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AP Calculus Bc

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. When f '(x) changes fro positive to negative - f(x) has a...
concave down
y' = sec(x)tan(x)
relative maximum
velocity is negative

2. p-series test
positive
use ratio test - set > 1 and solve absolute value equations - check endpoints
? v(t) over interval a to b
general term = 1/n^p - converges if p > 1

3. use substitution to integrate when

4. y = x cos(x) - state rule used to find derivative
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
? abs[v(t)] over interval a to b
f(x) has a relative minimum
product rule

5. trapezoidal rule
y' = 1/v(1 - x²)
use trapezoids to evaluate integrals (estimate area)
1/(b-a) ? f(x) dx on interval a to b
speed

6. If g(x) = ? f(t) dt on interval 2 to x - then g'(x) =...
draw short segments representing slope at each point
f(x)
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
relative minimum

7. y = cos(x) - y' =

8. When f '(x) is decreasing - f(x) is...
v(dx/dt)² + (dy/dt)² not an integral!
y' = -1/(1 + x²)
concave down
product rule

9. y = cos?¹(x) - y' =

10. Use partial fractions to integrate when...
integrand is a rational function with a factorable denominator
quotient rule
y' = 1/v(1 - x²)
y' = -csc²(x)

11. Find interval of convergence
use ratio test - set > 1 and solve absolute value equations - check endpoints
polynomial with infinite number of terms - includes general term
y' = 1/(1 + x²)
? v(t) over interval a to b

12. Particle is moving to the right/up
general term = 1/n^p - converges if p > 1
increasing
use trapezoids to evaluate integrals (estimate area)
velocity is positive

13. Quotient Rule

14. To find absolute maximum on closed interval [a - b] - you must consider...
undefined
critical points and endpoints
decreasing
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges

15. Area inside polar curve
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
general term = 1/n^p - converges if p > 1
v(dx/dt)² + (dy/dt)² not an integral!
Area of trapezoid

16. When f '(x) is negative - f(x) is...
e^x
? f(x) dx on interval a to b = F(b) - F(a)
decreasing
general term = a1r^n - converges if -1 < r < 1

17. Volume of solid of revolution - washer
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
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
increasing
y' = -sin(x)

18. To draw a slope field - plug (x -y) coordinates into differential equation...
f(x) has a relative minimum
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
draw short segments representing slope at each point
zero

19. If f '(x) = 0 and f'(x) > 0 -...
f(x) has a relative minimum
use tangent line to approximate values of the function
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
integrand is a rational function with a factorable denominator

20. y = csc(x) - y' =

21. Second derivative of parametrically defined curve
y' = -1/v(1 - x²)
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
y' = 1/x
logistic differential equation - M = carrying capacity

22. y = tan(x) - y' =

23. Product Rule

24. Eatio test
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
polynomial with infinite number of terms - includes general term
point of inflection

25. y = cos²(3x)
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)
draw short segments representing slope at each point
chain rule
has limits a & b - find antiderivative - F(b) - F(a)

26. Alternate definition of derivative
Limit as x approaches a of [f(x)-f(a)]/(x-a)
polynomial with infinite number of terms - includes general term
velocity is negative
uv' + vu'

27. y = e^x - y' = y' =
? v(1 + (dy/dx)²) dx over interval a to b
positive
e^x
use rectangles with right-endpoints to evaluate integrals (estimate area)

28. y = a^x - y' = y' =
a^x ln(a)
(uv'-vu')/v²
? v(t) over interval a to b
undefined

29. indefinite integral
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
v(dx/dt)² + (dy/dt)² not an integral!
use ratio test - set > 1 and solve absolute value equations - check endpoints
no limits - find antiderivative + C - use inital value to find C

30. use integration by parts when...
f(x)
two different types of functions are multiplied
increasing
integrand is a rational function with a factorable denominator

31. left riemann sum
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
use rectangles with left-endpoints to evaluate integral (estimate area)
Area of trapezoid
e^x

32. When f '(x) changes from increasing to decreasing or decreasing to increasing - f(x) has a...
a^x ln(a)
no limits - find antiderivative + C - use inital value to find C
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
point of inflection

33. Area inside one polar curve and outside another polar curve
1/2 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.
if integral converges - series converges
Limit as x approaches a of [f(x)-f(a)]/(x-a)
Alternating series converges and general term converges with another test

34. Converges absolutely
use rectangles with left-endpoints to evaluate integral (estimate area)
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
Alternating series converges and general term converges with another test
two different types of functions are multiplied

35. [(h1 - h2)/2]*base
use trapezoids to evaluate integrals (estimate area)
chain rule
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
Area of trapezoid

36. When f '(x) is increasing - f(x) is...
? v(1 + (dy/dx)²) dx over interval a to b
relative maximum
concave up
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x

37. Integral test
Alternating series converges and general term converges with another test
if integral converges - series converges
y' = 1/v(1 - x²)
concave up

38. y = cot?¹(x) - y' =

39. Average Rate of Change
y' = 1/(x lna)
use ratio test - set > 1 and solve absolute value equations - check endpoints
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
product rule

40. y = log (base a) x - y' =

41. y = cot(x) - y' =

42. Instantenous Rate of Change
general term = a1r^n - converges if -1 < r < 1
uv' + vu'
Slope of tangent line at a point - value of derivative at a point
uv - ? v du

43. P = M / (1 + Ae^(-Mkt))
1/(b-a) ? f(x) dx on interval a to b
logistic growth equation
y' = -csc(x)cot(x)
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative

44. y = sec(x) - y' =

45. When is a function not differentiable
? v(1 + (dy/dx)²) dx over interval a to b
corner - cusp - vertical tangent - discontinuity
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.
derivative

46. Length of curve
velocity is positive
y' = -1/v(1 - x²)
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
? v(1 + (dy/dx)²) dx over interval a to b

47. y = ln(x)/x² - state rule used to find derivative
f(x) has a relative minimum
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
quotient rule
1/2 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.

48. Converges conditionally
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
general term = a1r^n - converges if -1 < r < 1
Alternating series converges and general term diverges with another test

49. To find particular solution to differential equation - dy/dx = x/y...
use rectangles with right-endpoints to evaluate integrals (estimate area)
separate variables - integrate + C - use initial condition to find C - solve for y
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
use ratio test - set > 1 and solve absolute value equations - check endpoints

50. When f '(x) changes from negative to positive - f(x) has a...
uv' + vu'
f '(g(x)) g'(x)
if integral converges - series converges
relative minimum