1
Final Exam Review – Math 71
1. Simplify: |5 -12|
2. Simplify: 27 – 7(-2)2 - 30
3. Simplify: 2(3x – 13) – (x – 12)
4. Is x = -3 a solution of x2 – 2x = 3? Show your reason for full credit (“yes”/”no”
answers alone will only receive partial credit.
5. Solve 15 – 3y = 11
6. Solve: 4x + 6 = 7x – 5
15y 3

7. Solve:
8
4
8. Solve: 6x + 13 = -2(x – 5)
9. Six less than a number is equal to five times the sum of that number and 2. Find the
number.
10. Ed and Andy pick 157 pounds of peaches together. If Ed picks 33 pounds more
than Andy, how many pounds does each person pick?
11. It costs $100 to clean the carpet of a 1500 sq. ft. house. How much would it cost to
clean the carpet of a 2400 sq. ft. house at the same rate?
12. An area which is 13 feet long and 9 feet wide is sectioned off in a gymnasium.
How much rope is needed to surround this area?
13. Find the measure of the marked angles:
14. Hamburgers cost $2, and sodas cost $1. Twice as many hamburgers are bought
as sodas. If the total cost is $15, how many of each are bought?
15. Solve and graph the inequality: -3x > 12. Note: This is a number line graph.
16. Solve and graph the inequality –1 < 2x + 7 < 13.
17. Find the x and y intercepts of the line 3x – 4y = 12
18. Graph the equation 3x – 4y = 12
19. Graph the equation y = 2x – 5
20. Find the slope of the line passing through the points (5, -2) and (-3, -1)
21. Find the equation of the line with slope = -1 passing through the point (4, 3).
22. Graph the solution of x – 2y > -6
23. For the relation {(3,2), (5,1), (-1, 7), (3,0)}
a) Give the domain:
b) Give the range:
c) Is it a function?
24. Is (-2, 3) a solution to the system below? Justify your answer.
x+y=1
3x + y = 3
2
25. A cell phone company charges $2/month for service, plus 20 cents for each minute
of use. The monthly charge is represented by the function:
C(x) = 2 + .2x , where x is the number of minutes used
a) Find C(10)
b) Find C(600)
c) What are C(10) and C(600) in real-life terms?
26. Graph each of the 2 lines below. Then give the ordered pair solution to the
system.
2x – 3y = 12
x=3
27. Solve the system by the method of your choice:
4x + 3y = -5
x=y–3
28. Solve the system:
4x + 3y = 30
2x – 3y = 6
29. Solve the system:
x + 3y = 5
3x + 2y = - 6
30. Solve the system:
6x - 2y = 10
y = 3x - 5
31. A plane flies 160 mph with the wind. Against the wind, the plane flies at 120 mph.
Find the plane speed and the wind speed.
32. Cashews cost $5.60/lb and almonds cost $4/lb. To get 80 lb. of a mix costing $5/lb,
how much of each type (cashews and almonds) must be used?
33. Simplify: (2y4 – 5y3 + 7y – 4) – (y3 + 2y2 – 6)
34. Multiply: -5y2(3y3 –7y2 + 2y – 1)
35. Multiply: (3x + 2)(x2 + x – 6)
36. Simplify: (-2x3y5)2(x4y)
37. Simplify completely, using positive exponents only:
3x -3 y 2 z -1
2 -2 x 5 y 3 z -2
38. Write the following in scientific notation:
a) 30,709
b) .0000503
39. Multiply: (3x – 7)(3x + 7)
40. Divide: x  2 x 3  3x 2 - 4x  7