Test your basic knowledge |

AP Calculus Bc

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 re-enforces your understanding as you take the test each time.

1. If f '(x) = 0 and f'(x) < 0 -...
general term = 1/n^p - converges if p > 1
f(x) has a relative maximum
y' = -csc(x)
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0 - 8

2. [(h1 - h2)/2]*base
concave up
y' = 1/(1 + x)
Area of trapezoid
derivative

3. y = e^x - y' = y' =
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
1/(b-a) ? f(x) dx on interval a to b
e^x
y' = 1/(x lna)

4. y = cos(x) - y' =
A function and it's derivative are in the integrand
y' = -csc(x)cot(x)
y' = -sin(x)
p ? r dx over interval a to b - where r = distance from curve to axis of revolution

5. When is a function not differentiable
undefined
y' = 1/x
corner - cusp - vertical tangent - discontinuity
y' = cos(x)

6. left riemann sum
use rectangles with left-endpoints to evaluate integral (estimate area)
negative
p ? R - r 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
product rule

7. Chain Rule
decreasing
f '(g(x)) g'(x)
velocity is positive
f(x)

8. To draw a slope field - plug (x -y) coordinates into differential equation...
draw short segments representing slope at each point
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
y' = -1/v(1 - x)
e^x

9. Limit comparison test
y' = cos(x)
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite - then series behaves like comparison series
general term = 1/n^p - converges if p > 1
y' = 1/x

10. Particle is moving to the right/up
y' = -1/v(1 - x)
polynomial with infinite number of terms - includes general term
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
velocity is positive

11. If f '(x) = 0 and f'(x) > 0 -...
use trapezoids to evaluate integrals (estimate area)
f(x) has a relative minimum
e^x
y' = -sin(x)

12. Indeterminate forms
(uv'-vu')/v
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0 - 8
y' = 1/(1 + x)
If f(1)=-4 and f(6)=9 - then there must be a x-value between 1 and 6 where f crosses the x-axis.

13. Product Rule
logistic growth equation
uv' + vu'
no limits - find antiderivative + C - use inital value to find C
? f(x) dx on interval a to b = F(b) - F(a)

14. y = sin(x) - y' =
no limits - find antiderivative + C - use inital value to find C
two different types of functions are multiplied
y' = cos(x)
a^x ln(a)

15. Volume of solid of revolution - washer
p ? R - r 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/v(1 - x)
speed
f(x)

16. Instantenous Rate of Change
general term = a1r^n - converges if -1 < r < 1
f(x) has a relative minimum
Slope of tangent line at a point - value of derivative at a point
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint

17. absolute value of velocity
uv' + vu'
speed
y' = sec(x)
f(x) has a relative minimum

18. Fundamental Theorem of Calculus
? f(x) dx on interval a to b = F(b) - F(a)
relative maximum
use ratio test - set > 1 and solve absolute value equations - check endpoints
p ? R - r 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

19. use substitution to integrate when
uv' + vu'
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
A function and it's derivative are in the integrand
1/(b-a) ? f(x) dx on interval a to b

20. dP/dt = kP(M - P)
logistic differential equation - M = carrying capacity
velocity is negative
f '(g(x)) g'(x)
has limits a & b - find antiderivative - F(b) - F(a)

21. Average Rate of Change
zero
a^x ln(a)
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
chain rule

22. Formal definition of derivative
y' = 1/x
corner - cusp - vertical tangent - discontinuity
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
Limit as h approaches 0 of [f(a+h)-f(a)]/h

23. Second derivative of parametrically defined curve
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
negative
critical points and endpoints
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0 - 8

24. Alternating series tes
logistic differential equation - M = carrying capacity
y' = 1/v(1 - x)
lim as n approaches zero of general term = 0 and terms decrease - series converges
f '(g(x)) g'(x)

25. Given velocity vectors dx/dt and dy/dt - find speed
speed
negative
v(dx/dt) + (dy/dt) not an integral!
? v(t) over interval a to b

26. nth term test
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
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
1/2 ? R - r over interval from a to b - find a & b by setting equations equal - solve for theta.

27. y = cos?(x) - y' =
if terms grow without bound - series diverges
uv - ? v du
relative maximum
y' = -1/v(1 - x)

28. Particle is moving to the left/down
? f(x) dx on interval a to b = F(b) - F(a)
velocity is negative
relative minimum
polynomial with infinite number of terms - includes general term

29. ? u dv =
e^x
uv - ? v du
relative minimum
y' = -1/(1 + x)

30. Area inside one polar curve and outside another polar curve
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
1/2 ? R - r over interval from a to b - find a & b by setting equations equal - solve for theta.
use tangent line to approximate values of the function
uv - ? v du

31. Intermediate Value Theorem
Area of trapezoid
If f(1)=-4 and f(6)=9 - then there must be a x-value between 1 and 6 where f crosses the x-axis.
a^x ln(a)
product rule

32. Given v(t) find total distance travelled
negative
Slope of tangent line at a point - value of derivative at a point
? f(x) dx on interval a to b = F(b) - F(a)
? abs[v(t)] over interval a to b

33. When f '(x) changes from increasing to decreasing or decreasing to increasing - f(x) has a...
point of inflection
uv' + vu'
y' = -csc(x)cot(x)
? v(t) over interval a to b

34. Taylor series
Area of trapezoid
zero
polynomial with infinite number of terms - includes general term
Slope of tangent line at a point - value of derivative at a point

35. indefinite integral
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
e^x
y' = cos(x)

36. y = cot?(x) - y' =
y' = -1/(1 + x)
use rectangles with right-endpoints to evaluate integrals (estimate area)
Limit as x approaches a of [f(x)-f(a)]/(x-a)
general term = a1r^n - converges if -1 < r < 1

37. y = cos(3x)
A function and it's derivative are in the integrand
quotient rule
chain rule
a^x ln(a)

38. rate
derivative
if integral converges - series converges
? v (dx/dt) + (dy/dt) over interval from a to b
a^x ln(a)

39. average value of f(x)
y' = -1/v(1 - x)
1/(b-a) ? f(x) dx on interval a to b
lim as n approaches zero of general term = 0 and terms decrease - series converges
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta

40. Length of curve
use rectangles with right-endpoints to evaluate integrals (estimate area)
f(x) has a relative minimum
? v(1 + (dy/dx)) dx over interval a to b
Alternating series converges and general term converges with another test

41. area above x-axis is...
use rectangles with right-endpoints to evaluate integrals (estimate area)
Slope of tangent line at a point - value of derivative at a point
positive
point of inflection

42. y = cot(x) - y' =
concave up
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
y' = -csc(x)

43. Quotient Rule
increasing
quotient rule
f(x) has a relative maximum
(uv'-vu')/v

44. Volume of solid of revolution - no washer
p ? r dx over interval a to b - where r = distance from curve to axis of revolution
corner - cusp - vertical tangent - discontinuity
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 cross-section in terms of x

45. y = sec(x) - y' =
? v (dx/dt) + (dy/dt) over interval from a to b
y' = sec(x)tan(x)
two different types of functions are multiplied
chain rule

46. Converges absolutely
speed
Alternating series converges and general term converges with another test
velocity is positive
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)

47. If g(x) = ? f(t) dt on interval 2 to x - then g'(x) =...
chain rule
increasing
f(x)
y' = -sin(x)

48. p-series test
use rectangles with left-endpoints to evaluate integral (estimate area)
y' = sec(x)tan(x)
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
general term = 1/n^p - converges if p > 1

49. methods of integration
Slope of tangent line at a point - value of derivative at a point
substitution - parts - partial fractions
undefined
y' = -sin(x)

50. mean value theorem
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)
use tangent line to approximate values of the function
derivative
concave down

Test your basic knowledge |

AP Calculus Bc

13 Skills Types | 550 Pages | Only $9.95 | PDF / EPub, Kindle Ready

Link to This Test

Related Subjects