Old School
"Classify pi as being a natural (N), whole (W),"
"integer (I), rational (Q), and/or irrational number (Q’)."
"Pi is an irrational number (Q’)."
"Factor the following polynomial: " 81n^2-64
(9n+8)(9n-8)
"Does " y=x^2 " represent " y " as a function of "x"?"
"If so, is the function one-to-one?"
"Yes, it is a function since it passes the VLT."
"No, it is not one-to-one since it fails the HLT."
"Write the equation of the line, in slope-intercept form, that passes through "
(-4,2) " and " (2,5).
y=1/2x+4
bb"True or False:" " My middle name is Jean."
"False. I do no have a middle name."
"Express the following in scientific notation."
9990000000
9.99*10^9
"Expand the following polynomial: " (7r+4)^2
49r^2+56r+16
"Let "f(x) = sqrt(3-x)+5. "Evaluate: " f(-1)
f(-1)=7
"Determine whether the following lines are parallel or perpendicular. "
-x+2y=-5 " and " y=1/2x+4
"They are parallel."
"Evaluate " f(-4) ", " f(2) " and " f(4) " given that: "
k(x)={(-1/2x+5,if,x<0),(4,if,0<=x<=2),(1/2x-4,if,x>2):}
f(-4) = 7
f(2) = 4
f(4) = -2
"Evaluate the following expression."
(4^2-4)/(2/3)(2/9+2/18)^2+(20-4)^(1/4)
4
"Factor the following polynomial: " 27s^3+64
(3s+4)(9s^2-12s+16)
"Let "g(x) = 5-x^2. "Evaluate: "
(g(x+h)-g(x))/h
(g(x+h)-g(x))/h = -2x+h
"Given a slope of "1/2", write the equation of a perpendicular line,"
" in slope-intercept form, that contains " (1,-2).
y=-2x
"Solve the following equation."
s^(3/4) = 64
s = 256
"Simplify the following expression."
sqrt(8)/(sqrt(8)+sqrt(2))
2/3
"Factor the following polynomial: " (80t^11)^(1/4)
2t(5t^7)^(1/4)
"Write the domain, in interval notation, of: "
f(x) = (x+5)/(x^2-x-6)
"Domain: " (-oo,-2)cup(-2,3)cup(3,oo)
"Sonyville's population has been growing linearly. In 2014, the population was 4,200"
"people. Currently, the population has grown to 7,600 people."
"According to the function, predict the population for next year and interpret."
"The population will reach 8,280 people in 2020."
"AROC (Slope): The population has increased by 680 people per year."
"Solve the following system of equations. "
-2(12+4x)=12y
1+5/9y+7/18x=0
(6, -6)
"Solve. Write the solution in interval notation."
-1/2abs(4h-5)<-3
(-oo, -1/4)cup(11/4,oo)
"Solve. State extraneous solutions if any."
2x^-4 - x^-2 = 6
"Extraneous Solution: " x^-2=-3/2
x=+-sqrt(2)/2
"Let "f(x) = x^3-64. "Find the inverse. State the domains and ranges for both functions."
"Evaluate: " f^-1(0)
f^-1(0)=4
"Domain: " (-oo,oo)
"Range: " (-oo,oo)
"Same for both."
"Find the average rate of change of " y=(x^3-27)/(x-3)
"over the interval " [2,4].
9
"For four (4) points extra credit, differentiate the following function:"
f(x)=x+e^x
f'(x)=1+e^x