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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
differential
difference quotient
logarithmic function
logarithm laws
2. 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
integration by substitution
instantaneous rate of change
power series
differentiation
3. 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
optimization
position function
continuity on an interval
4. A variable occurring in a function - but on which the value of the function does not depend
position function
dummy variable of integration
constant function
endpoint extremum
5. Selection of a best element from some set of available alternatives.
differentiability
local linearity
optimization
partition of an interval
6. 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.
Rolle's Theorem
non removable discontinuity
continuous function
endpoint extremum
7. 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)
Mean Value theorem for derivatives
domain
related rates
limit at infinity
8. Dividing an interval into n sub-intervals
Mean Value theorem for derivatives
partition of an interval
infinite limit
limit at infinity
9. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
position function
complex number
conic section
10. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
continuous function
integration by substitution
logarithm laws
11. The value of the function approaches as x increases or decreases without bound
limit at infinity
cartesian coordinate system
axis of symmetry
root of an equation
12. The reciprocal of the sine function
cosecant function
constant function
trapezoidal rule
differential equation
13. Two curves that have perpendicular tangents at the point of tangency
leibniz notation
perpendicular curves
inflection point
Mean Value theorem for derivatives
14. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
trapezoidal rule
optimization
parameter
definite integral
15. A²=(b²+c²)-2(ab)Cos(A)
right hand limit
law of cosine
integration by substitution
differential
16. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
trapezoidal rule
absolute value
concave down
17. Ratio between the length of an arc and its radius
logarithm laws
integration by substitution
Algebraic function
Radian
18. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
differential equation
power series
cartesian coordinate system
left hand limit
19. A line that divides a figure in half so that each half is the mirror image of the other.
differentiation
even function
instantaneous velocity
axis of symmetry
20. N(1-r)^x
rational function
differential
decay model
first derivative test
21. 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)
linear approximation
distance formula
endpoint extremum
bounded above
22. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
continuity on an interval
difference quotient
bounded
23. 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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24. The limit of f as x approaches c from the right
cosecant function
even function
first derivative test
right hand limit
25. A function that is continuous at every point on the interval
average rate of change
continuity on an interval
second derivative test
related rates
26. 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
optimization
integrand
law of sines
Total change Theorem
27. 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
differentiability
average rate of change
constant of integration
root of an equation
28. If there is some number b that is less than or equal to every number in the range of f
critical point
bounded below
extreme value theorem
differential equation
29. 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
differentiability
difference quotient
cosecant function
natural logarithm
30. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
absolute maximum
initial condition
rational function
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
exponential function
natural logarithm
extreme value theorem
32. If there is some number B that is greater than or equal to every number in the range of f
endpoint extremum
bounded above
logarithm laws
Total change Theorem
33. The behavior of the graph of a function as x approaches positive infinity or negative infinity
left hand sum
odd function
end behavior
trapezoidal rule
34. A function whose domain is divided into several parts and a different function rule is applied to each part
amplitude
left hand sum
perpendicular curves
piecewise defined function
35. 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)
circular function
transcendental function
complex number
numerical derivative
36. Having the limits or boundaries established
bounded
continuous function
limit of integration
mean value theorem for definite integrals
37. 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
local linearity
Algebraic function
integrable function
38. A logarithm with the base e - written as ln
transcendental function
piecewise defined function
natural logarithm
absolute minimum
39. A measure of how a function changes as its input changes.
normal line
complex number
derivative
differential
40. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
odd function
extreme value theorem
Fundamental theorem of calculus
41. The mathematical process of obtaining the derivative of a function
perpendicular curves
Radian
law of cosine
differentiation
42. A point that represents the maximum value a function assumes over its domain
absolute maximum
leibniz notation
critical point
instantaneous velocity
43. A surface or shape exposed by making a straight cut through something at right angles to the axis.
inflection point
right hand sum
cross sectional area
piecewise defined function
44. Intervals in which the second derivative is positive
root of an equation
domain
concave up
local linearity
45. A function f that gives the position f(t) of a body on a coordinate axis at time t
absolute value
bounded
instantaneous velocity
position function
46. The value that a function is approaching as x approaches a given value through values less than x
optimization
complex number
left hand limit
numerical derivative
47. 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))
differential equation
integration by substitution
bounded
local linearity
48. The value of the function at a critical point
critical value
even function
endpoint extremum
instantaneous rate of change
49. A given value of x and f(x) used to find the constant of integration
initial condition
integrand
absolute value
end behavior
50. A point where a function changes concavity; also - where the second derivative changes signs
continuity at a point
perpendicular curves
inflection point
natural logarithm
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