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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. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
exponential growth and decay
instantaneous velocity
Fundamental theorem of calculus
position function
2. dy/dx
leibniz notation
law of sines
derivative
cosecant function
3. Zero of a function; a solution of the equation f(x)=0 is a zero of the function f or a root of the equation of an x-intercept of the graph
bounded
integration by substitution
root of an equation
trapezoidal rule
4. ex) dx - dy etc
indefinite integral
related rates
Rolle's Theorem
differential
5. If f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.
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6. The reciprocal of the sine function
cosecant function
complex number
Fundamental theorem of calculus
absolute minimum
7. Input of function
constant function
domain
logarithm laws
right hand sum
8. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
law of cosine
normal line
removable discontinuity
trapezoidal rule
9. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
parameter
integrand
initial condition
even function
10. The maximum distance that the particles of a wave's medium vibrate from their rest position
trapezoidal rule
amplitude
natural logarithm
bounded below
11. The local and global maximums and minimums of a function
leibniz notation
root of an equation
extremum
complex number
12. 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
absolute maximum
critical value
instantaneous velocity
concave up
13. The mathematical process of obtaining the derivative of a function
differential
logarithmic function
perpendicular curves
differentiation
14. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
Total change Theorem
cosecant function
antiderivative
implicit differentiation
15. A point that represents the maximum value a function assumes over its domain
root of an equation
mean value theorem for definite integrals
absolute maximum
Intermediate value theorem
16. A measure of how a function changes as its input changes.
derivative
instantaneous rate of change
leibniz notation
complex number
17. Curve whose points are at a fixed normal distance of a given curve
order of a derivative
left hand sum
parallel curve
position function
18. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
indefinite integral
local linearity
order of a derivative
definite integral
19. If f is continuous on [a -b] then at some point - c in [a -b] - f(c)= (1/(a-b))*?f(x)dx (with bounds a -b)
mean value theorem for definite integrals
right hand limit
normal line
partition of an interval
20. Having the limits or boundaries established
bounded
differential equation
absolute minimum
natural logarithm
21. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
constant of integration
circular function
extreme value theorem
concave up
22. A function that can be graphed w/ a line or smooth curve
continuity at a point
order of a derivative
continuous function
parameter
23. N(1-r)^x
critical value
parallel curve
right hand limit
decay model
24. A straight line that is the limiting value of a curve
parallel curve
right hand limit
continuous function
asymptote
25. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
right hand limit
differentiation
order of a derivative
26. 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)
parameter
average rate of change
linear approximation
bounded below
27. 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 right-most point of the sub-interval
mean value theorem for definite integrals
integrand
related rates
right hand sum
28. 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
Radian
related rates
domain
Total change Theorem
29. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
critical point
differential equation
absolute minimum
piecewise defined function
30. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
amplitude
concave down
indefinite integral
parameter
31. Dividing an interval into n sub-intervals
partition of an interval
absolute minimum
Mean Value theorem for derivatives
cartesian coordinate system
32. 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
Total change Theorem
inflection point
Intermediate value theorem
integration by substitution
33. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
domain
initial condition
difference quotient
absolute value
34. A function that is continuous at every point on the interval
infinite limit
continuous function
odd function
continuity on an interval
35. 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)
Fundamental theorem of calculus
root of an equation
difference quotient
law of cosine
36. The inverse of an eponential function
logarithmic function
related rates
Intermediate value theorem
linear approximation
37. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
definite integral
logarithm laws
mean value theorem for definite integrals
absolute maximum
38. The rate of change of a function occurring at or associated with a given instant - or as a limit as a time interval approaches zero; the derivative
Rolle's Theorem
limit of integration
instantaneous rate of change
integrand
39. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))
local linearity
Total change Theorem
cross sectional area
instantaneous rate of change
40. 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
left hand sum
trapezoidal rule
domain
Radian
41. A point where a function changes concavity; also - where the second derivative changes signs
bounded
inflection point
rational function
decay model
42. The value of the function approaches as x increases or decreases without bound
limit at infinity
cosecant function
local linearity
Fundamental theorem of calculus
43. 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
order of a derivative
distance formula
Total change Theorem
44. Ratio between the length of an arc and its radius
left hand sum
differential
parallel curve
Radian
45. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
continuity at a point
Mean Value theorem for derivatives
transcendental function
continuity on an interval
46. A function that is continuous on both the left and right side at that point
continuity at a point
average rate of change
definite integral
order of a derivative
47. Functions of angles
parallel curve
even function
circular function
left hand sum
48. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
Mean Value theorem for derivatives
continuous function
average rate of change
complex number
49. Two curves that have perpendicular tangents at the point of tangency
second derivative test
piecewise defined function
difference quotient
perpendicular curves
50. The value of the function at a critical point
infinite limit
critical value
numerical derivative
dummy variable of integration