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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. N(1-r)^x
decay model
differential equation
bounded above
left hand sum
2. 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
absolute maximum
logarithmic function
differentiability
3. Amount of change / time it takes (amount of change/ length of interval)
optimization
average rate of change
infinite limit
decay model
4. 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
extreme value theorem
Total change Theorem
parameter
Intermediate value theorem
5. 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)
critical value
linear approximation
implicit differentiation
acceleration
6. The smallest y-value of the function
absolute minimum
optimization
removable discontinuity
cross sectional area
7. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
limit at infinity
rational function
continuous function
average rate of change
8. ex) dx - dy etc
natural logarithm
Antidifferentiation- check
differential
piecewise defined function
9. A given value of x and f(x) used to find the constant of integration
odd function
initial condition
critical point
partition of an interval
10. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
position function
concave down
logarithmic function
11. A logarithm with the base e - written as ln
parameter
natural logarithm
cosecant function
position function
12. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
differential equation
integrand
absolute minimum
odd function
13. 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
instantaneous velocity
root of an equation
logarithmic function
asymptote
14. The mathematical process of obtaining the derivative of a function
bounded
differentiation
cartesian coordinate system
parameter
15. d = v[( x2 - x1)² + (y2 - y1)²]
end behavior
bounded above
distance formula
optimization
16. A function whose domain is divided into several parts and a different function rule is applied to each part
Total change Theorem
piecewise defined function
amplitude
related rates
17. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
extremum
parallel curve
transcendental function
natural logarithm
18. An undetermined constant added to every result of integration (the added +c)
constant of integration
power series
differentiability
extremum
19. A²=(b²+c²)-2(ab)Cos(A)
partition of an interval
law of cosine
Intermediate value theorem
optimization
20. The process of evaluating an indefinite integral
Radian
Antidifferentiation- check
right hand limit
concave up
21. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
bounded above
Mean Value theorem for derivatives
limit of integration
logarithm laws
22. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
optimization
even function
piecewise defined function
constant function
23. (geometry)A curve generated by the intersection of a plane or circular cone
cartesian coordinate system
Rolle's Theorem
conic section
inflection point
24. The value that a function is approaching as x approaches a given value through values less than x
indefinite integral
Algebraic function
average rate of change
left hand limit
25. 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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26. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
implicit differentiation
critical point
exponential function
27. The limit of f as x approaches c from the right
natural logarithm
right hand limit
logarithm laws
definite integral
28. A function that is continuous at every point on the interval
linear approximation
continuity on an interval
related rates
mean value theorem for definite integrals
29. 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
position function
cosecant function
critical value
left hand sum
30. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
right hand limit
acceleration
extremum
asymptote
31. A line that divides a figure in half so that each half is the mirror image of the other.
complex number
indefinite integral
axis of symmetry
law of sines
32. Intervals on which the second derivative is negative
concave down
conic section
right hand limit
leibniz notation
33. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
order of a derivative
cosecant function
absolute maximum
continuity on an interval
34. 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
local linearity
limit at infinity
concave down
35. 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
numerical derivative
parallel curve
trapezoidal rule
logarithmic function
36. sinA/a=sinB/b=sinC/c
law of sines
bounded below
transcendental function
exponential function
37. 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
mean value theorem for definite integrals
non removable discontinuity
instantaneous velocity
exponential function
38. The value of the function at a critical point
constant of integration
cartesian coordinate system
critical value
endpoint extremum
39. A function that can be graphed w/ a line or smooth curve
Fundamental theorem of calculus
continuous function
exponential function
infinite limit
40. 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
differential equation
decay model
antiderivative
Total change Theorem
41. A function that is a fixed numerical value for all elements of the domain of the function
constant function
extremum
endpoint extremum
Antidifferentiation- check
42. 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)
endpoint extremum
mean value theorem for definite integrals
implicit differentiation
instantaneous rate of change
43. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
indefinite integral
related rates
integration by substitution
44. 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
non removable discontinuity
absolute value
right hand sum
left hand sum
45. Input of function
left hand limit
domain
conic section
circular function
46. Dividing an interval into n sub-intervals
partition of an interval
trapezoidal rule
initial condition
concave up
47. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
distance formula
initial condition
difference quotient
Total change Theorem
48. The behavior of the graph of a function as x approaches positive infinity or negative infinity
cross sectional area
Fundamental theorem of calculus
end behavior
integrand
49. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
parameter
definite integral
piecewise defined function
initial condition
50. Ratio between the length of an arc and its radius
root of an equation
circular function
implicit differentiation
Radian