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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 line that divides a figure in half so that each half is the mirror image of the other.
axis of symmetry
continuity at a point
conic section
linear approximation
2. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
continuous function
odd function
logarithm laws
right hand sum
3. 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
inflection point
Intermediate value theorem
axis of symmetry
4. Ratio between the length of an arc and its radius
Radian
extreme value theorem
first derivative test
mean value theorem for definite integrals
5. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
position function
exponential growth and decay
second derivative test
antiderivative
6. A logarithm with the base e - written as ln
differentiation
cartesian coordinate system
logarithmic function
natural logarithm
7. 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
root of an equation
conic section
differential
exponential growth and decay
8. 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)
logarithm laws
numerical derivative
cartesian coordinate system
decay model
9. 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
parameter
non removable discontinuity
first derivative test
10. dy/dx
acceleration
leibniz notation
continuity at a point
continuity on an interval
11. Having the limits or boundaries established
differentiability
bounded
transcendental function
average rate of change
12. ex) dx - dy etc
Intermediate value theorem
differential
instantaneous rate of change
initial condition
13. 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
antiderivative
initial condition
local linearity
14. 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
limit of integration
differentiability
Algebraic function
piecewise defined function
15. N(1-r)^x
exponential growth and decay
decay model
absolute minimum
average rate of change
16. Any value in the domain where either the function is not differentiable or its derivative is 0.
critical point
cartesian coordinate system
odd function
law of cosine
17. The smallest y-value of the function
concave up
absolute minimum
concave down
instantaneous velocity
18. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
integrable function
law of cosine
antiderivative
Algebraic function
19. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
right hand limit
second derivative test
difference quotient
extreme value theorem
20. A surface or shape exposed by making a straight cut through something at right angles to the axis.
complex number
cross sectional area
differentiability
absolute value
21. The function that is integrated in an integral
integrand
difference quotient
first derivative test
root of an equation
22. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum
average rate of change
antiderivative
second derivative test
limit at infinity
23. 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.
mean value theorem for definite integrals
even function
complex number
non removable discontinuity
24. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives
exponential function
axis of symmetry
mean value theorem for definite integrals
differential equation
25. Intervals on which the second derivative is negative
concave down
differential
differentiability
definite integral
26. A straight line that is the limiting value of a curve
asymptote
endpoint extremum
end behavior
initial condition
27. The limit of f as x approaches c from the right
right hand sum
exponential function
average rate of change
right hand limit
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
concave down
extreme value theorem
differentiation
first derivative test
29. 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
bounded
mean value theorem for definite integrals
continuous function
Total change Theorem
30. A function that is a fixed numerical value for all elements of the domain of the function
continuous function
constant function
infinite limit
trapezoidal rule
31. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly
numerical derivative
absolute value
left hand limit
implicit differentiation
32. Dividing an interval into n sub-intervals
limit at infinity
law of cosine
partition of an interval
average rate of change
33. The maximum distance that the particles of a wave's medium vibrate from their rest position
amplitude
law of sines
logarithm laws
differentiation
34. Functions of angles
axis of symmetry
limit of integration
removable discontinuity
circular function
35. Input of function
root of an equation
absolute minimum
integrand
domain
36. d = v[( x2 - x1)² + (y2 - y1)²]
dummy variable of integration
amplitude
distance formula
end behavior
37. 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
conic section
instantaneous velocity
concave down
right hand sum
38. Either of the endpoints of an interval over which a definite integral is to be evaluated
limit of integration
Fundamental theorem of calculus
bounded above
Radian
39. The reciprocal of the sine function
absolute value
axis of symmetry
cosecant function
trapezoidal rule
40. 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
left hand sum
extreme value theorem
continuity at a point
conic section
41. 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)
initial condition
root of an equation
mean value theorem for definite integrals
exponential growth and decay
42. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve
piecewise defined function
order of a derivative
definite integral
trapezoidal rule
43. The process of evaluating an indefinite integral
extremum
related rates
end behavior
Antidifferentiation- check
44. An undetermined constant added to every result of integration (the added +c)
exponential growth and decay
conic section
normal line
constant of integration
45. The value of the function at a critical point
indefinite integral
Algebraic function
antiderivative
critical value
46. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
root of an equation
continuity on an interval
acceleration
implicit differentiation
47. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x
axis of symmetry
order of a derivative
continuous function
acceleration
48. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.
decay model
power series
parameter
bounded above
49. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
infinite limit
rational function
derivative
differential
50. The value that a function is approaching as x approaches a given value through values less than x
left hand limit
infinite limit
odd function
asymptote