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. right riemann sum
use rectangles with right-endpoints to evaluate integrals (estimate area)
use ratio test - set > 1 and solve absolute value equations - check endpoints
? v(t) over interval a to b
y' = -csc(x)cot(x)

2. Converges absolutely
positive
? v(t) over interval a to b
Alternating series converges and general term converges with another test
concave up

3. y = tan(x) - y' =
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta
? v (dx/dt) + (dy/dt) over interval from a to b
if integral converges - series converges
y' = sec(x)

4. dP/dt = kP(M - P)
negative
logistic differential equation - M = carrying capacity
f(x) has a relative maximum
Alternating series converges and general term diverges with another test

5. Chain Rule
f(x)
f(x) has a relative minimum
f '(g(x)) g'(x)
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit

6. Eatio test
draw short segments representing slope at each point
general term = 1/n^p - converges if p > 1
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
? v (dx/dt) + (dy/dt) over interval from a to b

7. y = ln(x)/x - state rule used to find derivative
y' = sec(x)
quotient rule
y' = -csc(x)cot(x)
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt

8. If f '(x) = 0 and f'(x) > 0 -...
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite - then series behaves like comparison series
f(x) has a relative minimum
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
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0 - 8

9. methods of integration
substitution - parts - partial fractions
undefined
concave down
use trapezoids to evaluate integrals (estimate area)

10. Limit comparison test
product rule
use rectangles with right-endpoints to evaluate integrals (estimate area)
two different types of functions are multiplied
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite - then series behaves like comparison series

11. ? u dv =
uv - ? v du
y' = -1/(1 + x)
y' = 1/(1 + x)
Alternating series converges and general term converges with another test

12. Length of curve
uv - ? v du
? v(1 + (dy/dx)) dx over interval a to b
A function and it's derivative are in the integrand
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges

13. nth term test
if terms grow without bound - series diverges
use rectangles with right-endpoints to evaluate integrals (estimate area)
a^x ln(a)
Area of trapezoid

14. Given v(t) find displacement
quotient rule
1/(b-a) ? f(x) dx on interval a to b
? v(t) over interval a to b
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta

15. Area inside polar curve
concave down
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - 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
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta

16. left riemann sum
a^x ln(a)
v(dx/dt) + (dy/dt) not an integral!
general term = a1r^n - converges if -1 < r < 1
use rectangles with left-endpoints to evaluate integral (estimate area)

17. Second derivative of parametrically defined 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' = sec(x)
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
product rule

18. Average Rate of Change
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
? f(x) dx integrate over interval a to b
draw short segments representing slope at each point

19. area below x-axis is...
negative
? v (dx/dt) + (dy/dt) over interval from a to b
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
relative minimum

20. Find radius of convergence
f(x) has a relative maximum
chain rule
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
y' = sec(x)tan(x)

21. To find particular solution to differential equation - dy/dx = x/y...
velocity is negative
f(x) has a relative minimum
separate variables - integrate + C - use initial condition to find C - solve for y
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta

22. When f '(x) changes from increasing to decreasing or decreasing to increasing - f(x) has a...
point of inflection
logistic differential equation - M = carrying capacity
substitution - parts - partial fractions
use rectangles with left-endpoints to evaluate integral (estimate area)

23. Alternate definition of derivative
use rectangles with right-endpoints to evaluate integrals (estimate area)
? abs[v(t)] over interval a to b
Limit as x approaches a of [f(x)-f(a)]/(x-a)
y' = -csc(x)

24. y = cos?(x) - y' =
negative
y' = -1/v(1 - x)
y' = 1/(1 + x)
relative minimum

25. y = a^x - y' = y' =
1/2 ? r over interval from a to b - find a & b by setting r = 0 - solve for theta
speed
a^x ln(a)
? f(x) dx on interval a to b = F(b) - F(a)

26. area above x-axis is...
? v(t) over interval a to b
positive
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 cross-section in terms of x

27. indefinite integral
no limits - find antiderivative + C - use inital value to find C
chain rule
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0 - 8
general term = a1r^n - converges if -1 < r < 1

28. average value of f(x)
e^x
1/(b-a) ? f(x) dx on interval a to b
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
speed

29. Instantenous Rate of Change
e^x
Slope of tangent line at a point - value of derivative at a point
concave up
y' = -1/(1 + x)

30. y = cot?(x) - y' =
quotient rule
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
y' = -1/(1 + x)
use trapezoids to evaluate integrals (estimate area)

31. y = cos(x) - y' =
draw short segments representing slope at each point
Limit as x approaches a of [f(x)-f(a)]/(x-a)
y' = 1/x
y' = -sin(x)

32. y = csc(x) - y' =
? f(x) dx on interval a to b = F(b) - F(a)
use rectangles with right-endpoints to evaluate integrals (estimate area)
y' = 1/(1 + x)
y' = -csc(x)cot(x)

33. Area between two curves
p ? r dx over interval a to b - where r = distance from curve to axis of revolution
velocity is negative
y' = -csc(x)cot(x)
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function

34. y = ln(x) - y' =
derivative
y' = 1/x
negative
y' = sec(x)

35. Volume of solid with base in the plane and given cross-section
e^x
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 cross-section in terms of x
relative minimum

36. When f '(x) is decreasing - f(x) is...
f '(g(x)) g'(x)
concave down
quotient rule
general term = 1/n^p - converges if p > 1

37. Particle is moving to the left/down
1/(b-a) ? f(x) dx on interval a to b
Slope of tangent line at a point - value of derivative at a point
velocity is negative
y' = -csc(x)cot(x)

38. Product Rule
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.
draw short segments representing slope at each point
uv' + vu'
f '(g(x)) g'(x)

39. slope of horizontal line
? v(1 + (dy/dx)) dx over interval a to b
use ratio test - set > 1 and solve absolute value equations - check endpoints
zero
Alternating series converges and general term converges with another test

40. y = sec(x) - y' =
a^x ln(a)
y' = sec(x)tan(x)
? abs[v(t)] over interval a to b
draw short segments representing slope at each point

41. To draw a slope field - plug (x -y) coordinates into differential equation...
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
separate variables - integrate + C - use initial condition to find C - solve for y
use trapezoids to evaluate integrals (estimate area)
draw short segments representing slope at each point

42. p-series test
general term = 1/n^p - converges if p > 1
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
substitution - parts - partial fractions
y' = sec(x)tan(x)

43. When f '(x) changes fro positive to negative - f(x) has a...
concave down
no limits - find antiderivative + C - use inital value to find C
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
relative maximum

44. definite integral
y' = sec(x)
increasing
has limits a & b - find antiderivative - F(b) - F(a)
1/(b-a) ? f(x) dx on interval a to b

45. Taylor series
polynomial with infinite number of terms - includes general term
y' = cos(x)
v(dx/dt) + (dy/dt) not an integral!
separate variables - integrate + C - use initial condition to find C - solve for y

46. Find interval of convergence
general term = a1r^n - converges if -1 < r < 1
velocity is positive
use ratio test - set > 1 and solve absolute value equations - check endpoints
1/(b-a) ? f(x) dx on interval a to b

47. Alternating series tes
lim as n approaches zero of general term = 0 and terms decrease - series converges
? v (dx/dt) + (dy/dt) over interval from a to b
(uv'-vu')/v
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x

48. When f '(x) changes from negative to positive - f(x) has a...
Area of trapezoid
y' = cos(x)
relative minimum
1/(b-a) ? f(x) dx on interval a to b

49. When f '(x) is increasing - f(x) is...
integrand is a rational function with a factorable denominator
concave up
Alternating series converges and general term diverges with another test
derivative

50. trapezoidal rule
relative minimum
negative
use trapezoids to evaluate integrals (estimate area)
y' = 1/x

Test your basic knowledge |

AP Calculus Bc

Communication skills, Self help skills, Self improvement skills, Productivity skills, Writing skills, Business skills, Thinking skills & More...

502 Pages | Only $12 | PDF / EPub, Kindle Ready

Link to This Test

Related Subjects