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Rate of Change: Precalculus Lesson Plans Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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Question 1 1. When driving over mountains, the grade of the road tells drivers how steep the climb is going up or down the mountain. The grade is the rate of change of _____.

Question 2 2. Your friend walks 15 minutes from her house to the school every day. What is her walking speed, if her house is 0.5 miles from her school?

Question 3 3. At how many points on the graph below is the derivative of f(x)=0?

Question 4 4.

Which of the following are rates of change?

a) the acceleration of an object

b) the position of an object

c) the velocity of an object

Question 5 5. Where is f(x) differentiable?

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Question 6 6. What is the rate of change at the point E in the graph below (for y in relation to x)?

Question 7 7. According to the mean value theorem, at how many points will the instantaneous rate of change equal the average rate of change between x = 1 and x = 3 on the following graph?

Question 8 8. Acceleration is the measure of how velocity changes over time. Acceleration is an example of _____.

Question 9 9. What is the rate of change at the point B in the graph below (for y in relation to x)?

Question 10 10. The derivative of f(x) is 0 at how many points on the graph below?

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Question 11 11. Velocity is a rate of change of _____.

Question 12 12. What is the average rate of change for the interval with endpoints A and B?

Question 13 13. Consider the function f(x) given below. According to Rolle's theorem, for how many values of x is the instantaneous rate of change equal to 0?

Question 14 14.

Which of the following statements are true?

a) d/dx f(x) = f'(x)

b) f'(x) is the derivative of the function f(x) with respect to x.

c) d/dx f(x) describes the instantaneous rate of change of f(x).

Question 15 15. When you blow up a balloon, the time that it takes to blow it up depends on how much pressure the inlet air is under. (AKA, how hard you blow!) If the pressure is higher, the rate of change of the balloon volume _____ as a function of time.

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Question 16 16.

If the continuous function g(t) equals 5 at the points t=2 and t=4, then what can you say about g(t)?

A) Between t=2 and t=4 there will be at least one point where the instantaneous rate of change is 0.

B) Between t=2 and t=4 the average rate of change is 0.

C) Between t=2 and t=4, g(t) is constant.

Question 17 17. What is the value of f(x) at the red circle?

Question 18 18. Consider the graph and question below..

Question 19 19. What is the rate of change at the point A in the graph below (for y in relation to x)?

Question 20 20. What is the derivative of the following?

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Question 21 21.

What is the rate of change at the point B in the graph below (for y in relation to x)?

(In other words, what is the slope of the line from x = 2 to x = 3?)

Question 22 22. Where is f(x) differentiable?

Question 23 23. According to Rolle's theorem, for a continuous function f(x), if the start point f(a) and the end point f(b) equal 0 then:

Question 24 24. What is the approximate instantaneous rate of change at point C?

Question 25 25. Consider the function f(x) given below. According to Rolle's theorem, between x=0 and x=pi, for how many values of x is the instantaneous rate of change equal to 0?

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Question 26 26. Consider the graph below. Between x=C and x=-C, for any value of C, will there be a point where the instantaneous rate of change is 0?

Question 27 27. Where is y differentiable?

Question 28 28.

Which of the following best describe(s) the derivative of a function?

a) It is the instantaneous rate of change.

b) It is the slope between any two points.

c) It is the tangent to the function.

Question 29 29. Where is f(x) differentiable?

Question 30 30. Which is greater, the derivative at a or the derivative at b?

Rate of Change: Precalculus Lesson Plans Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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