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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 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
continuity at a point
instantaneous rate of change
instantaneous velocity
cosecant function
2. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
exponential function
cartesian coordinate system
integrand
3. If there is some number b that is less than or equal to every number in the range of f
bounded below
difference quotient
related rates
constant of integration
4. 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)
Mean Value theorem for derivatives
distance formula
integrand
integration by substitution
5. 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
root of an equation
right hand sum
distance formula
left hand sum
6. The process of evaluating an indefinite integral
Antidifferentiation- check
piecewise defined function
integrable function
Total change Theorem
7. 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
Total change Theorem
left hand limit
trapezoidal rule
integration by substitution
8. A function that can be graphed w/ a line or smooth curve
Radian
end behavior
continuous function
perpendicular curves
9. An undetermined constant added to every result of integration (the added +c)
distance formula
differentiation
constant of integration
differential equation
10. The reciprocal of the sine function
end behavior
cosecant function
definite integral
acceleration
11. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
bounded below
differential equation
Fundamental theorem of calculus
difference quotient
12. d = v[( x2 - x1)² + (y2 - y1)²]
concave down
circular function
distance formula
instantaneous velocity
13. Two curves that have perpendicular tangents at the point of tangency
antiderivative
constant function
Total change Theorem
perpendicular curves
14. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
transcendental function
law of sines
amplitude
decay model
15. 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)
cross sectional area
Fundamental theorem of calculus
removable discontinuity
natural logarithm
16. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
limit of integration
instantaneous velocity
even function
difference quotient
17. The local and global maximums and minimums of a function
local linearity
difference quotient
extremum
instantaneous rate of change
18. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
odd function
initial condition
Algebraic function
19. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
inflection point
differential equation
odd function
instantaneous rate of change
20. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
rational function
position function
left hand limit
21. 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))
integrable function
definite integral
limit at infinity
local linearity
22. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
dummy variable of integration
Algebraic function
law of cosine
transcendental function
23. The inverse of an eponential function
parameter
trapezoidal rule
logarithmic function
asymptote
24. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
definite integral
right hand sum
complex number
25. sinA/a=sinB/b=sinC/c
Rolle's Theorem
power series
removable discontinuity
law of sines
26. 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)
cross sectional area
absolute maximum
concave down
mean value theorem for definite integrals
27. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
absolute value
Antidifferentiation- check
acceleration
28. 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)
linear approximation
decay model
absolute maximum
non removable discontinuity
29. ex) dx - dy etc
differential
odd function
exponential growth and decay
integrand
30. The maximum distance that the particles of a wave's medium vibrate from their rest position
constant of integration
amplitude
parameter
differential equation
31. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)
numerical derivative
parameter
Radian
cross sectional area
32. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
related rates
conic section
order of a derivative
integration by substitution
33. A function that is continuous on both the left and right side at that point
integration by substitution
continuity at a point
absolute minimum
differentiation
34. Amount of change / time it takes (amount of change/ length of interval)
second derivative test
concave down
average rate of change
even function
35. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
logarithmic function
limit at infinity
circular function
exponential growth and decay
36. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
leibniz notation
definite integral
power series
right hand limit
37. 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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38. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
limit at infinity
definite integral
order of a derivative
partition of an interval
39. 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
partition of an interval
root of an equation
asymptote
bounded
40. A function that is continuous at every point on the interval
end behavior
continuity on an interval
Rolle's Theorem
mean value theorem for definite integrals
41. A given value of x and f(x) used to find the constant of integration
initial condition
normal line
first derivative test
continuity at a point
42. 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
circular function
Mean Value theorem for derivatives
differentiability
cartesian coordinate system
43. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
Rolle's Theorem
right hand limit
amplitude
44. A²=(b²+c²)-2(ab)Cos(A)
end behavior
law of cosine
continuity at a point
continuous function
45. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
logarithm laws
integrable function
order of a derivative
antiderivative
46. 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
related rates
exponential growth and decay
first derivative test
circular function
47. Input of function
domain
logarithmic function
integrand
trapezoidal rule
48. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.
average rate of change
critical value
non removable discontinuity
natural logarithm
49. A measure of how a function changes as its input changes.
average rate of change
derivative
bounded above
limit at infinity
50. 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
constant of integration
bounded above
Algebraic function
Intermediate value theorem
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