Slope between two points?

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.

Net force relationship for constant mass in an inertial frame?

\sum\mathbf{F}=m\mathbf{a} Use a coherent unit system and include only external forces on the chosen body.

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

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

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

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

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

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

SI base unit of mass?

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

Linear equation from slope and intercept?

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

Velocity after time t under constant acceleration?

v=v_0+at This one-dimensional form requires constant a and a consistent positive direction.

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

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

How is the FE reference handbook available during the exam?

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.

Probability of A or B for possibly overlapping events?

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

Linear equation from one point and a slope?

y-y_1=m(x-x_1) Use it when the line passes through (x_1,y_1) and has slope m.

Position after time t under constant acceleration?

x=x_0+v_0t+\frac{1}{2}at^2 The acceleration is constant and all signed components use one coordinate direction.

A project assignment lies outside your competence. Proper response?

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.

Future amount under simple interest?

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.

Distance between two Cartesian points?

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} The coordinate components must use the same length unit.

Constant-acceleration relation without elapsed time?

v^2=v_0^2+2a(x-x_0) Use signed one-dimensional components and constant a.

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

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

Conditional probability of A given B?

P(A\mid B)=\frac{P(A\cap B)}{P(B)} This requires P(B)>0.

SI base unit of thermodynamic temperature?

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

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

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

Midpoint of two Cartesian points?

\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) Average corresponding coordinates.

Linear momentum of a particle?

\mathbf{p}=m\mathbf{v} For constant mass, SI units are kg\cdot m/s.

Future amount under compound interest?

F=P(1+i)^n The rate period must match the period used for n.

Should an FE search workflow depend on Ctrl+F?

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

Joint probability expressed with a conditional probability?

P(A\cap B)=P(A\mid B)P(B) This elementary formula requires P(B)>0.

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

(x-h)^2+(y-k)^2=r^2 The coordinate units and radius unit must match.

Impulse-momentum relationship?

\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.

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

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

Present worth of one future amount?

P=\frac{F}{(1+i)^n} Use an effective rate i per period consistent with n.

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

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} This form requires a\ne0.

When is total linear momentum conserved?

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

Why avoid memorizing FE handbook page numbers?

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

Probability condition that defines independence of A and B?

P(A\cap B)=P(A)P(B) Independence is not the same as mutual exclusivity.

SI unit of frequency in base-unit form?

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

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

P=A\frac{(1+i)^n-1}{i(1+i)^n} This requires i\ne0; at i=0, P=An.

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

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

Work done by a constant force through displacement?

W=\mathbf{F}\cdot\mathbf{s}=Fs\cos\theta Use the angle between force and displacement; SI units are joules.

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

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

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

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

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

P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)} This requires P(B)>0.

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

a^m a^n=a^{m+n} This form assumes a>0 and real exponents m and n.

Translational kinetic energy of a particle?

K=\frac{1}{2}mv^2 Mass and speed must use a coherent unit system.

SI unit of pressure in force-area form?

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

FE Exam Flashcards: Engineering Equations, Units & Handbook Skills

Review common FE equations, variable meanings, units, assumptions, conversions, and searchable handbook navigation.

Oleh penulis Open Study Contributor

Tentang dek ini

Build quick recall for broad topic families found across all seven FE discipline specifications: mathematics, probability and statistics, engineering economics, and ethics and professional practice. Individual subtopics vary by discipline. The deck also covers unit discipline, handbook navigation, and selected equations useful across multiple disciplines.

The 276 original cards practice equation → use, variable → meaning or unit, condition → applicable relationship, quantity → unit family, conversion setup → result, short scenario → handbook search cue, and equation behavior → interpretation. Answers come first, followed by the assumption, sign convention, unit condition, or practical check that keeps the relationship honest. Related variants are separated in a deterministic mixed sequence, while prerequisites stay ahead of dependent uses.

This is a common recall layer, not a compressed copy of the reference handbook. It deliberately leaves out mechanical reversals, exhaustive symbol permutations, long worked problems, handbook page numbers, discipline-specific design procedures, and claims that every equation appears in every FE discipline. Use it alongside your current FE discipline specification, the current reference handbook available through MyNCEES, and timed discipline-specific problem practice. The current NCEES Examinee Guide explains how the onscreen reference material is supplied and searched.

Independent and unofficial. Not affiliated with or endorsed by NCEES. No NCEES exam questions, answer keys, practice questions, handbook tables or prose, or exam-specification text were copied.

Kartu dalam dek ini

Kartu 1
Pertanyaan
SI base unit of length?
Jawaban
The metre, symbol $m$ .
Kartu 2
Pertanyaan
Slope between two points?
Jawaban
$m=\frac{y_2-y_1}{x_2-x_1}$
This requires $x_2\ne x_1$ ; slope is the change in the dependent variable per unit change in the independent variable.
Kartu 3
Pertanyaan
Net force relationship for constant mass in an inertial frame?
Jawaban
$\sum\mathbf{F}=m\mathbf{a}$
Use a coherent unit system and include only external forces on the chosen body.
Kartu 4
Pertanyaan
Cash-flow sign convention from the decision maker's viewpoint?
Jawaban
Receipts are positive and disbursements are negative. Choose one viewpoint and keep it consistent across the cash-flow diagram and equations.
Kartu 5
Pertanyaan
Where should an FE candidate get the current reference handbook for practice?
Jawaban
From the candidate's MyNCEES account. Use the current supplied file rather than an old indexed copy or a third-party mirror.
Kartu 6
Pertanyaan
Probability of the complement of event $A$ ?
Jawaban
$P(A^c)=1-P(A)$
Kartu 7
Pertanyaan
An engineering judgment conflicts with pressure to protect schedule or cost. First duty?
Jawaban
Protect public health, safety, and welfare. Document the technical concern and escalate through appropriate channels.
Kartu 8
Pertanyaan
SI base unit of mass?
Jawaban
The kilogram, symbol $kg$ . It is a mass unit, not a force unit.
Kartu 9
Pertanyaan
Linear equation from slope and intercept?
Jawaban
$y=mx+b$
Here $m$ is slope and $b$ is the value of $y$ where $x=0$ .
Kartu 10
Pertanyaan
Velocity after time $t$ under constant acceleration?
Jawaban
$v=v_0+at$
This one-dimensional form requires constant $a$ and a consistent positive direction.
Kartu 11
Pertanyaan
Where is an end-of-period cash flow placed?
Jawaban
At the boundary marking the end of that period. Interest factors assume consistent period lengths and cash-flow timing.
Kartu 12
Pertanyaan
How is the FE reference handbook available during the exam?
Jawaban
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.
Kartu 13
Pertanyaan
Probability of $A$ or $B$ for possibly overlapping events?
Jawaban
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Kartu 14
Pertanyaan
SI base unit of time?
Jawaban
The second, symbol $s$ .
Kartu 15
Pertanyaan
Linear equation from one point and a slope?
Jawaban
$y-y_1=m(x-x_1)$
Use it when the line passes through $(x_1,y_1)$ and has slope $m$ .
Kartu 16
Pertanyaan
Position after time $t$ under constant acceleration?
Jawaban
$x=x_0+v_0t+\frac{1}{2}at^2$
The acceleration is constant and all signed components use one coordinate direction.
Kartu 17
Pertanyaan
A project assignment lies outside your competence. Proper response?
Jawaban
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.
Kartu 18
Pertanyaan
SI base unit of electric current?
Jawaban
The ampere, symbol $A$ .
Kartu 19
Pertanyaan
Future amount under simple interest?
Jawaban
$F=P(1+in)$
Here $P$ is principal, $i$ is interest per period, and $n$ is the number of periods; interest is earned only on principal.
Kartu 20
Pertanyaan
Distance between two Cartesian points?
Jawaban
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
The coordinate components must use the same length unit.
Kartu 21
Pertanyaan
Constant-acceleration relation without elapsed time?
Jawaban
$v^2=v_0^2+2a(x-x_0)$
Use signed one-dimensional components and constant $a$ .
Kartu 22
Pertanyaan
Where do you search the supplied reference material in the exam interface?
Jawaban
Use the exam software's search box beside the supplied reference material.
Kartu 23
Pertanyaan
Conditional probability of $A$ given $B$ ?
Jawaban
$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
This requires $P(B)>0$ .
Kartu 24
Pertanyaan
SI base unit of thermodynamic temperature?
Jawaban
The kelvin, symbol $K$ . Kelvin is written without a degree sign.
Kartu 25
Pertanyaan
A client asks you to remove an unfavorable test result from a report. Proper response?
Jawaban
Keep the material result and explain it accurately. Engineering statements should be objective, complete enough to avoid deception, and supported by evidence.
Kartu 26
Pertanyaan
Midpoint of two Cartesian points?
Jawaban
$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
Average corresponding coordinates.
Kartu 27
Pertanyaan
Linear momentum of a particle?
Jawaban
$\mathbf{p}=m\mathbf{v}$
For constant mass, SI units are $kg\cdot m/s$ .
Kartu 28
Pertanyaan
Future amount under compound interest?
Jawaban
$F=P(1+i)^n$
The rate period must match the period used for $n$ .
Kartu 29
Pertanyaan
Should an FE search workflow depend on Ctrl+F?
Jawaban
No. The May 2026 NCEES Examinee Guide says Ctrl+F isn't available; practice with the exam interface's own search box.
Kartu 30
Pertanyaan
SI base unit of amount of substance?
Jawaban
The mole, symbol $mol$ .
Kartu 31
Pertanyaan
Joint probability expressed with a conditional probability?
Jawaban
$P(A\cap B)=P(A\mid B)P(B)$
This elementary formula requires $P(B)>0$ .
Kartu 32
Pertanyaan
Standard equation of a circle centered at $(h,k)$ ?
Jawaban
$(x-h)^2+(y-k)^2=r^2$
The coordinate units and radius unit must match.
Kartu 33
Pertanyaan
Impulse-momentum relationship?
Jawaban
$\int_{t_1}^{t_2}\sum\mathbf{F}\,dt=\mathbf{p}_2-\mathbf{p}_1$
The force is the net external force on the chosen system.
Kartu 34
Pertanyaan
You discover a financial interest that could affect your recommendation. Proper response?
Jawaban
Disclose the conflict promptly to affected parties and obtain appropriate consent or withdraw. Hidden personal interests undermine independent judgment.
Kartu 35
Pertanyaan
SI base unit of luminous intensity?
Jawaban
The candela, symbol $cd$ .
Kartu 36
Pertanyaan
Present worth of one future amount?
Jawaban
$P=\frac{F}{(1+i)^n}$
Use an effective rate $i$ per period consistent with $n$ .
Kartu 37
Pertanyaan
Roots of $ax^2+bx+c=0$ ?
Jawaban
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
This form requires $a\ne0$ .
Kartu 38
Pertanyaan
When is total linear momentum conserved?
Jawaban
When net external impulse on the system is zero. Internal forces can redistribute momentum but do not change the system total.
Kartu 39
Pertanyaan
Why avoid memorizing FE handbook page numbers?
Jawaban
Pagination and layout can change. Remember section names, concepts, and strong search terms instead.
Kartu 40
Pertanyaan
Probability condition that defines independence of $A$ and $B$ ?
Jawaban
$P(A\cap B)=P(A)P(B)$
Independence is not the same as mutual exclusivity.
Kartu 41
Pertanyaan
SI unit of frequency in base-unit form?
Jawaban
The hertz, $Hz=s^{-1}$ , applies to periodic phenomena. One hertz is one cycle per second.
Kartu 42
Pertanyaan
Present worth of an end-of-period uniform series $A$ ?
Jawaban
$P=A\frac{(1+i)^n-1}{i(1+i)^n}$
This requires $i\ne0$ ; at $i=0$ , $P=An$ .
Kartu 43
Pertanyaan
What does $b^2-4ac$ reveal for a real-coefficient quadratic?
Jawaban
It determines the root type: positive gives two distinct real roots, zero gives one repeated real root, and negative gives a complex-conjugate pair.
Kartu 44
Pertanyaan
Work done by a constant force through displacement?
Jawaban
$W=\mathbf{F}\cdot\mathbf{s}=Fs\cos\theta$
Use the angle between force and displacement; SI units are joules.
Kartu 45
Pertanyaan
A vendor offers a valuable gift while you evaluate bids. Proper response?
Jawaban
Decline it and follow the organization's disclosure policy. Even an intended courtesy can create an actual or apparent conflict.
Kartu 46
Pertanyaan
SI unit of force in base-unit form?
Jawaban
The newton, $N=kg\cdot m/s^2$ .
Kartu 47
Pertanyaan
First search cue for a named quantity such as coefficient of thermal expansion?
Jawaban
Search the exact technical noun phrase. Distinctive nouns usually narrow results better than a whole question sentence.
Kartu 48
Pertanyaan
Bayes' rule for $P(A\mid B)$ ?
Jawaban
$P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$
This requires $P(B)>0$ .
Kartu 49
Pertanyaan
Product of powers with the same positive base and real exponents?
Jawaban
$a^m a^n=a^{m+n}$
This form assumes $a>0$ and real exponents $m$ and $n$ .
Kartu 50
Pertanyaan
Translational kinetic energy of a particle?
Jawaban
$K=\frac{1}{2}mv^2$
Mass and speed must use a coherent unit system.
Kartu 51
Pertanyaan
SI unit of pressure in force-area form?
Jawaban
The pascal, $Pa=N/m^2$ . It is the SI derived unit for pressure and stress.
Kartu 52
Pertanyaan
Equivalent annual amount for present worth $P$ ?
Jawaban
$A=P\frac{i(1+i)^n}{(1+i)^n-1}$
For the displayed formula, $i\ne0$ ; at $i=0$ , $A=P/n$ . Payments occur at period ends and $i$ matches that period.
Kartu 53
Pertanyaan
May confidential client information be shared for personal benefit?
Jawaban
No. Protect it unless the client authorizes disclosure or law, safety, or professional duty requires it.
Kartu 54
Pertanyaan
A handbook search term returns too many results. Best refinement?
Jawaban
Add one meaningful qualifier, such as the phenomenon, geometry, distribution, or material property you need.
Kartu 55
Pertanyaan
Quotient of powers with the same positive base and real exponents?
Jawaban
$\frac{a^m}{a^n}=a^{m-n}$
This form assumes $a>0$ and real exponents $m$ and $n$ .
Kartu 56
Pertanyaan
Net work-energy relationship for a particle?
Jawaban
$W_{net}=K_2-K_1$
The net work includes the work of all forces represented in the particle model.
Kartu 57
Pertanyaan
Ordered selections of $r$ objects from $n$ distinct objects?
Jawaban
$P(n,r)=\frac{n!}{(n-r)!}$
Use this when order matters and selection is without replacement.
Kartu 58
Pertanyaan
Future worth of an end-of-period uniform series $A$ ?
Jawaban
$F=A\frac{(1+i)^n-1}{i}$
This requires $i\ne0$ ; at $i=0$ , $F=An$ .
Kartu 59
Pertanyaan
Power of a power for a positive base and real exponents?
Jawaban
$(a^m)^n=a^{mn}$
This form assumes $a>0$ and real exponents $m$ and $n$ .
Kartu 60
Pertanyaan
SI unit of energy in force-distance form?
Jawaban
The joule, $J=N\cdot m$ .
Kartu 61
Pertanyaan
A problem gives only an unfamiliar symbol. Best search preparation?
Jawaban
Translate the symbol into its likely quantity name and discipline context before searching; symbol-only searches are often ambiguous.
Kartu 62
Pertanyaan
Confidential information reveals an imminent public-safety risk. What comes first?
Jawaban
Take steps required to protect people, using appropriate legal and organizational channels. Share only what is necessary and document the basis for escalation.
Kartu 63
Pertanyaan
Unordered selections of $r$ objects from $n$ distinct objects?
Jawaban
$C(n,r)=\frac{n!}{r!(n-r)!}$
Use this when order does not matter and selection is without replacement.
Kartu 64
Pertanyaan
Change in gravitational potential energy near Earth's surface?
Jawaban
$\Delta U_g=mg\Delta h$
Use approximately constant $g$ and a clearly chosen height datum.
Kartu 65
Pertanyaan
Negative-exponent rule for a positive base and real exponent?
Jawaban
$a^{-n}=\frac{1}{a^n}$
This form assumes $a>0$ and real exponent $n$ .
Kartu 66
Pertanyaan
Uniform end-of-period deposit needed for future amount $F$ ?
Jawaban
$A=F\frac{i}{(1+i)^n-1}$
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 $n$ .
Kartu 67
Pertanyaan
A handbook search for an acronym fails. Next move?
Jawaban
Try the expanded term and a common alternate name. Acronyms vary by section and discipline.
Kartu 68
Pertanyaan
SI unit of power in energy-time form?
Jawaban
The watt, $W=J/s$ .
Kartu 69
Pertanyaan
Logarithm of a product?
Jawaban
$\log_b(xy)=\log_b x+\log_b y$
For real logarithms, $b>0$ , $b\ne1$ , and both arguments are positive.
Kartu 70
Pertanyaan
Conditions for a binomial model?
Jawaban
A fixed number of independent trials, two outcomes per trial, and the same success probability on every trial.
Kartu 71
Pertanyaan
Using another engineer's analysis in your deliverable?
Jawaban
Credit the source and verify the analysis before relying on it. Do not present someone else's work as your own.
Kartu 72
Pertanyaan
SI unit of electric charge in current-time form?
Jawaban
The coulomb, $C=A\cdot s$ .
Kartu 73
Pertanyaan
Average power from work over elapsed time?
Jawaban
$P_{avg}=\frac{W}{\Delta t}$
Use consistent energy and time units; watts are joules per second.
Kartu 74
Pertanyaan
Annual equivalent of cost $P$ with salvage $S$ after $n$ periods?
Jawaban
$A=P\frac{i(1+i)^n}{(1+i)^n-1}-S\frac{i}{(1+i)^n-1}$
The first factor converts present cost to an annual amount; the second converts future salvage. Use the same effective rate and period basis. At $i=0$ , $A=(P-S)/n$ .
Kartu 75
Pertanyaan
Logarithm of a positive quantity raised to a power?
Jawaban
$\log_b(x^p)=p\log_b x$
For real logarithms, $x>0$ , $b>0$ , and $b\ne1$ .
Kartu 76
Pertanyaan
SI unit of electric potential difference in energy-charge form?
Jawaban
The volt, $V=J/C$ .
Kartu 77
Pertanyaan
Instantaneous mechanical power delivered by a force?
Jawaban
$P=\mathbf{F}\cdot\mathbf{v}$
Use the velocity of the force's point of application.
Kartu 78
Pertanyaan
A precise handbook term gives no useful match. Next move?
Jawaban
Try a standard synonym or the broader parent concept, then narrow within the relevant section.
Kartu 79
Pertanyaan
Mean of $X\sim\operatorname{Binomial}(n,p)$ ?
Jawaban
$E[X]=np$
Kartu 80
Pertanyaan
SI unit of electrical resistance in voltage-current form?
Jawaban
The ohm, $\Omega=V/A$ .
Kartu 81
Pertanyaan
Moment of a force about a point?
Jawaban
$\mathbf{M}=\mathbf{r}\times\mathbf{F}$
Vector $\mathbf{r}$ runs from the moment point to a point on the force's line of action.
Kartu 82
Pertanyaan
Cash-flow pattern described by an arithmetic gradient $G$ ?
Jawaban
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.
Kartu 83
Pertanyaan
Inverse relationship between the natural log and exponential?
Jawaban
$\ln(e^x)=x,\qquad e^{\ln x}=x$
The second identity requires $x>0$ .
Kartu 84
Pertanyaan
SI prefix giga?
Jawaban
$G=10^9$ .
Kartu 85
Pertanyaan
Angular velocity after time $t$ under constant angular acceleration?
Jawaban
$\omega=\omega_0+\alpha t$
Use consistent angular sign convention and radians for angular measures.
Kartu 86
Pertanyaan
When should an engineer sign or seal technical work?
Jawaban
Only when authorized and when the work was prepared by the engineer or under the level of responsible charge required by the applicable jurisdiction.
Kartu 87
Pertanyaan
Best memory target for returning to a handbook formula?
Jawaban
The section or concept name plus a distinctive search phrase. That survives layout changes better than a page number.
Kartu 88
Pertanyaan
SI prefix mega?
Jawaban
$M=10^6$ . Uppercase matters: lowercase $m$ means milli.
Kartu 89
Pertanyaan
Convert degrees to radians?
Jawaban
$\theta_{rad}=\theta_{deg}\frac{\pi}{180}$
Use radians in calculus formulas unless a formula explicitly says otherwise.
Kartu 90
Pertanyaan
Variance of $X\sim\operatorname{Binomial}(n,p)$ ?
Jawaban
$\operatorname{Var}(X)=np(1-p)$
Kartu 91
Pertanyaan
Cash-flow pattern described by a geometric gradient rate $g$ ?
Jawaban
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.
Kartu 92
Pertanyaan
Where do licensure and sealing requirements come from?
Jawaban
The applicable jurisdiction's current laws and board rules. Confirm local requirements rather than assuming one state's rules apply everywhere.
Kartu 93
Pertanyaan
Rotational kinetic energy about a fixed axis?
Jawaban
$K_{rot}=\frac{1}{2}I\omega^2$
$I$ is the mass moment of inertia about that axis.
Kartu 94
Pertanyaan
SI prefix kilo?
Jawaban
$k=10^3$ .
Kartu 95
Pertanyaan
Right-triangle definition of sine?
Jawaban
Sine is opposite over hypotenuse. This definition applies to an acute angle in a right triangle.
Kartu 96
Pertanyaan
After search lands near a result, what should you scan first?
Jawaban
The section heading and nearby subheading. They establish whether the result belongs to the right model and subject.
Kartu 97
Pertanyaan
Rotational analogue of Newton's second law about a fixed principal axis?
Jawaban
$\sum M=I\alpha$
This scalar form assumes the stated fixed-axis model and a consistent sign convention.
Kartu 98
Pertanyaan
SI prefix milli?
Jawaban
$m=10^{-3}$ . Context distinguishes the prefix from the metre symbol.
Kartu 99
Pertanyaan
Meaning of a nominal annual rate compounded $m$ times per year?
Jawaban
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.
Kartu 100
Pertanyaan
Standardize an observation $x$ from a distribution with mean $\mu$ and standard deviation $\sigma$ ?
Jawaban
$z=\frac{x-\mu}{\sigma}$
This requires $\sigma>0$ ; using a normal probability table also assumes an appropriate normal model.
Kartu 101
Pertanyaan
Right-triangle definition of cosine?
Jawaban
Cosine is adjacent over hypotenuse. This definition applies to an acute angle in a right triangle.
Kartu 102
Pertanyaan
Force-displacement relation for an ideal linear spring?
Jawaban
$F=-kx$
The minus sign shows restoring direction; the model applies within the spring's linear range.
Kartu 103
Pertanyaan
May qualifications or project responsibility be exaggerated in a proposal?
Jawaban
No. State education, licensure, experience, and responsibility accurately, including the actual roles of collaborators.
Kartu 104
Pertanyaan
SI prefix micro?
Jawaban
$\mu=10^{-6}$ .
Kartu 105
Pertanyaan
A handbook symbol conflicts with your usual notation. What controls?
Jawaban
The definition beside the selected relationship. Symbols can represent different quantities in different sections.
Kartu 106
Pertanyaan
Periodic rate from nominal annual rate $r$ compounded $m$ times per year?
Jawaban
$i=\frac{r}{m}$
Use consistent decimal units, and pair this rate with the number of compounding periods.
Kartu 107
Pertanyaan
Right-triangle definition of tangent?
Jawaban
Tangent is opposite over adjacent, or $\sin\theta/\cos\theta$ where $\cos\theta\ne0$ .
Kartu 108
Pertanyaan
Average normal stress under centered axial load?
Jawaban
$\sigma=\frac{F}{A}$
$F$ is normal to area $A$ ; the average ignores local stress concentrations.
Kartu 109
Pertanyaan
Mean, median, and mode of a symmetric normal distribution?
Jawaban
They are equal and located at $\mu$ . The distribution is symmetric about that center.
Kartu 110
Pertanyaan
SI prefix nano?
Jawaban
$n=10^{-9}$ .
Kartu 111
Pertanyaan
Fundamental Pythagorean trigonometric identity?
Jawaban
$\sin^2\theta+\cos^2\theta=1$
Kartu 112
Pertanyaan
Engineering normal strain?
Jawaban
$\varepsilon=\frac{\Delta L}{L_0}$
It is dimensionless and uses original gauge length $L_0$ .
Kartu 113
Pertanyaan
A candidate retrieves a formula from the handbook. What must be checked with it?
Jawaban
Its applicability assumptions and variable definitions. A familiar equation used under the wrong model is still wrong.
Kartu 114
Pertanyaan
Technical duty to an employer or client?
Jawaban
Act as a faithful professional within lawful, ethical limits, communicate material risks, and preserve independent technical judgment.
Kartu 115
Pertanyaan
How does a length conversion factor apply to area?
Jawaban
Square it. If $1\,u=a\,v$ , then $1\,u^2=a^2\,v^2$ .
Kartu 116
Pertanyaan
Effective annual rate from nominal rate $r$ compounded $m$ times per year?
Jawaban
$i_{eff}=\left(1+\frac{r}{m}\right)^m-1$
Kartu 117
Pertanyaan
When is a Poisson count model reasonable?
Jawaban
For counts in a fixed interval when events occur independently at an approximately constant average rate and simultaneous events are negligible.
Kartu 118
Pertanyaan
Relationship for the third side of a non-right triangle?
Jawaban
$c^2=a^2+b^2-2ab\cos C$
Angle $C$ lies between sides $a$ and $b$ , opposite side $c$ .
Kartu 119
Pertanyaan
Linear elastic stress-strain relation in uniaxial loading?
Jawaban
$\sigma=E\varepsilon$
Use it in the material's linear elastic range; $E$ has stress units.
Kartu 120
Pertanyaan
How does a length conversion factor apply to volume?
Jawaban
Cube it. If $1\,u=a\,v$ , then $1\,u^3=a^3\,v^3$ .
Kartu 121
Pertanyaan
What should you record for every variable in a retrieved equation?
Jawaban
Its meaning and expected unit or dimension. This catches swapped symbols and incompatible substitutions.
Kartu 122
Pertanyaan
Effective annual rate for continuous compounding at nominal rate $r$ ?
Jawaban
$i_{eff}=e^r-1$
Here $r$ is expressed as a decimal per year.
Kartu 123
Pertanyaan
A supervisor directs an illegal engineering action. Proper response?
Jawaban
Refuse the illegal action, document the direction, and escalate through appropriate legal or organizational channels.
Kartu 124
Pertanyaan
Magnitude of a three-component vector $\mathbf{v}$ ?
Jawaban
$\lVert\mathbf{v}\rVert=\sqrt{v_x^2+v_y^2+v_z^2}$
All components must represent the same physical quantity in compatible units.
Kartu 125
Pertanyaan
Mass density?
Jawaban
$\rho=\frac{m}{V}$
Use mass, not weight, in the numerator.
Kartu 126
Pertanyaan
Inches in one foot?
Jawaban
$12\,in=1\,ft$ .
Kartu 127
Pertanyaan
Mean and variance of $X\sim\operatorname{Poisson}(\lambda)$ ?
Jawaban
Both equal $\lambda$ . The standard deviation is $\sqrt{\lambda}$ .
Kartu 128
Pertanyaan
How should subscripts be handled in a retrieved relationship?
Jawaban
Read what each subscript identifies—state, direction, phase, location, or reference—before substituting values.
Kartu 129
Pertanyaan
Dot product from vector magnitudes and included angle?
Jawaban
$\mathbf{a}\cdot\mathbf{b}=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\cos\theta$
The result is a scalar.
Kartu 130
Pertanyaan
Average normal pressure on an area?
Jawaban
$p=\frac{F_n}{A}$
$F_n$ is the normal force; pressure is scalar in a fluid at rest.
Kartu 131
Pertanyaan
Feet in one yard?
Jawaban
$3\,ft=1\,yd$ .
Kartu 132
Pertanyaan
When are two interest rates equivalent?
Jawaban
When they produce the same accumulation over the same time interval. Convert both rates to a common effective period before comparing them.
Kartu 133
Pertanyaan
You discover a material error in issued work. Proper response?
Jawaban
Notify responsible parties promptly, assess the safety impact, correct the record, and document the response. Do not hide the error.
Kartu 134
Pertanyaan
Expected value of a discrete random variable?
Jawaban
$E[X]=\sum_x xP(X=x)$
Sum over all possible values with a valid probability mass function.
Kartu 135
Pertanyaan
Dot-product test for perpendicular nonzero vectors?
Jawaban
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.
Kartu 136
Pertanyaan
Hydrostatic pressure change with vertical depth in a constant-density fluid?
Jawaban
$\Delta p=\rho g\Delta h$
Depth increases downward and the fluid is at rest.
Kartu 137
Pertanyaan
Feet in one statute mile?
Jawaban
$5280\,ft=1\,mi$ .
Kartu 138
Pertanyaan
Present-worth acceptance rule for an independent investment at the minimum attractive rate of return?
Jawaban
Accept it when net present worth is nonnegative. All cash flows must be discounted to the same time using the chosen comparison rate.
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Kartu 139
Pertanyaan
A retrieved formula contains signed quantities. What should you confirm?
Jawaban
The stated sign convention and positive direction. Do not mix magnitudes with signed components silently.
Kartu 140
Pertanyaan
Magnitude of a vector cross product?
Jawaban
$\lVert\mathbf{a}\times\mathbf{b}\rVert=\lVert\mathbf{a}\rVert\lVert\mathbf{b}\rVert\sin\theta$
The direction follows the right-hand rule.
Kartu 141
Pertanyaan
Exact inch-to-metre relationship?
Jawaban
$1\,in=0.0254\,m$ exactly.
Kartu 142
Pertanyaan
Volumetric flow rate through a cross-section?
Jawaban
$Q=Av_{avg}$
Velocity is the area-average component normal to the section.
Kartu 143
Pertanyaan
Variance from the mean $\mu$ ?
Jawaban
$\operatorname{Var}(X)=E[(X-\mu)^2]$
Variance has squared units; standard deviation has the original units.
Kartu 144
Pertanyaan
Future-worth acceptance rule for an independent investment?
Jawaban
Accept it when net future worth at the study horizon is nonnegative, using the minimum attractive rate of return consistently.
Kartu 145
Pertanyaan
What coordinate detail should be checked before using a vector or mechanics formula?
Jawaban
Axis directions and the reference point or origin. Components and moments depend on those choices.
Kartu 146
Pertanyaan
Exact foot-to-metre relationship?
Jawaban
$1\,ft=0.3048\,m$ exactly.
Kartu 147
Pertanyaan
How should important uncertainty be communicated?
Jawaban
State the assumptions, limits, and plausible consequences clearly enough for the decision maker to understand the risk.
Kartu 148
Pertanyaan
When is the matrix product $AB$ defined?
Jawaban
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 $m\times p$ .
Kartu 149
Pertanyaan
Steady one-inlet, one-outlet mass continuity?
Jawaban
$\rho_1A_1v_1=\rho_2A_2v_2$
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 $A_1v_1=A_2v_2$ .
Kartu 150
Pertanyaan
Sample mean of observations $x_1,\ldots,x_n$ ?
Jawaban
$\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i$
Kartu 151
Pertanyaan
Square feet in one acre?
Jawaban
$1\,acre=43{,}560\,ft^2$ .
Kartu 152
Pertanyaan
Determinant of $\begin{bmatrix}a&b\\c&d\end{bmatrix}$ ?
Jawaban
$ad-bc$
Kartu 153
Pertanyaan
Bernoulli relationship along a streamline for ideal steady flow?
Jawaban
$\frac{p}{\rho g}+\frac{v^2}{2g}+z=\text{constant}$
This basic form assumes steady, incompressible, negligible-viscosity flow with no shaft work or heat effects between points.
Kartu 154
Pertanyaan
May inconvenient measurements be discarded without a technical basis?
Jawaban
No. Use a documented, technically justified rule for excluding data and preserve the original record.
Kartu 155
Pertanyaan
Annual-worth acceptance rule for an independent investment?
Jawaban
Accept it when equivalent annual worth is nonnegative. Compare alternatives over compatible service assumptions.
Kartu 156
Pertanyaan
Before using a handbook equation, what unit-system check matters?
Jawaban
Confirm that every input and any embedded constant use one compatible unit system. Convert first when necessary.
Kartu 157
Pertanyaan
Cubic metres in one litre?
Jawaban
$1\,L=10^{-3}\,m^3$ .
Kartu 158
Pertanyaan
What does a zero determinant mean for a square matrix?
Jawaban
The matrix is singular and has no inverse. A corresponding linear system cannot have one unique solution.
Kartu 159
Pertanyaan
Reynolds number for internal flow using characteristic length $L$ ?
Jawaban
$Re=\frac{\rho vL}{\mu}=\frac{vL}{\nu}$
It is dimensionless; use consistent properties and the geometry-appropriate characteristic length.
Kartu 160
Pertanyaan
Unbiased sample variance for an independent sample from one population?
Jawaban
$s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2$
This requires at least two observations, so $n\ge2$ . The $n-1$ denominator estimates population variance after fitting the sample mean.
Kartu 161
Pertanyaan
How should mutually exclusive alternatives be compared?
Jawaban
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.
Kartu 162
Pertanyaan
Cubic centimetres in one millilitre?
Jawaban
$1\,mL=1\,cm^3$ .
Kartu 163
Pertanyaan
Why keep contemporaneous engineering records?
Jawaban
They preserve assumptions, decisions, calculations, approvals, and changes so the work can be checked and responsibilities understood.
Kartu 164
Pertanyaan
Fast check after substituting into a handbook formula?
Jawaban
Verify that the resulting dimensions match the requested quantity and that additive terms share dimensions.
Kartu 165
Pertanyaan
Matrix solution of $A\mathbf{x}=\mathbf{b}$ when $A$ is invertible?
Jawaban
$\mathbf{x}=A^{-1}\mathbf{b}$
In numerical work, direct factorization is usually preferable to explicitly forming the inverse.
Kartu 166
Pertanyaan
Sensible heat for constant specific heat and no phase change?
Jawaban
$Q=mc\Delta T$
$c$ must match the material, temperature range, mass unit, and temperature-difference unit.
Kartu 167
Pertanyaan
Standard error of the mean for an i.i.d. sample with population standard deviation $\sigma$ ?
Jawaban
$SE(\bar{x})=\frac{\sigma}{\sqrt{n}}$
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.
Kartu 168
Pertanyaan
Safe setup for converting $25\,ft^2$ to square metres?
Jawaban
$25\,ft^2\left(\frac{0.3048\,m}{1\,ft}\right)^2$
The squared length factor cancels $ft^2$ and leaves $m^2$ .
Kartu 169
Pertanyaan
Purpose of incremental analysis for mutually exclusive alternatives?
Jawaban
It tests whether the additional investment in the higher-cost option earns the required return compared with the lower-cost option.
Kartu 170
Pertanyaan
Physical meaning of $dy/dx$ ?
Jawaban
It is the instantaneous rate of change of $y$ with respect to $x$ , with units of the $y$ unit divided by the $x$ unit.
Kartu 171
Pertanyaan
One-dimensional steady conduction through a plane wall?
Jawaban
$\dot Q=-kA\frac{dT}{dx}$
The minus sign indicates heat flows toward lower temperature; $k$ is thermal conductivity.
Kartu 172
Pertanyaan
When should you algebraically rearrange a handbook relationship?
Jawaban
After confirming the correct equation, definitions, assumptions, and sign convention. Then isolate the requested variable without changing its domain restrictions.
Kartu 173
Pertanyaan
Safe setup for converting $2\,in^3$ to cubic metres?
Jawaban
$2\,in^3\left(\frac{0.0254\,m}{1\,in}\right)^3$
Cube the exact length conversion because the original quantity is volume.
Kartu 174
Pertanyaan
A client changes a safety-critical design requirement verbally. Proper response?
Jawaban
Confirm the change in writing, analyze its consequences, and obtain the required approvals before relying on it.
Kartu 175
Pertanyaan
Derivative of $x^n$ for constant $n$ ?
Jawaban
$\frac{d}{dx}x^n=nx^{n-1}$
Apply domain restrictions when $n$ is non-integer or negative.
Kartu 176
Pertanyaan
Convective heat-transfer rate at a surface?
Jawaban
$\dot Q=hA(T_s-T_\infty)$
$h$ depends on the flow and geometry; the sign follows the chosen temperature difference.
Kartu 177
Pertanyaan
What does the central limit theorem say about a sample mean?
Jawaban
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.
Kartu 178
Pertanyaan
Internal rate of return?
Jawaban
The discount rate that makes net present worth zero. Multiple sign changes in cash flow can produce multiple or no meaningful real rates.
Kartu 179
Pertanyaan
Several similar handbook equations appear together. How do you choose?
Jawaban
Match each equation's stated geometry, boundary conditions, material model, and variable definitions to the problem.
Kartu 180
Pertanyaan
Convert Celsius temperature to kelvin?
Jawaban
$T_K=T_{^\circ C}+273.15$
This conversion is for absolute temperature, not temperature difference.
Kartu 181
Pertanyaan
Derivative of a product $u(x)v(x)$ ?
Jawaban
$(uv)'=u'v+uv'$
Kartu 182
Pertanyaan
Internal escalation does not resolve a serious public-safety threat. Next step?
Jawaban
Use the next appropriate authority or reporting channel, consistent with law and the urgency of the hazard. Keep a factual record.
Kartu 183
Pertanyaan
Two-sided confidence interval for a population mean with known $\sigma$ ?
Jawaban
$\bar{x}\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$
Use the normal-model conditions and the critical value for confidence level $1-\alpha$ .
Kartu 184
Pertanyaan
Net thermal radiation from a small gray surface to large surroundings?
Jawaban
$\dot Q=\varepsilon\sigma A(T_s^4-T_{sur}^4)$
Use absolute temperatures; the model assumes the stated gray-surface surroundings.
Kartu 185
Pertanyaan
Basic benefit-cost acceptance rule for an independent public project?
Jawaban
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.
Kartu 186
Pertanyaan
Derivative of a composite function $f(g(x))$ ?
Jawaban
$\frac{d}{dx}f(g(x))=f'(g(x))g'(x)$
Kartu 187
Pertanyaan
Why inspect boundary or initial conditions near a formula?
Jawaban
They determine which solution form applies and can eliminate constants or terms. A formula without its conditions may be unusable.
Kartu 188
Pertanyaan
Convert Celsius temperature to Fahrenheit?
Jawaban
$T_{^\circ F}=\frac{9}{5}T_{^\circ C}+32$
Kartu 189
Pertanyaan
Ethical basis for expert technical testimony?
Jawaban
Offer opinions only within your competence, disclose important assumptions and limitations, and distinguish facts from professional judgment.
Kartu 190
Pertanyaan
Meaning of a breakeven value?
Jawaban
The value of a selected variable that makes two alternatives economically equivalent or makes net worth zero. Other assumptions are held fixed.
Kartu 191
Pertanyaan
Derivative of $e^x$ ?
Jawaban
$\frac{d}{dx}e^x=e^x$
Kartu 192
Pertanyaan
First-law energy balance for a closed system with work positive out?
Jawaban
$\Delta E=Q-W$
$Q$ is heat into the system and $W$ is work done by the system; state a different sign convention before using it.
Kartu 193
Pertanyaan
Frequentist meaning of a 95% confidence procedure?
Jawaban
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.
Kartu 194
Pertanyaan
A needed value falls between handbook table entries. What is the cue?
Jawaban
Check whether interpolation is appropriate, keep both axes and units straight, and avoid extrapolating unless the source supports it.
Kartu 195
Pertanyaan
Derivative of $\ln x$ over the real domain?
Jawaban
$\frac{d}{dx}\ln x=\frac{1}{x}$
This real-valued form requires $x>0$ .
Kartu 196
Pertanyaan
Relationship between Celsius and kelvin temperature differences?
Jawaban
$1\,K$ of temperature difference equals $1\,^{\circ}C$ of temperature difference. Do not add $273.15$ to a difference.
Kartu 197
Pertanyaan
How should credit for team engineering work be assigned?
Jawaban
Accurately recognize each contributor's work and responsibility. Do not claim sole credit for a collaborative result.
Kartu 198
Pertanyaan
Main limitation of simple payback period?
Jawaban
It ignores the time value of money and usually ignores cash flows after payback. Discounted payback fixes the first issue, not the second.
Kartu 199
Pertanyaan
Roles of the null and alternative hypotheses?
Jawaban
The null states the baseline parameter claim tested; the alternative states the competing direction or difference supported when evidence is strong enough.
Kartu 200
Pertanyaan
Ideal-gas equation of state?
Jawaban
$pV=nRT$
Use absolute temperature and a gas constant consistent with pressure, volume, amount, and energy units.
Kartu 201
Pertanyaan
First check when reading a handbook table?
Jawaban
Read the title, column headings, units, notes, and basis conditions before selecting a value.
Kartu 202
Pertanyaan
Candidates for absolute extrema of a continuous function on a closed interval?
Jawaban
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.
Kartu 203
Pertanyaan
How should a sunk cost affect a current engineering-economy decision?
Jawaban
It should not affect the choice because it cannot be changed by the decision. Use future incremental cash flows instead.
Kartu 204
Pertanyaan
Convert Fahrenheit absolute temperature to Rankine?
Jawaban
$T_{^\circ R}=T_{^\circ F}+459.67$
Rankine uses the Fahrenheit-sized degree from absolute zero.
Kartu 205
Pertanyaan
Ohm's law for an ideal resistor?
Jawaban
$V=IR$
Use a consistent passive sign convention; $R$ is constant only over the assumed operating range.
Kartu 206
Pertanyaan
You have confidential details about a competitor's bid. Proper response?
Jawaban
Do not use or disclose improperly obtained information. Notify the appropriate procurement or ethics contact.
Kartu 207
Pertanyaan
Physical meaning of a definite integral $\int_a^b f(x)\,dx$ ?
Jawaban
It is signed accumulation of $f$ from $a$ to $b$ . Its units are the units of $f$ multiplied by the units of $x$ .
Kartu 208
Pertanyaan
Is a radian dimensionless?
Jawaban
Yes. It is the ratio of arc length to radius, so the length units cancel; keep $rad$ when it clarifies angular meaning.
Kartu 209
Pertanyaan
Electrical power absorbed under the passive sign convention?
Jawaban
$P=VI$
For a resistor, this also gives $P=I^2R=V^2/R$ when Ohm's law applies.
Kartu 210
Pertanyaan
Meaning of a p-value?
Jawaban
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.
Kartu 211
Pertanyaan
First check when reading a handbook graph?
Jawaban
Identify both axes, scales, units, curve labels, and any log scale before estimating a value.
Kartu 212
Pertanyaan
Difference between mass and weight?
Jawaban
Mass measures inertia; weight is gravitational force on that mass. Their dimensions and units are different.
Kartu 213
Pertanyaan
Kirchhoff's current law at a node?
Jawaban
The algebraic sum of currents at a node is zero. Choose one sign convention, such as currents entering positive, and apply it consistently.
Kartu 214
Pertanyaan
Evaluate $\int_a^b f(x)\,dx$ from an antiderivative $F$ ?
Jawaban
$\int_a^b f(x)\,dx=F(b)-F(a)$
This applies when $F'=f$ on the interval under the usual continuity conditions.
Kartu 215
Pertanyaan
Opportunity cost?
Jawaban
The value of the best forgone alternative. Include it when choosing one use of a scarce resource prevents another valuable use.
Kartu 216
Pertanyaan
Weight from mass in a gravitational field?
Jawaban
$W=mg$
Use compatible units; $g$ is local gravitational acceleration, not a universal constant for every location.
Kartu 217
Pertanyaan
Kirchhoff's voltage law around a closed loop?
Jawaban
The algebraic sum of voltage rises and drops around the loop is zero. Traverse the loop once with a consistent polarity convention.
Kartu 218
Pertanyaan
Decision rule using significance level $\alpha$ ?
Jawaban
Reject the null when the p-value is at most $\alpha$ ; otherwise fail to reject it. Failing to reject does not prove the null.
Kartu 219
Pertanyaan
Can proprietary methods from a former employer be reused freely?
Jawaban
Only if you have the legal right or permission to use them. General skill and experience may transfer; confidential proprietary material does not.
Kartu 220
Pertanyaan
Pound-force to newtons?
Jawaban
$1\,lbf\approx4.44822\,N$ . Use more digits only when the required precision justifies them.
Kartu 221
Pertanyaan
When does a definite integral equal ordinary geometric area?
Jawaban
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.
Kartu 222
Pertanyaan
Charge-voltage relation for an ideal capacitor?
Jawaban
$q=CV$
$C$ is capacitance in farads; $V$ is the voltage across the capacitor under the chosen polarity.
Kartu 223
Pertanyaan
Searching for a material or fluid property: what qualifiers often matter?
Jawaban
Material identity, phase, temperature, pressure, and composition. Use only the qualifiers relevant to that property source.
Kartu 224
Pertanyaan
Force produced when one slug accelerates at $1\,ft/s^2$ ?
Jawaban
$1\,lbf$ . Equivalently, $1\,lbf=1\,slug\cdot ft/s^2$ .
Kartu 225
Pertanyaan
Relationship among nominal rate $i$ , real rate $r$ , and inflation $f$ ?
Jawaban
$1+i=(1+r)(1+f)$
Keep cash-flow dollars and discount rates on the same real-or-nominal basis.
Kartu 226
Pertanyaan
Antiderivative of $x^n$ for $n\ne-1$ ?
Jawaban
$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C$
Kartu 227
Pertanyaan
Time constant of a first-order resistor-capacitor circuit?
Jawaban
$\tau=RC$
Use the resistance seen by the capacitor in the applicable first-order linear circuit.
Kartu 228
Pertanyaan
What physical quantity does pound-mass measure?
Jawaban
Mass. Do not substitute $lbm$ directly where a force unit such as $lbf$ is required.
Kartu 229
Pertanyaan
Type I error?
Jawaban
Rejecting a true null hypothesis. Its probability is controlled by the chosen significance level under the test assumptions.
Kartu 230
Pertanyaan
A search hit contains the right words. Is that enough?
Jawaban
No. Read the surrounding definition, equation label, units, and notes to confirm the hit answers the actual question.
Kartu 231
Pertanyaan
Annual straight-line depreciation from basis $B$ to salvage $S$ over $n$ years?
Jawaban
$D=\frac{B-S}{n}$
This is an accounting allocation, not a market-value forecast.
Kartu 232
Pertanyaan
Purpose of $g_c$ in some US customary force-mass equations?
Jawaban
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.
Kartu 233
Pertanyaan
Recognizable form of a separable first-order differential equation?
Jawaban
$\frac{dy}{dx}=g(x)h(y)$
Rearrange to place the $y$ terms with $dy$ and the $x$ terms with $dx$ , while checking for solutions lost by division.
Kartu 234
Pertanyaan
Using unverified software output in a safety-relevant calculation?
Jawaban
Check inputs, assumptions, units, and results with an independent method appropriate to the risk. The engineer remains responsible for professional judgment.
Kartu 235
Pertanyaan
Equivalent resistance of ideal resistors in series?
Jawaban
$R_{eq}=\sum_i R_i$
Series elements carry the same current with no branching node between them.
Kartu 236
Pertanyaan
Pressure conversion from psi to pascals?
Jawaban
$1\,psi\approx6894.76\,Pa$ . Keep enough significant figures for the problem's data.
Kartu 237
Pertanyaan
Type II error?
Jawaban
Failing to reject a false null hypothesis. Its probability is $\beta$ for a specified alternative.
Kartu 238
Pertanyaan
Useful flashcard to make after a failed handbook search?
Jawaban
A short scenario-to-search-cue card recording the section name and terms that eventually worked—not a copied problem or page number.
Kartu 239
Pertanyaan
Standard form of a first-order linear differential equation?
Jawaban
$\frac{dy}{dx}+P(x)y=Q(x)$
An integrating factor is $e^{\int P(x)\,dx}$ .
Kartu 240
Pertanyaan
Equivalent resistance of ideal resistors in parallel?
Jawaban
$\frac{1}{R_{eq}}=\sum_i\frac{1}{R_i}$
Parallel elements share the same two nodes and therefore the same voltage.
Kartu 241
Pertanyaan
Book value after $k$ years of straight-line depreciation?
Jawaban
$BV_k=B-kD$
Apply it within the depreciable life and do not depreciate below the assumed salvage value.
Kartu 242
Pertanyaan
Standard atmosphere in pascals?
Jawaban
$1\,atm=101{,}325\,Pa$ exactly.
Kartu 243
Pertanyaan
Using AI-generated technical content in engineering work?
Jawaban
Treat it as unverified input: protect confidential data, check sources and calculations, disclose use when required, and keep accountable human review.
Kartu 244
Pertanyaan
Trial form for a homogeneous linear ODE with constant coefficients?
Jawaban
Use $y=e^{rx}$ to obtain the characteristic polynomial in $r$ . Repeated or complex roots require the corresponding standard solution forms.
Kartu 245
Pertanyaan
Wave-speed relationship among frequency and wavelength?
Jawaban
$v=f\lambda$
Use frequency in cycles per second and wavelength in compatible length units.
Kartu 246
Pertanyaan
Statistical power?
Jawaban
The probability of rejecting the null when a specified alternative is true: $1-\beta$ . Larger effects, larger samples, or lower variability commonly increase power.
Kartu 247
Pertanyaan
Bar in pascals?
Jawaban
$1\,bar=100{,}000\,Pa$ exactly.
Kartu 248
Pertanyaan
How should handbook navigation be practiced before the FE exam?
Jawaban
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.
Kartu 249
Pertanyaan
Is depreciation itself a cash outflow?
Jawaban
No. It is a noncash accounting expense, though it can affect taxes and therefore after-tax cash flow.
Kartu 250
Pertanyaan
First-order linear approximation of $f(x)$ near $x=a$ ?
Jawaban
$f(x)\approx f(a)+f'(a)(x-a)$
It is most accurate for $x$ close to $a$ when higher derivatives stay bounded.
Kartu 251
Pertanyaan
Relationship between period and frequency?
Jawaban
$T=\frac{1}{f}$
This requires $f>0$ ; $T$ has time units.
Kartu 252
Pertanyaan
How should foreseeable environmental harm enter an engineering decision?
Jawaban
Identify and communicate it, follow applicable requirements, and consider practicable ways to reduce harm without compromising public safety.
Kartu 253
Pertanyaan
Foot-pound-force in joules?
Jawaban
$1\,ft\cdot lbf\approx1.35582\,J$ . This is a work or energy conversion; keep torque labeled as force times distance even though its dimensions match energy.
Kartu 254
Pertanyaan
Allowed range and sign meaning of Pearson correlation $r$ ?
Jawaban
$-1\le r\le1$ . The sign gives the direction of linear association, and magnitude measures its linear strength.
Kartu 255
Pertanyaan
When should you search instead of relying on recall?
Jawaban
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.
Kartu 256
Pertanyaan
After-tax effect of a deductible expense $E$ at marginal tax rate $t$ ?
Jawaban
The net cost is $E(1-t)$ under the simplified assumption that the deduction can be used fully in that period.
Kartu 257
Pertanyaan
Centered finite-difference approximation to $f'(x)$ ?
Jawaban
$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}$
For smooth $f$ , truncation error is proportional to $h^2$ before roundoff dominates.
Kartu 258
Pertanyaan
General material balance on a control volume?
Jawaban
$\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}$
At steady state, accumulation is zero; generation and consumption depend on reactions or sources.
Kartu 259
Pertanyaan
Approximate joules in one International Table Btu?
Jawaban
$1\,Btu_{IT}\approx1055.06\,J$ . Identify the Btu convention when precision matters.
Kartu 260
Pertanyaan
What is the defender in a replacement analysis?
Jawaban
The currently owned asset being compared with a proposed replacement. Its current market value is an opportunity cost; its original purchase price is sunk.
Kartu 261
Pertanyaan
Speaking publicly about a technical matter outside your expertise?
Jawaban
Limit claims to what you can support, identify the boundary of your expertise, and avoid implying qualifications you do not have.
Kartu 262
Pertanyaan
Single-interval trapezoidal approximation to an integral?
Jawaban
$\int_a^b f(x)\,dx\approx\frac{b-a}{2}[f(a)+f(b)]$
It is exact for linear $f$ .
Kartu 263
Pertanyaan
Energy efficiency of a device?
Jawaban
$\eta=\frac{\text{useful output energy}}{\text{input energy}}$
Use the same energy basis in numerator and denominator; a real passive device has $0\le\eta\le1$ .
Kartu 264
Pertanyaan
Purpose of sensitivity analysis in engineering economics?
Jawaban
It shows how the decision changes when an uncertain input changes. Vary inputs over plausible ranges while preserving units and model relationships.
Kartu 265
Pertanyaan
Can a strong correlation establish causation?
Jawaban
No. Correlation alone cannot rule out confounding, reverse direction, selection effects, or coincidence.
Kartu 266
Pertanyaan
Where should you confirm the tested topics for your FE discipline?
Jawaban
Use the discipline specification linked from the official NCEES FE exam hub. This common deck does not replace that discipline-specific boundary.
Kartu 267
Pertanyaan
Mechanical horsepower in watts?
Jawaban
$1\,hp\approx745.7\,W$ , based on $550\,ft\cdot lbf/s$ . Distinguish it from metric horsepower.
Kartu 268
Pertanyaan
Combine independent standard uncertainties $u_1,\ldots,u_n$ in a sum or difference?
Jawaban
$u_c=\sqrt{u_1^2+u_2^2+\cdots+u_n^2}$
This root-sum-square form assumes uncorrelated inputs and coefficients of magnitude one; otherwise include sensitivities and covariance.
Kartu 269
Pertanyaan
Newton iteration for a root of $f(x)=0$ ?
Jawaban
$x_{k+1}=x_k-\frac{f(x_k)}{f'(x_k)}$
It requires $f'(x_k)\ne0$ and a suitable starting value; convergence is not guaranteed.
Kartu 270
Pertanyaan
Meaning of slope in simple linear regression of $y$ on $x$ ?
Jawaban
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.
Kartu 271
Pertanyaan
Kilowatt-hour in joules?
Jawaban
$1\,kW\cdot h=3.6\times10^6\,J$ . It is energy, not power.
Kartu 272
Pertanyaan
Percent error relative to an accepted nonzero value?
Jawaban
$\%\,error=\left|\frac{x_{measured}-x_{accepted}}{x_{accepted}}\right|100\%$
The accepted value must be nonzero and both values must use compatible units.
Kartu 273
Pertanyaan
Does legal compliance alone settle an engineering ethics question?
Jawaban
No. Law sets mandatory boundaries, while professional duties can require stronger action, especially when safety, honesty, or conflicts are involved.
Kartu 274
Pertanyaan
Does handbook fluency replace discipline-specific problem practice?
Jawaban
No. Pair navigation and common recall with the current discipline specification and timed, rights-safe problems that match your selected FE discipline.
Kartu 275
Pertanyaan
Linear interpolation between $(x_1,y_1)$ and $(x_2,y_2)$ ?
Jawaban
$y\approx y_1+(y_2-y_1)\frac{x-x_1}{x_2-x_1}$
Use it between distinct $x$ values when local linear behavior is reasonable.
Kartu 276
Pertanyaan
Dimensional requirement for a physically meaningful additive equation?
Jawaban
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.

Open notebook with a calculator, ruler, drafting compass, and geometric solids on a dark engineering desk.

276 kartu