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# The Derivative at a Point Chapter Exam

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. 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?

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Question 2
2.
Which of the following equations represent(s) a line that goes through the points (2,3) and (1,1)?

I) y = 2(x - 2) + 3

II) y = 2x - 1

III) y = 2(x - 1) + 1

#### Question 3 3. A(n) _____ is a comparison of two values, usually x and y, and the consistent change between those values.

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Question 4
4.
What is the slope of the line represented by the following formula?

y = 2 + 6(x - 3)

#### Question 5 5. Which of the following graphs MOST likely represents the equation y = 5.2x-2?

### Page 2

#### Question 6 6. What is the slope of the line normal to f(x) at x=1?

#### Question 7 7. In the equation y = 4x +15, what does 15 represent?

#### Question 8 8. What is the slope intercept formula?

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

#### Question 10 10. 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.

### Page 3

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

#### Question 12 12. Acceleration is the measure of how velocity changes over time. Acceleration is an example of _____.

#### Question 13 13. Consider the slope of the lines given by the following functions. Which function has the steepest slope?

#### Question 14 14. A _____ attempts to predict the relationship between two points.

#### Question 15 15. What is the slope of a line normal to f(x)?

### Page 4

#### Question 16 16. Which of the following equations represents a line that passes through the point (0, 1) and has a slope of -4?

#### Question 17 17. What is the slope of the tangent to r(s) at s = 0?

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Question 18
18.
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 19 19. What is the equation of the line normal to f(x) at the point x=1?

#### Question 20 20. Which of the following equations has a slope equal to -1/4?

### 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. What is the slope of the line given by the equation y + 3x = 2?

#### Question 23 23. 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 24 24. What is the rate of change at the point A in the graph below (for y in relation to x)?

#### Question 25 25. What is the slope of the line tangent to the curve given by the equation y = (x-1)²+2 at the point (1,2)?

### Page 6

#### Question 26 26. The _____ refers to the consistent change between x and y in a formula.

#### Question 27 27. What is the equation of the line tangent to f(x) at the point x=0?

#### Question 28 28. Which equation represents a line that goes through the points (0, 1) and (1, 0)?

#### Question 29 29. What is the rate of change at the point B in the graph below (for y in relation to x)?

#### Question 30 30. What is the point-slope form of the equation that goes through the origin and has a slope of 1.5?

#### The Derivative at a Point 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!