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
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)
? abs[v(t)] over interval a to b
? v(t) over interval a to b
speed


2. Area between two curves
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
Area of trapezoid
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)
? f(x) - g(x) over interval a to b - where f(x) is top function and g(x) is bottom function


3. left riemann sum
? f(x) dx integrate over interval a to b
y' = 1/v(1 - x²)
concave down
use rectangles with left-endpoints to evaluate integral (estimate area)


4. average value of f(x)
concave up
1/(b-a) ? f(x) dx on interval a to b
f(x) has a relative minimum
Slope of secant line between two points - use to estimate instantanous rate of change at a point.


5. y = ln(x)/x² - state rule used to find derivative
? v(t) over interval a to b
quotient rule
if integral converges - series converges
decreasing


6. y = sin?¹(x) - y' =

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


7. trapezoidal rule
use trapezoids to evaluate integrals (estimate area)
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta
quotient rule
y' = -sin(x)


8. Instantenous Rate of Change
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
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
relative maximum
Slope of tangent line at a point - value of derivative at a point


9. Chain Rule

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


10. L'Hopitals rule
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit
product rule
use rectangles with left-endpoints to evaluate integral (estimate area)
y' = -1/(1 + x²)


11. P = M / (1 + Ae^(-Mkt))
? f(x) dx on interval a to b = F(b) - F(a)
logistic growth equation
1/(b-a) ? f(x) dx on interval a to b
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit


12. To find absolute maximum on closed interval [a - b] - you must consider...
use ratio test - set > 1 and solve absolute value equations - check endpoints
relative minimum
critical points and endpoints
point of inflection


13. use integration by parts when...
no limits - find antiderivative + C - use inital value to find C
A function and it's derivative are in the integrand
two different types of functions are multiplied
relative maximum


14. Given v(t) find total distance travelled
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
Limit as x approaches a of [f(x)-f(a)]/(x-a)
? abs[v(t)] over interval a to b
y' = cos(x)


15. slope of horizontal line
zero
velocity is negative
v(dx/dt)² + (dy/dt)² not an integral!
critical points and endpoints


16. Indeterminate forms
logistic growth equation
negative
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
y' = 1/x


17. Product Rule

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


18. Particle is moving to the left/down
velocity is negative
corner - cusp - vertical tangent - discontinuity
Slope of tangent line at a point - value of derivative at a point
general term = 1/n^p - converges if p > 1


19. Formal definition of derivative
undefined
Limit as h approaches 0 of [f(a+h)-f(a)]/h
logistic growth equation
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges


20. dP/dt = kP(M - P)
has limits a & b - find antiderivative - F(b) - F(a)
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
polynomial with infinite number of terms - includes general term
logistic differential equation - M = carrying capacity


21. Volume of solid of revolution - no washer
relative minimum
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
general term = a1r^n - converges if -1 < r < 1
1/(b-a) ? f(x) dx on interval a to b


22. y = cot?¹(x) - y' =

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


23. y = e^x - y' = y' =
derivative
e^x
concave up
corner - cusp - vertical tangent - discontinuity


24. To find particular solution to differential equation - dy/dx = x/y...
f(x) has a relative maximum
separate variables - integrate + C - use initial condition to find C - solve for y
two different types of functions are multiplied
v(dx/dt)² + (dy/dt)² not an integral!


25. use substitution to integrate when

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


26. Use partial fractions to integrate when...
product rule
? v (dx/dt)² + (dy/dt)² over interval from a to b
integrand is a rational function with a factorable denominator
draw short segments representing slope at each point


27. Area inside one polar curve and outside another polar curve
corner - cusp - vertical tangent - discontinuity
1/2 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.
y' = -1/v(1 - x²)
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.


28. When f '(x) is positive - f(x) is...
f(x)
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
increasing
negative


29. Quotient Rule

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


30. If f '(x) = 0 and f'(x) > 0 -...
two different types of functions are multiplied
concave down
f(x) has a relative minimum
A function and it's derivative are in the integrand


31. Length of parametric curve
? v (dx/dt)² + (dy/dt)² over interval from a to b
concave up
y' = -1/v(1 - x²)
critical points and endpoints


32. To draw a slope field - plug (x -y) coordinates into differential equation...
draw short segments representing slope at each point
Alternating series converges and general term diverges with another test
derivative
y' = 1/(x lna)


33. methods of integration
substitution - parts - partial fractions
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)
chain rule
? v(t) over interval a to b


34. Average Rate of Change
decreasing
Area of trapezoid
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
y' = 1/(x lna)


35. Find radius of convergence
y' = -csc(x)cot(x)
undefined
logistic growth equation
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint


36. Length of curve
? v(1 + (dy/dx)²) dx over interval a to b
y' = 1/x
no limits - find antiderivative + C - use inital value to find C
A function and it's derivative are in the integrand


37. y = a^x - y' = y' =
a^x ln(a)
v(dx/dt)² + (dy/dt)² not an integral!
y' = 1/x
positive


38. When f '(x) is decreasing - f(x) is...
substitution - parts - partial fractions
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.
concave down
? v (dx/dt)² + (dy/dt)² over interval from a to b


39. y = x cos(x) - state rule used to find derivative
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
product rule
no limits - find antiderivative + C - use inital value to find C


40. Find interval of convergence
use ratio test - set > 1 and solve absolute value equations - check endpoints
derivative
y' = cos(x)
? v(t) over interval a to b


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

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


42. 6th degree Taylor Polynomial
polynomial with infinite number of terms - includes general term
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
positive
Area of trapezoid


43. Given velocity vectors dx/dt and dy/dt - find total distance travelled
1/2 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
? v (dx/dt)² + (dy/dt)² over interval from a to b
f(x) has a relative minimum


44. area above x-axis is...
positive
general term = a1r^n - converges if -1 < r < 1
relative maximum
1/2 ? r² over interval from a to b - find a & b by setting r = 0 - solve for theta


45. Alternate definition of derivative
Alternating series converges and general term converges with another test
e^x
y' = 1/x
Limit as x approaches a of [f(x)-f(a)]/(x-a)


46. nth term test
? f(x) dx integrate over interval a to b
if terms grow without bound - series diverges
use trapezoids to evaluate integrals (estimate area)
speed


47. slope of vertical line
no limits - find antiderivative + C - use inital value to find C
f(x)
undefined
general term = a1r^n - converges if -1 < r < 1


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

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


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

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


50. y = ln(x) - y' =

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