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Test your basic knowledge |
AP Calculus Ab
Start Test
Study First
Subjects
:
math
,
ap
,
calculus
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. The function that is integrated in an integral
critical point
integrand
asymptote
trapezoidal rule
2. Intervals on which the second derivative is negative
endpoint extremum
concave down
absolute minimum
limit of integration
3. (geometry)A curve generated by the intersection of a plane or circular cone
instantaneous velocity
conic section
root of an equation
partition of an interval
4. Input of function
critical point
integrable function
domain
continuity on an interval
5. If y=f(x) is continuous at every point of the close interval [a -b] and differentiable at every point of its interior (a -b) - then there is at least one point c in (a -b) at which f'(c)= [f(b)-f(a)]/(b-a)
implicit differentiation
Mean Value theorem for derivatives
bounded above
cross sectional area
6. N(1-r)^x
decay model
removable discontinuity
Radian
law of cosine
7. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point - L(x) = f(a) + f'(a)(x - a)
critical value
implicit differentiation
linear approximation
integrable function
8. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N
Intermediate value theorem
critical point
continuous function
continuity at a point
9. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
mean value theorem for definite integrals
differentiation
order of a derivative
integration by substitution
10. Imaginary line drawn perpendicular to the surface of a mirror or any surface
related rates
normal line
conic section
optimization
11. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives
mean value theorem for definite integrals
removable discontinuity
Total change Theorem
parallel curve
12. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
derivative
Mean Value theorem for derivatives
instantaneous rate of change
exponential function
13. Functions of angles
axis of symmetry
circular function
instantaneous rate of change
distance formula
14. The value of the function at a critical point
indefinite integral
critical value
first derivative test
integrand
15. Selection of a best element from some set of available alternatives.
optimization
Mean Value theorem for derivatives
constant function
related rates
16. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
extreme value theorem
law of cosine
order of a derivative
17. The value of the function approaches as x increases or decreases without bound
critical value
law of cosine
limit at infinity
difference quotient
18. An undetermined constant added to every result of integration (the added +c)
constant of integration
differential
acceleration
continuity at a point
19. A function f that gives the position f(t) of a body on a coordinate axis at time t
Rolle's Theorem
instantaneous velocity
odd function
position function
20. dy/dx
distance formula
endpoint extremum
leibniz notation
trapezoidal rule
21. Any value in the domain where either the function is not differentiable or its derivative is 0.
differential
critical point
cross sectional area
differential equation
22. Intervals in which the second derivative is positive
left hand limit
concave up
right hand sum
non removable discontinuity
23. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates
rational function
complex number
absolute value
related rates
24. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
difference quotient
endpoint extremum
implicit differentiation
25. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
amplitude
position function
rational function
dummy variable of integration
26. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
Intermediate value theorem
derivative
partition of an interval
27. The smallest y-value of the function
infinite limit
absolute minimum
instantaneous rate of change
differential equation
28. A function that is continuous at every point on the interval
dummy variable of integration
cross sectional area
normal line
continuity on an interval
29. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)
logarithmic function
law of cosine
related rates
Fundamental theorem of calculus
30. A point that represents the maximum value a function assumes over its domain
root of an equation
conic section
absolute maximum
critical value
31. Curve whose points are at a fixed normal distance of a given curve
decay model
parallel curve
Radian
odd function
32. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
continuity at a point
power series
non removable discontinuity
even function
33. Having the limits or boundaries established
bounded
instantaneous velocity
absolute minimum
root of an equation
34. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
exponential growth and decay
linear approximation
absolute minimum
complex number
35. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
optimization
non removable discontinuity
local linearity
36. sinA/a=sinB/b=sinC/c
law of sines
absolute maximum
continuous function
differentiation
37. If f is continuous at x = a and lim f'(x) (from the left) = lim f'(x) (from the right) - then f is differentiable at x = a
exponential function
Total change Theorem
differentiability
numerical derivative
38. Limit of an average velocity - as the time interval gets smaller and smaller. Let s (t) be the position of an object at time t. The instantaneous velocity at t = a is defined as lim(h goes to 0) [s(a+h)-s(a)] / h
natural logarithm
domain
instantaneous velocity
non removable discontinuity
39. The maximum distance that the particles of a wave's medium vibrate from their rest position
instantaneous velocity
amplitude
cartesian coordinate system
implicit differentiation
40. A function F is called an __________ of a function f on a given open interval if F'(x) = f(x) for all x in the interval - Add + c at the end
dummy variable of integration
exponential growth and decay
continuity on an interval
antiderivative
41. ex) dx - dy etc
differential
logarithm laws
amplitude
odd function
42. A given value of x and f(x) used to find the constant of integration
parallel curve
initial condition
cartesian coordinate system
difference quotient
43. T = ?X / 2 (yo + 2y1 + 2y2 ... + 2y + y) - A method of approximating to an intergral as the limit of a sum of areas of trapezoids. Can be done by averaging a left hand sum and a right hand sum
order of a derivative
trapezoidal rule
limit of integration
removable discontinuity
44. The limit of f as x approaches c from the right
right hand limit
domain
order of a derivative
Algebraic function
45. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
axis of symmetry
removable discontinuity
domain
parameter
46. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
natural logarithm
absolute value
endpoint extremum
logarithmic function
47. A function whose domain is divided into several parts and a different function rule is applied to each part
differentiation
transcendental function
piecewise defined function
partition of an interval
48. A rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the left most point of the sub-interval
distance formula
left hand sum
axis of symmetry
law of cosine
49. A function that is a fixed numerical value for all elements of the domain of the function
constant of integration
constant function
absolute minimum
definite integral
50. A variable occurring in a function - but on which the value of the function does not depend
power series
dummy variable of integration
critical value
integrand