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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. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
integrable function
linear approximation
derivative
logarithm laws
2. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
differentiation
Algebraic function
rational function
constant of integration
3. 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))
transcendental function
removable discontinuity
dummy variable of integration
local linearity
4. The behavior of the graph of a function as x approaches positive infinity or negative infinity
continuity on an interval
end behavior
root of an equation
derivative
5. The function that is integrated in an integral
constant function
Intermediate value theorem
integrand
law of sines
6. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
implicit differentiation
axis of symmetry
acceleration
derivative
7. The value that a function is approaching as x approaches a given value through values less than x
even function
left hand limit
constant function
absolute minimum
8. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
difference quotient
even function
conic section
continuity on an interval
9. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
indefinite integral
complex number
numerical derivative
exponential function
10. Functions of angles
inflection point
root of an equation
differential
circular function
11. A function that is continuous on both the left and right side at that point
constant of integration
exponential growth and decay
logarithmic function
continuity at a point
12. Input of function
logarithm laws
trapezoidal rule
parallel curve
domain
13. 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)
integration by substitution
logarithm laws
Mean Value theorem for derivatives
definite integral
14. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
absolute value
extreme value theorem
normal line
parallel curve
15. 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
left hand limit
critical point
Total change Theorem
transcendental function
16. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
Radian
Algebraic function
dummy variable of integration
17. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
order of a derivative
odd function
antiderivative
law of sines
18. A point that represents the maximum value a function assumes over its domain
absolute maximum
odd function
trapezoidal rule
average rate of change
19. N(1-r)^x
decay model
normal line
Mean Value theorem for derivatives
bounded below
20. Intervals on which the second derivative is negative
differential equation
extremum
law of cosine
concave down
21. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
piecewise defined function
constant of integration
removable discontinuity
bounded above
22. The inverse of an eponential function
mean value theorem for definite integrals
logarithmic function
exponential function
difference quotient
23. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
law of sines
power series
linear approximation
amplitude
24. dy/dx
law of cosine
leibniz notation
Rolle's Theorem
exponential function
25. A function whose domain is divided into several parts and a different function rule is applied to each part
leibniz notation
first derivative test
cartesian coordinate system
piecewise defined function
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
right hand limit
related rates
linear approximation
critical point
27. Amount of change / time it takes (amount of change/ length of interval)
absolute minimum
average rate of change
order of a derivative
differential
28. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
even function
piecewise defined function
derivative
29. A²=(b²+c²)-2(ab)Cos(A)
right hand limit
exponential function
integrable function
law of cosine
30. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
Mean Value theorem for derivatives
axis of symmetry
end behavior
31. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
normal line
differential equation
differentiation
32. A point where a function changes concavity; also - where the second derivative changes signs
Algebraic function
amplitude
extremum
inflection point
33. 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)
rational function
derivative
linear approximation
Intermediate value theorem
34. The limit of f as x approaches c from the right
integrand
right hand limit
asymptote
partition of an interval
35. 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)
leibniz notation
concave down
mean value theorem for definite integrals
rational function
36. 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
continuous function
continuity at a point
acceleration
instantaneous velocity
37. 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
perpendicular curves
transcendental function
instantaneous rate of change
law of cosine
38. The process of evaluating an indefinite integral
domain
decay model
implicit differentiation
Antidifferentiation- check
39. A function that is continuous at every point on the interval
continuity on an interval
indefinite integral
circular function
instantaneous velocity
40. A function that can be graphed w/ a line or smooth curve
law of sines
trapezoidal rule
normal line
continuous function
41. A logarithm with the base e - written as ln
natural logarithm
inflection point
domain
integrable function
42. A limit in which f(x) increases or decreases without bound - as x approaches c
infinite limit
critical value
exponential function
leibniz notation
43. 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
first derivative test
normal line
position function
amplitude
44. Dividing an interval into n sub-intervals
law of cosine
absolute value
partition of an interval
bounded below
45. 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
root of an equation
initial condition
Intermediate value theorem
46. A function f that gives the position f(t) of a body on a coordinate axis at time t
related rates
differentiability
position function
numerical derivative
47. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
initial condition
integrand
Algebraic function
first derivative test
48. An undetermined constant added to every result of integration (the added +c)
constant of integration
difference quotient
odd function
leibniz notation
49. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
right hand limit
integrable function
transcendental function
local linearity
50. The local and global maximums and minimums of a function
extremum
law of cosine
cartesian coordinate system
bounded