Math 203 Practice Test 2
No cell phones, tablets, translators, mp3 players, or earphones are allowed on the test. I will not answer any questions during the test. Bring a calculator to the test.
1. A dietician in a hospital prepares meals under the guidance of a physician. Suppose that for a particular patient a physician prescribes a meal to have 800 calories, 55 g of protein, and 220 mg of vitamin C. The dietician prepares a meal of roast beef, baked potatoes, and broccoli according to the data in the following table. Set up the system of equations to determine how many servings of each food are needed in order to satisfy the doctor’s orders? Only set up the system of equations. There is no need to solve the system. (Sec 8.5)
Serving Size / Calories / Protein(in grams) / Vitamin C
(in milligrams)
Roast Beef / 300 / 20 / 0
Baked Potato / 100 / 5 / 20
Broccoli / 50 / 5 / 100
2. Find each indicated intersection or union. (Sec 9.2)
a.b.
3. Solve. (Sec 9.3)
a. b. c.
4. Edy is about to take a test that contains short answer questions worth 7 points each and word problems worth 14 points each. She must do at least 3 short answer questions, but does not have time to do more than 6. She must do at least 11 word problems, but does not have time to do more than 20. She can do no more than 25 questions altogether. How many of each type of question must Edy do in order to maximize her score? (Sec 9.5)
a. Identify the unknowns and name them.
b. Write the objective function (the function that needs to be maximized).
c. Write the constraints (the inequalities).
d. Graph the system of inequalities.
e. Find the vertices.
f. Plug the vertices into the objective function.
g. How many of each type of question must Edy do in order to maximize her score? Write your answer in a sentence.
h. What is her maximum score? Write your answer in a sentence.
5. Determine the domain of each function. Write your answers in interval notation. (9.2, 10.1)
a. b. c.
6. Write an equivalent expression using radical notation and, if possible, simplify. (Sec 10.2)
a.b.
7. Simplify (Extract roots). Assume no radicands were formed by raising negative numbers to even powers. (Sec 10.3, 10.4)
a.b.
8. Perform the indicated operation and simplify. (Sec 10.5)
a.b.
9. Solve. (Sec 10.6)
10. Find the distance between the points (17, 8) and (14, 7). Round to the nearest thousandth. (three decimal places). (Sec 10.7)
11. Perform the indicated operation and simplify. (Sec 10.8)