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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 at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
derivative
law of sines
mean value theorem for definite integrals
2. 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
right hand limit
root of an equation
integrable function
bounded
3. The process of evaluating an indefinite integral
exponential function
Antidifferentiation- check
bounded below
definite integral
4. 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
integration by substitution
exponential function
piecewise defined function
5. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
non removable discontinuity
conic section
complex number
first derivative test
6. The distance a number is from 0 on a number line
difference quotient
inflection point
absolute value
complex number
7. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
Antidifferentiation- check
right hand sum
differential
8. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
amplitude
order of a derivative
exponential growth and decay
differential
9. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
transcendental function
extreme value theorem
conic section
instantaneous rate of change
10. A logarithm with the base e - written as ln
exponential growth and decay
natural logarithm
integrand
removable discontinuity
11. 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
Radian
instantaneous rate of change
left hand limit
12. ex) dx - dy etc
bounded above
initial condition
differential
differentiation
13. A point where a function changes concavity; also - where the second derivative changes signs
decay model
bounded
absolute maximum
inflection point
14. A measure of how a function changes as its input changes.
transcendental function
limit at infinity
derivative
exponential growth and decay
15. A function that is continuous at every point on the interval
continuity on an interval
Antidifferentiation- check
right hand sum
local linearity
16. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
instantaneous velocity
left hand limit
absolute value
17. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
bounded above
cartesian coordinate system
implicit differentiation
18. d = v[( x2 - x1)² + (y2 - y1)²]
cartesian coordinate system
Fundamental theorem of calculus
law of cosine
distance formula
19. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
order of a derivative
antiderivative
indefinite integral
normal line
20. 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)
parallel curve
differentiability
linear approximation
definite integral
21. 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
left hand sum
integrable function
numerical derivative
22. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
power series
absolute minimum
non removable discontinuity
amplitude
23. Ratio between the length of an arc and its radius
Radian
instantaneous rate of change
absolute value
parallel curve
24. 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
Algebraic function
absolute value
first derivative test
differentiability
25. A function that can be graphed w/ a line or smooth curve
Algebraic function
parameter
concave up
continuous function
26. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
decay model
parallel curve
complex number
27. A variable occurring in a function - but on which the value of the function does not depend
initial condition
dummy variable of integration
continuous function
right hand limit
28. A straight line that is the limiting value of a curve
mean value theorem for definite integrals
asymptote
Radian
exponential growth and decay
29. 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
logarithmic function
Intermediate value theorem
Radian
constant function
30. 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
bounded above
removable discontinuity
infinite limit
31. The inverse of an eponential function
limit at infinity
critical value
logarithmic function
constant function
32. A surface or shape exposed by making a straight cut through something at right angles to the axis.
non removable discontinuity
critical point
cross sectional area
difference quotient
33. 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)
concave down
first derivative test
Fundamental theorem of calculus
continuity at a point
34. The smallest y-value of the function
instantaneous velocity
absolute minimum
parallel curve
instantaneous rate of change
35. A given value of x and f(x) used to find the constant of integration
differentiability
instantaneous rate of change
initial condition
trapezoidal rule
36. The value of the function at a critical point
partition of an interval
Intermediate value theorem
parameter
critical value
37. Two curves that have perpendicular tangents at the point of tangency
removable discontinuity
related rates
perpendicular curves
definite integral
38. The value of the function approaches as x increases or decreases without bound
limit at infinity
rational function
extreme value theorem
perpendicular curves
39. A line that divides a figure in half so that each half is the mirror image of the other.
cross sectional area
axis of symmetry
endpoint extremum
linear approximation
40. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
logarithm laws
average rate of change
axis of symmetry
second derivative test
41. 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
concave down
differential
parameter
42. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
limit of integration
domain
decay model
43. 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))
differential
complex number
local linearity
optimization
44. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
logarithm laws
dummy variable of integration
circular function
45. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
left hand sum
exponential growth and decay
parallel curve
Radian
46. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
differential equation
Intermediate value theorem
Mean Value theorem for derivatives
limit at infinity
47. A function that is a fixed numerical value for all elements of the domain of the function
integrand
absolute value
constant function
piecewise defined function
48. Intervals on which the second derivative is negative
parameter
concave down
difference quotient
Algebraic function
49. N(1-r)^x
decay model
Algebraic function
amplitude
inflection point
50. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
exponential growth and decay
distance formula
Radian