This document provides sample questions and answers for the MAT 209 Final Exam. It includes 20 multiple choice or short answer math problems testing skills like performing operations, solving equations, and word problems involving speed, area, and geometry. For each problem, the steps to solve are shown along with the final numerical answer. The document provides a full worked example of the thought process and calculations for each question on the exam.

1. MAT 209 Final Exam
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MAT 209 Final Exam Answers
Demo content and sample answers

2. Perform the indicated operation:
1. 19×2 - 13x + 31 - 12×2 - 24x - (16×2 - 27x + 25)
2. 7xy2(5×3 – 4x2y2 + 3xy4)
3. (13x + 5)(9x - 13)
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4. (25x - 12)2
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5. (13a + 15b)(13a - 15b)
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6. (25×4 - 35×3 + 45×2) / (5×2)
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3. 7. (9.63 x 1035)(8.56 x 10-26) answer in scientific notation
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8. 2x / (x + 5) – 150 / (x2 - 25) + 3x / (x – 5)
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9. x / (x - y) – y / (x + y)
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10. 5 / [sqrt(5) + sqrt(7)] – 7 / [sqrt(5) – sqrt(7)]
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sqrt(7)][ sqrt(5) + sqrt(7)]

4. -
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Solve the equations for x.
11. (2x – 3)2 -
2x-3-
2x-
x-
12. 125×2 -
x2-
x-
x-
13. 8×2 + 6x - 5 -
(2x-1)(4x+5)-
2x-1-
x-
14. 5×2 – 4x – 3 -
X-

5. X-
15. 24×2 + 32x - 96 -
3×2 + 4x – 12-
X-
X-
16. 4.56×2 + 7.89x – 7.65 -
X-
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X-
17. x2 -
x2 + 3x -6-
x-
x-
18. x / (x + 7) -
x2 + 6x – 7-
the LCD for the denominators is (x+7)(x-1)
multiply both sides by (x+7)(x-1)
x(x - 1)-
x2-x-

6. x2+11x-12-
(x+12)(x-1)-
x-
when x-
So the solution to the equation is x-
19. Jim made a 350 mile trip in his car at a certain speed. If he had gone 10 mph fa
ster, he could have
made the trip in one hour less time. Find his speed.
Let x represent his speed.
The time he made a 350 mile trip is 350/x hour.
If he had gone 10 mph faster, the speed is (x+10) mph, then the time he made a 35
0 mile trip is
350/(x+10) hour, which is 1 hour less. So we can make an equation:
350/x - 350/(x+10)-
Multiply both sides by x(x+10):
350(x + 10) - 350x-
x2 + 10x - 3500-
x-
x-
Jim’s speed is 54.37 mph

7. 20. The Monahan’s garden is 20 feet by 30 feet.
They wish to lay a uniform border of pine bark
around the garden. How large a strip should they lay if they only have enough bark
to cover 420
square feet? (…and don’t tell me to buy more pine bark…:) )
let x represent the width of the border
the overall dimensions of border and garden is: (2x+20)feet by (2x+30)feet
the area of the garden is 20 * 30 -
The total area of border & garden is (420 + 600) sq ft, which can also express
ed as: (2x+20)(2x+30).
So here is the equation:
(2x+20) * (2x+30) -
4×2 + 100x + 600-
X2 + 25x -105-
(x+26)(x-1)-
X-
So the strip should be 1 foot.
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