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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. 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)
transcendental function
Mean Value theorem for derivatives
removable discontinuity
parallel curve
2. 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
leibniz notation
cartesian coordinate system
parallel curve
first derivative test
3. The value that a function is approaching as x approaches a given value through values less than x
initial condition
second derivative test
normal line
left hand limit
4. 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
second derivative test
limit of integration
antiderivative
odd function
5. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
concave up
definite integral
average rate of change
parameter
6. The distance a number is from 0 on a number line
absolute value
domain
second derivative test
implicit differentiation
7. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
definite integral
Algebraic function
law of cosine
8. dy/dx
bounded above
piecewise defined function
instantaneous rate of change
leibniz notation
9. A limit in which f(x) increases or decreases without bound - as x approaches c
piecewise defined function
instantaneous velocity
infinite limit
bounded above
10. A function that is continuous at every point on the interval
acceleration
trapezoidal rule
continuity on an interval
position function
11. A function that is continuous on both the left and right side at that point
asymptote
cartesian coordinate system
continuity at a point
trapezoidal rule
12. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
trapezoidal rule
Intermediate value theorem
second derivative test
13. The value of the function at a critical point
left hand limit
acceleration
indefinite integral
critical value
14. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
parallel curve
limit at infinity
differential
15. N(1-r)^x
decay model
indefinite integral
natural logarithm
differentiability
16. The behavior of the graph of a function as x approaches positive infinity or negative infinity
removable discontinuity
end behavior
implicit differentiation
perpendicular curves
17. 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
differentiation
extremum
absolute minimum
Intermediate value theorem
18. 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
integrable function
bounded
instantaneous velocity
endpoint extremum
19. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
Algebraic function
circular function
infinite limit
power series
20. Functions of angles
first derivative test
circular function
law of sines
distance formula
21. Dividing an interval into n sub-intervals
rational function
Algebraic function
partition of an interval
absolute value
22. 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
bounded
dummy variable of integration
23. A function that can be graphed w/ a line or smooth curve
domain
constant of integration
continuous function
bounded above
24. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
continuity on an interval
exponential function
removable discontinuity
local linearity
25. A straight line that is the limiting value of a curve
asymptote
transcendental function
removable discontinuity
cartesian coordinate system
26. 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
position function
endpoint extremum
limit of integration
related rates
27. Having the limits or boundaries established
bounded
mean value theorem for definite integrals
law of sines
differential equation
28. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
absolute minimum
decay model
inflection point
rational function
29. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
Total change Theorem
non removable discontinuity
limit at infinity
30. If there is some number B that is greater than or equal to every number in the range of f
first derivative test
cartesian coordinate system
bounded above
Total change Theorem
31. d = v[( x2 - x1)² + (y2 - y1)²]
numerical derivative
position function
distance formula
right hand sum
32. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
continuity on an interval
Algebraic function
differential equation
parameter
33. A function that is a fixed numerical value for all elements of the domain of the function
critical point
constant function
even function
Algebraic function
34. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
right hand sum
acceleration
linear approximation
extremum
35. Intervals on which the second derivative is negative
concave down
limit at infinity
antiderivative
Total change Theorem
36. A line that divides a figure in half so that each half is the mirror image of the other.
law of cosine
axis of symmetry
critical value
Antidifferentiation- check
37. Ratio between the length of an arc and its radius
Radian
power series
instantaneous rate of change
continuity at a point
38. The value of the function approaches as x increases or decreases without bound
limit at infinity
linear approximation
continuity on an interval
initial condition
39. The function that is integrated in an integral
power series
piecewise defined function
integrand
implicit differentiation
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 right-most point of the sub-interval
right hand sum
integration by substitution
decay model
bounded above
41. A measure of how a function changes as its input changes.
integration by substitution
derivative
concave down
limit of integration
42. A²=(b²+c²)-2(ab)Cos(A)
complex number
absolute value
non removable discontinuity
law of cosine
43. A point where a function changes concavity; also - where the second derivative changes signs
parameter
Fundamental theorem of calculus
inflection point
logarithmic function
44. A variable occurring in a function - but on which the value of the function does not depend
dummy variable of integration
piecewise defined function
limit at infinity
definite integral
45. If there is some number b that is less than or equal to every number in the range of f
bounded below
linear approximation
absolute maximum
dummy variable of integration
46. sinA/a=sinB/b=sinC/c
exponential growth and decay
law of sines
continuity at a point
complex number
47. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
average rate of change
derivative
piecewise defined function
exponential growth and decay
48. Curve whose points are at a fixed normal distance of a given curve
decay model
acceleration
definite integral
parallel curve
49. 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))
infinite limit
non removable discontinuity
definite integral
local linearity
50. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
definite integral
bounded
average rate of change