AP Calculus BC Final Exam Questions
and Answers
taking a continuous object and breaking it up to approximate (advantages,
disadvantages) - Correct Answers -disadvantage- more pieces to deal with
advantage- more accurate estimate
Calculus - Correct Answers -all about limits and the attempt of closing in on an exact
value of an answer by using finer and finer approximations
limit - Correct Answers -the idea of a limit is that we are attempting to see what the
output (y) approaches, if anything, as the input (x) approaches a particular value
limit (L) can be one of four things - Correct Answers --a number (if f(x) closes in on a
number)
-∞ (if f(x) goes up forever without approaching a horizontal asymptote)
- - ∞ (if f(x) goes down forever without approaching a horizontal asymptote)
-does not exist (if f(x) doesn't stabilize or imaginary or jumps)
three ways to determine limits - Correct Answers --graphically (examine the plot)
-numerically (substitute closer and closer values into x with calculator)
-algebraically (manipulating equations into a simpler form and sometimes use direct
substitution)
determine limits algebraically - Correct Answers -look at what's happening to the y-
coordinate as you close in on a particular x-value
two-sided limits - Correct Answers -function needs to be approaching the same y-value
from both the left and right to exist
one-sided limits - Correct Answers -only focus on the y-value from one particular side
determine limits numerically - Correct Answers -substitute in numbers closer and closer
to "c" and watching what happens to L
Determining Limits Algebraically (when x is not heading to infinite or - infinite) - Correct
Answers -break single large limit into several smaller easier limits
Sandwich or Squeeze Theorem - Correct Answers -if you are trying to determine the
limit of f(x) and can find a function g(x) ≤ f(x) and another function h(x) ≥ f(x), if g(x) and
h(x) have the same limit as c, then f(x) must also have the same limit as c
, rational function - Correct Answers -polynomial/polynomial
degree - Correct Answers -highest power x is raised to in a polynomial
leading coefficient - Correct Answers -coefficient in front of the highest power of x
# horizontal asymptotes for rational functions - Correct Answers -1
graphs get interrupted by discontinuities - Correct Answers -hole, single-point jump,
piecewise equations jumps, vertical asymptotes
removeable discontinuity - Correct Answers -if you could redefine just one point, can
turn into function with no breaks
non-removeable discontinuity - Correct Answers -limit at discontinuity is either infinite, -
infinite, or DNE→ non-removable- either jump discontinuities (limit does not exist) or
infinite discontinuities (limit is infinite or - infinite)
Intermediate Value Theorem (for continuous functions) - Correct Answers -if f(x) is
continuous everywhere on [a,b] then the graph visits every y-value from f(a) to f(b) at
least once
velocity - Correct Answers -vector (direction and magnitude)
speed - Correct Answers -scalar (only magnitude)
average speed - Correct Answers -distance traveled/ change in time
Initial Value Problem (IVP) - Correct Answers -need 1) differential equation 2) any point
the solution goes through (initial value condition)
Slope Fields - Correct Answers -visual representation of all solutions by showing lots of
little slopes (dashed lines of road)
Euler's Method - Correct Answers -a graphical approach to approximating the solution
to an IVP
indefinite integral - Correct Answers -does not include limits of integration
U-Substitution - Correct Answers -a technique to undo the chain rule
U Substitution with Definite Integrals - Correct Answers -change limits of integration
before integrating because the limits need to also be for u, not for x
and Answers
taking a continuous object and breaking it up to approximate (advantages,
disadvantages) - Correct Answers -disadvantage- more pieces to deal with
advantage- more accurate estimate
Calculus - Correct Answers -all about limits and the attempt of closing in on an exact
value of an answer by using finer and finer approximations
limit - Correct Answers -the idea of a limit is that we are attempting to see what the
output (y) approaches, if anything, as the input (x) approaches a particular value
limit (L) can be one of four things - Correct Answers --a number (if f(x) closes in on a
number)
-∞ (if f(x) goes up forever without approaching a horizontal asymptote)
- - ∞ (if f(x) goes down forever without approaching a horizontal asymptote)
-does not exist (if f(x) doesn't stabilize or imaginary or jumps)
three ways to determine limits - Correct Answers --graphically (examine the plot)
-numerically (substitute closer and closer values into x with calculator)
-algebraically (manipulating equations into a simpler form and sometimes use direct
substitution)
determine limits algebraically - Correct Answers -look at what's happening to the y-
coordinate as you close in on a particular x-value
two-sided limits - Correct Answers -function needs to be approaching the same y-value
from both the left and right to exist
one-sided limits - Correct Answers -only focus on the y-value from one particular side
determine limits numerically - Correct Answers -substitute in numbers closer and closer
to "c" and watching what happens to L
Determining Limits Algebraically (when x is not heading to infinite or - infinite) - Correct
Answers -break single large limit into several smaller easier limits
Sandwich or Squeeze Theorem - Correct Answers -if you are trying to determine the
limit of f(x) and can find a function g(x) ≤ f(x) and another function h(x) ≥ f(x), if g(x) and
h(x) have the same limit as c, then f(x) must also have the same limit as c
, rational function - Correct Answers -polynomial/polynomial
degree - Correct Answers -highest power x is raised to in a polynomial
leading coefficient - Correct Answers -coefficient in front of the highest power of x
# horizontal asymptotes for rational functions - Correct Answers -1
graphs get interrupted by discontinuities - Correct Answers -hole, single-point jump,
piecewise equations jumps, vertical asymptotes
removeable discontinuity - Correct Answers -if you could redefine just one point, can
turn into function with no breaks
non-removeable discontinuity - Correct Answers -limit at discontinuity is either infinite, -
infinite, or DNE→ non-removable- either jump discontinuities (limit does not exist) or
infinite discontinuities (limit is infinite or - infinite)
Intermediate Value Theorem (for continuous functions) - Correct Answers -if f(x) is
continuous everywhere on [a,b] then the graph visits every y-value from f(a) to f(b) at
least once
velocity - Correct Answers -vector (direction and magnitude)
speed - Correct Answers -scalar (only magnitude)
average speed - Correct Answers -distance traveled/ change in time
Initial Value Problem (IVP) - Correct Answers -need 1) differential equation 2) any point
the solution goes through (initial value condition)
Slope Fields - Correct Answers -visual representation of all solutions by showing lots of
little slopes (dashed lines of road)
Euler's Method - Correct Answers -a graphical approach to approximating the solution
to an IVP
indefinite integral - Correct Answers -does not include limits of integration
U-Substitution - Correct Answers -a technique to undo the chain rule
U Substitution with Definite Integrals - Correct Answers -change limits of integration
before integrating because the limits need to also be for u, not for x
