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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. 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
antiderivative
cross sectional area
limit of integration
trapezoidal rule
2. N(1-r)^x
normal line
constant function
order of a derivative
decay model
3. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
extremum
definite integral
natural logarithm
4. The reciprocal of the sine function
absolute value
cosecant function
definite integral
law of sines
5. Selection of a best element from some set of available alternatives.
implicit differentiation
parameter
order of a derivative
optimization
6. Intervals in which the second derivative is positive
first derivative test
Rolle's Theorem
even function
concave up
7. A function that is continuous on both the left and right side at that point
absolute value
parallel curve
initial condition
continuity at a point
8. Intervals on which the second derivative is negative
circular function
concave down
exponential function
average rate of change
9. A limit in which f(x) increases or decreases without bound - as x approaches c
natural logarithm
distance formula
parameter
infinite limit
10. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
integrable function
indefinite integral
law of sines
complex number
11. A surface or shape exposed by making a straight cut through something at right angles to the axis.
domain
bounded
cross sectional area
dummy variable of integration
12. A function that can be graphed w/ a line or smooth curve
constant function
continuous function
differentiation
infinite limit
13. A point that represents the maximum value a function assumes over its domain
acceleration
absolute maximum
even function
Total change Theorem
14. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
cartesian coordinate system
bounded above
parameter
end behavior
15. Amount of change / time it takes (amount of change/ length of interval)
endpoint extremum
antiderivative
mean value theorem for definite integrals
average rate of change
16. The distance a number is from 0 on a number line
even function
law of sines
absolute value
continuous function
17. A line that divides a figure in half so that each half is the mirror image of the other.
absolute maximum
optimization
axis of symmetry
exponential function
18. If there is some number b that is less than or equal to every number in the range of f
bounded below
cartesian coordinate system
odd function
Intermediate value theorem
19. The process of evaluating an indefinite integral
left hand limit
related rates
Antidifferentiation- check
Radian
20. An undetermined constant added to every result of integration (the added +c)
constant of integration
trapezoidal rule
concave down
end behavior
21. The smallest y-value of the function
instantaneous velocity
related rates
absolute minimum
Antidifferentiation- check
22. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
constant function
extremum
left hand sum
23. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
acceleration
even function
position function
order of a derivative
24. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
first derivative test
left hand limit
circular function
25. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
antiderivative
definite integral
integration by substitution
mean value theorem for definite integrals
26. The behavior of the graph of a function as x approaches positive infinity or negative infinity
axis of symmetry
concave down
end behavior
bounded
27. The local and global maximums and minimums of a function
continuity at a point
extremum
perpendicular curves
Intermediate value theorem
28. A logarithm with the base e - written as ln
parameter
limit at infinity
natural logarithm
asymptote
29. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
concave up
decay model
transcendental function
instantaneous rate of change
30. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
instantaneous velocity
removable discontinuity
instantaneous rate of change
initial condition
31. 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
amplitude
logarithm laws
perpendicular curves
32. 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)
optimization
critical point
mean value theorem for definite integrals
linear approximation
33. The value of the function approaches as x increases or decreases without bound
limit at infinity
differentiability
left hand limit
difference quotient
34. 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
differentiability
leibniz notation
local linearity
Mean Value theorem for derivatives
35. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
complex number
cartesian coordinate system
infinite limit
extreme value theorem
36. If there is some number B that is greater than or equal to every number in the range of f
cosecant function
bounded above
complex number
initial condition
37. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
continuous function
parameter
initial condition
38. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
absolute minimum
position function
definite integral
endpoint extremum
39. 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
logarithmic function
instantaneous rate of change
even function
40. 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)
root of an equation
constant of integration
linear approximation
dummy variable of integration
41. 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
root of an equation
partition of an interval
bounded above
initial condition
42. 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
transcendental function
right hand limit
non removable discontinuity
instantaneous rate of change
43. The inverse of an eponential function
parameter
axis of symmetry
piecewise defined function
logarithmic function
44. 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)
transcendental function
numerical derivative
complex number
root of an equation
45. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
Fundamental theorem of calculus
right hand sum
cross sectional area
46. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
critical point
trapezoidal rule
acceleration
differential equation
47. Input of function
derivative
rational function
domain
differentiability
48. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
law of sines
definite integral
local linearity
implicit differentiation
49. When testing critical values - if the first derivative changes from negative to zero to positive - then that critical value is a local minimum of the function. If the first derivative changes from positive to zero of negative - then that critical val
amplitude
first derivative test
extreme value theorem
absolute minimum
50. 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
continuity at a point
exponential function
distance formula
right hand sum