MTE 180 Place label hereel her

Phil Clark

Test #1 - Covers Chapter 1 and Section 2.2

No note cards!

Scratch paper is provided.

Use of calculators is encouraged.

This test is 9 pages and includes 10 problems and one extra credit problem.

Instructions:

To receive credit, you must show all work and explain all your reasoning. If you use you calculator, tell me how. If you guess-and-check, tell me how.

Honor Statement:

By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s program memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor.

Signature Date

1. True and False [2 pts each]

a) If a sequence is geometric then a linear function can be found to model it. T F

b) The Fibonacci sequence is geometric. T F

c) A function is a process that maps an element of one set to exactly one T F

element of another set.

d) A sequence can be both arithmetic and geometric. T F

e) According to the book, Trial + Error and Guess–Check–Revise T F

are examples of problem

2. The George W bush has one berry when it is a year old, and then twice as many berries each subsequent year as the year before.

a) Write the first six terms of the sequence that represents the number of berries on the bush each year (starting with the first year). [4 pts]

b) What type of sequence is this (circle one) ? [2 pts]

ARITMETIC GEOMETRIC NEITHER

c) Write a formula for the nth term of your sequence in part (a). Is this sequence arithmetic, geometric, or neither? [4pts]

d) What is the youngest age the bush can be in order for it to produce more than 100 berries? [4 pts]

3. Consider the sequence 6, 11, 9, 14, 12, …

a) Determine the next three numbers in the sequence. [3 pts]

b) What type of sequence is this (circle one) ? [2 pts]

ARITMETIC GEOMETRIC NEITHER

c) Describe the sequence in such a way that someone could recreate it from your description. (Do not just restate the numbers in order.) [3 pts]

4. Exactly 8,000 fans attended a Rush concert at Desert Sky Pavilion. If lower level tickets cost $25, lawn tickets cost $15, and ticket receipts totaled $147,750, how many people sat on the lawn? How many sat in the lower level? Explain your reasoning. [8 pts]

5. There is a small town in Ohio called Shelbyville with a population of 150 people. An advertising firm found that a certain ad than ran on both radio and TV was heard only by 78 of the people in Shelbyville and was seen by only 46 of the people in Shelbyville. Just 31 of the people both heard the radio ad and saw the TV ad.

a) How many people from Shelbyville had neither seen nor heard the ad? Explain your reasoning. (hint: you can use a Venn Diagram to explain your reasoning.) [4 pts]

b) What percent of the people in the area only heard the ad on radio or saw the ad on TV? Explain your reasoning. [4 pts]

6. Determine whether the arguments below are valid or invalid. If a problem is invalid give a brief explanation of why it is invalid. Circle the correct answer. [3 pts each]

a) All squares are quadrilaterals.

All quadrilaterals are polygons.

Therefore, all squares are polygons.

VALID INVALID

b) If a student is a freshman, then the student takes mathematics.

Jane is a sophomore.

Therefore, Jane does not take mathematics.

VALID INVALID

c) If a teacher is intelligent, he/she will do a good job.

Phil will do a good job therefore he is intelligent.

VALID INVALID

d) If a building is made of straw, the big bad wolf can blow it over.

The big bad wolf could not blow over the physical sciences building, therefore it is not mad of straw.

VALID INVALID

7. Consider the following statement:

If the test is difficult then George will not pass the exam.

Using the statement above give the:

[2 pts each]

a) Converse

b) Inverse

c) Contrapositive

d) Which of the above (a-c) is logically equivalent to the original statement?

8. A “complete toast” is when everyo9nein a room clinks glasses exactly once with everyone else. If there are 22 people in the room, how many clinks will be heard for a complete toast? Explain your reasoning. (Hint: start with a small number of people and look for the pattern). [10 pts]

9. A health club charges a one-time initiation fee of $200 plus a membership fee of $30 per month.

a) Write an expression for the cost function C(x) that gives the total cost for membership at the health club for x months. [4 pts]

b) Draw a graph of the function in part (a) for the first 12 months. [4 pts]

c) The health club decided to give its members an option of a higher initiation fee but a lower monthly membership fee. If the initiation fee is $500 and the monthly membership fee is $10, determine after how many months the second plan is less expensive for the member. Explain your reasoning. [4 pts]

10. Use the above graph which gives a time-distance graph of a student using a CBR motion detecting device (like we used in class).

a) Give the walking strategy necessary to create the above graph. Describe the strategy as if you were telling another member of your group how to make the same graph. [6 pts]

b) At what time is the student traveling the fastest? [2 pts]

c) At what time is the student traveling the slowest? [2 pts]

Extra Credit!!!

You are given a 5-gallon pail and a 3-gallon pail. You are asked to fetch exactly 4 gallons of water. How can you do this? (Note: You must not estimate. For instance, you cannot fill the pails "half-full" because you do not know where half-full is.) [3 pts]