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Test your basic knowledge 
AP Calculus Bc
Start Test
Study First
Subjects
:
math
,
ap
,
calculus
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it reenforces your understanding as you take the test each time.
1. Length of parametric curve
use ratio test  set > 1 and solve absolute value equations  check endpoints
logistic growth equation
? v (dx/dt)² + (dy/dt)² over interval from a to b
Limit as h approaches 0 of [f(a+h)f(a)]/h
2. If f '(x) = 0 and f'(x) < 0 ...
f(x) has a relative maximum
decreasing
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
? v(1 + (dy/dx)²) dx over interval a to b
3. dP/dt = kP(M  P)
logistic differential equation  M = carrying capacity
A function and it's derivative are in the integrand
Limit as h approaches 0 of [f(a+h)f(a)]/h
? abs[v(t)] over interval a to b
4. definite integral
concave down
velocity is positive
use rectangles with rightendpoints to evaluate integrals (estimate area)
has limits a & b  find antiderivative  F(b)  F(a)
5. Volume of solid of revolution  washer
(uv'vu')/v²
y' = csc²(x)
1/(ba) ? f(x) dx on interval a to b
p ? R²  r² dx over interval a to b  where R = distance from outside curve to axis of revolution  r = distance from inside curve to axis of revolution
6. 6th degree Taylor Polynomial
use ratio test  set > 1 and solve absolute value equations  check endpoints
if f(x) is continuous and differentiable  slope of tangent line equals slope of secant line at least once in the interval (a  b) f '(c) = [f(b)  f(a)]/(b  a)
polynomial with finite number of terms  largest exponent is 6  find all derivatives up to the 6th derivative
negative
7. Converges absolutely
uv  ? v du
negative
Alternating series converges and general term converges with another test
f(x) has a relative minimum
8. Quotient Rule
9. y = sin(x)  y' =
10. y = csc(x)  y' =
11. left riemann sum
Slope of tangent line at a point  value of derivative at a point
concave up
use rectangles with leftendpoints to evaluate integral (estimate area)
logistic growth equation
12. Geometric series test
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
Area of trapezoid
? v (dx/dt)² + (dy/dt)² over interval from a to b
general term = a1r^n  converges if 1 < r < 1
13. If g(x) = ? f(t) dt on interval 2 to x  then g'(x) =...
use ratio test  set > 1 and solve absolute value equations  check endpoints
f(x)
y' = 1/x
speed
14. Fundamental Theorem of Calculus
e^x
? f(x) dx on interval a to b = F(b)  F(a)
y' = sec(x)tan(x)
polynomial with finite number of terms  largest exponent is 6  find all derivatives up to the 6th derivative
15. To draw a slope field  plug (x y) coordinates into differential equation...
draw short segments representing slope at each point
logistic differential equation  M = carrying capacity
y' = csc(x)cot(x)
relative minimum
16. y = cot(x)  y' =
17. average value of f(x)
1/(ba) ? f(x) dx on interval a to b
y' = sin(x)
draw short segments representing slope at each point
? abs[v(t)] over interval a to b
18. When f '(x) is decreasing  f(x) is...
logistic differential equation  M = carrying capacity
if f(x) is continuous and differentiable  slope of tangent line equals slope of secant line at least once in the interval (a  b) f '(c) = [f(b)  f(a)]/(b  a)
concave down
? v(1 + (dy/dx)²) dx over interval a to b
19. trapezoidal rule
general term = a1r^n  converges if 1 < r < 1
use trapezoids to evaluate integrals (estimate area)
two different types of functions are multiplied
undefined
20. Indeterminate forms
y' = sin(x)
y' = cos(x)
0/0  8/8  8*0  8  8  1^8  0°  8°
? A(x) dx over interval a to b  where A(x) is the area of the given crosssection in terms of x
21. y = tan(x)  y' =
22. pseries test
y' = csc²(x)
general term = 1/n^p  converges if p > 1
f(x) has a relative minimum
positive
23. rate
polynomial with infinite number of terms  includes general term
f(x)
derivative
decreasing
24. Alternating series tes
if terms grow without bound  series diverges
use to find indeterminate limits  find derivative of numerator and denominator separately then evaluate limit
lim as n approaches zero of general term = 0 and terms decrease  series converges
relative minimum
25. Alternate definition of derivative
Limit as x approaches a of [f(x)f(a)]/(xa)
Alternating series converges and general term diverges with another test
? v (dx/dt)² + (dy/dt)² over interval from a to b
? f(x)  g(x) over interval a to b  where f(x) is top function and g(x) is bottom function
26. When is a function not differentiable
0/0  8/8  8*0  8  8  1^8  0°  8°
e^x
relative maximum
corner  cusp  vertical tangent  discontinuity
27. To find absolute maximum on closed interval [a  b]  you must consider...
general term = a1r^n  converges if 1 < r < 1
Alternating series converges and general term diverges with another test
critical points and endpoints
e^x
28. To find particular solution to differential equation  dy/dx = x/y...
f(x) has a relative maximum
y' = cos(x)
separate variables  integrate + C  use initial condition to find C  solve for y
if integral converges  series converges
29. Converges conditionally
use ratio test  set > 1 and solve absolute value equations  radius = center  endpoint
? abs[v(t)] over interval a to b
Alternating series converges and general term diverges with another test
polynomial with infinite number of terms  includes general term
30. y = x cos(x)  state rule used to find derivative
concave up
v(dx/dt)² + (dy/dt)² not an integral!
y' = 1/(1 + x²)
product rule
31. Particle is moving to the right/up
velocity is positive
negative
Alternating series converges and general term diverges with another test
e^x
32. y = a^x  y' = y' =
a^x ln(a)
A function and it's derivative are in the integrand
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
y' = 1/(x lna)
33. y = cos?¹(x)  y' =
34. Average Rate of Change
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
undefined
35. Length of curve
? v(1 + (dy/dx)²) dx over interval a to b
p ? R²  r² dx over interval a to b  where R = distance from outside curve to axis of revolution  r = distance from inside curve to axis of revolution
Limit as x approaches a of [f(x)f(a)]/(xa)
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
36. When f '(x) changes fro positive to negative  f(x) has a...
Area of trapezoid
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
y' = sec(x)tan(x)
relative maximum
37. y = tan?¹(x)  y' =
38. P = M / (1 + Ae^(Mkt))
y' = 1/(1 + x²)
find first derivative  dy/dx = dy/dt / dx/dt  then find derivative of first derivative  then divide by dx/dt
zero
logistic growth equation
39. Intermediate Value Theorem
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
y' = sec(x)tan(x)
? v (dx/dt)² + (dy/dt)² over interval from a to b
lim as n approaches 8 of ratio of (n+1) term/nth term > 1  series converges
40. use integration by parts when...
two different types of functions are multiplied
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
if terms grow without bound  series diverges
41. slope of vertical line
A function and it's derivative are in the integrand
general term = a1r^n  converges if 1 < r < 1
undefined
critical points and endpoints
42. When f '(x) changes from negative to positive  f(x) has a...
relative minimum
critical points and endpoints
two different types of functions are multiplied
point of inflection
43. Area between two curves
e^x
uv' + vu'
Area of trapezoid
? f(x)  g(x) over interval a to b  where f(x) is top function and g(x) is bottom function
44. When f '(x) is increasing  f(x) is...
lim as n approaches zero of general term = 0 and terms decrease  series converges
concave up
velocity is negative
Limit as h approaches 0 of [f(a+h)f(a)]/h
45. Find interval of convergence
use ratio test  set > 1 and solve absolute value equations  check endpoints
? abs[v(t)] over interval a to b
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
find first derivative  dy/dx = dy/dt / dx/dt  then find derivative of first derivative  then divide by dx/dt
46. Linearization
use tangent line to approximate values of the function
negative
0/0  8/8  8*0  8  8  1^8  0°  8°
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
47. right riemann sum
y' = sin(x)
? v (dx/dt)² + (dy/dt)² over interval from a to b
uv' + vu'
use rectangles with rightendpoints to evaluate integrals (estimate area)
48. Eatio test
Alternating series converges and general term diverges with another test
lim as n approaches 8 of ratio of (n+1) term/nth term > 1  series converges
y' = 1/v(1  x²)
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
49. Instantenous Rate of Change
velocity is negative
logistic growth equation
Slope of tangent line at a point  value of derivative at a point
uv' + vu'
50. [(h1  h2)/2]*base
? v(1 + (dy/dx)²) dx over interval a to b
use rectangles with rightendpoints to evaluate integrals (estimate area)
Area of trapezoid
Alternating series converges and general term converges with another test