Mr. Reed's Math 30 Applied Website

LearnAlberta Online Lessons - Alberta students may get the userID/password from their instructor.

Formula Sheet - may be used with all course assignments and final exam. Print a copy and use regularly. The digital copy has links to formula notes that may help make the printed copy even more useful.

TI-83 Calculator

Math 30 Projects - August 2008 - Farming in Alberta

• Complete the Module Project Assignment for Assignment Booklet 4B only.

Module 1 - Probability

• omit Module Project Assignment in Assignment Booklet 1B

Alberta Education Resources

• FOURIER.XLS
• GARDEN.XLT
• SHELVINGSYSTEMS.XLT

Assignment Booklet 1A, page 5, Q8

There is logic to the box design. Answers may vary. You may use the following to help you with the dimensions of the box. From this information you will find the rest of solution is simpler.

The cardboard box must be at least 44 inches long and 24 inches wide to fit the hardboard back. It is best to make the box 48 inches long to fit the two shelves and a top beside each other in the box. The box will have to be deep enough to hold four layers of melamine pieces (each ½ -inch thick) plus the thin hardboard back (assuming it is 1/8-inch thick). The bag of connectors will fit into any of the empty spaces created. Therefore, the dimensions of the box is 48 inches by 24 inches by 2 1/8 inches.

Assignment Booklet 1A, page 8, Q12b

Key Strokes:

[MATH]   PRB   7:randBin   1, 3 / 26, 50 )   [ENTER]

Store the data in L1 and find the sum of the list

[2nd]   [ANS]   [STO> ]   [2nd]   [L1]   [ENTER]

[2nd]   [LIST]   MATH 5: sum(   [2nd]   [L2]  )  [ENTER]

Enter output into the calculator display screen provided.

Module 2 - Matrices

• Assignment Booklet 2A, question 10: It is confusing and time consuming to find the data for Tables A,B, D, E and G. The completed tables and reference source are provided below.

Project Book (pages 25-26): Number of each type of branch required - take first 4 rows from each chart. Complete the Total column by adding the entries in the 4 rows above..

Coiled Module 2 Booklet (page 26): Monthly orders:

Coiled Module 2 Booklet (page 73, questions 9 and 10): Building time:

Coiled Module 2 Booklet (page 26, questions 9 and 10): Labour rate:

Coiled Module 2 Booklet (page 27, questions 9 and 10): Material costs:

• omit Module Project Assignment in Assignment Booklet 2B

Module 3 - Statistics

• Shade Norm
• Module 3A, page 2, #2. You need to do look at the textbook (page 1-4) solutions for 6a and 6b before completing question 6c. I will reproduce these answers here.

  Key for 6a)

Key for 6b) This is not a bionomial experiment, because there are 3 outcomes

Support for 6c) This is the queestion from the booklet. You need to enter the data from 6a) into your graphing calculator. Select:

[STAT] EDIT 1: Edit.

Enter the values 0, 1, and 2 into L1 to represent the three light colors. Enter the probability values for each light into L2. Note: if you enter 75/140 [ENTER], the decimal equivalent will be displayed.

To display a histogram:

[2nd] [Y=] STAT PLOTS 1: Plot 1...Off [ENTER]

Change to the following settings:

Note: if you need to change frequence to L₂ , select [2nd] [2]

[WINDOW] --> x: [0, 3, 1], y: [0, 0.6, 1]

[GRAPH]

• Module 3A, page 7, #11. The screens on the right side of the question are hints.

  Screen 1: There is enough information to generate 2 equations (retail cost/80-m bolt cost). Enter these into Y1 and Y2. . Note: x is the number of jeans and y refers to money. The 80-m bolt cost has two parts to the cost: $400 and the cost recovery of the excess material.

  Screen 2: Use the graphing calculator intersect feature to determine the solution for the system of equations. Your answer will have to be "rounded up" because the question refers to the number of (completed) pairs of jeans. Note: the discount of 15% on 5 or more bolts. is not relevant to this question, because the question refers to 1 bolt.

• Module 3A, page 8, #12. The "jeans under each condition of denim purchase" is not in the question you are referred to. You must go back to question 3 to get this informaiton. Start with this chart. The headings of the last 3 columns are the "jeans under each condition of denim purchase".
  • The per meter retail cost for denim is given in question 3..
  • Question 3 also gives the information of the cost of 80 m of denim. You will need to convert this to a per meter cost.
  • The discount for Wholesale bulk order is also given in question 3. You will need to convert this to a per meter cost.
  • Assume as in question 3 that a pair of medium jeans takes 2.5 m of denim. to make you denim cost calculation for each condition.

• Module 3A, page 8, #13: Read the directions closely. This chart will help you organize the data..

• omit Module Project Assignment in Assignment Booklet 3B
• Module 3B - page 5, question 8

Module 4 - Personal Finance

4A, page 4, question 4 a)

• Spreadsheet - Investigation 1: The Power of RRSPs
• Spreadsheet - Life of the Loan

Module 4A, page 4, question 4 b)

• Spreadsheet - Registered Plan

Module 4B, page 3, question 3 - Answer 5b from page 189 of Addison Wesley: Applied Math 12 by completing the chart included in 5a from page 189 of Addison Wesley: Applied Math 12.

• Charts

Spreadsheets:

• RRSP
• RRSP2
• Mortgage
• Retire
• LeaseBuy
• RentBuy

Module 4, Page 4

• 4_1
• 4_2
• 4_3

LearnAlberta Resources:

• Investments: An Individual Portfolio Part 1
• Investments: An Individual Portfolio Part 2
• Investments: An Institutional Portfolio
• Renting Versus Buying a Home
• Spreadsheet Templates

Module 5 - Sinusoidal Data

• omit Module Project Assignment in Assignment Booklet 5B

Booklet 5A, page 1, Q3a. The parabola shown for each day provides the data for the number of hours a day that a shadow is cast.

Booklet 5A, page 2, Q3c. The y-axis is Length (m) of the shadow. Find the minimum value of the parabola.

Booklet 5A, page 2, Q4. The y-axis is Length (m) of the shadow. Find the minimum value of the parabola.

• Move the sliders to change the angle and radius size.
• Study the effect (if any) on the arc length.

Booklet 5A, page 3, Q6 (textbook p 226 #7-8). These questions will make more sense if you have completed the previous 6 questions. The answer key for these previous questions is found in the back of the textbook.

Booklet 5A, page 3, Q7 (Textbook p 227 #6-7). These questions will make more sense if you have completed/looked at the answer key for the previous 5 questions. The answer key for these previous questions is found in the back of the textbook. The formula for frequency is:

Frequency =         1        
                        period

Booklet 5A, page 4, Q8 (Textbook Discussing Ideas p 229 #1-2). To answer #1 look at the data table in the textbook (p 227), then the sine curve (p 228). your answer should refer to the repeating pattern of the data. To answer #2, look at #6 on page 361 of the textbook. This tells to input an estimate for the period. It does not tell you that if the data is evenly spaced, the regressions will work properly without the period. More importantly in the answering of this question, you need to know that if the data is not spaced evenly, the predicted regression will be off if the period is not given. If you are in my class, you are welcome to use this information in your response.

Booklet 5A, page 4, Q9 (Textbook pp 227-228). The directions for SinReg is given in the textbook on page 361-362. Input the values from the table on page 227. Use the graphing calculator minimum feature to determine the answer to this question.

It may be worth to look at some additional properties of sine waves before continuing in the assignment booklet.

Booklet 5A, page 5, Q10 (Project Book p 83, Q4). Input the values from the table on page 83. Look at the data and determine the period (remember that if data starts in the middle of the curve, it will go up to the maximum value, then drop to the mid-line, continue to the minimum and finaly climb back to the mid-line to complete one period. The directions for SinReg is given in the textbook on page 361-362. Enter the period value you calculated in the appropriate place. Recall amplitude = a, period = (2)/ b, Maximum sea level = Median sea level + Amplitude and Minimum seal level = Median sea level - Amplitude.

Note: resources may refer to a "Refined" SinReg. The most significant change here is entering the period value. The first run will generate a b value. The period value in the "Refined" SinReg will be (2)/ b, since this is how period is calculated.

Booklet 5A, page 5, Q10 (Project Book p 83, Q5). For the following applet, the h slider changes the c-value and the k slider changes the d-value. The other sliders are for letters a and b.Hopefully this does not confuse you. The letter used is not as important as understanding what the change in the value will mean. In this question horizontal shifts and vertical stretches are referred to. Use the applet below to check which sliders control horizontal shift and vertical stretch. Armed with this knowledge, you should be able to answer this question.

Linked Source - Ron Blond

Booklet 5A, page 6, Q11 (Textbook p 237, Q12) - Do the best you can for this question. Your guesses will be correct, but you may have difficulty confirming your answer. Sometime in the future I may be able to provide more support.

Booklet 5A, page 6, Q12 - Enter the graph shown. Initially use the first Xscl-value, then graph. Repeat the process for the second Xscal-value and compare the graphs. Note: The first Xscl-value ()/3) can be entered [2nd] [ ^ ][ / ] [3].

Booklet 5A, page 6, Q13 (Textbook p 238, Q2a, 2b, 2c, 2d) - Use the graphic at the top of page 237 and Example 1 on page 237 if you need additional support.

Booklet 5A, pages 7-10, Q14 (Textbook p 238-240 Q 1c, 1e, 2b, 2c and 7) - Use the graphic at the top of page 237 as well as Example 1 (p 237) and Example 2 (page 238) for additional support.

Booklet 5B, page 1, Q1

Booklet 5B, page 1, Q3 - make sure your calculator is in degree mode: [2nd] [MODE] Radian

Booklet 5B, page 2, Q4 - a little guess and check will solve this one. Remember amplitude is a measure of the greatest angle of declination. Looking at the chart you will see the a value will occur between June 18 and July 4. Substitute in thevalues between 170 and 186 until you find the closest value to the amplitude (23.553).

Booklet 5B, page 2, Q5 - Remember a + d will be the maximum height. and a - d will be the minimum height. Calculate period using:

period =

Check your calculations to those given to the answers for this question in the back of the textbook.

Booklet 5B, page 3, Q6 - The easiest way to answer this question is to start at x = 0. Follow the graph to the location where the sine wave starts to repeat the original position (midline) and direction (upwards). The x-value at that point is the period.

Booklet 5B, page 3, Q7a

Sine: y = a sin [ b( x - c) ] + d

| a | = amplitude =

period = The easiest way to answer this part of the question is to start at x = 0. Follow the graph to the location where the sine wave starts to repeat the original position (midline) and direction (upwards).

c = horizontal phase shift - not required for this question

d = vertical displacement/Midline/Median) d =

Booklet 5B, page 4, Q7b. The x-axis is labelled incorrectly/inconsistently. Every increment should be 1/2. Look closely - there are 3 divisons between & 2 and between 2 &  3, while there are 2 divisions between all of the other labels. Should be:

         |___|___|___|___|___|___|___|___|___|___|___|___|___|___|___|
         |      |      |      |      |      |      |      |      |      |      |      |      |      |      |      |

           -2     -          0                  2      3      4    5 

Sine: y = a sin [ b( x - c) ] + d

| a | = amplitude =

period = The easiest way to answer this part of the question is to start at x = 0. Follow the graph to the location where the sine wave starts to repeat the original position (midline) and direction (upwards).

c = horizontal phase shift - not required for this question

d = vertical displacement/Midline/Median) d =

Booklet 5B, page 4, Q8a - Note the y-coordinate position of the graph at x = 0. Follow the graph to the location where the sine wave starts to repeat the original position (bottom/midline/top) and direction (upwards/downwards). This will give the period (wavelength)

Booklet 5B, page 5, Q8b - Note the y-coordinate position of the graph at x = 0. Follow the graph to the location where the sine wave starts to repeat the original position (bottom/midline/top) and direction (upwards/downwards). This will give the period (wavelength)

Booklet 5B, pages 5-6, Q9a & Q9b- The directions for SinReg is given in the textbook on page 361-362. Enter the period value you calculated for 8a and 8b in the appropriate place.

Note: The question shows a screen for the"Refined" SinReg. The most significant change here is entering the period value. The first run generated a b value. Repeat the same steps as completed in the "Initial" calculation, except enter (2)/ b for the period, because:

period =

Booklet 5B, page 6, Q10a

Sine: y = a sin [ b( x - c) ] + d

| a | = amplitude = - a is given in the question

period = . so b = - need to calculate b

c = horizontal phase shift - no information: c = 0

d = vertical displacement/Midline/Median) d = or d = maximum - amplitude

Booklet 5B, page 6, Q10b

Sine: y = a sin [ b( x - c) ] + d

Start point = (-c/b, d) - Use this data to determine d. Use -c/b to calculate c after b is calculated

| a | = amplitude = or amplitude = Maximum value - Median value(d)

period = . so b = - need to calculate b

Booklet 5B, pages 7-17 - try these on your own.

LearnAlberta Resources:

• Simple Estimation Techniques
• Periodic Events

Module 6 - Patterns

• omit Module Project Assignment in Assignment Booklet 6B

Booklet 6A, page 2, Q3 - Regression equation instructions

Booklet 6A, pages 4-5, Q7 - spreadsheets

Booklet 6A, pages 6-7, Q7 - spreadsheet/graph

Booklet 6A, page 8, Q8 - spreadsheet

Booklet 6A, page 11, Q13 - spreadsheet

Note: spreadsheet needs only show 1-5 cm. The volume of each can must be 355 cm³.

Booklet 6B, page 4, Q6

Iteration	Length of One Side (cm)	Perimeter (cm)	Total Perimeter (cm)
Original	10	6 x 10 = 60	60
1
2
3
4

Assignment Booklet 6B, page 12, NR 2 and 3 - This is an extension of the chart provided at the beginning of page 12 -spreadsheet

Booklet 6B, page 15, Q9

• The starting does at 7:00 A.M. is 200 mg. The half-life is 4 hours. Use this information to complete the following chart. Include the chart in your answer for 9a. You can use this chart to help generate the solution for 9b.

Booklet 6B, page 16, Q10

• spreadsheet

Module 7 - Vectors

• omit Module Project Assignment in Assignment Booklet 7B

LearnAlberta Resources:

• Vectors and Navigation
• Vectors Supporting Structures

Diploma Exam

• Alberta Diploma Previous Exams and Keys
• Alberta Diploma Applied Math 30 Exam Details
• Diploma Exams General Information
• Diploma Exam Rewrites