# Exam: 250316RR – Introduction to Calculus & Exam: 250315RR – Conic Sections and Analytic Geometry

Exam: 250315RR – Conic Sections and Analytic Geometry

1. What is the vertex of the parabola y

A. (-2,11)

B. (-11,2)

C. (0,0)

D. (2,11)

2. If the conic section Ax

A. A hyperbola

B. An ellipse

C. A parabola

D. A circle

3. Translate the ellipse to be centered at (3, -1).

4. Where are the foci of the hyperbola ?

5. If an ellipse has foci (±2,0) and vertices (±3,0), locate the vertices of its minor axis.

6. Which of the following is symmetrical about the polar (or x) axis?

7. Eliminate the parameter from the parametric form of the following equation.

8. Express the parametric equations without the parameter.

9. Convert the equation of the ellipse 5x

A. The equation isn’t that of an ellipse.

10. How many asymptotes does a hyperbola have?

11. What are the substitution equations for rotating the axes back 30°?

12. Where are the foci for the ellipse ?

13. What is the equation for the directrix of the parabola y

A. x = -5

B. x = 5

C. y = -5

D. y = 5x

14. A piece of string is hung from the points (-6,3) and (6,3) in the plane so that it hangs “down” (in the -y direction) to just touch the origin at its vertex. How high above the x axis is the string over x = 2?

15. Which of the following is the polar graph of ?

16. Which conic section is comprised of two branches?

A. Parabola

B. Hyperbola

C. Circle

D. Ellipse

17. What kind of conic section is -6x

A. Circle

B. Ellipse

C. Parabola

D. Hyperbola

18. What is the equation of the directrix for the conic section ?

A. y = -6

B. y = 6

C. x = –3

D. x = 2

19. To determine which is the major axis of , which of these should you do?

A. Plug in 0 for x to find the y intercepts; these will be the vertices of the major axis.

B. Find c using the relationship c

2 to determine the locations of the foci.

C. Compare a to b, and the larger goes with the major axis.

D. Translate the ellipse to the origin using (-a,-b).

20. What is a parameterized version of the curve given by y – 3 = x + sin x?

A. y = -3t, x = y + sint

B. t = x, sinx – y + 3

C. t = – 3 = y, t + sint = x

D. x = t, y = t + sint + 3

Exam: 250316RR – Introduction to Calculus

1. The table shown gives some evidence that which mathematical statement is true?

x 7 7.9 7.9999 8.001 8.1 9

f(x) -6 -6.2 -6.297 -6.303 -6.37 -7

2. At which points is the function shown in the graph discontinuous?

A. 3.5

B. 1,3

C. -3,-1,1,3

D. Nowhere

3. Consider the figure shown. What is the value of ?

A. 3

B. 4

C. 0

D. Doesn’t exist

A. 30

B. 30x

C. 10x

D. 30x

5. Compute .

A. Doesn’t exist

B. 0.01

C. 0.11

D. 0.1

6. What is the slope of the tangent line to

A.

1

B. –

C. –

D. 1

7. Compute .

A. Doesn’t exist

B. 6

C. 7

D.

8. Find the average velocity from time t = 0 to t = 1 of a car whose position p(t) along a horizontal track is given by the equation p(t) = 4 – (t – 2)

A. 2

B. 3

C. 4

D. 1

9. Let . Is there a value of a that would make ƒ(x) continuous everywhere?

A. No

B. Yes, a = 1.

C. Yes, a = 0.

D. Yes, a = e.

10. Compute .

A. 6

B. 3

C. Doesn’t exist

D. -1

11. The area of a square with side length x is x and increasing?

A. 10

B. 5

C. 25

D. 20

12. Compute .

A. 4

B. 9

C. 1

D. 6

. What is the instantaneous rate of change in area if x is 5 13.

A. 3x

B. 13

C. 3

D. x

14. Which of these is a tangent line to y = -x

A. y = -8x + 16

B. y = -8x + 80

C. y = -16x + 80

D. y = -16x + 72

15. Compute .

A. 2

B. 0

D. Doesn’t exist

16.

A. 2x – 1

B. x – 1

C. x

D. 4x – 1

17. Where is y = lnx discontinuous?

A. Only where it’s undefined, which is for all

B. Only at zero

C. Only where it’s undefined, which is for all x < 0

D. Nowhere. It’s a smooth curve on its entire domain.

2 at x = 4?

18. Consider the figure shown here. What is the value of ?

A. 3

B. Doesn’t exist

C. 4

D. 0

19. Which of the following statements is true about the function ƒ shown in the graph below? Assume the viewing window extends from (-6,-6) to (6,6).

20. Compute .

A. 4

B. Doesn’t exist

C. 1

D. 6

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