College of Arts and Sciences



Math 101 Final Exam Review Sheet

Room Sections

Matheson 109 011, 013, 016, 017

Matheson 208 009, 010

Exam coverage: 1.1-3.5

Date: Friday, June 12 1-3 p.m.

Problems:

1. Write an equation of the line passing through (2,7) and (-1,1)

2. Vertical line passing through the point (1,-1)

3. On the Fahrenheit temperature scale, water freezes at 32 degrees and boils at 212 degrees. On the Celsius scale, water freezes at 0 and boils at 100.

a. Use the data points (0,32) and (100,212) to find the linear relationship between x=Celsius temperature and y=Fahrenheit temperature.

b. Find the Fahrenheit temperature that corresponds to 20 degrees Celsius.

4. Determine if this is a function:

[pic]

5. Evaluate and find the domain: [pic]

6. Graph: [pic]

[pic]

7. Find the vertex and graph: [pic]

[pic]

8. Solve: [pic]

9. A company rents out cars for $45 per day and $0.12 per mile. Find a function, C(x) for the cost of a rented car driven for x miles in a day.

10. A store that installs satellite TV receivers finds that if it installs x receivers per week, then its costs will be C(x)=80x+1950 and its revenue will be [pic] (both in dollars).

a. Find the store's break-even points.

b. Find the number of receivers the store should install to maximize profit and the maximum profit.

11. Find the domain of [pic]

12. Graph: [pic]

[pic]

13. Use the properties of natural logarithms to simplify: [pic]

14. After 4 years and 9 months of monthly mortgage payments on their 30-year $150,000 mortgage at 8.75%, the Jones family has to relocate to Atlanta and must sell their nice house in the suburbs. How much do they still owe on their mortgage?

15. How much must you deposit each month into a stock fund earning 11.2% interest to accumulate $150,000 in 20 years?

16. How much should be invested now at 5.6% simple interest if $5200 is needed in 2 years, 9 months?

17. During the mid-1990's the Brandywine long-term grown fund returned 19.6% compounded quarterly. How much would a %5,000 investment be worth after 4 years?

18. How long must you save $275 each month in a 6.2% money market fund to accumulate %19,500 for a new car?

19. Solve: [pic]

20. The pharmacist at the Charter Drug Shop filled 92 prescriptions today for antibiotics and cough suppressants. If there were 34 more prescriptions for antibiotics than cough suppressants, how many prescriptions for each were filled?

21. Solve: [pic]

Use the given matrices to find each matrix expression:

[pic], [pic], [pic]

22. Find AC

23. Find AB

24. Find A+2C

25. Find [pic]

26. A proud grandmother's record book shows that her grandson Thomas is now 61 inches tall and weighs 90 pounds, while last year he was 58 inches tall and weighed 80 pounds. Her grandson Richard is now 54 inches tall and weighs 75 pounds, while last year he was 52 inches tall and weighed 70 pounds; and her granddaughter Harriet is now 47 inches tall and weighs 60 pounds, while last year she was 46 inches tall and weighed 55 pounds. Represent these facts as a "this year" matrix and "last year" matrix. Use these matrices to find how much each child grew.

27. Are these two matrices inverses of one another: [pic]

28. Find the inverse of [pic]

29. Rewrite the system of equations as a matrix equation AX=B and use the inverse of A to find the solution.

[pic]

30. The Art Museum Of Philadelphia sells children's tickets for $6 and adult tickets for $12. On Saturday, 180 tickets were sold with gross receipts totaling $1560. On Sunday, 120 tickets were sold with gross receipts totaling $1140. How many of each type of ticket was sold on each day?

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