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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. A logarithm with the base e - written as ln
natural logarithm
odd function
endpoint extremum
left hand limit
2. 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
acceleration
right hand sum
normal line
concave down
3. 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
average rate of change
related rates
law of cosine
exponential growth and decay
4. A function that is continuous on both the left and right side at that point
continuity at a point
continuous function
perpendicular curves
right hand limit
5. A function that can be graphed w/ a line or smooth curve
leibniz notation
absolute value
continuous function
definite integral
6. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
continuity at a point
continuous function
endpoint extremum
exponential growth and decay
7. 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)
decay model
left hand limit
Fundamental theorem of calculus
absolute maximum
8. The value of the function approaches as x increases or decreases without bound
cross sectional area
limit at infinity
Algebraic function
continuity at a point
9. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
even function
perpendicular curves
differentiation
continuity at a point
10. 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
Fundamental theorem of calculus
partition of an interval
trapezoidal rule
bounded above
11. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions
position function
circular function
local linearity
transcendental function
12. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
parallel curve
implicit differentiation
logarithm laws
even function
13. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
continuity on an interval
second derivative test
inflection point
integrand
14. A function whose domain is divided into several parts and a different function rule is applied to each part
trapezoidal rule
continuity at a point
conic section
piecewise defined function
15. Functions of angles
end behavior
circular function
partition of an interval
first derivative test
16. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
order of a derivative
second derivative test
piecewise defined function
17. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
extremum
left hand sum
law of sines
18. The distance a number is from 0 on a number line
absolute value
circular function
mean value theorem for definite integrals
average rate of change
19. A function that is a fixed numerical value for all elements of the domain of the function
difference quotient
limit of integration
constant function
root of an equation
20. The process of evaluating an indefinite integral
linear approximation
removable discontinuity
power series
Antidifferentiation- check
21. Intervals on which the second derivative is negative
limit of integration
concave down
endpoint extremum
natural logarithm
22. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
left hand limit
root of an equation
critical point
exponential function
23. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
domain
second derivative test
right hand sum
implicit differentiation
24. 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
continuous function
conic section
mean value theorem for definite integrals
25. A function that is continuous at every point on the interval
parameter
continuity on an interval
critical point
position function
26. A straight line that is the limiting value of a curve
inflection point
concave up
bounded below
asymptote
27. 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
exponential function
domain
odd function
instantaneous rate of change
28. A line that divides a figure in half so that each half is the mirror image of the other.
instantaneous velocity
parameter
inflection point
axis of symmetry
29. 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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30. Dividing an interval into n sub-intervals
endpoint extremum
amplitude
linear approximation
partition of an interval
31. 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
instantaneous velocity
continuous function
inflection point
Rolle's Theorem
32. An undetermined constant added to every result of integration (the added +c)
complex number
decay model
perpendicular curves
constant of integration
33. A point where a function changes concavity; also - where the second derivative changes signs
integrable function
law of cosine
local linearity
inflection point
34. A²=(b²+c²)-2(ab)Cos(A)
bounded
parameter
derivative
law of cosine
35. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
differentiability
mean value theorem for definite integrals
piecewise defined function
odd function
36. The value of the function at a critical point
cosecant function
critical value
conic section
normal line
37. The local and global maximums and minimums of a function
instantaneous rate of change
extremum
cross sectional area
logarithm laws
38. ex) dx - dy etc
rational function
numerical derivative
indefinite integral
differential
39. Having the limits or boundaries established
related rates
transcendental function
bounded
integrable function
40. Selection of a best element from some set of available alternatives.
optimization
circular function
implicit differentiation
differential equation
41. The behavior of the graph of a function as x approaches positive infinity or negative infinity
decay model
bounded
constant function
end behavior
42. The limit of f as x approaches c from the right
mean value theorem for definite integrals
concave up
right hand limit
absolute minimum
43. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
left hand sum
differentiability
constant of integration
44. 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)
linear approximation
concave up
numerical derivative
differentiation
45. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
optimization
critical point
absolute maximum
parameter
46. 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
antiderivative
critical value
piecewise defined function
first derivative test
47. 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)
local linearity
concave down
linear approximation
logarithm laws
48. The inverse of an eponential function
linear approximation
partition of an interval
logarithmic function
instantaneous rate of change
49. If there is some number B that is greater than or equal to every number in the range of f
bounded above
concave up
Fundamental theorem of calculus
constant of integration
50. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
differentiation
domain
definite integral
transcendental function