Final Practice Test



Final Practice Test Solutions MAT 142

1. Determine whether the argument is valid or fallacy (use the truth table)

If I’ll get all A’s on the tests, I’ll get a good grade in the class

I didn’t get all A’s on the tests

Therefore, I wont get a good grade in the class

a) State what p and q represent

p: I get all A’s on the tests

q: I get a good grade in the class

b) Write the argument as a compound statement

[pic]

c) Construct a truth table for the argument (not all the columns might be used)

|p |q |~p |~q |[pic] |[pic] |[pic] |

|T |T |F |F |T |F |T |

|T |F |F |T |F |F |T |

|F |T |T |F |T |T |F |

|F |F |T |T |T |T |T |

d) Is the argument valid? Invalid – one row contains F

2. Construct a truth table for the following compound statement

[pic]

|p |q |r |~p |~q |[pic] |[pic] |

|T |T |T |F |F |F |T |

|T |T |F |F |F |F |T |

|T |F |T |F |T |T |T |

|T |F |F |F |T |T |T |

|F |T |T |T |F |T |T |

|F |T |F |T |F |T |T |

|F |F |T |T |T |T |T |

|F |F |F |T |T |T |T |

3. Construct a Venn diagram to determine the validity of the following argument

All officers are gentlemen

Paul is not an officer

Paul is not a gentleman

The statement is invalid, since on the Venn diagram

Paul is not an officer, but he could be a gentlemen.

This is a fallacy of inverse.

4. Write the negation of the following statement (Remember DeMorgans’ laws)

a) Every weekday I have to go to work

Some days I don’t have to go to work

b) All the students of math department have good math teachers

Some of the students of math department don’t have good math teachers

c) I’ll go to work now or I’ll loose my job.

I wont go to work and I wont loose my job

5. Determine if the pairs of statements are equivalent by using a truth tables

a) If it is not a weekend, I go to work.

b) If I go to work, it is not a weekend

c) If I don’t go to work, it is a weekend

d) If it is a weekend, I don’t go to work

p: It is a weekend q: I go to work

Statements a) and c) are equivalent, statements b) and d) are equivalent

|p |q |~p |~q |[pic] |[pic] |[pic] |[pic] |

|T |T |F |F |T |F |T |F |

|T |F |F |T |T |T |T |T |

|F |T |T |F |T |T |T |T |

|F |F |T |T |F |T |F |T |

6. Using the symbolic representation

p: I am an A student

q: I take physics

r: I don’t like chemistry

express the following statements in words (the sentence might not make much sense):

a) [pic] I’m not an A student or I don’t take physics

b) [pic] If I’m an A student and I don’t take physics then I like chemistry

7. How many different phone numbers are possible if the number has 7 digits and the first digit can not be 0 or 1

[pic]

8. Given sets U={1,3,5,7,9,11,13,15,17,19,21,23,25}, A={1,3,5,7,9,15,23,25}, B={3,9,13,15}, Find the following sets

A(B={3,9,15}

A(B={1,3,5,7,9,13,15,23,25}

A(={11,13,17,19,21}

B(={1,5,7,11,17,19,21,23,25}

(A(B) (={11,17,19,21}

9. How many different 5 card hands could be selected from a deck of 52 cards

[pic]

10. Draw a Venn diagram and fill the number of elements for each region

n(A)=27, n(A(B(C)=5, n(A(C)=10, n(A(B)=13, n(B(C)=14, n(B)=35, n(C)=29, n(A((B((C()=4

[pic]

11. Draw a Venn diagram and fill it completely

A survey asked the students about the classes they are enrolled in and the following results were obtained: 206 were enrolled in math, 211 were enrolled in physics and 122 were enrolled in ceramics. 64 had were enrolled in all 3 of them,

27 were enrolled in none, 79 were enrolled in math and ceramics, 10 were enrolled in ceramics only and 25 were enrolled in math and physics but not in ceramics.

What percentage of all the students was enrolled in math?

What percentage of all the students was enrolled only in ceramics?

Total number of surveyed students is 365

Percentage of the students enrolled in math is

[pic]

Percentage of the students enrolled in ceramics only

[pic]

12. How many different lottery ticket selections can you make if you have to select 5 out of 36 numbers?

[pic]

13. Find the probability and the odds of being dealt a jack or a king from the well-shuffled deck of 52 cards:

Probability[pic] Odds [pic]

14. A box contains 3 red marbles, 4 blue marbles and 5 orange marbles. Find the probability of a selection of 3 marbles taken at random having marbles of all different colors.

[pic]

15. In a lottery to pick 4 correct numbers out of 32 find the probability of picking 4 correct numbers

[pic]

16. A pair of dice is rolled. Find the probability of the following result

The sum of dice is more than 7 or the first die is 3. Fill up the table for outcomes and use it to calculate the probability

| 2nd die |1 |2 |3 |4 |5 |6 |

|1st die | | | | | | |

|1 |2 |3 |4 |5 |6 |7 |

|2 |3 |4 |5 |6 |7 |8 | |

|Frequency |5 |1 |5 |2 |3 |3 |3 |

Rearrange the data in increasing order 3,3,3,3,3,4,5,5,5,5,5,6,6,7,7,7,8,8,8,9,9,9

a) Find the mean, median and the mode of the data

Mean[pic]

Median[pic] Mode 3,5

b) Find the standard deviation of the data

s=[pic]

17. If the scores on your first 4 tests are 67,84,74 and 89, what score do you need to get on the fifth test to have your overall mean to be at least 80 (to get at least B). What score should you get on the last test to get overall mean of 82?

x-score on the fifth test, then in order to get an overall mean of

80[pic] 82[pic]

x=86 x=96

18. The average daily temperature during the first week of the month is given by

|Weekday |1 |2 |3 |4 |5 |6 |7 |

|Temp., F |72 |75 |79 |85 |89 |73 |70 |

Find the mean, median and mode of the temperatures

Mean [pic] Median=75 Mode - none

Find the standard deviation of the temperatures

[pic]

1. Find how much money would the investment of $150 into the account with an annual interest of 5% invested for 15 years be worth if the accounts interest is

a) Compounded weekly b) Compounded monthly

[pic] [pic]

2. Find the future value of the annuity due with an annual interest rate of 3.5% and monthly payments of $200 made for 20 years

[pic]

3. Find the maturity value of the loan of $1000 borrowed at 5.5% simple interest for 3 years

[pic]

4. Find the future value of an ordinary annuity with monthly payments of $300 per month that earns 4.5% annual interest rate after 25 years

[pic]

5. You want to buy a car for $12,000. You get a simple interest amortized loan for the rest at 4.9% interest for 4 years

Determine

a) Monthly payments

[pic]

b) Total interest paid at the end of the loan [pic]

c) Prepare amortization schedule for the first 3 month of the loan

|Payment |Principal portion |Interest portion |Total payment |Balance |

|1 |226.81 |49 |275.81 |11773.19 |

|2 |227.14 |48.07 |275.81 |11545.45 |

|3 |228.67 |47.14 |275.81 |11316.78 |

6. If you are setting a payout annuity with the investment of $100000, how much would be the monthly payments for the next 10 years if the annuity has 4% annual interest rate?

[pic]

7. Buying a car for $20,000 you get a 5-year simple interest amortized loan at 5.5% for 75% of the needed amount from the bank. How large would be your monthly payments?

75% of $20000 is$15000

[pic]

-----------------------

gentlemen

Officers

X - Paul

13

9

5

9

C

A

10

[pic]5

B

U

8

4

107

33

25

102

Physics

Math

89

[pic]64

Ceramics

U

15

27

27

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download