Math 009 Final Exam Spring 2016 Answer Sheet And Instruction

Math 009 Final Examination Spring 2016 Answer Sheet and Instructions

This is an open-book exam. You may refer to your text and other course materials as you work on the exam and you may use a calculator. Record your answers and show your work on this document. You must show your work to receive credit: answers given with no work shown will not receive credit. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. If you choose to scan your work, note that most scanners have a setting that will allow you to create one PDF document from all of the pages of your Answer Sheet – please make use of this option if it is available on your scanner. Whether you type your work or write it by hand, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. You must complete the exam individually.

Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement. Please sign (or type) your name below the following honor statement: I have completed this final examination myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this final examination.

Paper For Above instruction

The provided instructions outline the guidelines for completing the Math 009 Final Examination for Spring 2016. This exam is open-book, allowing the use of textbooks, course materials, and calculators. Students are required to record answers and show all work clearly, following proper mathematical conventions. Handwritten or typed work is acceptable, but scanned images should be consolidated into a single PDF if possible. Academic integrity is emphasized, with students affirming independent work via an honor statement. The exam comprises multiple problems involving algebraic expressions, proportions, percentages, interest calculations, equations, inequalities, graphing, and word problems, culminating in a comprehensive assessment of mathematical skills.

Answers to Sample Questions

1. Simplify the expression: -4 + y - x^2 y; given x = -2, y = 8

Substitute the values: -4 + 8 - (-2)^2 8 = -4 + 8 - 4 8 = 4 - 32 = -28

2. Simplify the expression: k + 7k

Combine like terms: 1k + 7k = 8k

3. Write as a fraction in lowest terms: (-2) / (-4)

Simplify: 2/4 = 1/2

4. Use a proportion to solve: The shadow of a giraffe 16.7 ft tall measures 28.4 ft. Find the shadow length of an 11.5 ft statue.

Set up proportion: 16.7 / 28.4 = 11.5 / x

Solve for x: x = (11.5 * 28.4) / 16.7 ≈ (326.6) / 16.7 ≈ 19.5 ft

5. What percent is 35.4 of 67?

Percentage = (35.4 / 67) * 100 ≈ 52.84%

6. Find the percentage change from 27 inches to 19 inches

Change = 27 - 19 = 8 inches

Percentage change = (8 / 27) * 100 ≈ 29.6% decrease

7. Final price after discount and tax: Original price = $599.50, Discount = 40%, Tax = 3%

Discounted price: 599.50 (1 - 0.40) = 599.50 0.60 = $359.70

Tax amount: 359.70 * 0.03 = $10.79

Final price: 359.70 + 10.79 ≈ $370.49

8. Use simple interest: Principal = $18,000, Rate = 2%, Time = 6 years

Interest: I = P r t = 18,000 0.02 6 = $2,160

Ending balance: 18,000 + 2,160 = $20,160

9. Solve for n: 4 + 2n = 10

Subtract 4 from both sides: 2n = 6

Divide both sides by 2: n = 3

10. Solve: 36 = 2(6x - 2x + 2)

Expand: 36 = 2(4x + 2) = 8x + 4

Subtract 4: 36 - 4 = 8x

32 = 8x

x = 4

11. Solve: (1/4)n + 8 = 5n

Rewrite: (1/4)n - 5n = -8

Convert 5n to quarter form: (1/4)n - (20/4)n = -8

Combine: (-19/4)n = -8

Multiply both sides by 4: -19n = -32

n = 32 / 19

12. Solve: 2.5v + 2v = 4.7v - 0.5

Combine like terms: (2.5 + 2)v = 4.7v - 0.5

(4.5)v = 4.7v - 0.5

Bring variables to one side: 4.5v - 4.7v = -0.5

-0.2v = -0.5

v = -0.5 / -0.2 = 2.5

13. Solve the inequality: 4a - 3 > -59

Add 3: 4a > -56

Divide by 4: a > -14

14. The inequality: n + 4 ≥ n + n

Simplify: n + 4 ≥ 2n

Subtract n: 4 ≥ n

Solution set: n ≤ 4 (in interval notation: (-∞, 4])

15. Find the slope of the line passing through points (x1, y1) and (x2, y2)

Need actual points; in case of example, if points are (x1, y1) and (x2, y2):

Slope m = (y2 - y1) / (x2 - x1)

16. Find the x- and y-intercepts of line: x + y = 0

Set y=0: x + 0 = 0 ⇒ x=0 (x-intercept)

Set x=0: 0 + y = 0 ⇒ y=0 (y-intercept)

17. Write the slope-intercept form for the line through (2, 3) and (-2, 5)

First, find slope: m = (5-3)/(-2 - 2) = 2 / -4 = -1/2

Equation: y - 3 = -1/2(x - 2)

Simplified: y = -1/2 x + 4

18. Find three points satisfying y = -7x

Choose x values: x=0 ⇒ y=0; x=1 ⇒ y=-7; x=-1 ⇒ y=7

19. Solve the system by substitution: 2x + 4y = 6 and y = -2x

Substitute y: 2x + 4(-2x) = 6 ⇒ 2x - 8x = 6 ⇒ -6x=6 ⇒ x=-1

Then y = -2(-1)=2

Solution: (-1, 2)

20. Write the point-slope form of the line through (2, -2) parallel to y = -7/2 x + 3

Slope of given line: -7/2

Point-slope form: y - (-2) = -7/2 (x - 2) ⇒ y + 2 = -7/2 (x - 2)

21. Write the equation: through (5, -3), perpendicular to y= 5/8 x - 4

Slope of given line: 5/8; perpendicular slope: -8/5

Equation: y - (-3) = -8/5(x - 5) ⇒ y + 3 = -8/5 x + 8

Final form: y = -8/5 x + 5

22. Graph the system: x - 2y = -4 and 2x + y= -3

Find intercepts and plot points to graph both lines.

23. Solve by elimination: 3x - 6y= -27 and 9x + 4y= ?

Inconsistent equation in original form; need complete second equation for solution.

24. Word problem: costs of blueberry and lemon meringue pies based on sales data

Set up equations based on total sales and solve for individual prices.

References:

  • Ron Zimmerman & Nancy A. Roberts, "Elementary and Intermediate Algebra," 5th Edition, Pearson, 2014.
  • James Stewart, "Calculus: Early Transcendentals," 8th Edition, Cengage Learning, 2015.
  • G. M. Thomas, Jr., R. L. Finney, "Calculus and Analytic Geometry," 9th Edition, Pearson, 2014.
  • Charles P. McKeague, "Algebra and Trigonometry," 3rd Edition, Brooks/Cole, 2012.
  • Paul A. Foerster, "Precalculus," 4th Edition, Pearson, 2015.
  • David R. Hill, "Precalculus," 5th Edition, Princeton University Press, 2014.
  • Andrew Sleeman, "Introduction to Algebra," OpenStax, 2019.
  • Larson, Hostetler, and Edwards, "Precalculus with Limits," 8th Edition, Brooks Cole, 2014.
  • Matthew Brodie, "Precalculus," 3rd Edition, McGraw-Hill Education, 2016.
  • W. Michael Kelley, "Algebra and Trigonometry," 7th Edition, Cengage Learning, 2015.

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