Final Exam Review – Math 72
1. Factor: x2 + 7x + 10
2. Factor: 25a2 – 49b2
3. Factor: y2 – 13y + 2
4. Factor: 5x2 - 21x + 4
5. Factor: x3 + 125
6. Factor: x2 + 5x – xy – 5y
7. Factor: -3x3 + 12x2 – 9x
8. Solve: p3 – 2p2 – 15p = 0
9. A room is 2 ft. longer than twice its width. If the area of the room is 144 ft2, find the
length and width.
10. A ladder is 2 feet longer than the height of a window it reaches. If the ladder is 6 ft
from the building along the ground, find the height of the window.
x  18
is undefined.
x - 7x 3  12x 2
x 2  4x  3 7x - 7x 2

12. Multiply:
x2 - 1
5x 2
y 2  3y - 18 y 2 - 5y  6
13. Divide:

2y  12
y4
2x
-4
 2
14. Simplify, writing as one fraction:
x -1 x - 1
2
y -4
y3
15. Simplify:
3y  6
6y
16. Solve the equation, checking for bad points:
20
5

r -7 r 2
17. Solve the equation, checking for bad points:
x
4
18

 2
x-3 x3 x -9
18. A plane flies 500 miles with the wind in the same time it takes to fly 450 miles
against the wind. If the wind speed is 30 mph, find the speed of the plane in still air.
19. Ed takes 6 hours to paint a room by himself, and Al takes 7 hours. How long does
it take them to paint the room working together?
20. F varies directly as the square of x, and F = 100 when x = 5.
a) Find the proportionality constant, k, and write a specific formula with F and x.
b) Find F for x = 8.
11. Find the values where
4
1
21. a) What 2 whole numbers does 72 fall between?
b) Simplify 72 , leaving your final answer in radical form.
22. If the hypotenuse of a triangle is 10.5 ft. long and one of its legs is 8.8 ft. long, find
the length of the other leg, to the nearest tenth (calculator recommended).
10.5
x
8.8
23. Simplify:
75x 2 y 9
3
24. Simplify:
120
3
3
25. Simplify: 2 18 - 48 + 5 75
26. Simplify:
7
5 2
27. Write in lowest terms:
6  48
12
28. Solve: 2x  5  1  8
29. Solve: y  5  y  3
30. Simplify: 165/4
y 2/7  y -3/7
31. Simplify:
y 5/7
32. Solve: x2 + 8x + 2= 0
33. Solve: (2y + 3)2 = 13
34. Solve: x2 – 8x + 15 = 0
35. Solve: 3x2 + 6x + 8 = 0
36. Solve: z2 = 48
37. Solve: (p – 4)(p + 1) = 3
38. a) Solve x2 + 11x + 2
b) Write the values as decimal solutions to the nearest hundredth.
39. For the equation y = x2 – 6x + 7
a) Give the coordinates of the vertex.
b) Graph the equation
40. Decide from the graph how many solutions f(x) = 0 has. Then give the x values of
the solution or solutions.