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