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.

Tác giả Open Study Contributor

Về bộ thẻ này

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.

Thẻ trong bộ này

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