Topics covered so far in the course.

· Organizing and diagramming deductive and inductive arguments; applying the terms valid, sound, strong and weak to these arguments.

· Using numbers in decimal, fraction, and percentage forms; and doing calculations (+,-, × , ÷ ) with numbers in these forms.

· Finding changes and making comparisons in quantities in absolute, fractional and percentage terms. Solving practical problems involving percentages.

· Using units of length, area, volume, time, weight, capacity, and currency in both the USCS and metric systems to solve problems and do conversions.

The midterm exam will be a 75-minute open-book, open-note, in-class exam to be held on Thursday, March 11 at 11:00 am. To help you study for the midterm exam, I have included a sample exam.

Your solutions to all questions must be detailed and complete, showing all of your work and thinking.

1. In the following two arguments, identify the premises and conclusion; if possible, state whether the premises and conclusion are true of false; state whether the argument is deductive or inductive; and determine if the argument is valid, sound, strong or weak.

P: If the tomatoes are not fertilized, then they will die. P: The tomatoes died. C: The tomatoes were not fertilized.

P: All dogs have four legs. P: Poodles have four legs. C: Poodles are dogs.

2. Suppose that spending for education in a particular state has increased by 5% in the last year to $33 million. How much was spent on education last year?

3. A friend tells you that her take home salary (after taxes) is $27,000 per year and that she is in a 24% tax bracket. What is her gross (before taxes) salary?

4. Answer the following questions and support your answer with an explanation or example.

(a) If the value of your stamp collection increases by 20% in 1996 and then decreases by 20% of its value in 1997, is it worth more than, less than, or the same as its original value at the beginning of 1996?


(b) Do three successive 10% tax cuts over three years amount to a 30% tax cut?


(c) If 60% of the class scores above 80% on an exam, does 40% of the class score at or below 80% on the exam?


(d) If 40% of the people in the room are English and 50% of the people in the room are women, does it follow that 40% × 50% = 20% of the people in the room are English women?

5. How many cubic centimeters are there in a cubic inch?

6. Suppose that 1 German mark = $0.72.

(a) Which is larger, 1 mark or $1? Explain
(b) How many marks are there in $1?
(c) If oranges cost 1.50 marks per kilogram, how much do they cost in dollars per pound?

Sample Mid-Term Exam Answers

Some of these answers are not the detailed solutions that you would need to provide on a real exam to receive full credit.

1a. The first two propositions are the premises of this deductive argument and the last proposition is the conclusion. Since the first proposition is if the tomatoes are not fertilized, then they will die, this is an argument with a conditional proposition. The second proposition affirms the consequent of the conditional proposition, which makes the argument invalid. Since the argument is invalid, it cannot be sound.

1b. The first two propositions are the premises and the last proposition is the conclusion. All of the propositions are true. This is an deductive argument, and a Venn diagram will show that it is invalid. (to see that the argument is invalid, replace poodles by, say, rabbits).

2. The amount spent on education this year is 5% more than last year, so the amount spent on education this year is 105% times the amount spent last year. This means that this year's amount = 1.05 × last year's amount. We know that this year's amount is $33 million. Dividing both sides of the equal sign by 1.05, we can find that

Check that indeed, $33 million is 5% more than $31.4 million.

3. Her take-home pay is 24% less than her gross pay, so her take-home pay is 100% 24% = 76% times her gross income. Therefore, gross income × 0.76 = $27,000. Dividing both side of the equal sign by 0.76, we have

Check that indeed $27,000 is 24% less than $35,526.

4a. An example will suffice. Suppose the stamp collection is worth $100 at the beginning of 1996. At the end of 1996 it is worth $100 + (0.20 × $100) = $120. At the end of 1997, it is worth $120 (0.20 × $120) = $96. The collection is worth less than its original value!

4b. You should provide an example to show that three successive 10% tax cuts amounts to a total of a 27.1% tax cut.

4c. Yes! Those who do not score above 80% must score at or below 80%. The percentages must add up to 100%.

4d. We are not told that 50% of English people are women. Unless 50% of English people are women, the statement is false.

5. Since 1 in = 2.54 cm, (1 in)3 = (2.54 cm)3. This means that 1 in3 = 16.3 cm3.

6a. One dollar is worth more than 1 mark because there is less than $1 in a mark.

6b. We can write the conversion factor as 1 mark = $0.72 or

Notice that in the last case we divided 1/0.72 to find that there are 1.39 marks in $1.

6c. We can convert the price just as we have done in class using 1 mark = $0.72 and 1 kg = 2.2 lbs. The oranges cost $0.49 per pound.