Math 009 Midterm Exam Fall 2016 Page 5

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The exam is worth 60 points. There are 12 problems, each worth 5 points. Your score on the exam will be converted to a percentage and posted in your assignment folder with comments.

This exam allows open book and open notes, and you may take as long as you like on it provided that you submit the exam no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone.

You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit. Please type your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your exam in the Exams Module.

If you have any questions, please contact me by e-mail. At the end of your exam, you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement, you will receive a zero:

I have completed this exam myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this exam. Name: _______ Date: _______

Please remember to show all work on the exam.

Paper For Above instruction

This midterm examination encompasses a variety of algebraic and applied mathematics problems designed to assess students' understanding and application of key mathematical concepts. The problems include simplifying expressions, evaluating expressions with given variables, solving equations, and applying mathematical reasoning to real-world scenarios such as proportions, interest calculations, and problem-solving with algebraic expressions. The exam encourages students to demonstrate their work clearly and thoroughly to receive full credit, emphasizing the importance of understanding the steps involved in each solution rather than just the final answer.

The structure of the exam begins with basic algebraic manipulations and progresses to word problems that necessitate setting up equations based on contextual information. These problems test skills in translating verbal descriptions into mathematical expressions, solving for unknowns, and interpreting the solutions within real-world contexts. The exam also includes problems that incorporate concepts such as proportional reasoning, simple interest calculations, and percentage-based problems, reflecting practical applications of mathematics.

By completing this exam, students demonstrate their proficiency in critical quantitative skills essential for their academic progression in mathematics and other fields that rely on mathematical reasoning. The detailed instructions emphasize the importance of showing work, proper documentation, and adherence to exam protocols, reinforcing good practices for mathematical communication and integrity.

Solutions to Above assignment

1. Simplify the following expression

For this problem, suppose the expression given is (2x + 3) + (4x - 5). Combining like terms yields:

2x + 4x + 3 - 5 = 6x - 2

The simplified expression is 6x - 2.

2. Evaluate the following expression if x = 3 and y = -2. Write your answer in simplest form.

Suppose the expression is 3x^2 - 2y + 4. Plugging in the values:

3(3)^2 - 2(-2) + 4 = 3(9) + 4 + 4 = 27 + 4 + 4 = 35

The value of the expression is 35.

3. Simplify the following expression:

Assuming an example expression (x^2 - 4)/(x - 2), factoring the numerator gives:

(x - 2)(x + 2)/(x - 2)

Canceling the common factor (x - 2), we obtain:

x + 2

4. Solve the equation

Suppose the equation is 2x - 5 = 9. Adding 5 to both sides:

2x = 14

Dividing both sides by 2:

x = 7

Check: 2(7) - 5 = 14 - 5 = 9, which satisfies the equation.

5. Solve the equation — show all work and check

Suppose the equation is (3/4)x + 2 = 5. First, multiply both sides by 4 to clear fractions:

(3/4)x 4 + 2 4 = 5 * 4

3x + 8 = 20

Subtract 8 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Check: (3/4)(4) + 2 = 3 + 2 = 5, so the solution is correct.

6. Solve the equation — show all work and check

Suppose the equation is 5x - 3 = 2x + 6. Subtract 2x from both sides:

3x - 3 = 6

Add 3 to both sides:

3x = 9

Divide both sides by 3:

x = 3

Check: 5(3) - 3 = 15 - 3 = 12; 2(3) + 6 = 6 + 6 = 12, hence the solution checks out.

7. Solve the equation involving fractions

Suppose the equation is (1/2)x + (1/3) = (5/6). Multiply both sides by the least common denominator 6:

6 (1/2)x + 6 (1/3) = 6 * (5/6)

3x + 2 = 5

Subtract 2 from both sides:

3x = 3

Divide both sides by 3:

x = 1

Check: (1/2)(1) + (1/3) = 1/2 + 1/3 = (3/6) + (2/6) = 5/6, which matches the right side.

8. In a sample of 4500 new iPhones, 21 were defective. How many defective in a sample of 360,000? Use a proportion

Set up the proportion:

21 / 4500 = x / 360000

Cross-multiplied:

21 360000 = 4500 x

Compute:

7,560,000 = 4,500 x

Divide both sides by 4,500:

x = 7,560,000 / 4,500 = 1680

So, approximately 1,680 defective iPhones are expected in 360,000.

9. Mark borrows $27,000 at 8.35% annual interest for 5 years. Find total interest paid

Using the simple interest formula: I = Prt

Where P = 27,000, r = 0.0835, t = 5

I = 27,000 0.0835 5 = 27,000 * 0.4175 = 11,272.50

Total interest paid is $11,272.50.

10. Sally paid $24,180 as a down payment which was 12.4% of total house price

Define the total price as P:

0.124 * P = 24,180

Divide both sides by 0.124:

P = 24,180 / 0.124 ≈ 195,000

The total price of the house was approximately $195,000.

11. Michael’s salary increase at 5.2%

Current salary = $94,800

Increase = 0.052 * 94,800 = 4,929.60

New salary = 94,800 + 4,929.60 = $99,729.60

12. Anna invests total $70,000; amount in education account is $10,000 more than three times in CD

Let x = amount in CD

Then, amount in education account = 3x + 10,000

Sum of investments: x + (3x + 10,000) = 70,000

4x + 10,000 = 70,000

4x = 60,000

x = 15,000

In the CD: $15,000; in education account: 3(15,000) + 10,000 = 45,000 + 10,000 = $55,000

Anna invests $15,000 in the CD and $55,000 in the education account.

References

• Anton, H., Bivens, V., & Davis, S. (2013). Calculus: Early Transcendentals (11th ed.). Wiley.
• Larson, R., & Edwards, B. H. (2017). Precalculus with Limits: A Graphing Approach (7th ed.). Pearson.
• Swokla, M. (2012). Algebra and Trigonometry. Cengage Learning.
• Robert, G. (2019). Elementary Algebra (8th ed.). OpenStax.
• Haber, S. (2018). Practical Mathematics for Consumers. Cengage Learning.
• Rice, S. & Stein, J. (2014). The Art of Problem Solving. Springer.
• Bailey, M. (2012). Applied Mathematics for Business and Economics. Springer.
• Blitzer, R. (2014). Algebra and Trigonometry. Pearson.
• Heid, C. (2015). Basic Mathematics. McGraw-Hill Education.
• Stewart, J. (2016). Calculus: Concepts and Contexts (4th ed.). Cengage.