10/16/20 Test Solutions

For each numbered task, rewrite the problem. When appropriate, provide your analysis of the problem and your proof of the solution. You may not consult anyone or anything except your own brain. Once you begin, you have four hours to complete the test. Good luck and think well!

1. Name a goal and present your plan for meeting it.
Solution: My goal is to squat 500 lbs before I reach 50 years of age. My plan is to add 15 lbs to my squat each week, sleep 9-10 hours each night, and eat 3600 C each day.

2. Describe three techniques for controlling your emotions.
Solution: I can rescue my thoughts from the exacerbating stimulus by doing some calisthenics, meditating, or journaling about what I'm feeling.

3. List twelve fractions which are equivalent to 5/15. Include and identify the irreducible among them.
Solution: 5/15 = 1/3 = 2/6 = 3/9 = 4/12 = 6/18 = 7/21 = 8/24 = 9/27 = 10/30 = 11/33 = 12/36 = 13/39

4. Write 5/8 in decimal.
Solution: 5/8 = 625/1000 = 0.625

5. Determine the rectangle with perimeter 80 feet which has the greatest area.
Solution: By inductive reasoning, we know a square encloses the most area for a fixed rectangular perimeter. The length of each side of the square is one fourth of 80 feet, which gives us 20 feet. Thus, a 20' by 20' rectangle will have the required perimeter and enclose the greatest area.

6. Construct a parallelogram and a rectangle with equal areas.
Solution: A rectangle and a parallelogram with the same base and height will have the same area.

7. Write (2120.2)4 in hexadecimal.
Solution: (2120.2)4 = 2⋅64 + 16 + 2⋅4 + 2/4 = 152½. Since 152½ = 9⋅16 + 8 + 8/16, therefore, (2120.2)4 = (98.8)16.

8. Find all solutions of xn = 81.
Solution: 81 = 92. Since 9 = (32), we get 81 = (32)2. Thus, we also have 81 = 34.

9. List the classifications and states of matter. Give an example of each.
Solution: The states of matter are solid (e.g. ice), liquid (e.g. water), and gas (e.g. steam). The classes of matter are heterogeneous (mixtures (e.g. ocean), homogeneous (mixtures (e.g. salt water) and pure substances (elements (e.g. hydrogen) and compounds (e.g. salt)). For example,

10. Draw a simple Bohr model of 21N, a stable isotope of neon.
Solution: none; N is the symbol for nitrogen, not neon (Ne).

11. Discuss your current understanding of the past, present, and future.
Solution: Subjective, but should include some remarks about important historical periods/developments, current events, and the probable future.

12. Below is a paragraph that is full of errors. There may be spelling, punctuation, capitalization, or grammar errors. Rewrite the paragraph correcting all the errors.
Solution: At the start of school, Dora was afraid of her new teacher. Mrs. Davis seemed nice, but she had so many rules for the class to follow. It's enough to scare someone to pieces. As the school year continued, Dora began to understand how the teacher came up with the rules. The rules were there so students would be respectful of themselves and each other. By the end of the year, Dora thought Mrs. Davis was the best teacher she ever had!