M121 Fall 95  Exam I  Sept. 15, 1995

Name (Print) SSN: Circle the name of your TA and Discussion Hour:

David Krebes  8 AM  11 AM
Qihui Liu:  8am  9am
Jukun Ying  9am  11 am

M121 Fall 95  Exam I  Sept. 15, 1995

Answer all questions and SHOW ALL WORK. No credit for answers only.

Part I: Multiple choice. No partial credit but SHOW WORK! Circle the letter corresponding to

the correct answer.

1. A wheel with a diameter of 15 inches revolves through 720^{0} degrees. About how far has the wheel moved.

(A) 47 inches (B) 60 inches (C) 94 inches (D) 188 inches (E) 377 inches

2. Solve exactly |x − 5| > 3:

(A) (8, ∞) (B) (2, 8) (C) (−∞, 2) ∪ (8, ∞) (D) (∞, 1.93) ∪ (8.06, ∞) (E) (−∞, −8) ∪ (2, ∞)

M121 Fall 95  Exam I  Sept. 15, 1995

3. Let θ be an angle in the third quadrant whose terminal side is given by the equation y = x/2. What is cos θ?

(A) \frac{√5}{5}
(B) \frac{2√5}{5}
(C) \frac{−2√5}{5}
(D) \frac{√3}{2}
(E) \frac{−√3}{2}

4. The angle of elevation of the top of a building from a point 50m away from the building is 53^{∘}. Determine the building’s height.

M121 Fall 95  Exam I  Sept. 15, 1995

(A) 66.4m (B) 40m (C) 30.1m (D) .03m (E) .01m 5. The graph of y = 2 sin(3x − π) can be obtained from the graph of y = sin x by applying in

order the following three transformations.

1. vertical stretch by a factor of a.

2. horizontal shrink by a factor of b units.

3. horizontal shift of c units left or right. What are the values of a, b, c and in which directions is the shift?

(A) a = 2, b = 3, c = π left

(B) = 2, b = 3, c = π/3 right

(C) a = 3, b = 2, c = π

(D) a = 2, b = 3, c = π/3 left

(E) a = 2, b = 3, c = π right

(Partial credit) Write complete solutions and indicate your answers clearly.

6. The vertices of a triangle are located as follows. Vertex A is at the origin. Vertex B is the intersection of the line y = x and the parabola y = −x^{2} + x + 1. Vertex C is the point on the x-axis directly below B. Find the area of the triangle. Your solution must include a diagram locating the vertices of the triangle.

Ans:

M121 Fall 95  Exam I  Sept. 15, 1995

7. Find exactly all real zeros of the polynomial f(x) = 2x^{3} + 14x + 20x. For which x is f(x) > 0?

8. The sketch below is of one of the following five functions, which one? (A) (x^{2} − 5)/(x + 1)(x^{2} + 1) (B) (x^{2} + 5)/(x + 1)(x^{2} + 1) (C) (x^{2} − 5)/(x − 1)(x^{2} + 1) (D) (x^{2} − 5)/(x + 1)(x^{2} + 1) (E) (x^{2} + 5)/(x − 1)(x^{2} + 1))

Added November 1997. In the original problem we had provided a sketch. For practice graph each of the above.

Part II : (Partial credit) Write complete solutions and indicate your answers clearly.

9. Consider the function f(x) = x^{4} − x^{2} − 1. Sketch the complete graph of f(x). Half the credit on this problem will be awarded for your argument that this graph is complete. Explain why your sketch identifies all the zero’s of f.