Mathematics
Let's start off with a typical basic calculus question for a warmup. What is the slope of the tangent line to the graph of y = x^3 at the point (2,8) ?
12
The derivative function gives the slope of the tangent line to a function at a given point. In this case, dy/dx = 3x^2, which when evaluated at x = 2 gives 3*2^2 = 12.
What is the most common isotope of hydrogen?
A. Protium
B. Deuterium
C. Tritum
D. Hydrogen only has one isotope
A. Protium
•Rainbow is produced when sunlight fall on drops of rain. Which of the following physical phenomena are responsible for this?
I.Diffusion
II.Refraction
III.Internal reflection
II and III
How many founders are there?
7
Which of the following is not a known series used in calculus?
Simpson's Rule
A series is the sum of the terms in a sequence and can be definite or indefinite. Simpson's Rule is used to approximate definite integrals, not series.
All of the following elements are liquids around room temperature except which one?
A. Gallium
B. Magnesium
C. Bromine
D. Mercury
B. Magnesium
When light bends as it enters a different medium the process is known as what?
Refraction
What is NSBE Mission Statement?
"To increase the number of culturally responsible Black Engineers who excel academically, succeed professionally and positively impact the community."
What is the integral from -pi over 7 to Pi over 7 of Sin(x cubed)?
0
Please say you did NOT try to actually find the antiderivative here! Sin(xcubed)=-Sin((-x)cubed), so the area below the axis to the left of 0 is the same as the area above the axis to the right, and vice versa, so everything cancels leaving 0. On a somewhat related note, if a teacher or professor ever gives you a really really ugly integral, try answering 0. If they ask you how you got it, smile and say 'by symmetry'. They might be impressed!
Find dy/dx if y = e^a and a is constant.
0
Since there is no x-dependence in the equation, y is equal to a constant. Therefore, the derivative equals zero.
A drop of food coloring spreading out in a cup of water is an example of which transport process?
A. Diffusion
B. Osmosis
C. Vapor Pressure
D. Effusion
A. Diffusion
•Out of the following pairs, choose the pair in which the physical quantities do not have identical dimension?
A. Pressure and Young's modules
B.Planck's constant and Angular momentum
C. Impulse and moment of force
D. Force and rate of change of linear momentum
C. Impulse and moment of force
Two of the Founders of NSBE are?
Who is : Arthur Bond (Deceased)
Stanley L. Kirtley (Deceased)
John W. Logan, Jr
George A. Smith
Edward A. Coleman
Brian Harris
Anthony Harris (Brother founder)
Are the following statements true or false:
A. If a function is differentiable at 0, it is continuous there.
B. If a function is differentiable at 0, its derivative is continuous there?
A is true, but not B
For A: If f was NOT continuous, f(x+h)-f(x) would not approach 0, so the limit defined as the derivative could not exist. Therefore f must be continuous. For B: Take a function g to be 0 at 0 and (x squared times Sine (1 over x)) elsewhere. For x not 0, g' is 2x*Sine(1 over x)+Cos(1 over x), which oscillates wildly around 0. For x equals 0, we can compute the derivative limit directly and find it is 0. Therefore the derivative exists but is not continuous!
One of the essential minerals in the human body is salt. How much salt (NaCl) is in the average adult human body?
A. 1 Kg
B. 500 g
C. 250 g
D. none
C. 250g
True or false? Iron is attracted by magnets.
True
When was NSBE Founded?
When was 1975
If f(x) = x^3 - 2x^2 + 4x + 1, how many inflection points does this graph have?
1
It has one at x = 2/3, where the second derivative equals zero. The point is indeed an inflection point because the second derivative, 6x - 4, changes signs at x = 2/3 and thus the graph changes concavity.
Water-based liquids can be described as acidic, neutral, or basic, with respect to pH. Which of these describes milk?
A. Slightly Acidic
B. Stron Acid
C. Strong Basic
D. Milk does not have a pH
A. Slightly Acidic
Light year is a unit of what?
Distance
Explain the significance of the NSBE Logo.
The NSBE Torch symbolizes our everlasting burning desire to achieve success in this competitive society and to affect a positive change on the quality of life for all people. The lightning bolts represent the striking impact that will be felt by the Society and industry due to the contributions and accomplishments made by dedicated members of the National Society of Black Engineers.