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]

1, 2, 4, 8, 16, 32,…

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). [4pts]

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

n = 7

Since it is 1 year old when it has one berry it must be 8 years old to have at least 100.

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

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

17, 15, 20, …

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]

Every other number is increased by 3. You start with 6 and an 11 which means the next two numbers will be 6 + 3 = 9 and 11 + 3 = 14. You continue to do this to create the sequence.

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]

a = # of lower level tickets, b = # of lawn tickets

a + b = 8000

25a + 15b = 147,750

a = 2775 tickets

b = 5225 tickets

note: methods may vary for this problem.

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]

There are 31 who did both, 15 t.v. only and 47 radio only so 93 either saw or heard ad. Thus, 150 – 93 = 57 people who neither saw nor heard the ad.

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]

62 people either only saw or only heard the ad so the percent of people who either saw or heard the add is = 41.3%

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

The fact that she is a sophomore does not tell us whether or not she takes a math class.

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

Just because Phil does a good job does not necessarily mean he is intelligent (but he is so don’t worry about it ;-)

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

If George does not pass the exam, then the test is difficult.

b) Inverse

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

c) Contrapositive

If George passes the exam, then the test is not difficult.

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

c) the contrapositive

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]

There will be 231 clinks. Methods may vary.

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]

C(x) = 200 + 30x

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]

200 + 30x = 500 + 10x

x = 15 months for them to be equal so after 15 months.

Methods may vary.

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]

Walk slowly towards the CBR then a little more quickly between 1 and 2 seconds then slow down between 2 and 3 seconds. Speed up a lot at 4 seconds (still walking towards the CBR). Slow down around 5 seconds and stand still close to the CBR for the last second.

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

At about 4 seconds.

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

Either when the person first starts or at the end between 5 and 6 seconds. (either answer will do)

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]

Fill the 5-gallon pail and use it to fill the 3-gallon pail. You will then have exactly 2 gallons left in the 5-gallon pail. Empty the 3-gallon pail and then pour the remaining 2 gallons from the 5-gallon pail into the 3-gallon pail. Now the 5-gallon pail is empty and the 3-gallon pail has exactly 2 gallons in it. Now fill the 5-gallon pail to the top. Use the 5-gallon pail to fill up the 3-gallon pail to the top. Since there was room in the 3-gallon pail for 1 more gallon this will take 1 gallon away from the 5-gallon pail leaving exactly 4 gallons!!!