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Calculus practice

Instantaneous and average rate worksheets

Compare finite-interval and lower-endpoint rates for polynomial, rational and radian trigonometric functions with blank and keyed graphs.

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Find average change on [a,b] and instantaneous change at a. Round only final nonterminating values to three decimals.

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Practice with exact answers

Keep fractions, radicals and pi exact. Round only when a question asks for a decimal answer, and check every original domain restriction.

Instantaneous-rate student pages contain blank grids. Answer pages draw the actual function in separate continuous branches without joining across poles.

Learning objective

What this activity builds

Calculate both requested rates from one bounded function and inspect its discontinuities.

Worked example

How does a rate arise from a function?

Compare function values, then divide by the matching input change when the task asks for a rate.

Delta y, average rate, a derivative limit and an instantaneous rate are related but distinct quantities. Read the requested form before calculating.

Teaching notes

Make the practice count

  • Keep exact values through the final step.
  • Retain every original domain restriction.
  • Treat trigonometric inputs as radians.
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Math SheetInstantaneous and Average Rate of ChangeFind average change on [a,b] and instantaneous change at a. Round final nonterminating values to 3 decimals.1.f(x) = -x^2-3x-5; [0, 1]-10010x100-10y2.f(x) = (1)/(x-2); [1, 3]-10010x100-10y3.f(x) = -x^2+2x+1; [0, 1]-10010x100-10y4.f(x) = 4sin(2/7x+6); [0, 2]-10010x100-10ymath-sheet.comPage 1 of 1

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