SUBDOMAIN 206.2 . 1.Solve linear equations in one unknown both algebraically and graphically.

Given:

A person cuts a rope into two pieces that are equal in length. The first piece is 4 times the length of the person’s forearm minus 1 inch. The second piece is 3 times the length of the person’s forearm plus 15 inches.

Task:

1. Construct the linear equation that represents the situation in the given using x as the variable for the person’s forearm.
2. Solve the linear equation you constructed both algebraically and graphically to find the length of the person’s forearm. Show your work.
3. Briefly discuss whether or not your answer is reasonable.

Note: To draw the graph, you may use one or a combination of the following:

- A spreadsheet program, such as Excel (*. xls )

- A graphics program, such as Paint (*.jpeg, *.gif)

- A word processing program, such as Word (*.rtf)

- A scanned hand-drawn sketch (*.jpeg, *.gif)

SUBDOMAIN 206.2 02. Solve quadratic equations in one unknown both algebraically and graphically.

Task:

1. Solve the following quadratic equations. Make sure to show all your work. Do not use any method (e.g., factoring, completing the square, quadratic formula, graphing) more than twice. Use the graphing method at least once .

1. 3 x 2 + 11 x – 20 = 0
2. x 2 + 3 x – 4 = 0
3. 3 x 2 – x – 1 = 0

B. State the different methods you used to solve each equation. Make sure that your work demonstrates both algebraic and graphing methods.

S UBDOMAIN 206.2 04 : Explain why an answer to an algebraic or numerical calculation is unreasonable.

Task:

1. A school bus holds 57 students but is only 40% full. How many students are on the bus?

1. Explain why the answer of 22.8 students is unreasonable.
2. Give a reasonable answer in its place.
3. Explain why your answer is more reasonable.

B. The length of a rectangular field is 2 yards more than its width. Find the width if the area of the field is 120 yd 2 .

1. Explain why the answer of a width of –12 yards is unreasonable.
2. Give a reasonable answer in its place.
3. Explain why your answer is more reasonable.

Task:

1. Graph the function f( x ) = –3 x + 7. Be sure to properly label the graph, which includes labeling the axes and the line with its equation.
2. Graph the function f( x ) = –3 x 2 + x – 5. Be sure to properly label the graph, which includes labeling the axes and the graph with its equation.

Note: To draw the graph, you may use one or a combination of the following:

- A spreadsheet program, such as Excel (*. xls )

- A graphics program, such as Paint (*.jpeg, *.gif)

- A word processing program, such as Word (*.rtf)

- A scanned hand-drawn sketch (*.jpeg, *.gif)

Objective 206.4.1-02: Explain randomization, replication, comparison, and control in experiments.

Given:

A scientist was hired to determine which brand of toothpaste is more effective in preventing cavities in children. Thirty children volunteered to participate in the experiment from which the scientist randomly created two groups of 15 children. The first group was given Brand A toothpaste, and the second group was given Brand B toothpaste. All of the children were given detailed directions describing when and how they should brush their teeth. After six months the children were taken to the same dentist and the number of cavities each child had was recorded. This data was used to determine which toothpaste is more effective.

Task:

1. Identify something the scientist tried to control in this experiment. Identify something the scientist did not consider controlling or was unable to control in this experiment and explain the adverse effects this might have had on the collected data.
2. Explain how replication was used in this experiment and why it is important.
3. The scientist randomly created the two groups. Instead, the scientist could have created the two groups based on some common characteristic, such as age or gender. Explain the adverse effects this might have had on this experiment.
4. Explain the role comparison plays in experiments and specify what was compared in this experiment.

Objective 206.4.1-08: Task:

Write a brief essay ( suggested length of 2 pages ) in which you address the following:

1. Define "association" in statistics. Explain how association is identified and demonstrated.
2. Define "causation" in statistical analysis. Describe at least two factors that influence relationships between two variables and can lead to misinterpretation of data analysis.
3. Explain when it is appropriate to use averages when computing correlations. Explain what statisticians should be aware of when doing this.

12: Explain the Law of Large Numbers.

Task:

Write a brief essay ( suggested length of 2 pages ) in which you:

1. Define the Law of Large Numbers, citing a credible source.
2. Explain the Law of Large Numbers in your own words using a coin toss as an example.
3. Apply the Law of Large Numbers

Using the example of a coin, assume that we repeatedly toss a fair coin, and we record the number of tails. The relative frequency corresponds to the number of tails divided by the total number of repetitions. This fraction should approximate to 0.5 as the sample size gets large, because 0.5 is the probability of getting a tail, for the case of a fair coin.

1. Using a coin toss and fictitious data, explain how the following scenario is possible: As the number of trials increases, the differences between the number of actual and expected successes tends to grow, but the difference between the percentage of actual and expected successes tends to decrease.
2. Explain your answer to the following question: Is it true that if I flip a coin 1,000 times I will get heads 500 times?
3. Explain your answer to the following question: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?

Objective 206.4.1-15: Explain why random samples are preferred.

Describe the advantages and limitations of commonly used sampling techniques.

Task:

Write a brief essay ( suggested length of 2 pages ) in which you:

1. Explain why random samples are preferred to nonrandom samples.
2. Describe the advantages and limitations of the following commonly used sampling techniques:

1. Simple random sampling
2. Stratified sampling
3. Cluster sampling
4. Multi-stage sampling

Objective 206.4.1-17: Construct simple hypothesis tests for means and proportions.

Given:

A potato chip company packages its potato chips into 12.0 ounce bags. You find it hard to believe that the bag contains enough potato chips to weigh 12.0 ounces and would like to make an official complaint. Before doing so, you decide to run an experiment so that you can have some confidence that the company’s claim is incorrect. Over the next several months you buy 30 bags of potato chips and weigh the contents of each one. You discover that the mean weight is 11.9 ounces with a standard deviation of 0.4 ounces. You decide that you will only complain if you can be 95% sure that the bags do not contain at least 12.0 ounces of potato chips. You decide to construct a hypothesis test.

Task:

1. Determine if this is a one-tailed or two-tailed test. Justify your decision.
2. State the null hypothesis and alternative hypothesis. Your null hypothesis should assume the company’s claim is correct.
3. Define the term Type I error and explain what a Type I error is in terms of this problem.
4. Define the term level of significance and identify the level of significance for this problem.
5. Calculate the test statistic as a z-score. Show all relevant work.
6. Using a standard table, you determine that the critical value is –1.645. Determine if you are able to reject the null hypothesis and explain how you reached this conclusion. ( Your conclusion should include a comment relating the results to the original problem. )
   Objective 206.5.1-08: Use relevant quantitative problem-solving strategies and techniques to solve multi-step problems.
   Given:
   There are two companies that sell widgets. Both companies sell the widgets to the general public for the same price. In order to earn business, Company A offers a special 25% discount on each order. In response, Company B offers a 35% discount on every dollar the customer spends over $50. Both discounts are rounded to the nearest cent. If you place an order for $50 or less, it is less expensive to order from Company A. If you place a large enough order, it will be less expensive to order from Company B. At what price does it become less expensive to order from Company B?
   Task:
   1. You can estimate the answer by considering hypothetical orders and comparing the discounts each company would provide.
      1. Create and properly label a table of data demonstrating this technique. The table should include at least four hypothetical orders and should estimate the answer within a $50 range. Each row will represent a hypothetical order. The first row will represent a $50 order and each additional row will represent orders in $50 increments (i.e., $100, $150). The table should include three columns. The first column is the order amount, the second column is the discount that Company A would give, and the third column is the discount Company B would give.
      2. Specify the $50 range that the answer could be within.
      3. Explain how you used your table to determine this.
   2. Determine algebraically the actual price at which Company B offers you the same discount as Company A. Make sure to show all relevant work.
   3. Determine the actual price at which Company B will give you a greater discount than Company A.
      1. Explain how you reached this conclusion.

O bjectives:

206.6.1-01: Describe given mathematical procedures clearly and correctly.

206.6.1-03: Communicate mathematical reasoning in written form.

206.6.1-05: Communicate mathematical equations in written form .

206.6.1-06: Communicate the results of a calculation in written form.

Given:

By using a ruler, you determine that the distance between two cities on a map is 3.4 inches. According to the map’s scale, 2 inches represents 75 miles. What is the actual distance between the two cities?

Task:

Write an essay ( suggested length of 1 page ) in which you communicate mathematical information in written form. Include the following:

A.  Briefly explain the general procedure used to identify and set up a proportion problem.

B.  Write a proportion that correctly represents the problem in the Given.

1. Solve the proportion, showing all relevant work.

C.  Explain the reasoning behind the equation you set up (e.g., how did you determine the two ratios in the problem, and how do you know if they are equivalent?).

D.  Explain each step used to solve the equation. Your explanation should include the original equation, the equation at each step, and the final equation with the unknown equal to some number. ( Use complete sentences, not mathematical symbols, to explain the steps. )

E.  Briefly explain ( in 1–2 sentences ) what the answer means in terms of the original problem.

Objectives:

206.7.1-02: Use appropriate technological tools to carry out basic arithmetic and algebraic operations.

206.7.1-04: Use appropriate technological tools to represent quantitative information and relationships in the form of formulas, tables, and graphs.

206.7.1-05: Use appropriate technological tools to represent data and model situations.

206.7.1-06: Use appropriate technological tools to perform calculations related to a posed problem.

Given:

Your students’ test scores are as follows:

86, 75, 50, 95, 93, 45, 88, 78, 100, 94, 64, 50, 87, 67, 98, 68, 66, 72, 94, 82

The class grade spread is as follows:

Grade       Score

A          90–100

B           80–89

C           70–79

D           60–69

F             0–59

Task:

Create a Microsoft Excel spreadsheet in which you:

A.  Create a properly labeled table showing the individual student test scores.

B.  Create a properly labeled table showing the number of students who received each letter grade.

C.  Using Excel, calculate the class average. ( You must use Excel to do the calculation; typing in the answer is insufficient.)

D.  Create a pie chart using the table from B which demonstrates the percent of the class that received each letter grade. ( You must use the table to create the pie chart .)

Objective 206.7.1-07: Use flow charts and logic diagrams to solve mathematical problems.
Objective 206.7.1-08: Select appropriate technological tools and problem-solving strategies for solving non-routine, multi-step problems.
Objective 206.7.1-09: Use appropriate technological tools and problem-solving strategies to solve non-routine, multi-step problems.

Given:

Currently, Person A has $60 and Person B has $135. Person A decides to save $5 of his/her paycheck each week, while Person B decides to spend all of his/her paycheck and an additional $10 each week. How long will it be before Person A and Person B have the same amount of money? The following represents the situation:

Task:

A.  Write an equation describing the situation in the Given.

B.  Solve the equation written in A.

C.  Using an appropriate technological tool of your choice, make a properly labeled graph of the situation. Is your solution from B correct? Explain your reasoning.

D.  Based on your graph, what can you conclude about the difference in amounts of money each person has after week 5?

Price: $49.99

Solution: The downloadable solution consists of 23 pages, 3598 words and 8 charts.
Deliverable: Word Document