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. Find interval of convergence
use ratio test - set > 1 and solve absolute value equations - check endpoints
derivative
if terms grow without bound - series diverges
e^x


2. When f '(x) is increasing - f(x) is...
increasing
concave up
velocity is positive
general term = a1r^n - converges if -1 < r < 1


3. If f '(x) = 0 and f'(x) < 0 -...
y' = -csc²(x)
negative
f(x) has a relative maximum
critical points and endpoints


4. [(h1 - h2)/2]*base
uv - ? v du
y' = sec²(x)
relative minimum
Area of trapezoid


5. Given v(t) find total distance travelled
use rectangles with left-endpoints to evaluate integral (estimate area)
? abs[v(t)] over interval a to b
? f(x) dx integrate over interval a to b
lim as n approaches zero of general term = 0 and terms decrease - series converges


6. ? u dv =
(uv'-vu')/v²
? v (dx/dt)² + (dy/dt)² over interval from a to b
y' = 1/(x lna)
uv - ? v du


7. area under a curve
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 rectangles with right-endpoints to evaluate integrals (estimate area)
quotient rule
? f(x) dx integrate over interval a to b


8. Fundamental Theorem of Calculus
? f(x) dx on interval a to b = F(b) - F(a)
speed
relative maximum
polynomial with infinite number of terms - includes general term


9. slope of horizontal line
Alternating series converges and general term diverges with another test
zero
two different types of functions are multiplied
? abs[v(t)] over interval a to b


10. Particle is moving to the left/down
? abs[v(t)] over interval a to b
Slope of tangent line at a point - value of derivative at a point
velocity is negative
y' = cos(x)


11. Given velocity vectors dx/dt and dy/dt - find speed
critical points and endpoints
? v(t) over interval a to b
general term = 1/n^p - converges if p > 1
v(dx/dt)² + (dy/dt)² not an integral!


12. Taylor series
zero
Area of trapezoid
? abs[v(t)] over interval a to b
polynomial with infinite number of terms - includes general term


13. y = ln(x)/x² - state rule used to find derivative
quotient rule
point of inflection
corner - cusp - vertical tangent - discontinuity
product rule


14. nth term test
relative minimum
uv - ? v du
velocity is negative
if terms grow without bound - series diverges


15. 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
product rule
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
y' = -sin(x)


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

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17. y = tan?¹(x) - y' =

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18. rate
derivative
? f(x) dx integrate over interval a to b
lim as n approaches zero of general term = 0 and terms decrease - series converges
? v (dx/dt)² + (dy/dt)² over interval from a to b


19. Converges absolutely
Alternating series converges and general term converges with another test
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function
(uv'-vu')/v²
lim as n approaches zero of general term = 0 and terms decrease - series converges


20. Intermediate Value Theorem
Alternating series converges and general term diverges with another test
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
(uv'-vu')/v²
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.


21. If f '(x) = 0 and f'(x) > 0 -...
general term = a1r^n - converges if -1 < r < 1
separate variables - integrate + C - use initial condition to find C - solve for y
if terms grow without bound - series diverges
f(x) has a relative minimum


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

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23. 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
? v(1 + (dy/dx)²) dx over interval a to b
zero
f(x)


24. Formal definition of derivative
two different types of functions are multiplied
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
Limit as h approaches 0 of [f(a+h)-f(a)]/h
uv' + vu'


25. Area inside polar curve
1/(b-a) ? f(x) dx on interval a to b
y' = 1/(x lna)
has limits a & b - find antiderivative - F(b) - F(a)
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta


26. y = sin(x) - y' =

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27. p-series test
negative
general term = 1/n^p - converges if p > 1
concave up
logistic differential equation - M = carrying capacity


28. y = cos?¹(x) - y' =

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29. mean value theorem

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30. Find radius of convergence
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 - radius = center - endpoint
critical points and endpoints
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta


31. Integral test
y' = -sin(x)
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
if integral converges - series converges
use tangent line to approximate values of the function


32. When f '(x) changes from negative to positive - f(x) has a...
undefined
point of inflection
y' = 1/(1 + x²)
relative minimum


33. use integration by parts when...
two different types of functions are multiplied
logistic differential equation - M = carrying capacity
y' = -1/(1 + x²)
has limits a & b - find antiderivative - F(b) - F(a)


34. Alternating series tes
A function and it's derivative are in the integrand
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
lim as n approaches zero of general term = 0 and terms decrease - series converges


35. Quotient Rule

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36. y = sin?¹(x) - y' =

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37. y = x cos(x) - state rule used to find derivative
uv - ? v du
product rule
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
use rectangles with left-endpoints to evaluate integral (estimate area)


38. right riemann sum
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 rectangles with right-endpoints to evaluate integrals (estimate area)
increasing
logistic differential equation - M = carrying capacity


39. Use partial fractions to integrate when...
concave up
derivative
integrand is a rational function with a factorable denominator
Alternating series converges and general term diverges with another test


40. When f '(x) is positive - f(x) is...
Area of trapezoid
(uv'-vu')/v²
corner - cusp - vertical tangent - discontinuity
increasing


41. To find absolute maximum on closed interval [a - b] - you must consider...
y' = sec²(x)
Limit as x approaches a of [f(x)-f(a)]/(x-a)
y' = -1/v(1 - x²)
critical points and endpoints


42. trapezoidal rule
use trapezoids to evaluate integrals (estimate area)
f(x)
substitution - parts - partial fractions
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint


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

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44. area below x-axis is...
lim as n approaches zero of general term = 0 and terms decrease - series converges
A function and it's derivative are in the integrand
draw short segments representing slope at each point
negative


45. y = cos²(3x)
logistic growth equation
chain rule
f(x)
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges


46. y = a^x - y' = y' =
no limits - find antiderivative + C - use inital value to find C
a^x ln(a)
product rule
y' = 1/(1 + x²)


47. use substitution to integrate when

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48. y = e^x - y' = y' =
y' = cos(x)
negative
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
e^x


49. area above x-axis is...
Limit as h approaches 0 of [f(a+h)-f(a)]/h
positive
polynomial with infinite number of terms - includes general term
y' = -sin(x)


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

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