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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. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit
extreme value theorem
complex number
Intermediate value theorem
constant function
2. The local and global maximums and minimums of a function
first derivative test
amplitude
linear approximation
extremum
3. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
numerical derivative
power series
Rolle's Theorem
4. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
cartesian coordinate system
absolute maximum
implicit differentiation
Fundamental theorem of calculus
5. 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
left hand sum
extreme value theorem
trapezoidal rule
integration by substitution
6. 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
root of an equation
removable discontinuity
constant function
7. 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
Fundamental theorem of calculus
odd function
integrand
instantaneous rate of change
8. A straight line that is the limiting value of a curve
cosecant function
Fundamental theorem of calculus
limit at infinity
asymptote
9. Ratio between the length of an arc and its radius
implicit differentiation
differentiation
Radian
decay model
10. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
Rolle's Theorem
normal line
implicit differentiation
11. Having the limits or boundaries established
leibniz notation
bounded
average rate of change
linear approximation
12. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
right hand limit
mean value theorem for definite integrals
left hand limit
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)
absolute maximum
Radian
inflection point
Mean Value theorem for derivatives
14. The value that a function is approaching as x approaches a given value through values less than x
root of an equation
law of sines
odd function
left hand limit
15. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
Rolle's Theorem
logarithm laws
second derivative test
critical value
16. The value of the function at a critical point
right hand limit
root of an equation
logarithm laws
critical value
17. Intervals in which the second derivative is positive
second derivative test
concave up
right hand limit
rational function
18. An undetermined constant added to every result of integration (the added +c)
first derivative test
extremum
exponential growth and decay
constant of integration
19. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
end behavior
complex number
order of a derivative
Fundamental theorem of calculus
20. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
Algebraic function
cartesian coordinate system
local linearity
acceleration
21. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
critical value
parameter
Intermediate value theorem
domain
22. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
difference quotient
second derivative test
exponential function
concave down
23. The limit of f as x approaches c from the right
right hand limit
continuous function
logarithm laws
circular function
24. A surface or shape exposed by making a straight cut through something at right angles to the axis.
cross sectional area
exponential function
instantaneous velocity
inflection point
25. A logarithm with the base e - written as ln
differentiation
extremum
related rates
natural logarithm
26. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
integration by substitution
differential
law of cosine
difference quotient
27. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
removable discontinuity
non removable discontinuity
differential
continuity on an interval
28. 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
difference quotient
first derivative test
extremum
instantaneous velocity
29. A²=(b²+c²)-2(ab)Cos(A)
non removable discontinuity
law of cosine
mean value theorem for definite integrals
leibniz notation
30. Input of function
initial condition
domain
absolute value
concave down
31. The value of the function approaches as x increases or decreases without bound
endpoint extremum
limit of integration
limit at infinity
exponential function
32. A function that is continuous on both the left and right side at that point
circular function
constant function
differential equation
continuity at a point
33. dy/dx
infinite limit
bounded above
leibniz notation
constant of integration
34. The function that is integrated in an integral
integrand
trapezoidal rule
absolute maximum
piecewise defined function
35. 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
asymptote
average rate of change
differential equation
right hand sum
36. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
even function
initial condition
law of cosine
transcendental function
37. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
axis of symmetry
constant of integration
logarithmic function
difference quotient
38. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
root of an equation
cartesian coordinate system
bounded
exponential growth and decay
39. 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
related rates
asymptote
continuity at a point
even function
40. The inverse of an eponential function
logarithmic function
differentiation
antiderivative
circular function
41. Curve whose points are at a fixed normal distance of a given curve
parallel curve
critical value
transcendental function
bounded
42. A measure of how a function changes as its input changes.
derivative
Algebraic function
extremum
continuity at a point
43. Any value in the domain where either the function is not differentiable or its derivative is 0.
infinite limit
critical point
Intermediate value theorem
average rate of change
44. A function f that gives the position f(t) of a body on a coordinate axis at time t
Fundamental theorem of calculus
Antidifferentiation- check
position function
acceleration
45. 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))
Total change Theorem
initial condition
local linearity
bounded below
46. A function that can be graphed w/ a line or smooth curve
extreme value theorem
numerical derivative
concave up
continuous function
47. 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
circular function
bounded
parameter
Total change Theorem
48. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
Mean Value theorem for derivatives
logarithm laws
extremum
order of a derivative
49. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
normal line
logarithmic function
power series
piecewise defined function
50. 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)
parallel curve
mean value theorem for definite integrals
indefinite integral
cosecant function
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