Study Guide for Exam 1

Note that this is a study guide, not a sample exam - it is much longer than your exam will be. However, the ideas and the question types represented here (along with your homework) will help prepare you for your exam.

This exam covers material from 1.1 to 2.4.

1. A pet shop has a total of 18 dogs and birds. Altogether there are 52 feet. How many dogs are there and how many birds?

2. The flower peddler has red flowers with five petals each and white flowers with eight petals each. He has a total of 9 flowers with a total of 54 petals. How many red flowers are there and how many white flowers?

3. How many different ways can you make change for a 50-cent coin using nickels and dimes?

4. How many posts does it take to support a straight fence 210 feet long if posts are placed every 10 feet? Justify your answer.

5. How many cuts are needed to divide a 10-foot pole into 1-foot sections? Justify your answer.

6. Find the number of terms in the following arithmetic progression:
     1, 3, 5, 7, ..., 55

7. Find the number of terms in the following arithmetic progression:
     8, 11, 14, 17, ..., 65

8. Find the sum of the arithmetic progression:
     10 + 11 + 12 + ... 300

9. Find the sum of the arithmetic progression:
     11 + 13 + ... 201

Questions 10 - 11: Solve the problems using Polya's Principles. Explain your solution as a step-by-step process, listing each of the four principles in the appropriate place and describing briefly how you applied each principle to the problem.

10. April forgot which chapter she has math homework for. She knows it is within chapters 3 to 7 and deals with exponents. She knows that her homework is not from chapter 3. Last month they worked on chapter 4 so they're at least two chapters ahead by now. The final will not be for another month. She estimates that they do two chapters a month and the book has 8 chapters. When the final comes, they will have just finished the entire book. Which chapter should April look in to do the homework assignment?

11. The scores of a math test for five students were posted on the bulletin board. The students' names are Jake, Penny, Jim, John and Rob. Jake and Rob scored the same number of points. Penny did not get the highest score. John's score was 5 points lower than Jim's. The scores were 73, 50, 90, 50 and 85. Which student received what score?

12. Use indirect reasoning to show that if n² is odd, then n is also odd.

13. If you choose any 6 whole numbers from 1 to 10, there are two of them have an odd sum. Explain why this must be true. (Hint: Try a number of particular cases. Try to choose numbers that show that the conclusion is false. What must be the case if the sum of two natural numbers is odd?)

14. Find the 65th term in the number sequence corresponding to this dot sequence:

15. Discuss the validity of the argument. If it is a valid argument, explain why. If it is not valid, change the second and third statements of the argument as needed to make a valid claim.

(a) All businessmen wear suits. 
     Aaron wears suits. 
     Therefore Aaron is a businessman.

(b) Martians are green.
      Roger is not green.
      Therefore Roger is not a Martian.

16. Use the clues provided about the sequence to fill in the missing information. Give the expression for the n^th term using the term number n. 

(a)
 

(b)
 

(c)
 

17. Write the set in set-builder notation:

(a) {2, 4, 6, 8}
(b){18, 19, 20, 21}
(c) The odd natural numbers less than 20

             Determine whether the following statements are true or false.

(a) C  D
(b) DB
(c) A = {1, 7, 3, 5}
(d) {5} D
(e) {0} D
(f) C  D
(g) {5} D
(h) 5 D

            (a )Place the set elements in the proper location on the Venn diagram.

(b) List the elements in A B.
(c) List the elements in A  B.
(d) List the elements in.

(a) 
(b) 
(c) 

(a) If A  B = A  C for nonempty sets A, B, and C, must B = C?
(b) If A  B = A  C for nonempty sets A, B, and C, must B = C?

(a) n(A  B) = n(B  A)
(b) n(A B) = n(A) + n(B) – n(AB) 
(c) n(A  B) = n(A) – n(B) 
(d) n(A  B) + n(A B) = n(A) + n(B) 

99 had a dog;
76 had a cat;
34 had a dog and a cat;
18 had a dog and a parakeet;
10 had a cat and a parakeet;
98 had neither a cat nor a dog nor a parakeet;
8 had a cat and dog and a parakeet.

How many had a parakeet only?

24. Find the cardinal number (number of elements) of the indicated sets.

(a) A = {red, green, yellow, black, orange}
     B = { red, yellow, orange, blue, white}
     Find  n(A  B).
(b) If n(A) = 32, n(B) = 93 and n(A  B) = 109, find n(A  B).
(c) If n(B) = 60, n(A  B) = 11, and n(A  B) = 105, find n(A).

(a)
(b) 4 + 8 = 8 + 4
(c) (2 + 3) + 9 = 2 + (3 + 9)
(d) 5 + 0 = 5
(e) 5 + 998 is a whole number
(f) 7*1 = 7 
(g) 4(x + 3) = 4x + 4 * 3 
(h) (1 * 2)* 9 = 1 * (2 * 9) 
(i) 3 * 97 = a whole number 
(j) 

(k) 

(a) {1, 3, 5, 7, …}
(b) {0}
(c) {n  N | n > 20}

(a) {1, 3, 5, 7,...} 
(b) {0, 1} 
(c) {1, 2, 3, 4, ... 33} 

29. Illustrate 7 * 1 = 1 * 7 using repeated addition on a number line.

30. Simplify by rewriting as a single exponential: 

(a) 13⁴13³

(b) 5⁴5⁰

(c) (z⁴)⁶

(d) (5³)²

Look at the solutions