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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. 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.
non removable discontinuity
domain
antiderivative
continuity at a point
2. Intervals on which the second derivative is negative
concave down
right hand limit
constant function
constant of integration
3. 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
mean value theorem for definite integrals
logarithmic function
absolute minimum
4. 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
instantaneous velocity
differentiation
left hand sum
Mean Value theorem for derivatives
5. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
order of a derivative
limit at infinity
cartesian coordinate system
6. 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)
difference quotient
decay model
linear approximation
endpoint extremum
7. 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
cartesian coordinate system
Antidifferentiation- check
logarithmic function
8. Amount of change / time it takes (amount of change/ length of interval)
average rate of change
removable discontinuity
instantaneous rate of change
implicit differentiation
9. 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
circular function
removable discontinuity
root of an equation
domain
10. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
initial condition
bounded
parameter
Algebraic function
11. Input of function
Rolle's Theorem
domain
difference quotient
endpoint extremum
12. sinA/a=sinB/b=sinC/c
perpendicular curves
bounded above
law of sines
differential equation
13. Having the limits or boundaries established
transcendental function
logarithm laws
bounded
constant of integration
14. A straight line that is the limiting value of a curve
asymptote
local linearity
exponential function
bounded below
15. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
cross sectional area
infinite limit
Total change Theorem
second derivative test
16. The value of the function at a critical point
local linearity
power series
critical value
parallel curve
17. 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
Fundamental theorem of calculus
Algebraic function
Total change Theorem
integrable function
18. The mathematical process of obtaining the derivative of a function
differentiability
integrable function
bounded
differentiation
19. 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
antiderivative
decay model
absolute maximum
Mean Value theorem for derivatives
20. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
differentiation
absolute maximum
law of cosine
exponential function
21. 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
circular function
average rate of change
domain
trapezoidal rule
22. The behavior of the graph of a function as x approaches positive infinity or negative infinity
non removable discontinuity
mean value theorem for definite integrals
end behavior
position function
23. 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)
optimization
Mean Value theorem for derivatives
concave down
derivative
24. The inverse of an eponential function
difference quotient
complex number
leibniz notation
logarithmic function
25. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
complex number
linear approximation
removable discontinuity
concave down
26. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
constant of integration
endpoint extremum
cosecant function
parameter
27. 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
integrable function
asymptote
conic section
28. If there is some number b that is less than or equal to every number in the range of f
removable discontinuity
instantaneous velocity
first derivative test
bounded below
29. Selection of a best element from some set of available alternatives.
removable discontinuity
law of sines
optimization
local linearity
30. An undetermined constant added to every result of integration (the added +c)
differential
left hand limit
complex number
constant of integration
31. Ratio between the length of an arc and its radius
Radian
non removable discontinuity
transcendental function
instantaneous rate of change
32. Imaginary line drawn perpendicular to the surface of a mirror or any surface
bounded
optimization
normal line
extremum
33. The distance a number is from 0 on a number line
average rate of change
limit of integration
absolute value
asymptote
34. 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
conic section
right hand sum
concave up
35. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
conic section
odd function
critical value
definite integral
36. The value of the function approaches as x increases or decreases without bound
piecewise defined function
constant function
limit at infinity
continuity at a point
37. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
implicit differentiation
asymptote
order of a derivative
integrable function
38. Curve whose points are at a fixed normal distance of a given curve
Algebraic function
complex number
parallel curve
related rates
39. If there is some number B that is greater than or equal to every number in the range of f
bounded above
non removable discontinuity
antiderivative
rational function
40. 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
perpendicular curves
decay model
differentiability
Radian
41. 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
Intermediate value theorem
differentiability
piecewise defined function
42. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
local linearity
partition of an interval
order of a derivative
absolute minimum
43. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
left hand sum
acceleration
transcendental function
difference quotient
44. A function that can be graphed w/ a line or smooth curve
continuous function
order of a derivative
acceleration
conic section
45. 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
even function
related rates
indefinite integral
first derivative test
46. The maximum distance that the particles of a wave's medium vibrate from their rest position
critical point
definite integral
partition of an interval
amplitude
47. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
inflection point
absolute minimum
differential equation
integrable function
48. A function that is continuous at every point on the interval
integration by substitution
bounded
continuity on an interval
Intermediate value theorem
49. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
axis of symmetry
amplitude
absolute value
logarithm laws
50. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
Algebraic function
transcendental function
end behavior
trapezoidal rule