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FTCE Mathematics 6-12 (026): Practice & Study Guide  /  Math Courses

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FTCE Math: Rate of Change 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!

Page 1

Question 1 1. What is the derivative of the following?

Question 2 2. What is the rate of change at the point B in the graph below (for y in relation to x)?

Question 3 3. Velocity is a rate of change of _____.

Question 4 4. What is the average rate of change for the interval with endpoints A and B?

Question 5 5. What is the rate of change at the point A in the graph below (for y in relation to x)?

Page 2

Question 6 6. 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 7 7. What is the approximate instantaneous rate of change at point C?

Question 8 8. Which is greater, the derivative at a or the derivative at b?

Question 9 9. At how many points on the graph below is the derivative of f(x)=0?

Question 10 10. Acceleration is the measure of how velocity changes over time. Acceleration is an example of _____.

Page 3

Question 11 11. What is the value of f(x) at the red circle?

Question 12 12.

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

Question 14 14. 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 15 15. Where is f(x) differentiable?

Page 4

Question 16 16.

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 17 17. 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 18 18. Where is f(x) differentiable?

Question 19 19. Where is f(x) differentiable?

Question 20 20.

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

Page 5

Question 21 21. What is the rate of change at the point A in the graph below (for y in relation to x)?

Question 22 22.

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 23 23. Where is f(x) differentiable?

Question 24 24. Consider the graph and question below..

Question 25 25. Where t= time, what is the derivative of f(t)?

Page 6

Question 26 26. 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.

Question 27 27. Which point on the following graph satisfies the mean value theorem between x = 0 and x = 3?

Question 28 28. The derivative of f(x) is equal to 0 at how many points on the graph below?

Question 29 29. Where is y differentiable?

Question 30 30. According to the mean value theorem, which of the following is true for a function f(x) that is continuous and differentiable between the points A and B?

FTCE Math: Rate of Change 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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