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AP Calculus BC 2.1: Rates of Change

Practice AP Calculus BC questions on calculating average rates and connecting them with instantaneous rate of change at a point.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Covered syllabus points

CHA-2.A—Determine average rates of change using difference quotientsCHA-2.B—Represent the derivative of a function as the limit of a difference quotient

2.1 Defining Average and Instantaneous Rates of Change at a Point question 1

[Maximum number: 1]

Grass clippings are placed in a bin, where they decompose. For 0≤t≤300 \leq t \leq 30, the amount of grass clippings remaining in the bin is modeled by A(t)=6.687(0.931)tA(t)=6.687(0.931)^{t}, where A(t) is measured in pounds and t is measured in days.

Find the average rate of change of A(t) over the interval 0≤t≤300 \leq t \leq 30. Indicate units of measure.

2.1 Defining Average and Instantaneous Rates of Change at a Point question 2

[Maximum number: 1]

lim⁡h→025+h−5h\lim _{h \rightarrow 0} \frac{\sqrt{25+h}-5}{h}

A

(A)=0(\mathrm{A})=0

B

(B) =110=\frac{1}{10}

C

(C) =1

D

(D) does not exist

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