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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 function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0
rational function
integrand
trapezoidal rule
initial condition
2. The distance a number is from 0 on a number line
linear approximation
absolute value
bounded below
numerical derivative
3. The behavior of the graph of a function as x approaches positive infinity or negative infinity
exponential function
end behavior
difference quotient
continuous function
4. Any value in the domain where either the function is not differentiable or its derivative is 0.
Mean Value theorem for derivatives
Intermediate value theorem
critical point
absolute maximum
5. A variable occurring in a function - but on which the value of the function does not depend
Intermediate value theorem
trapezoidal rule
dummy variable of integration
continuous function
6. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.
exponential function
linear approximation
continuity on an interval
mean value theorem for definite integrals
7. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)
law of sines
critical value
removable discontinuity
piecewise defined function
8. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined
law of cosine
asymptote
endpoint extremum
inflection point
9. If there is some number b that is less than or equal to every number in the range of f
Fundamental theorem of calculus
inflection point
antiderivative
bounded below
10. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change
dummy variable of integration
acceleration
Rolle's Theorem
numerical derivative
11. 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
derivative
distance formula
right hand sum
12. If there is some number B that is greater than or equal to every number in the range of f
conic section
bounded above
parameter
initial condition
13. A measure of how a function changes as its input changes.
parallel curve
inflection point
derivative
linear approximation
14. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0
difference quotient
infinite limit
first derivative test
piecewise defined function
15. 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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16. 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
extremum
absolute value
axis of symmetry
instantaneous velocity
17. The mathematical process of obtaining the derivative of a function
domain
integrand
bounded below
differentiation
18. 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
limit at infinity
position function
indefinite integral
19. Input of function
linear approximation
domain
position function
order of a derivative
20. Having the limits or boundaries established
average rate of change
bounded
differential equation
constant function
21. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.
amplitude
natural logarithm
integration by substitution
derivative
22. A function that is a fixed numerical value for all elements of the domain of the function
initial condition
antiderivative
cartesian coordinate system
constant function
23. The value of the function at a critical point
removable discontinuity
Fundamental theorem of calculus
critical value
normal line
24. 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
limit at infinity
removable discontinuity
leibniz notation
antiderivative
25. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0
Fundamental theorem of calculus
limit at infinity
Algebraic function
logarithm laws
26. 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
first derivative test
exponential function
critical value
right hand limit
27. A straight line that is the limiting value of a curve
absolute value
domain
related rates
asymptote
28. The inverse of an eponential function
rational function
critical point
logarithmic function
instantaneous velocity
29. N(1-r)^x
acceleration
complex number
decay model
infinite limit
30. A function whose domain is divided into several parts and a different function rule is applied to each part
related rates
piecewise defined function
antiderivative
removable discontinuity
31. 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
circular function
critical point
absolute maximum
left hand sum
32. 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)
amplitude
numerical derivative
concave down
right hand sum
33. A function f that gives the position f(t) of a body on a coordinate axis at time t
position function
instantaneous velocity
parallel curve
Intermediate value theorem
34. A function that is continuous on both the left and right side at that point
Intermediate value theorem
order of a derivative
concave down
continuity at a point
35. d = v[( x2 - x1)² + (y2 - y1)²]
distance formula
exponential growth and decay
optimization
absolute value
36. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1
critical point
Rolle's Theorem
dummy variable of integration
exponential growth and decay
37. Imaginary line drawn perpendicular to the surface of a mirror or any surface
normal line
difference quotient
exponential growth and decay
extreme value theorem
38. A given value of x and f(x) used to find the constant of integration
initial condition
limit of integration
first derivative test
definite integral
39. 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)
asymptote
cartesian coordinate system
critical point
mean value theorem for definite integrals
40. 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
integrand
root of an equation
critical value
differentiability
41. 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
related rates
cross sectional area
difference quotient
distance formula
42. A function that possesses a finite integral; the function must be continuous on the interval of integration
left hand limit
integrable function
related rates
acceleration
43. The limit of f as x approaches c from the right
law of sines
right hand limit
absolute maximum
axis of symmetry
44. A limit in which f(x) increases or decreases without bound - as x approaches c
infinite limit
power series
differentiability
average rate of change
45. Intervals in which the second derivative is positive
concave up
absolute maximum
absolute minimum
second derivative test
46. sinA/a=sinB/b=sinC/c
endpoint extremum
law of sines
complex number
left hand limit
47. Functions of angles
instantaneous rate of change
circular function
differential
rational function
48. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables
instantaneous rate of change
Algebraic function
even function
distance formula
49. Two curves that have perpendicular tangents at the point of tangency
circular function
local linearity
perpendicular curves
parameter
50. A logarithm with the base e - written as ln
integration by substitution
natural logarithm
limit of integration
instantaneous velocity