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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. 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
logarithm laws
end behavior
Algebraic function
2. The inverse of an eponential function
right hand sum
limit of integration
cross sectional area
logarithmic function
3. Graph is symmetrical with respect to the origin; f(-x)=-f(x)
odd function
left hand limit
exponential growth and decay
order of a derivative
4. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
conic section
integration by substitution
indefinite integral
5. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
definite integral
continuity at a point
antiderivative
first derivative test
6. 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
extreme value theorem
related rates
first derivative test
partition of an interval
7. A²=(b²+c²)-2(ab)Cos(A)
law of cosine
extremum
inflection point
infinite limit
8. An undetermined constant added to every result of integration (the added +c)
constant of integration
logarithm laws
circular function
Antidifferentiation- check
9. 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)
antiderivative
critical point
leibniz notation
linear approximation
10. 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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11. The smallest y-value of the function
left hand limit
linear approximation
instantaneous rate of change
absolute minimum
12. A function that is a fixed numerical value for all elements of the domain of the function
parallel curve
concave down
constant function
Intermediate value theorem
13. ex) dx - dy etc
integration by substitution
constant function
differential
exponential function
14. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
non removable discontinuity
Algebraic function
right hand sum
continuous function
15. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
acceleration
complex number
exponential function
odd function
16. Dividing an interval into n sub-intervals
right hand sum
partition of an interval
Intermediate value theorem
antiderivative
17. A straight line that is the limiting value of a curve
continuity at a point
related rates
asymptote
cosecant function
18. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)
even function
optimization
numerical derivative
root of an equation
19. (geometry)A curve generated by the intersection of a plane or circular cone
conic section
exponential function
optimization
continuity at a point
20. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
rational function
end behavior
average rate of change
second derivative test
21. Ratio between the length of an arc and its radius
extremum
Mean Value theorem for derivatives
perpendicular curves
Radian
22. A function that is continuous on both the left and right side at that point
normal line
cross sectional area
differentiability
continuity at a point
23. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
bounded above
derivative
acceleration
difference quotient
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
differentiability
Rolle's Theorem
non removable discontinuity
Intermediate value theorem
25. A surface or shape exposed by making a straight cut through something at right angles to the axis.
perpendicular curves
bounded below
cross sectional area
infinite limit
26. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
cartesian coordinate system
exponential growth and decay
acceleration
axis of symmetry
27. If there is some number b that is less than or equal to every number in the range of f
average rate of change
natural logarithm
bounded below
definite integral
28. Functions of angles
initial condition
concave up
axis of symmetry
circular function
29. A given value of x and f(x) used to find the constant of integration
derivative
initial condition
dummy variable of integration
perpendicular curves
30. The reciprocal of the sine function
inflection point
initial condition
bounded
cosecant function
31. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
mean value theorem for definite integrals
complex number
cartesian coordinate system
non removable discontinuity
32. 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
right hand sum
related rates
Mean Value theorem for derivatives
critical point
33. If there is some number B that is greater than or equal to every number in the range of f
end behavior
bounded above
extremum
complex number
34. A function whose domain is divided into several parts and a different function rule is applied to each part
removable discontinuity
normal line
extreme value theorem
piecewise defined function
35. The process of evaluating an indefinite integral
numerical derivative
Antidifferentiation- check
instantaneous rate of change
absolute maximum
36. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].
law of cosine
extreme value theorem
definite integral
linear approximation
37. Two curves that have perpendicular tangents at the point of tangency
perpendicular curves
differential equation
absolute value
endpoint extremum
38. Selection of a best element from some set of available alternatives.
left hand limit
optimization
left hand sum
non removable discontinuity
39. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
dummy variable of integration
logarithm laws
average rate of change
related rates
40. 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
law of cosine
inflection point
Total change Theorem
continuity at a point
41. 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)
antiderivative
exponential growth and decay
Fundamental theorem of calculus
parameter
42. Having the limits or boundaries established
bounded
dummy variable of integration
axis of symmetry
related rates
43. 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
extremum
continuity on an interval
root of an equation
second derivative test
44. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
complex number
parallel curve
left hand sum
removable discontinuity
45. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
asymptote
limit at infinity
cartesian coordinate system
differential equation
46. Curve whose points are at a fixed normal distance of a given curve
circular function
parallel curve
continuous function
antiderivative
47. A measure of how a function changes as its input changes.
cartesian coordinate system
dummy variable of integration
local linearity
derivative
48. The value of the function at a critical point
dummy variable of integration
definite integral
critical value
extreme value theorem
49. The behavior of the graph of a function as x approaches positive infinity or negative infinity
end behavior
normal line
odd function
optimization
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
infinite limit
complex number
right hand sum
order of a derivative