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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. y = ln(x)/x²  state rule used to find derivative
quotient rule
y' = 1/(x lna)
relative minimum
velocity is negative
2. slope of vertical line
logistic differential equation  M = carrying capacity
y' = 1/x
undefined
Alternating series converges and general term diverges with another test
3. Length of curve
? v(1 + (dy/dx)²) dx over interval a to b
polynomial with infinite number of terms  includes general term
Alternating series converges and general term converges with another test
velocity is negative
4. Particle is moving to the left/down
p ? r² dx over interval a to b  where r = distance from curve to axis of revolution
velocity is negative
Area of trapezoid
y' = 1/(x lna)
5. Intermediate Value Theorem
f(x) has a relative maximum
if terms grow without bound  series diverges
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
polynomial with finite number of terms  largest exponent is 6  find all derivatives up to the 6th derivative
6. Product Rule
7. Given velocity vectors dx/dt and dy/dt  find speed
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
critical points and endpoints
v(dx/dt)² + (dy/dt)² not an integral!
integrand is a rational function with a factorable denominator
8. trapezoidal rule
use trapezoids to evaluate integrals (estimate area)
y' = sin(x)
v(dx/dt)² + (dy/dt)² not an integral!
f(x) has a relative minimum
9. slope of horizontal line
zero
two different types of functions are multiplied
positive
general term = a1r^n  converges if 1 < r < 1
10. Taylor series
(uv'vu')/v²
y' = 1/x
y' = csc²(x)
polynomial with infinite number of terms  includes general term
11. Limit comparison test
f(x) has a relative maximum
p ? r² dx over interval a to b  where r = distance from curve to axis of revolution
if integral converges  series converges
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
12. Alternate definition of derivative
? f(x)  g(x) over interval a to b  where f(x) is top function and g(x) is bottom function
use tangent line to approximate values of the function
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
Limit as x approaches a of [f(x)f(a)]/(xa)
13. indefinite integral
no limits  find antiderivative + C  use inital value to find C
(uv'vu')/v²
use ratio test  set > 1 and solve absolute value equations  radius = center  endpoint
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
14. If g(x) = ? f(t) dt on interval 2 to x  then g'(x) =...
? v (dx/dt)² + (dy/dt)² over interval from a to b
separate variables  integrate + C  use initial condition to find C  solve for y
? v (dx/dt)² + (dy/dt)² over interval from a to b
f(x)
15. To draw a slope field  plug (x y) coordinates into differential equation...
? v(1 + (dy/dx)²) dx over interval a to b
draw short segments representing slope at each point
f(x)
y' = 1/x
16. Use partial fractions to integrate when...
f(x) has a relative maximum
y' = sec(x)tan(x)
integrand is a rational function with a factorable denominator
y' = 1/v(1  x²)
17. y = cos(x)  y' =
18. use integration by parts when...
negative
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
two different types of functions are multiplied
y' = 1/v(1  x²)
19. Volume of solid of revolution  washer
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
if integral converges  series converges
negative
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
20. Find interval of convergence
? v(1 + (dy/dx)²) dx over interval a to b
logistic differential equation  M = carrying capacity
use ratio test  set > 1 and solve absolute value equations  check endpoints
y' = sin(x)
21. Area inside one polar curve and outside another polar curve
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
separate variables  integrate + C  use initial condition to find C  solve for y
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
v(dx/dt)² + (dy/dt)² not an integral!
22. Area inside polar curve
corner  cusp  vertical tangent  discontinuity
? v (dx/dt)² + (dy/dt)² over interval from a to b
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
? v(1 + (dy/dx)²) dx over interval a to b
23. When f '(x) changes from negative to positive  f(x) has a...
relative minimum
p ? r² dx over interval a to b  where r = distance from curve to axis of revolution
use rectangles with leftendpoints to evaluate integral (estimate area)
find first derivative  dy/dx = dy/dt / dx/dt  then find derivative of first derivative  then divide by dx/dt
24. Alternating series tes
lim as n approaches zero of general term = 0 and terms decrease  series converges
decreasing
uv' + vu'
substitution  parts  partial fractions
25. Converges absolutely
has limits a & b  find antiderivative  F(b)  F(a)
f(x) has a relative minimum
Alternating series converges and general term converges with another test
integrand is a rational function with a factorable denominator
26. y = sec(x)  y' =
27. area under a curve
relative minimum
derivative
? f(x) dx integrate over interval a to b
Alternating series converges and general term converges with another test
28. When f '(x) is positive  f(x) is...
increasing
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
use tangent line to approximate values of the function
lim as n approaches zero of general term = 0 and terms decrease  series converges
29. Formal definition of derivative
A function and it's derivative are in the integrand
Limit as h approaches 0 of [f(a+h)f(a)]/h
two different types of functions are multiplied
if integral converges  series converges
30. y = ln(x)  y' =
31. area above xaxis is...
two different types of functions are multiplied
Slope of tangent line at a point  value of derivative at a point
positive
y' = sec²(x)
32. definite integral
has limits a & b  find antiderivative  F(b)  F(a)
? abs[v(t)] over interval a to b
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
zero
33. y = cos?¹(x)  y' =
34. y = tan?¹(x)  y' =
35. When is a function not differentiable
corner  cusp  vertical tangent  discontinuity
use ratio test  set > 1 and solve absolute value equations  radius = center  endpoint
f(x) has a relative maximum
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
36. Area between two curves
use to find indeterminate limits  find derivative of numerator and denominator separately then evaluate limit
polynomial with infinite number of terms  includes general term
? f(x)  g(x) over interval a to b  where f(x) is top function and g(x) is bottom function
y' = sin(x)
37. Volume of solid with base in the plane and given crosssection
p ? r² dx over interval a to b  where r = distance from curve to axis of revolution
y' = 1/(1 + x²)
? A(x) dx over interval a to b  where A(x) is the area of the given crosssection in terms of x
f(x) has a relative minimum
38. Eatio test
undefined
lim as n approaches 8 of ratio of (n+1) term/nth term > 1  series converges
derivative
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
39. rate
derivative
a^x ln(a)
y' = 1/v(1  x²)
1/(ba) ? f(x) dx on interval a to b
40. When f '(x) is negative  f(x) is...
(uv'vu')/v²
y' = 1/v(1  x²)
decreasing
relative minimum
41. To find particular solution to differential equation  dy/dx = x/y...
derivative
separate variables  integrate + C  use initial condition to find C  solve for y
? v(1 + (dy/dx)²) dx over interval a to b
uv  ? v du
42. Find radius of convergence
use ratio test  set > 1 and solve absolute value equations  radius = center  endpoint
use tangent line to approximate values of the function
? v(t) over interval a to b
Alternating series converges and general term diverges with another test
43. y = sin?¹(x)  y' =
44. When f '(x) is decreasing  f(x) is...
concave down
integrand is a rational function with a factorable denominator
polynomial with infinite number of terms  includes general term
logistic differential equation  M = carrying capacity
45. y = cos²(3x)
use tangent line to approximate values of the function
uv' + vu'
chain rule
use to find indeterminate limits  find derivative of numerator and denominator separately then evaluate limit
46. Particle is moving to the right/up
velocity is positive
logistic growth equation
y' = sec²(x)
critical points and endpoints
47. Linearization
integrand is a rational function with a factorable denominator
use trapezoids to evaluate integrals (estimate area)
uv' + vu'
use tangent line to approximate values of the function
48. 6th degree Taylor Polynomial
use ratio test  set > 1 and solve absolute value equations  check endpoints
A function and it's derivative are in the integrand
logistic differential equation  M = carrying capacity
polynomial with finite number of terms  largest exponent is 6  find all derivatives up to the 6th derivative
49. Indeterminate forms
quotient rule
use rectangles with leftendpoints to evaluate integral (estimate area)
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
0/0  8/8  8*0  8  8  1^8  0°  8°
50. use substitution to integrate when
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