ALL Flashcards
What is a Complex number?
combination of a real number added with an imaginary number (a+bi)
What are Real numbers? Are they a subset of any other types?
All numbers except imaginary (not a subset)
What are Rational Numbers? Are they a subset of any other types?
All numbers that are real (not i) and do not extend forever (pi, Sqrt(2)) - this is a subset of Real numbers
What are Irrational Numbers? Are they a subset of any other types?
Numbers that extend forever (pi, sqrt(2)) - this is a subset of Real numbers.
What are Natural Numbers? Are they a subset of any other types?
Whole, positive numbers (also called Whole Numbers? counting numbers?) - this is the most exclusive subset of numbers.
What are Integers? Are they a subset of any other types?
Whole numbers (includes negatives, I.E. Natural Numbers and their additive inverse). - This is a subset of Real numbers and a subset of Rational Numbers.
What are Imaginary numbers? Are they a subset of any other types?
sqrt of negative numbers, i. (not a subset)
What is a Conjugate?
Two sets of numbers that, for one set are added and the second set subtracted. (2+sqrt(2) and 2-sqrt(2) are conjugates).
You can multiply something by it’s conjugate to get squares (E.G., (x-y)*(x+y) = x^2 - y^2. This becomes even more useful when dealing with complex numbers (5-4i multiplied with it’s conjugate becomes 41)
Sometimes annotated with a line over the variable, sometimes with an asterisk*
What is a quotient?
“results obtained by dividing”
What are other names for the length and angle of a vector?
Length: Magnitude, Absolute Value, Modulus
Angle: Argument note: argument is also the name of the term/expression on which a function operates (e.g. for y=LOGa(x), x is the argument.
What is the Quadratic Formula?
[-b +/- sqrt(b^2 - 4ac)]/2a
Which is the difference between <2, 3> and (2, 3)
<2, 3> is a vector whereas (2, 3) is an ordered pair (which could be a point on a graph rather than the vector from (0, 0) to that point)
What is the equation of a parabola written in Vertex Form?
y = a(x-h)^2 + k (I think this is also called standard form? The other is called the general form..)
the vertex of the parabola is (h, k), and a is where the parabola crosses the y axis (set x=0 and solve).
If the vertex is not known but the “roots” (y=0) are, then you can write the equation as y = a(x-r1)(x-r2) where r1 and r2 are the two roots, then you can expand this to the quadratic formula, use algebra to equate h and k to b and c (a is still a), and then re-write in vertex form.. spoiler alert: h=b/(-2a) and k=c-ah^2. This process is known as “completing the square”
what is the general form of a parabola?
y = ax^2 + bx + c
What are Permutations (probability), and what is the basic equation?
Used when forming a subset and order matters (e.g., listing number of options for filling out a baseball lineup where batting order matters given a certain roster size)
n!/(n-k)! where n = number of options & k = number of selections. (e.g., for a baseball team with 26 players, the number of 9-man lineup permutations is 26!/(26-9)!
)
What are Combinations (probability)
Used when forming a subset and order does not matter (e.g., listing the number of options for starters of a soccer match given a certain roster size)
n!/(k!(n-k)!) where n = number of options and k = number of selections. (e.g. for establishing 11 starters from a 16 man roster - ignoring positions - the number of possible combinations is 16!/(11!(16-11)! )
What is the Euclidean Algorithm and how do you use it?
It is a method for determining the highest possible common divisor. To do it, you divide the larger number by the smaller number which results in a number and a remainder. You then divide the previous denominator by the remainder and continue this until the remainder is 0. At that point, your previous remainder is the highest common divisor.
E.G. for 21 and 35: 35/21=1r14 21/14=1r7 14/7=2r0 so the highest common divisor is 7.
The highest number of possible steps required is 5 times the number of digits in the smaller number, so in the example that would be 5x2, or 10 steps. If you go 10 steps and still have a remainder, the numbers have no common divisor.
What is Least Common Multiple (LCM)?
The lowest number that can be divided by two given numbers.
E.G, the LCM of 45 and 120 is 360
What is an additive inverse
The number you would add to get back to zero. E.G. The additive inverse of 69 is -69
What is a geometric sequence?
In a geometric sequence, any term (other than the first) can be divided by the previous term to obtain a common ratio. The next term is then determined by multiplying by that ratio.
What is an arithmetic sequence?
A sequence where each term differs from the previous term by a constant amount (e.g., 3, 6, 9, 12,…)
An=n(x) where x is the difference in each step (3 for the example above)
What is a Fibonacci sequence?
A sequence where each term is the sum of the two previous terms, and the first two terms are both 1
(1, 1, 2, 3, 5, 8,…)
What is a Lucas sequence?
A sequence where each term is the sum of the two previous terms, and the first two terms are 1 & 3
(1, 3, 4, 7, 11, …)
What does “Composition of Functions” describe?
using the output of one function as input for another e.g. g(f(x)) ; This is different from g(x)*f(x) or g(x)+f(x)
What is the Associative Process?
States that the sum or product of two real numbers is the same regardless of order.
What does “take the square” mean?
take the square root (not ‘square the value’)
What is the Range of a function?
It describes the possible output of a function (if y=ax+b, the range would be all possible values of y)
What is the domain of a function?
It describes the possible input of a function (if y=ax+b, the domain would be all possible values of x)
If a parabola’s vertex is on the x-axis, what do we know?
We know that (b^2-4ac) = 0 (because there is only one root: [-b^2+/-sqrt(b^2-4ac)] / 2a would solve for the roots, and if b^2-4ac is equal to anything other than zero, then there would be two different answers..)
We know that k=0 (if written in vertex form).
What is the slope of a line perpendicular to the line y=ax+b?
the slope of a perpendicular line must be the negative reciprocal, meaning when multiplied by the slope of the known line, the product must equal -1. So the answer is -1/a
what is the equation for a line in slope-intercept form?
y=ax+b
what is the equation for a line in standard form?
ax+by=c where a is always a positive whole number (must multiply everything by -1 if a is negative, and must multiply by the denominator if it’s a fraction or decimal)
solve for x where y=LOGb(x)
x=b^y
solve for x where y=a^x
x=LOGa(y)
True or False: A logarithm can yield a negative value
True: log(a)=y can be rewritten as a=10^y, so if y can be negative if a is less than 1
True or False: A logarithm can process a negative value
False: log(a)=y can be rewritten as a=10^y, so a will never be negative or zero.
True or False: Log(ax)=Log(a)+Log(x)
True
True or False: Log(a/x)=Log(a)+Log(x)
False: Log(a/x)=Log(a)-Log(x) (minus, not plus)
True or False: Log(ax)=Log(a)*Log(x)
False: Log(ax)=Log(a)+Log(x)
Compute LOG4(32)
2.5: LOG4(32) = LOG(32)/LOG(4)
What is the derivative of 5/(2x^3)?
rewrite as 5/2(x^-3), then the derivative becomes -3(5/2)*(x^-4), which is -15/(2x^4)
How do you determine the equation for the line tangent to a curve at a given point on the curve?
Take the derivative of the function, then plug in the X value for the point you are interested in. This is the slope of the line. You then plug that X into the original equation to determine Y for that X: you now know the slope of the line and one point that the line crosses through so you can use that to determine the y-intercept and write the line in slope-intercept form.
eg. if f’(x) @ x=3 = (2/3) and f(x) @ x=3 = 7, we can plug this into the equation to get 7=(2/3)(3)+b, so b=5 making the slope-intercept equation of the line become y=(2/3)x+5
How do you determine the instantaneous rate of change of a line?
Take the derivative of the equation and plug in the x for the given point of interest (same as determining the slope of the tangent line at that point)
What is the equation to determine the average rate of change of a function over a given interval?
[f(a+h)-f(a)]/h where a=starting point and h=difference between starting and ending point (e.g. if finding the average from x=2 to x=5, a=2, h=3). THERE IS NO NEED TO TAKE A DERIVATIVE! This uses the ‘position’ function and estimates average velocity change without using calculus.
If the equation represents position, this is literally just finish position minus starting position divided by time to get from start to finish, which would be your average speed (velocity) over that distance.
How do you determine the maximum value of an equation?
Take the derivative and set it = 0. The derivative is the rate of change, so any time a function reaches a max/min, the slope of the line will be 0 at that point so you can find all max/mins by setting the derivative = 0.
How do you determine max/min point of a function, and how do you know if those points are local maximums or minimums?
Take the derivative and set it equal to zero to find local max/mins, then take another derivative and plug in those Xs to determine if the slope was positive or negative.
If the second derivative at that point is negative, it’s a local maximum, and if the second derivative is positive it’s a local maximum.
What is lim(x->2) asking
What does the function approach as x goes to 2 from the right side of x (i.e. counting backwards).
If you want to know the limit as you approach from the “left” (counting forwards) you would write lim(x->2^-) where there is a minus in the exponent position to indicate you want to approach it from the left.
How do you write the equation for a secant line?
You would be asked to find the secant line through two x values, so just solve the equation for those given values to find the corresponding y values. At that point you have two known points of a line and you just write the equation for that line (solve for the rise/run (m) between those two points, then use one point to solve for b and you’ll have y=mx+b)
What is the point of a secant line?
Secant lines are intro to calculus. you pick two points on a curve and determine the slope, then continue moving one point towards the other and watch what the slope does as you approach. This is equivalent to taking a derivative, but assumes you don’t yet know how to do that.
What is the difference between hyperbolic geometry and euclidean geometry?
1) Where Euclidean geometry says that, for a given line and a point not on that line, there exists only one line which can run through point P and be parallel to the line, hyperbolic geometry says there are at least two parallel lines, plus an infinite level of ultra-parallels (which I envision as projections onto the original two lines, but I don’t fully understand yet)
2) the sum of all angles in a triangle must be LESS than 180 (they must equal 180 for Euclidean geometry). In fact, you can use the formula pi-(sum of the angles) to calculate the surface area of a polygon in hyperbolic geometry.
Define Similar and Congruent
These terms are used in reference to geometry. Congruent means exactly the same (same size and shape). Similar means same shape (angles) but different sizes.
What is the difference between elliptic geometry and euclidean geometry?
Elliptic geometry is basically spherical geometry, which is, for the most part, opposite of hyperbolic geometry.
One key difference is that Euclidean says there can only be one line that goes through point P that is not on line L which is parallel to line L, but elliptic geometry says no parallel lines exist (picture drawing two lines around a sphere - eventually they have to cross twice)
What is the equation of a circle with a center point of (5,3) and a radius of 7?
(x-5)^2+(y-3)^2=49 (the equation is (x-h)^2+(y-k)^2=r^2
What are the lifespan requirements for engineering facilities?
80 years or more for the building, 20-40 years for the “support” equipment (HVAC, Boilers, etc.)
What is the art and science of measurement and control of the process variables in a production or manufacturing area?
Instrumentation
What does an Ammeter measure?
electrical current (amps!) in a circuit.
can consider Ammeter to be the shortened version of Amp-meter
What does a Voltmeter measure?
voltage or potential difference between two points in a circuit
What does an Ohmmeter measure?
electrical resistance through a circuit
What is the process of manufacturing a material in multiple layers to achieve improved properties (strength, sound insulation, etc) in a composite material called?
Lamination. This is an example of molding.
What manufacturing processes is inkjet printing an example of?
imaging and coating
What manufacturing process is shell molding an example of?
Casting - it uses an expendable sand mold
What manufacturing process is stamping an example of?
Forming
In programing, what is the difference between “while” and “do..while”
“while” checks for a given condition before executing a statement.
“Do…while” allows for execution of a loops before checking a condition
What does a Break Statement do in programming?
It forces a stop to a loop and resumes programming at the next statement.
What does a Continue Statement do in programming?
It forces the next iteration of a loop to begin without processing the remaining statements within the loop.
If a molecule accepts H+ ions, is it an acid or a base?
It’s a base: higher acidity means more hydrogen ions, so if a molecule is accepting additional hydrogen it must be more basic.
If a molecule is an H+ donor, is it an acid or a base?
An H+ donor is an acid
Which theory states that acids are substances that produce Hydrogen ions and bases produce hydroxide ions?
Lewis, Arrhenius, or Bronsted-Lowry
Arrhenius Theory
An Arrhenius acid increases the number of protons in a solution.
HCL dissolved in water is an Arrhenius acid because Hydrogen and Chloride disassociate in solution.
Which theory states that acids are proton donors and bases are proton acceptors?
Lewis, Arrhenius, or Bronsted-Lowry
Bronsted-Lowry Theory
Which theory states that acids are electron pair acceptors and bases are electron pair donors?
Lewis, Arrhenius, or Bronsted-Lowry
Lewis Theory
What is the hydronium ion concentration if pH=1? what about pH=3?
pH=-LOG(H+) so H+=10^(-pH)
pH=1 corresponds to a concentration of 0.1 moles/L (10^-1)
pH=3 corresponds to a concentration of 0.001 moles/L (10^-3)
What is the pH of something described as alkaline?
greater than 7 (7 is neutral, less than 7 is acidic. greater than 7 may also be described as basic..)
How do you calculate pH if you know the concentration of hydrogen ions?
pH = -log(H+)
Which of the following is the color range change for Bromthymol Blue, and what colors does it change from/to?
- 0-9.8
- 0-7.6
- 8-5.4
- 1-4.4
6.0-7.6, changes from yellow (acidic) to blue (basic)
Which of the following is the color range change for Phenolphthalein, and what colors does it change from/to?
- 0-9.8
- 0-7.6
- 8-5.4
- 1-4.4
8.0-9.8, changes from colorless (acidic) to pink (basic)
Which of the following is the color range change for Bromcresol Green, and what colors does it change from/to?
- 0-9.8
- 0-7.6
- 8-5.4
- 1-4.4
3.8-5.4, changes from yellow (acidic) to blue (basic)
Which of the following is the color range change for Methyl Orange, and what colors does it change from/to?
- 0-9.8
- 0-7.6
- 8-5.4
- 1-4.4
3.1-4.4, changes from red (acidic) to yellow (basic)
In probability, what does “intersection” mean and what is it’s symbol?
It means the set of outcomes that are in both sets. The symbol is upside-down capital U.
If A={1, 2, 3} and B={3, 4, 5} the intersection would be {3}
In probability, what does “union” mean and what is it’s symbol?
It means the combination of all outcomes of two sets, the Symbol is U.
If A={1, 2, 3} and B={3, 4, 5} the Union (A U B) would be {1, 2, 3, 4, 5}
in probability, what does capital C mean?
It means “choose”. 16C10 means you have 16 options and you choose 10 from those.
The equation for this is the same as a combination: n!/(k!*(n-k)!).
If you have 13 HB eggs and 10 “normal eggs”, and you select 6 eggs, how would you calculate the probability that all eggs are hard boiled?
13’C’6 / 23’C’6
The probability is the number of combinations (not permutations) that could be made from only selecting from HB eggs, divided by the number of possible combinations when selecting from both eggs.
Define random sampling
using a sampling method in which each member of the sampling pool has an equal chance of being selected.
Define systematic sampling
sampling one ever ‘nth’. So if you have 100 people and you want to sample 5, you might sample #12, 24, 36, 48, and 60.
Define convenience sampling
use data that is readily and easily obtained.
Define descriptive statistics
collecting, organizing, and analyzing data and not making generalizations and predictions from the data collected.
What is the elementary charge of an electron?
1.60 x 10^-19 Coulomb
True or False: Joules = Watts * Seconds
True. Watts = Joules / second
What is the equivalent total resistance of resistors R1 and R2 when connected in parallel?
1/Req = 1/R1 + 1/R2 - resistance can be measured in ohms
What is the equivalent total resistance of resistors R1 and R2 when connected in series?
R1 + R2 - resistance can be measured in ohms
True or False: V=I/R
False: V=IR (voltage = current * resistance)
Voltage measured in volts, current measured in amps, and resistance measured in ohms
What is a Coulomb?
The quantity of electricity conveyed in one second by a current of 1A.
What is the relationship between Coulomb, Joule, and Volt?
Coulomb = Joule/Volt = Joule / (amp * ohm)
Define Coulomb’s Law
Determines the magnitude of electrostatic force exerted by A on B at a distance r.
Fe = kqAqB/r^2 where
- qA and qB are the charges of A and B
- k is the Coulomb constant (8.9910^9 Nm^2/C^2)
- Fe is the electrostatic force
What is the 1st law of Thermodynamics?
Energy and Matter cannot be created or destroyed, but can change forms.
What is the 2nd law of Thermodynamics?
Total entropy of an isolated system can never decrease over time. Entropy remains constant, or is undergoing a reversible process.
Which has more entropy? Ice, Water, or Steam?
Steam - entropy is a measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work. Gas particles have higher kinetic energy than a liquid or solid, and have more space available to move faster and more randomly
Symbol for entropy is S:
Sgas»_space; Sliquid > Ssolid
Describe Metallic Bonding
Metallic Bonding is a type of covalent bonding that specifically occurs between atoms of metals in which the electrons are free to move throughout the lattice.
Why is water able to dissolve many different substances?
since water is polar (and therefore partially charged) its molecules attract ions that are oppositely charged and the charged parts of other polar substances.
Dissolving into solution has more to do with bonding and charges than molecular mass or the size of a molecule
Which is stronger: Ionic or Covalent bonds?
Covalent bonds are stronger: they occur when one subatomic particle is shared between two atoms keeping them very tightly bonded.
Metallic bonds are similar to covalent, except instead of sharing an electron pair, one electron from each atom is free to “roam” throughout the lattice. This is a strong bond, but slightly weaker than covalent bonds
Ionic bonds occur between two oppositely charged particles (ions).
All of these are stronger than hydrogen bonding (a dipole-dipole bond), which is stronger than Van der Waals forces (which are the weakest type of bond).
True or False: Metals lose electrons
True: metals lose electrons to form cations (positively charged ions) in order to form stable octlet (8 electrons in outer shell). They absorb energy in an endothermic process to lose these electrons.
Therefor, a metal’s electron affinity (how tightly it holds onto electrons) is lower than that of non-metals
True of False: Non-Metals lose electrons
False: non-metals gain electrons to form anions (negatively charge ions) so they can have a stable octlet (8 electrons in outer shell)
Non-metals release energy (exothermic) in order to gain electrons.
True or False: a Non-Metal’s electron affinity is higher than a Metal’s
True: a metal is prepared to lose an electron to form cations, so it must hold on less-tightly to it’s electrons which means metals have lower affinity than non-metals
True or False: Electron Affinity increases as you move upward and from left to right on the periodic table
True. This is also true for increasing electronegativity.
True or False: Electron Affinity increases as you move downward and from right to left on the periodic table
False - it’s the opposite.
How many electrons can be present in each of the first three rings?
First ring = 2
Second ring = 8
Third ring = 18
4th = 32
Looking at the periodic table can help remember this: the rows correspond to the number of rings. The first row only has two elements, the 2nd has 8, and the 4th has 18 (not sure why the 3rd doesn’t also have 18
What is a valence electron?
Number of electrons in an outer shell.
If the outer shell is full, the element tends to be inert.
If it has one or two electrons more than a full shell, it tends to be highly reactive due to the ease of removing those electrons to form cations.
If it is one or two electrons short of a full shell, it tends to be reactive due to the ease of gaining missing electrons and forming anions or alternatively covalent bonds.
What happens under Alpha decay?
The element basically loses a Helium atom, therefore Mass decreases by 4 and protons reduce by 2.
What happens under -Beta decay?
Beta decay is the addition/subtraction of neutrons without changing the mass. Negative beta means it’s losing a neutron, so the element must gain a proton to maintain its mass.
What happens under +Beta decay?
Beta decay is the addition/subtraction of neutrons without changing the mass. Positive beta means it’s gaining a neutron, so the element must lose a proton to maintain its mass.
What happens under gamma decay?
Mass and protons stay the same.
Which reaction requires more energy to sustain: fission or fusion
Fusion produces more energy, but also requires more energy to continue.
Which reaction produces less radioactive waste: fission or fusion
fusion would produce less radioactive waste
Which reaction’s reactants are more easily obtainable: fission or fusion
Fusion: it uses lighter molecules which are much more plentiful than the heavy molecules used in fission.
Which reaction continues indefinitely on its own: fission or fusion
Fission: it is started by bombarding a particle with a neutron, and the reaction produces additional neutrons which will then spark their own fission reaction, and so on..
When an element is listed with two numbers to the left of it, what is the top number and what is the bottom number?
The top number is the mass, and the bottom number is the atomic number. This is opposite of how it is displayed in the periodic table.
Which is stronger: hydrogen bonding or dipole-dipole
They are the same. Hydrogen bonding is a form of dipole-dipole attraction
What is the equation for the force applied by a spring
F=kx where k is the spring constant and x is the distance compressed
What is the equation for kinetic energy?
0.5*mv^2 where m is mass and v is velocity.
It’s the integral of momentum. Momentum (p) is p=mv integrating for velocity results in 1/2mv^2.
What is the inverse of -5?
The additive inverse (aka “opposite”) is 5
The multiplicative inverse is -1/5 (multiplying by the multiplicative inverse should yield 1)
What is Successive Approximation
Successive Approximation is an approach to problem solving where repeated approximations are performed. Each approximation builds on the preceding one until the desired degree of accuracy is achieved.
What is the result of multiplying a matrix by its inverse?
The result is the identity matrix, which has 1s from the top left to the bottom right with zeros everywhere else. For a 2x2 matrix that’s [(1,0);(0,1)]
How would you solve LOG(x) = 3/2LOG(16)-2/3LOG(8)
3/2log(16) can be re-written as Log(16^(3/2)) or log(sqrt(16^3)). Similarly, -2/3LOG(8) can be re-written as -LOG(8^(2/3))
The two LOGs can be combined into one to be LOG((sqrt(16^3)/(8^(2/3)).
In this equation, X is inside the log so you only have to solve for the portion on the right inside the log, which equates to 16.
Which mathematician proved the Pythagorean theorem and that the sum of the angles of a triangle = 180?
Euclid
Describe a histogram that is “skewed left”
This means that the mean and median is to the left of the mode. Or, more easily understood, the “tail” of the graph is on the left. This would put the “spike” of the bell curve on the right side of the distribution.
In Thermodynamics, define:
c
C
Q
c is specific heat (heat required to raise one gram by 1*). Equal to C/m
C is heat capacity (heat needed to raise the temperature of a body 1* - in SI this is Kelvin..). Equal to c*m.
Q is heat gained or lost by the system. Q=C(T2-T1)
Define extensive property
A property that depends on mass or quantity.
Examples: Mass, Volume, Entropy
What is the standard temperature for an ideal gas?
0C, or 273K
What is standard pressure for an ideal gas?
1 ATM, or 101.3kpa
What is the volume of 1 mole of gas at STP?
22.4L
What is the Ideal Gas equation?
PV=nRT
PressureVolume = substance amountideal gas constant*Temp
What is enthalpy?
Measure of the change in heat. Exothermic reactions are giving off heat, and therefore enthalpy is decreasing. E.G., a burning candle is giving off heat, which means enthalpy is decreasing.
What reactions occur in an electrochemical cell and where?
Oxidation and Reduction.
The reduction reaction occurs at the positive location (Cathode).
The oxidation reaction occurs at the negative location (anode).
What reactions occur in an electrochemical cell and where?
Oxidation and Reduction.
The reduction reaction occurs at the positive location (Cathode).
The oxidation reaction occurs at the negative location (anode).
Define intensive property.
Properties of a (thermodynamic) system that do not depend on the quantity of matter (non-extensive). An example is boiling point.
How do you calculate the length change of a given beam/bar due to force?
convert the force to pressure/stress (F/A) and divide by E, then multiply by initial length.
strain = deformation / initial length = stress / E (young’s modulus)
Key things to know:
Stress = Force/Area (pressure, basically..)
Strain = deltaL / L (change in length divided by original length)
Young’s Modulus = stress/strain - sometimes annotated as E, sometimes as Y
If you can remember this, then you can solve for what’s missing out of the group (either force, area, change in length, initial length, or young’s modulus)
define strain
change in length divided by initial length
This is the same as stress (pressure) / E (young’s modulus)
define stress
F/A
Define Abstraction (estimation practice)
Abstraction is choosing compact representations that hide unimportant details to reveal important features.
Define Divide and Conquer (estimation practice)
Divide and Conquer reasoning is dividing a large problem into manageable sub-problems.
What is a realistic constraint?
Anything that might be a constraint/restriction to engineering solutions. Examples can include safety features, costs, environmental impact, available resources, or political opposition. However, if, for example, the estimated cost is $10M and the budget is $30M, cost is no longer a constraint.
What are the major steps to the iterative design process.
identifying the design problem, formulate the design concept, make improvements to selected designs, and fully developing one idea.
In QA, what is an example of validation?
developing a process that can control specifications within a tight range
in QA, what is an example of assuring product specifications?
Identifying specifications derived from a customer survey; Creating a set of specification or procedures to control production.
In QA, what is an example of gathering customer input?
Talking to friends/family/customers about what characteristics they look for in a product.
What are the guiding principles for engineers?
- uphold the dignity of man
- avoid buttressing social systems that perform poorly and should be replaced
- avoid dangerous or uncontrolled side effects and by-products
- make provisions for consequence when technology fails
- participate in formulating the “why” of technology
What are the levels of Bloom’s Taxonomy?
From bottom to top: remember ; understand ; apply ; analyze ; evaluate ; create
How do you do synthetic division of polynomials? (e.g. (x^3+2x+3)/(x-3)
first you set the divisor = 0 and solve (find the root) - the solution is placed outside the “L” (in this example it is 3). Inside you put the coefficient for each of the “Xs” (in this example it would be 1 0 2 3).
You then start by carrying down the leading coefficient unchanged (in this example the 1 moves down). For the rest, you multiply the carried down number by the root (outside the L), and add it to the next number (0+13) and carry that down. The last number is the remainder For this problem it’s 2+33=11, 3+11*3=36).
The final answer is 1 3 11 r36. This can be re-written as x^2+3x+11+36/(x-3)
What is the equation for the potential energy of a compressed spring?
f=0.5*kx^2 where k is the spring constant and x is the distance compressed.
This is the integral of the force required to compress it (f=kx).
Which is a key principle of ethics, equity, and responsibility?
1) Society drives technological change, while changing technologies in turn shape society.
2) Some Technological Decisions put environmental and economic concerns in competition with one another, while others have positive effects for both the economy and the environment.
3) Information technology is evolving rapidly, enabling ever-increasing amounts of information and data to be stored, managed, enhanced, analyzed, and accessed through a wide array of devices in various media formats.
4) Technology by itself is neither good nor bad, but its use may affect others.
Technology by itself is neither good nor bad, but its use may affect others
Which is a key principle of the interaction of technology and humans?
1) Information technology is evolving rapidly, enabling ever-increasing amounts of information and data to be stored, managed, enhanced, analyzed, and accessed through a wide array of devices in various media formats.
2) Some Technological Decisions put environmental and economic concerns in competition with one another, while others have positive effects for both the economy and the environment.
3) Society drives technological change, while changing technologies in turn shape society.
4) Technology by itself is neither good nor bad, but its use may affect others.
Society drives technological change, while changing technologies in turn shape society.
Which is a key principle of the effects of technology on the natural world?
1) Technology by itself is neither good nor bad, but its use may affect others.
2) Information technology is evolving rapidly, enabling ever-increasing amounts of information and data to be stored, managed, enhanced, analyzed, and accessed through a wide array of devices in various media formats.
3) Society drives technological change, while changing technologies in turn shape society.
4) Some Technological Decisions put environmental and economic concerns in competition with one another, while others have positive effects for both the economy and the environment.
Some Technological Decisions put environmental and economic concerns in competition with one another, while others have positive effects for both the economy and the environment.
Which is a key principle of the effects of technology on the world of information and knowledge?
1) Information technology is evolving rapidly, enabling ever-increasing amounts of information and data to be stored, managed, enhanced, analyzed, and accessed through a wide array of devices in various media formats.
2) Some Technological Decisions put environmental and economic concerns in competition with one another, while others have positive effects for both the economy and the environment.
3) Technology by itself is neither good nor bad, but its use may affect others.
4) Society drives technological change, while changing technologies in turn shape society.
Information technology is evolving rapidly, enabling ever-increasing amounts of information and data to be stored, managed, enhanced, analyzed, and accessed through a wide array of devices in various media formats.
Which is a materials factor that influences the design of engineering products?
1) Smart Technology
2) Customer Requirements
3) Values
4) Recycling
Smart Technology
Which is a customer specification factor that influences the design of engineering products?
1) Smart Technology
2) Customer Requirements
3) Values
4) Recycling
Customer Requirements
Which is a cultural factor that influences the design of engineering products?
1) Smart Technology
2) Customer Requirements
3) Values
4) Recycling
Values
Which is an environmental need that influences the design of engineering products?
1) Smart Technology
2) Customer Requirements
3) Values
4) Recycling
Recycling
How many years of work experience must an engineer have to sit for the PE Exam?
4 years
Which of the following tests options in ethical decision making?
- harm
- publicity
- reversibility
- defensibility
- virtue
All except for (maybe?) virtue.
Which is an example of Team Communication in a multidisciplinary team environment?
1) Participation: Understanding of and willingness to be fully involved in team efforts.
2) Feedback: Giving and receiving constructive criticism.
3) Defining a Problem: Identifying and articulating the problem to be solved.
4) Judgement / Using Facts: Reaching conclusions based upon clear analysis of facts and ideas.
5) Conflict Management: Principles of problem-based conflict management
Feedback.
Which is an example of Collaboration?
1) Participation: Understanding of and willingness to be fully involved in team efforts.
2) Feedback: Giving and receiving constructive criticism.
3) Defining a Problem: Identifying and articulating the problem to be solved.
4) Judgement / Using Facts: Reaching conclusions based upon clear analysis of facts and ideas.
5) Conflict Management: Principles of problem-based conflict management
Participation
AND
Conflict Management
Which is an example of Team Decision Making?
1) Participation: Understanding of and willingness to be fully involved in team efforts.
2) Feedback: Giving and receiving constructive criticism.
3) Defining a Problem: Identifying and articulating the problem to be solved.
4) Judgement / Using Facts: Reaching conclusions based upon clear analysis of facts and ideas.
5) Conflict Management: Principles of problem-based conflict management
Defining the Problem
AND
Judgement
Which is an example of how and engineer can demonstrate they only perform services in the area of their competence?
1) Engineers shall approve only those engineering documents that are in conformity with applicable standards
2) Engineers shall undertake assignments only when qualified by education or experience in the specific technical fields involved.
3) Engineers may express publicly technical opinions that are founded upon knowledge of the facts and competence in the subject matter.
4) Engineers shall disclose all known potential conflicts of interest that could influence or appear to influence their judgement or the quality of their services.
Engineers shall undertake assignments only when qualified by education or experience in the specific technical fields involved.
Which is an example of how and engineer can demonstrate they hold paramount the safety, health, and welfare of the public?
1) Engineers shall approve only those engineering documents that are in conformity with applicable standards
2) Engineers shall undertake assignments only when qualified by education or experience in the specific technical fields involved.
3) Engineers may express publicly technical opinions that are founded upon knowledge of the facts and competence in the subject matter.
4) Engineers shall disclose all known potential conflicts of interest that could influence or appear to influence their judgement or the quality of their services.
Engineers shall approve only those engineering documents that are in conformity with applicable standards
Which is an example of how and engineer can demonstrate they only issue public statements in an objective and truthful manner?
1) Engineers shall approve only those engineering documents that are in conformity with applicable standards
2) Engineers shall undertake assignments only when qualified by education or experience in the specific technical fields involved.
3) Engineers may express publicly technical opinions that are founded upon knowledge of the facts and competence in the subject matter.
4) Engineers shall disclose all known potential conflicts of interest that could influence or appear to influence their judgement or the quality of their services.
Engineers may express publicly technical opinions that are founded upon knowledge of the facts and competence in the subject matter.
Which is an example of how an engineer can demonstrate they act for each employer or client as faithful agents or trustees?
1) Engineers shall approve only those engineering documents that are in conformity with applicable standards
2) Engineers shall undertake assignments only when qualified by education or experience in the specific technical fields involved.
3) Engineers may express publicly technical opinions that are founded upon knowledge of the facts and competence in the subject matter.
4) Engineers shall disclose all known potential conflicts of interest that could influence or appear to influence their judgement or the quality of their services.
Engineers shall disclose all known potential conflicts of interest that could influence or appear to influence their judgement or the quality of their services.
How many ‘Fundamental Canons’ of Engineering Ethics are there, and what are they?
6:
1) hold paramount the safety, health, and welfare of the public.
2) Perform services only in the area of competence
3) Issue public statements only in an objective and truthful manner
4) Act for each employer or client as faithful agents or trustees
5) Avoid deceptive acts.
6) Conduct themselves honorably, responsibly, ethically, and lawfully so as to enhance the honor, reputation, and usefulness of the profession.
Which is an example of validation?
1) Improving a process that can control a cookies diameter in a tight range.
2) Specifications for a cookie that are derived from a customer survey and include size and texture.
3) Talking to friends and family about what characteristics they look for when buying cookies
4) Creating a set of instructions or procedures to control the production of cookies
Improving a process that can control a cookies diameter in a tight range.
Which is an example of assuring correct product specifications in quality assurance?
1) Improving a process that can control a cookies diameter in a tight range.
2) Specifications for a cookie that are derived from a customer survey and include size and texture.
3) Talking to friends and family about what characteristics they look for when buying cookies
4) Creating a set of instructions or procedures to control the production of cookies
Specifications for a cookie that are derived from a customer survey and include size and texture.
AND
Creating a set of instructions or procedures to control the production of cookies
Which is an example of gathering customer input in a quality assurance program?
1) Improving a process that can control a cookies diameter in a tight range.
2) Specifications for a cookie that are derived from a customer survey and include size and texture.
3) Talking to friends and family about what characteristics they look for when buying cookies
4) Creating a set of instructions or procedures to control the production of cookies
Talking to friends and family about what characteristics they look for when buying cookies
A -> B+C is an example of which kind of chemical reaction?
1) Decomposition
2) Synthesis
3) Single Replacement
4) Double Replacement
5) Combustion
Decomposition
A+B -> B is an example of which kind of chemical reaction?
1) Decomposition
2) Synthesis
3) Single Replacement
4) Double Replacement
5) Combustion
Synthesis
A+BC -> AC+B is an example of which kind of chemical reaction?
1) Decomposition
2) Synthesis
3) Single Replacement
4) Double Replacement
5) Combustion
Single Replacement
AB+CD -> AC+BD is an example of which kind of chemical reaction?
1) Decomposition
2) Synthesis
3) Single Replacement
4) Double Replacement
5) Combustion
Double Replacement
CHO+O2 -> CO2+H20+Energy is an example of which kind of chemical reaction?
1) Decomposition
2) Synthesis
3) Single Replacement
4) Double Replacement
5) Combustion
Combustion
Combustion occurs when any carbon compound made of C, H, and O is burned in the presence of oxygen and produced carbon dioxide and water along with energy.
Is c3h6o3 a valid empirical formula?
No - an empirical formula represents the lowest whole-number ratio of elements in a compound. In this case it needs to be divided by 3 to form ch2o.
Definition of Empirical Formula: A formula giving the proportions of the elements present in a compound but not the actual numbers or arrangement of atoms.
Who first arranged the periodic table based on atomic number rather than increasing atomic mass?
John Dalton Henry Moseley Dmitri Mendeleev Neils Bohr Geiger-Marsden Alexander Fleming Louis Pasteur
Henry Moseley
Dmitri Mendeleev is credited with first arranging the elements in order of increasing atomic mass
Geiger-Marsden discovered that the nucleus of the atom is solid
Alexander Fleming discovered penicillin
Louis Pasteur discovered that microorganisms cause diseases, as well as the development of vaccines to inoculate against diseases such as small pox.
John Dalton developed the early spherical model of the atom
Niels Bohr developed the theory of quantized nature of the electron orbital.
What distinguishes computer-integrated manufacturing from other principles of manufacturing?
1) means for data storage, retrieval, manipulation, and presentation
2) mechanisms for sensing state and modifying process
3) algorithms for uniting the data processing component with the sensor/modification component
Note: use of robotic technology is (apparently..) used in several manufacturing methods..
How do you find the quotient of two vectors?
Divide the magnitude, subtract the angles/arguments.
E.G.: (12,60) / (6,15) = (2,45*)
How do you determine how long it will take for money to double when compounded continuously at 3.5%?
The equation to use is A=Pe^(rt) where A is the total value, P is the starting value, r is the rate, and t is time (usually in years).
For this question, A = 2P (double the starting value), so the equation becomes 2P = Pe^(.035t). Solve for t..
LN(2)/0.035 = t= 19.8 years
What is a Rhombus?
A shape with four equal sides. Squares are a subset of Rhombuses.
What is a Parallelogram?
A quadrilateral with two pairs of parallel sides. This results in two sets of equal (same length) sides.
What are the minor and major axes of the following:
y=sqrt[(-x^2 + 16)/16]
Do this one of two ways. One is to set y=0 and solve for X, then set x=0 and solve for y. Each should yield two equal and opposite numbers, and the axes is the sum of the two (diameter, not radius..). Note that if the center of the ellipse is not (0,0), then you’ll have to set (x-h)=0 and (y-k)=0.
The schools will want you to remember the equation for an ellipse as:
(x-h)^2/a^2 + (y-k)^2/b^2=1
and have you re-write the equation in this form. a and b are the “radii” so double them to get the axes.
In this example, the equation becomes x^2+16y^2=16, which means a=4 and b=1, so the minor and major axes are 2 and 8.
Use calculator to determine the variance of the following set of ages of 11 men:
31 42 38 34 37 38 60 37 39 47 49
Put the list into the calculator (stat -> edit), then have the calculator run the statistics (stat -> calc -> 1-var stats). This will report the standard deviation as SIGMAx and the sample deviation as Sx.
Since this is a complete set (nothing to suggest this is meant to be a sample-set of a larger set of men), the variance can be found by squaring the standard devation (SIGMAx). You can type that number in manually and square it, or pull it directly (vars -> statistics -> SIGMAx) and square it that way.
Answer = 60.45
Note that if it were a sample, you’d do it exactly the same way, but you’d square Sx instead.
Other key 1-var statistics reported are Xbar (the average), and lower down are min, med, max
Complete the square:
Ax^2+Bx+C=0
Completing the Square means converting into the form A(x+d)^2+e=0.
You can do this by recognizing that x^2+bx is a square that is x by x plus a rectangle that is x by b. You can then create an ‘almost’ square by adding half the rectangle to each side so that you end up with (x+b/2)^2. But, this is missing the bottom right square which is (b/2)^2. So… x^2+Bx can be re-written as (x+b/2)^2 - (b/2)^2.
Using some algebra from here you find that d=b/2a and e = c - b^2/4a. a is still a.
Describe Natural Transmutation
Transmutation is the conversion of one element into another by a process taking place in the nucleus. In Natural Transmutation, the element changes without another entity. There is only one element/entity on the left side of the equation/arrow (the reactant side).
Describe Artificial Transmutation
Transmutation is the conversion of one element into another by a process taking place in the nucleus. In Artificial Transmutation, there is a change in the number of protons of an element caused by another element/entity. There would be one or more element/entity on the left side of the equation/arrow (the reactant side).
What is Oxidation?
What is the oxidation number of oxygen in the carbonate ion found in Cu2CO3(OH)2
Oxidation is the loss of electrons. It does not have to involve oxygen.
The easiest way to determine the oxidation number for an element is to use the periodic table. Elements in column 1 will tend to lose one electron to form a stable outer ring, and will therefore have +1 Oxidation Number. Similarly elements in column 17 will gain one electron resulting in a -1 Oxidation Number.
Oxygen is in column 16, so it will tend to gain two electrons and have an oxidation number of -2.
How does the Proportional Reasoning method of estimation work?
Proportional reasoning involves thinking about relationships and making comparisons of quantities or values. For me, this type of estimation is really just using common sense or basic math. You might use proportional reasoning to estimate the cost of a tank of gas knowing the volume of the tank and the price/gallon..
How does the Symmetry and Conservation method of estimation work?
The key concept seems to be that symmetry greatly simplifies any problem to which it can be applied.
Other than this definition, this one is poorly defined and a google search produces nothing usable. The only example is the Gauss example where he recognizes that the sum of 1+2+3..+100 can be easily calculated by recognizing that adding them in reverse (1+100, 2+99, etc.) can be easily summed as 100x101 (they all add to 101), and you can then divide by 2.
What does NSTA stand for
National Science Teaching Association
What is the octet rule?
The octet rule refers to the tendency of atoms to prefer to have eight electrons in the valence shell.
How many molecules are in 1 mol?
6.022*10^23 This is Avogadro’s number
A beaker holds 50ml of a gas at 25C and 736mmHg. What would the volume be if the temperature were increased to 60C?
V1/T1=V2/T2 in Kelvin.
50/(25+273) = V2/(60+273) V2=55.8ml
Given a fixed container starting at the same pressure and temperature with a pinhole leak, which is correct?
1) Helium would leak faster than Argon
2) Argon would leak faster than Helium
3) They would leak at the rate
Helium would leak faster. Since Argon is heavier, it moves slower at the same temperature.
