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Name (printed) Section Name (signature) Assigned Seat ZID. NO. MATH 101 EXAM 3 FORM B April, 2004 3:00-3:50 p.m. INSTRUCTIONS:
- Use a No. 2 pencil.
- Write your last name and initials in the appropriate boxes on the answer form, and fill in the corresponding letter ovals.
- Write your ZID number in the appropriate boxes on the answer form starting at the left end, and fill in the corresponding number ovals.
- Write your recitation section (01, ..., 08) in the boxes marked “Section”. Fill in the appropriate ovals.
- Fill in the oval corresponding to your Form number (A or B).
- Write your REGULAR row and set number in the space marked DEPT.
- There are 20 questions. It is YOUR responsibility to see that you have a complete examination form.
- When you have finished, you are to turn in your answer form, and your signed exami- nation copy. Have your identification card ready. BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
- The number of points with integer coordinates which lie in the solution set of the system (^) { x + y ≤ 4 x ≥ 0 , y ≥ 2 is (a) infinite (b) 0 (c) 3 (d) 6 (e) impossible to determine
- The vertex of the parabola y = (x − 3)^2 + 4 is at x equals (a) 1 (b) 6 (c) 3 (d) 4 (e) 9
- One factor of the polynomial 2 x^2 + x − 3 is (a) x + 1 (b) x − 3 (c) (x − 1) (d) 2x − 3 (e) x + 3
- If the area of a square is 48 square feet, how long is a side of the square? (a) 6.93 ft. (b) 2304 ft. (c) 8 ft. (d) 12 ft. (e) 6 ft.
- The x coordinate for the solution of the system
{ x + y = 12 2 x − y = 9 is (a) 4.5 (b) 7 (c) 6 (d) 5 (e) 4
- If a tree casts a shadow of 18.9 feet at the same time an 8 foot flag pole casts a shadow of 5.6 feet, how high is the tree? (a) 105.8 ft. (b) 44.8 ft. (c) 151.2 ft. (d) 27 ft. (e) 13.2 ft.
- A survey asked newspaper readers which of the following three newspapers they read daily: New York Times (NYT), Washington Post (WP), and Wall Street Journal (WSJ). The results were:
Papers Readers Papers Readers NYT only 24 NYT and WSJ only 14 WSJ only 27 NYT and WP only 16 WP only 26 WP and WSJ only 13 None 15 All three 8
How many people read NYT or WSJ? (a) 51 (b) 67 (c) 29 (d) 81 (e) 92
- Zeke is building an apartment complex as an investment. He knows an electrician gets $6.50 more per hour than his assistant. Zeke receives a bill for $3,860 for a 40-hour week for their combined work. If x = the hourly wage of the electrician and y = the hourly wage of the assistant, which system below could be used to determine these wages?
(a)
y = 6.5 + x
- 5 x + 40y = 3860 (^) (d)
x = 6.5 + y 40 x + 40y = 3860
(b)
x + y = 6. 50 40 x + 40y = 3860 (^) (e)
40 x + 33. 5 y = 3860 x = 6.5 + y
(c)
y = 6.5 + x 40 x + 40y = 3860
- Amy and Kara are putting together two packages to use as treats for families of children in their after school care center. The Choco package is to have 6 ounces of chocolates and 2 ounces of peanuts, whereas the Nutty package is to have 4 ounces of chocolates and 4 ounces of peanuts. If they have 80 ounces of chocolates and 72 ounces of peanuts available, which system below describes the number of packages of each type they can put together assuming x = # of Choco packages and y = # of Nutty packages?
(a)
6 x + 4y ≤ 80 2 x + 4y ≤ 72 x ≥ 0 , y ≥ (^0) (d)
4 x + 6y ≤ 80 4 x + 2y ≤ 72 x ≥ 0 , y ≥ 0
(b)
6 x + 4y ≤ 72 2 x + 4y ≤ 80 x ≥ 0 , y ≥ (^0) (e)
80 ≤ 6 x + 4y 72 ≤ 2 + 4y x ≥ 0 , y ≥ 0
(c)
6 x + 2y ≤ 80 4 x + 4y ≤ 72 x ≥ 0 , y ≥ 0
- The gate into Jenny’s farm yard measures 4 feet high and 8 feet wide. There is a heavy steel wire running from the top corner of the gate (by the hinge) to the bottom corner on the opposite side for support. How many feet long is the wire? (a) 6 (b) 8.94 (c) 12 (d) 3.46 (e) 6.
- Holly has a brick decorative circular region with radius 4 feet in her yard. She put a sidewalk around it which extends 2 feet out from the circular region. How many square feet is sidewalk? (a) 113. (b) 6. (c) 100. (d) 62. (e) 50.
- The minimum for the expression 3x + 4y subject to
2 x − y ≥ 18 4 x + y ≥ 12 x ≥ 0 , y ≥ 0
is
(a) 48 (b) 27 (c) 3 (d) 12 (e) 9
- If B^2 − 4 AC < 0 and A 6 = 0 the quadratic equation Ax^2 + Bx + C = 0 has
(a) two solutions (b) no solution (c) at least one solution (d) one solution (e) either one solution or two solutions
y
x
III
I
IV
V
II
1 2 PSfrag replacements
5 x = 2y + 10
2 x + 3y = 18
The solution set for the system of inequalities
2 x + 3y ≤ 18 5 x ≤ 2 y + 10 x ≥ 0 , y ≥ 0 is (a) I (b) II (c) III (d) IV (e) V
