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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 mathematical process of obtaining the derivative of a function
differentiation
decay model
law of cosine
natural logarithm
2. 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
position function
differentiation
decay model
3. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
order of a derivative
indefinite integral
Total change Theorem
non removable discontinuity
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
Intermediate value theorem
integrable function
continuity on an interval
rational function
5. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
decay model
limit at infinity
removable discontinuity
left hand limit
6. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
parallel curve
integration by substitution
difference quotient
differential
7. Intervals in which the second derivative is positive
implicit differentiation
absolute maximum
position function
concave up
8. Selection of a best element from some set of available alternatives.
critical point
continuity at a point
Fundamental theorem of calculus
optimization
9. An undetermined constant added to every result of integration (the added +c)
Intermediate value theorem
removable discontinuity
non removable discontinuity
constant of integration
10. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
exponential function
acceleration
integrable function
root of an equation
11. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
Fundamental theorem of calculus
difference quotient
indefinite integral
differentiation
12. sinA/a=sinB/b=sinC/c
law of sines
integrable function
absolute minimum
power series
13. 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
Algebraic function
average rate of change
related rates
Mean Value theorem for derivatives
14. 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
leibniz notation
root of an equation
order of a derivative
absolute minimum
15. 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
local linearity
exponential growth and decay
differentiability
natural logarithm
16. The value that a function is approaching as x approaches a given value through values less than x
bounded
integration by substitution
optimization
left hand limit
17. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
acceleration
bounded above
odd function
differential equation
18. The value of the function approaches as x increases or decreases without bound
continuous function
complex number
limit at infinity
endpoint extremum
19. If there is some number b that is less than or equal to every number in the range of f
bounded below
integration by substitution
critical point
cosecant function
20. A function that is continuous on both the left and right side at that point
cartesian coordinate system
parallel curve
continuity at a point
critical point
21. (geometry)A curve generated by the intersection of a plane or circular cone
numerical derivative
instantaneous rate of change
conic section
rational function
22. 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)
bounded above
leibniz notation
numerical derivative
mean value theorem for definite integrals
23. The distance a number is from 0 on a number line
law of cosine
inflection point
Radian
absolute value
24. d = v[( x2 - x1)² + (y2 - y1)²]
optimization
distance formula
definite integral
acceleration
25. The maximum distance that the particles of a wave's medium vibrate from their rest position
related rates
definite integral
continuity at a point
amplitude
26. ex) dx - dy etc
infinite limit
differential
critical point
axis of symmetry
27. Imaginary line drawn perpendicular to the surface of a mirror or any surface
bounded below
odd function
normal line
removable discontinuity
28. A given value of x and f(x) used to find the constant of integration
initial condition
instantaneous velocity
continuity on an interval
absolute minimum
29. A variable occurring in a function - but on which the value of the function does not depend
differential equation
dummy variable of integration
continuity at a point
mean value theorem for definite integrals
30. Two curves that have perpendicular tangents at the point of tangency
bounded above
even function
asymptote
perpendicular curves
31. 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
Algebraic function
left hand sum
concave down
32. 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)
Total change Theorem
integrable function
integrand
Fundamental theorem of calculus
33. 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
extreme value theorem
concave down
Total change Theorem
left hand sum
34. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
critical value
inflection point
left hand limit
35. A point that represents the maximum value a function assumes over its domain
instantaneous velocity
average rate of change
absolute maximum
differentiability
36. Ratio between the length of an arc and its radius
local linearity
continuity at a point
continuity on an interval
Radian
37. A straight line that is the limiting value of a curve
asymptote
amplitude
continuous function
antiderivative
38. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
cartesian coordinate system
related rates
complex number
mean value theorem for definite integrals
39. 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
instantaneous rate of change
Radian
right hand sum
partition of an interval
40. Amount of change / time it takes (amount of change/ length of interval)
transcendental function
instantaneous velocity
average rate of change
indefinite integral
41. A function f that gives the position f(t) of a body on a coordinate axis at time t
numerical derivative
critical value
position function
Antidifferentiation- check
42. 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)
cosecant function
linear approximation
bounded below
left hand limit
43. A limit in which f(x) increases or decreases without bound - as x approaches c
domain
continuity on an interval
infinite limit
linear approximation
44. The behavior of the graph of a function as x approaches positive infinity or negative infinity
logarithmic function
end behavior
perpendicular curves
first derivative test
45. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
exponential growth and decay
normal line
Fundamental theorem of calculus
46. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
second derivative test
cross sectional area
implicit differentiation
law of cosine
47. The process of evaluating an indefinite integral
continuous function
antiderivative
Antidifferentiation- check
infinite limit
48. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
limit at infinity
differential equation
local linearity
49. dy/dx
right hand sum
difference quotient
inflection point
leibniz notation
50. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
initial condition
domain
left hand limit
complex number