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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 = cot(x)  y' =
2. methods of integration
y' = 1/(1 + x²)
? v(t) over interval a to b
1/(ba) ? f(x) dx on interval a to b
substitution  parts  partial fractions
3. y = ln(x)  y' =
4. trapezoidal rule
use tangent line to approximate values of the function
a^x ln(a)
v(dx/dt)² + (dy/dt)² not an integral!
use trapezoids to evaluate integrals (estimate area)
5. Quotient Rule
6. y = csc(x)  y' =
7. y = a^x  y' = y' =
derivative
a^x ln(a)
y' = 1/v(1  x²)
uv' + vu'
8. left riemann sum
use rectangles with leftendpoints to evaluate integral (estimate area)
0/0  8/8  8*0  8  8  1^8  0°  8°
logistic differential equation  M = carrying capacity
use ratio test  set > 1 and solve absolute value equations  check endpoints
9. Volume of solid with base in the plane and given crosssection
uv' + vu'
? A(x) dx over interval a to b  where A(x) is the area of the given crosssection in terms of x
Alternating series converges and general term converges with another test
y' = csc²(x)
10. Particle is moving to the right/up
velocity is positive
p ? r² dx over interval a to b  where r = distance from curve to axis of revolution
decreasing
zero
11. Average Rate of Change
Slope of secant line between two points  use to estimate instantanous rate of change at a point.
lim as n approaches zero of general term = 0 and terms decrease  series converges
? v(1 + (dy/dx)²) dx over interval a to b
use trapezoids to evaluate integrals (estimate area)
12. Second derivative of parametrically defined curve
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
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)
e^x
find first derivative  dy/dx = dy/dt / dx/dt  then find derivative of first derivative  then divide by dx/dt
13. Integral test
use ratio test  set > 1 and solve absolute value equations  check endpoints
if integral converges  series converges
v(dx/dt)² + (dy/dt)² not an integral!
y' = 1/x
14. Given v(t) find total distance travelled
e^x
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
? abs[v(t)] over interval a to b
chain rule
15. y = cos?¹(x)  y' =
16. y = e^x  y' = y' =
y' = csc(x)cot(x)
y' = 1/(x lna)
e^x
If f(1)=4 and f(6)=9  then there must be a xvalue between 1 and 6 where f crosses the xaxis.
17. slope of horizontal line
quotient rule
zero
general term = a1r^n  converges if 1 < r < 1
y' = 1/(1 + x²)
18. If f '(x) = 0 and f'(x) > 0 ...
Limit as x approaches a of [f(x)f(a)]/(xa)
critical points and endpoints
f(x) has a relative minimum
draw short segments representing slope at each point
19. definite integral
critical points and endpoints
0/0  8/8  8*0  8  8  1^8  0°  8°
has limits a & b  find antiderivative  F(b)  F(a)
? abs[v(t)] over interval a to b
20. indefinite integral
Slope of tangent line at a point  value of derivative at a point
no limits  find antiderivative + C  use inital value to find C
f(x) has a relative minimum
use rectangles with rightendpoints to evaluate integrals (estimate area)
21. Area inside one polar curve and outside another polar curve
y' = 1/v(1  x²)
uv  ? v du
y' = sin(x)
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
22. Volume of solid of revolution  washer
(uv'vu')/v²
? v (dx/dt)² + (dy/dt)² over interval from a to b
increasing
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
23. If g(x) = ? f(t) dt on interval 2 to x  then g'(x) =...
velocity is negative
uv' + vu'
f(x)
y' = cos(x)
24. Product Rule
25. To find absolute maximum on closed interval [a  b]  you must consider...
y' = csc(x)cot(x)
negative
relative minimum
critical points and endpoints
26. If f '(x) = 0 and f'(x) < 0 ...
f(x) has a relative maximum
concave down
e^x
A function and it's derivative are in the integrand
27. average value of f(x)
? f(x) dx integrate over interval a to b
integrand is a rational function with a factorable denominator
general term = 1/n^p  converges if p > 1
1/(ba) ? f(x) dx on interval a to b
28. [(h1  h2)/2]*base
A function and it's derivative are in the integrand
Area of trapezoid
positive
y' = csc²(x)
29. Fundamental Theorem of Calculus
general term = a1r^n  converges if 1 < r < 1
corner  cusp  vertical tangent  discontinuity
use trapezoids to evaluate integrals (estimate area)
? f(x) dx on interval a to b = F(b)  F(a)
30. When f '(x) is positive  f(x) is...
relative minimum
y' = 1/x
draw short segments representing slope at each point
increasing
31. use substitution to integrate when
32. P = M / (1 + Ae^(Mkt))
point of inflection
logistic growth equation
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)
uv  ? v du
33. dP/dt = kP(M  P)
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
use ratio test  set > 1 and solve absolute value equations  check endpoints
logistic differential equation  M = carrying capacity
concave up
34. When f '(x) is decreasing  f(x) is...
concave down
find first derivative  dy/dx = dy/dt / dx/dt  then find derivative of first derivative  then divide by dx/dt
critical points and endpoints
f(x)
35. Length of curve
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
y' = csc²(x)
y' = csc(x)cot(x)
? v(1 + (dy/dx)²) dx over interval a to b
36. y = sin(x)  y' =
37. 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
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.
general term = a1r^n  converges if 1 < r < 1
38. Formal definition of derivative
1/2 ? R²  r² over interval from a to b  find a & b by setting equations equal  solve for theta.
polynomial with infinite number of terms  includes general term
Limit as h approaches 0 of [f(a+h)f(a)]/h
point of inflection
39. To draw a slope field  plug (x y) coordinates into differential equation...
corner  cusp  vertical tangent  discontinuity
Limit as h approaches 0 of [f(a+h)f(a)]/h
draw short segments representing slope at each point
Alternating series converges and general term converges with another test
40. nth term test
if terms grow without bound  series diverges
? v(t) over interval a to b
y' = sin(x)
y' = sec(x)tan(x)
41. Limit comparison test
concave up
y' = csc(x)cot(x)
product rule
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite  then series behaves like comparison series
42. y = cos²(3x)
y' = csc(x)cot(x)
chain rule
y' = 1/v(1  x²)
relative minimum
43. Area inside polar curve
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
use trapezoids to evaluate integrals (estimate area)
critical points and endpoints
use rectangles with leftendpoints to evaluate integral (estimate area)
44. area below xaxis is...
negative
0/0  8/8  8*0  8  8  1^8  0°  8°
decreasing
uv  ? v du
45. Taylor series
polynomial with infinite number of terms  includes general term
y' = 1/v(1  x²)
use to find indeterminate limits  find derivative of numerator and denominator separately then evaluate limit
v(dx/dt)² + (dy/dt)² not an integral!
46. Use partial fractions to integrate when...
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
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)
integrand is a rational function with a factorable denominator
e^x
47. y = sin?¹(x)  y' =
48. area under a curve
y' = csc(x)cot(x)
1/2 ? r² over interval from a to b  find a & b by setting r = 0  solve for theta
Slope of tangent line at a point  value of derivative at a point
? f(x) dx integrate over interval a to b
49. y = tan?¹(x)  y' =
50. use integration by parts when...
if terms grow without bound  series diverges
separate variables  integrate + C  use initial condition to find C  solve for y
two different types of functions are multiplied
Limit as x approaches a of [f(x)f(a)]/(xa)