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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. sinA/a=sinB/b=sinC/c
law of sines
concave up
Radian
logarithm laws
2. 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
cartesian coordinate system
Intermediate value theorem
optimization
piecewise defined function
3. 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
optimization
root of an equation
differentiation
perpendicular curves
4. The value that a function is approaching as x approaches a given value through values less than x
endpoint extremum
instantaneous velocity
distance formula
left hand limit
5. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
Rolle's Theorem
related rates
local linearity
exponential growth and decay
6. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
acceleration
absolute minimum
asymptote
constant function
7. Either of the endpoints of an interval over which a definite integral is to be evaluated
parameter
limit of integration
even function
logarithmic function
8. A function that possesses a finite integral; the function must be continuous on the interval of integration
integrable function
Radian
endpoint extremum
extreme value theorem
9. A function that is continuous on both the left and right side at that point
continuity at a point
circular function
non removable discontinuity
left hand sum
10. The maximum distance that the particles of a wave's medium vibrate from their rest position
absolute value
amplitude
partition of an interval
indefinite integral
11. A surface or shape exposed by making a straight cut through something at right angles to the axis.
logarithmic function
implicit differentiation
cross sectional area
bounded above
12. 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))
infinite limit
absolute value
local linearity
conic section
13. The local and global maximums and minimums of a function
numerical derivative
dummy variable of integration
extremum
non removable discontinuity
14. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
endpoint extremum
Radian
non removable discontinuity
axis of symmetry
15. 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
right hand limit
differentiability
Rolle's Theorem
cross sectional area
16. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
definite integral
integrand
first derivative test
17. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative
indefinite integral
parallel curve
cross sectional area
constant of integration
18. The smallest y-value of the function
differentiability
exponential function
amplitude
absolute minimum
19. The inverse of an eponential function
Mean Value theorem for derivatives
differential
logarithmic function
non removable discontinuity
20. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
natural logarithm
cartesian coordinate system
decay model
21. 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)
decay model
transcendental function
Mean Value theorem for derivatives
continuity on an interval
22. Intervals in which the second derivative is positive
optimization
continuous function
concave up
absolute value
23. Intervals on which the second derivative is negative
natural logarithm
trapezoidal rule
limit at infinity
concave down
24. 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
differentiation
antiderivative
cross sectional area
related rates
25. A function that is a fixed numerical value for all elements of the domain of the function
even function
related rates
constant function
leibniz notation
26. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)
absolute maximum
related rates
cartesian coordinate system
differential equation
27. Ratio between the length of an arc and its radius
second derivative test
first derivative test
right hand limit
Radian
28. The behavior of the graph of a function as x approaches positive infinity or negative infinity
distance formula
extremum
end behavior
right hand limit
29. The mathematical process of obtaining the derivative of a function
differentiability
difference quotient
differentiation
leibniz notation
30. 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
continuous function
logarithm laws
left hand sum
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
transcendental function
inflection point
initial condition
instantaneous velocity
32. Functions of angles
root of an equation
extremum
circular function
law of sines
33. ex) dx - dy etc
critical point
Antidifferentiation- check
differential
trapezoidal rule
34. Imaginary line drawn perpendicular to the surface of a mirror or any surface
limit of integration
normal line
antiderivative
Radian
35. Dividing an interval into n sub-intervals
partition of an interval
parallel curve
root of an equation
bounded
36. The process of evaluating an indefinite integral
right hand limit
indefinite integral
Antidifferentiation- check
instantaneous velocity
37. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary
left hand sum
acceleration
Radian
parameter
38. Amount of change / time it takes (amount of change/ length of interval)
non removable discontinuity
leibniz notation
parallel curve
average rate of change
39. (geometry)A curve generated by the intersection of a plane or circular cone
continuity at a point
law of cosine
conic section
root of an equation
40. If there is some number B that is greater than or equal to every number in the range of f
bounded above
inflection point
linear approximation
integration by substitution
41. 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
Mean Value theorem for derivatives
power series
instantaneous rate of change
end behavior
42. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
perpendicular curves
cross sectional area
normal line
43. 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
trapezoidal rule
logarithmic function
decay model
right hand limit
44. The reciprocal of the sine function
mean value theorem for definite integrals
absolute value
cosecant function
transcendental function
45. 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
trapezoidal rule
concave up
exponential growth and decay
first derivative test
46. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
critical point
integrable function
order of a derivative
second derivative test
47. Selection of a best element from some set of available alternatives.
initial condition
perpendicular curves
dummy variable of integration
optimization
48. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
logarithm laws
piecewise defined function
related rates
amplitude
49. 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)
Fundamental theorem of calculus
domain
differential equation
left hand sum
50. 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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