AP Calculus BC Flashcards: Exploring Accumulations of Change
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
A car's velocity is measured in meters/second and time is in seconds. What are the units of the area under the velocity graph?
The units are (meters/second) × (seconds), which results in meters. This represents the total distance traveled.
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A car's velocity is measured in meters/second and time is in seconds. What are the units of the area under the velocity graph?
The units are (meters/second) × (seconds), which results in meters. This represents the total distance traveled.
If a graph shows the rate of oil leaking from a tank in liters per hour, what does the area under the graph from t=0 to t=3 represent?
The area represents the total amount of oil in liters that has leaked from the tank during the first three hours.
When can the accumulation of change be evaluated using geometry?
In some cases, such as when the graph of the rate of change function forms simple geometric shapes like triangles or rectangles, accumulation can be evaluated using geometry.
How are the units for an accumulation of change determined?
The unit for the accumulation (area) is the unit for the rate of change multiplied by the unit for the independent variable.
What does the area of the region between the graph of a rate of change function and the x-axis represent?
The area of the region between the graph of a rate of change function and the x-axis gives the accumulation of change.
How do you interpret the meaning of the area under the graph of a rate of change in a specific context?
In a given context, the area represents the total accumulated change of a quantity over an interval.
If the rate at which a city's population is changing is negative for a decade, what does this imply about the total population change?
This implies the accumulated change is negative, meaning the city's population has decreased over that decade.
Why is the area under a rate of change graph considered an 'accumulation'?
It is an accumulation because it represents the sum of all the small changes occurring over each moment in an interval, resulting in the total net change.
Accumulation of Change
The net change in a quantity over an interval, which is represented by the area of the region between the graph of its rate of change and the x-axis.
The graph of a company's rate of profit, in dollars per month, forms a triangle above the x-axis for the first 6 months. How would you find the total profit for that period?
The total profit is the accumulation of change, which can be found by using geometry to calculate the area of the triangle.
What is the relationship between the sign of a rate of change and the sign of the accumulated change?
If a rate of change is positive over an interval, the accumulated change is positive. If the rate is negative, the accumulated change is negative.