaningful additive equation?

     Jawapan

     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.