## MATH 114N Week 8 Final Exam

**1. Question:** Factor the trinomial.

c2 + 2c – 24

**2. Question: **Factor the trinomial.

a2 + 6a – 16

**3. Question: **Factor by grouping.

12c2 – 25c + 12

**4. Question: **Factor the trinomial completely.

20c2 + 11c – 3

**5. Question:** Factor Completely.

s2 – 9

**6. Question:** Factor the binomial completely.

25a2 – 36

**7. Question:** Solve using the zero-factor property.

6b(11b + 5) = 0

**8. Question: **Find all solutions by factoring.

v2 + 11v + 28 = 0

**9. Question:** The length of the top of the table is 6m greater than the width. The area is 91m^{2}. Find the dimensions of the table.

**10. Question:** Rosa works due north of Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 7 miles from home, the distance between them is one mile more than Ray’s distance from home. How far from home is Ray?

**11. Question: **Determine whether the given ordered pair is a solution of the system of equations. Remember to use alphabetically ordered variables.

Mary works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Mary is 5 miles from home, the distance between them is one mile more than Juan’s distance from home. How far from home is Juan?

(8, -8); – 3y = x + 16

3y = 4x – 56

**12. Question:** Solve the following system of equations by graphing.

x – 2y = – 2

x + 2y = 10

**13. Question:** Solve the following system of equations by graphing.

3x – 4y = 12

y = – 2x – 3

**14. Question: **Solve the following system by the substitution method.

6x + 5 = – y

5x + y = 0

**15. Question:** Solve the following system by the substitution method. Check the solution (s).

4x + y = 9

y = 9 – 4x

**16. Question:** Solve the following system by the substitution method. Check the solution (s).

0.1x + 0.8y = – 3.1

0.4x – 0.3y = 6.9

**17. Question:** Solve the following system by the elimination method.

8x + 8y = – 24

– 7x + 6y = 21

**18. Question:** Solve the following system by the elimination method.

4x – 7y = 7

16x – 28y = 31

**19. Question:** A baseball team has home games on Wednesday and Saturday. The two games together earn $5142.50 for the team. Wednesday’s game generates $782.50 less than Saturday’s game. How much money was taken in at each game?

- … much money did Wednesday’s game generate?
- How much money did Saturday’s game generate?

**20. Question:** A boat takes 4 hours to go 20 miles upstream. It can go 32 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)

**21. Question:** Find

– √(100/49)^{ }

**22. Question:** In the right triangle, find the length of the side not given.

a = 4, b = 6

**23. Question:** Multiply and simplify by factoring.

√(15 ). √10

**24. Question:** Multiply and simplify by factoring.

√(21 ). √15

**25. Question:** Use the square root property to solve the equation.

m2 = 14

**26. Question:** Use the square root property to solve the equation.

(x – 2)2 = 36

**27. Question:** Use the quadratic formula to solve the following equation.

x2 + 8x + 16 = 0

**28. Question: **Solve by using the quadratic formula.

4p2 = – 15p – 9

**29. Question: **Use the quadratic formula to solve the equation.

x2 – = 1

**30. Question: **Graph the quadratic equation.

y = – 3×2

**31. Question: Question:** Give the coordinates of the vertex. Sketch the graph of the equation.

y = x2+ 2x + 6

**32. Question:** Given the function f(x) = x^{2} – x + 10, find each of the following.

f(4), f(- 2), f(0)