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. absolute value of velocity
speed
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function
y' = 1/(x lna)
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


2. methods of integration
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
substitution - parts - partial fractions
concave down
y' = -1/(1 + x²)


3. To find absolute maximum on closed interval [a - b] - you must consider...
derivative
f(x) has a relative minimum
critical points and endpoints
use trapezoids to evaluate integrals (estimate area)


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


5. L'Hopitals rule
y' = 1/x
integrand is a rational function with a factorable denominator
uv' + vu'
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit


6. If f '(x) = 0 and f'(x) < 0 -...
? f(x) dx integrate over interval a to b
f(x) has a relative maximum
two different types of functions are multiplied
if terms grow without bound - series diverges


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


8. rate
derivative
v(dx/dt)² + (dy/dt)² not an integral!
Alternating series converges and general term diverges with another test
e^x


9. slope of vertical line
undefined
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)
has limits a & b - find antiderivative - F(b) - F(a)
draw short segments representing slope at each point


10. indefinite integral
polynomial with infinite number of terms - includes general term
y' = cos(x)
if integral converges - series converges
no limits - find antiderivative + C - use inital value to find C


11. When f '(x) is decreasing - f(x) is...
velocity is positive
concave down
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
logistic growth equation


12. Quotient Rule

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


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

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


14. Product Rule

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


15. Find radius of convergence
if integral converges - series converges
increasing
y' = -sin(x)
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint


16. To find particular solution to differential equation - dy/dx = x/y...
zero
relative minimum
separate variables - integrate + C - use initial condition to find C - solve for y
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.


17. Indeterminate forms
general term = 1/n^p - converges if p > 1
velocity is negative
positive
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°


18. To draw a slope field - plug (x -y) coordinates into differential equation...
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
draw short segments representing slope at each point
y' = 1/v(1 - x²)
(uv'-vu')/v²


19. Particle is moving to the left/down
velocity is negative
a^x ln(a)
e^x
integrand is a rational function with a factorable denominator


20. Use partial fractions to integrate when...
zero
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
integrand is a rational function with a factorable denominator


21. Find interval of convergence
speed
two different types of functions are multiplied
use ratio test - set > 1 and solve absolute value equations - check endpoints
? v(t) over interval a to b


22. Area inside polar curve
use trapezoids to evaluate integrals (estimate area)
substitution - parts - partial fractions
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
two different types of functions are multiplied


23. When is a function not differentiable
speed
Limit as h approaches 0 of [f(a+h)-f(a)]/h
corner - cusp - vertical tangent - discontinuity
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x


24. Intermediate Value Theorem
use ratio test - set > 1 and solve absolute value equations - check endpoints
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.
f(x) has a relative minimum
positive


25. Fundamental Theorem of Calculus
y' = -1/v(1 - x²)
v(dx/dt)² + (dy/dt)² not an integral!
? f(x) dx on interval a to b = F(b) - F(a)
uv - ? v du


26. Integral test
if integral converges - series converges
? v (dx/dt)² + (dy/dt)² over interval from a to b
? v(1 + (dy/dx)²) dx over interval a to b
corner - cusp - vertical tangent - discontinuity


27. y = cos²(3x)
chain rule
negative
Limit as h approaches 0 of [f(a+h)-f(a)]/h
f '(g(x)) g'(x)


28. Length of parametric curve
Limit as x approaches a of [f(x)-f(a)]/(x-a)
substitution - parts - partial fractions
zero
? v (dx/dt)² + (dy/dt)² over interval from a to b


29. Given velocity vectors dx/dt and dy/dt - find total distance travelled
increasing
? v (dx/dt)² + (dy/dt)² over interval from a to b
has limits a & b - find antiderivative - F(b) - F(a)
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt


30. Volume of solid with base in the plane and given cross-section
Area of trapezoid
zero
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
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x


31. Volume of solid of revolution - no washer
logistic differential equation - M = carrying capacity
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
uv - ? v du
Alternating series converges and general term converges with another test


32. Instantenous Rate of Change
Slope of tangent line at a point - value of derivative at a point
Limit as x approaches a of [f(x)-f(a)]/(x-a)
relative minimum
Slope of secant line between two points - use to estimate instantanous rate of change at a point.


33. mean value theorem

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


34. Formal definition of derivative
quotient rule
Limit as h approaches 0 of [f(a+h)-f(a)]/h
relative maximum
draw short segments representing slope at each point


35. When f '(x) is increasing - f(x) is...
concave up
logistic differential equation - M = carrying capacity
negative
y' = 1/(1 + x²)


36. Second derivative of parametrically defined curve
? f(x) dx integrate over interval a to b
a^x ln(a)
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
? v (dx/dt)² + (dy/dt)² over interval from a to b


37. y = ln(x)/x² - state rule used to find derivative
quotient rule
f '(g(x)) g'(x)
f(x) has a relative maximum
? v(1 + (dy/dx)²) dx over interval a to b


38. Eatio test
uv - ? v du
polynomial with infinite number of terms - includes general term
use tangent line to approximate values of the function
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges


39. area above x-axis is...
positive
y' = -csc²(x)
velocity is positive
a^x ln(a)


40. Geometric series test
velocity is negative
Limit as h approaches 0 of [f(a+h)-f(a)]/h
general term = a1r^n - converges if -1 < r < 1
relative maximum


41. Length of curve
? v(1 + (dy/dx)²) dx over interval a to b
use rectangles with left-endpoints to evaluate integral (estimate area)
y' = 1/(1 + x²)
a^x ln(a)


42. Chain Rule

Warning: Invalid argument supplied for foreach() in /var/www/html/basicversity.com/show_quiz.php on line 183


43. Area between two curves
use tangent line to approximate values of the function
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
logistic differential equation - M = carrying capacity
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function


44. Particle is moving to the right/up
increasing
Limit as x approaches a of [f(x)-f(a)]/(x-a)
velocity is positive
uv - ? v du


45. Average Rate of Change
no limits - find antiderivative + C - use inital value to find C
? v (dx/dt)² + (dy/dt)² over interval from a to b
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite - then series behaves like comparison series


46. Given velocity vectors dx/dt and dy/dt - find speed
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
Area of trapezoid
v(dx/dt)² + (dy/dt)² not an integral!
? f(x) dx integrate over interval a to b


47. When f '(x) is negative - f(x) is...
logistic growth equation
decreasing
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
product rule


48. 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 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function
f '(g(x)) g'(x)


49. nth term test
if terms grow without bound - series diverges
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
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°


50. y = e^x - y' = y' =
(uv'-vu')/v²
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
e^x
? v(1 + (dy/dx)²) dx over interval a to b