Week 9, Part 1
Look at the following triangles. They will be used in the problems below:
Triangles
Week 9, Part 1 Continued:
1. In the top pair of similar triangles, assume a=12, y =6, b = 10, z = 4 Find c. Find x.
2. In the top pair of similar triangles, assume c = 9, z = 6, x = 5, a = 6. Find b. Find y.
3. Know the definition of opposite, adjacent and hypotenuse from you text, Chapter 6
In the bottom triangle, assume it is a right triangle. Assume side B is 3, C is 4 and side A is 5
4. What is the sin of angle b? express as a fraction and as a decimal number
5. What is the cos of angle b as a fraction and as a decimal?
6. What is the tan of angle b as a fraction and as a decimal?
7. How are the sin of angle b and the cos of the angle between sides A and B related?
8. Do you think if you know that sin of b was .214, and that side B was 7, could you find the length of side A? How?
9. What is an arcsin? Why would you use it?
10. If side B = 5 and side A = 8, find the measure of angle b using arcsin
11. If only knew the length of sides B and C, could you find the measure of angle b? How?
12. You see Mt Rainier in the distance. You know it is 14,000 feet tall. You measure the angle from where you are standing to the top of the mountain at 12 degrees. Use tan to find how far you are from the mountain in miles. (5280 feet in a mile)
13. Make a right triangle. Measure 2 sides. Measure one of the non-right angles in your triangle. Use trig to find the length of the 3rd side. Measure to see if you are correct.
14. Review quizzes and practice quizzes. Come with lingering questions to your group.
Week 8, Part 1
1. Use gcalc.net to graph the following functions: log(x): log(8x): 8(log(x)): log(.01x): 1/log(x) Try to explain this behavior
2. For the next examples, assume log means log base 10. ln means log base e. If another base it will be written: log(base7) or log(base3) etc.
3. Change the following into base 10 numbers: 10110 (base2) = ___________ 104(base5) = ___________ 72(base 
= ________
110101(base2) = ___________ 210(base3) = ___________
4. Change the following base 10 numbers into the given bases: 34 = _______(base 6) 51 = __________ (base 2) 50 = ________ (base 7)
85 = ___________ (base 3)
5. 10^3 = 1000 can be rewritten as: log(1000) = 3. Rewrite the following: 7^2 = 49 is ___________; 2^3 = 8 is _________
3^4 = 81 is ___________ e^1 = 2.72 is ________ (use ln in your notation) Make up your own examples
6. Express as an exponent equation, the opposite of #5 above: log(base7) 49 = 2 is ___________; log(base2) 32 = 5 is _________
log(81) = 1.9 is __________ ; log(211) = 2.32 is __________; ln(75) = 4.32 is __________;
7. Estimate without using a calculator: log(base7) 50 log(base3) 26 log(base5) 30 log(850) log(50)
8. Rewrite using the product of a logarithm rule:
log(xy) log(21) log(12) log(xyz) log(6xy)
9. Rewrite using the quotient rule of logarithms: log(x/y) log(6/5) log (3/2z)
10. rewrite as a single log function:
1. log(2) + log(5) + log(3)
2. log(x) – (log(4) + log(z))
3. ( log(2z) + log(3y)) – (log(2) + log(7))
11. Simplify using the power property of logs
1. log(base3) x^(1/2)
2. log(base5) x^3
3. ln t^2
4. log 3y^2/x^3
12. Rewrite as a single log expression: 2log(5) + 3log(2) 3ln(4) - (4ln(5) + 2ln(3))
Week 7, Part 1
1. Spend time testing yourself on your understanding of Polynomials. Use the graphing website or your graphing calculator to find 2 polynomials that have 2 bumps up. Find one with 1 bump down and one bump up. (as we did in class). Use mathway.com to test your understanding on simplification rules: Examples to try: 1. (3x-2)^2 2. (2x^3 – x + 1)(x^2 – 2x -2) 3. (x^3)(y^-2)/((x^-3)(y^5)) 4. 2^(-3/4) 5. (x^(-2/3))^(3/4) Make up your own and check with mathway.com. If you get stumped, first try to find your mistake, then check with others in the class, quasr, IM or email me.
2. Review old practice tests and solutions
3. Make a table, from x = 1 to 6 for the equation ( y = 10 (1.03^x) ) What is the value when x = 6?
4. For each value in your table, divide f(x) by f(x-1), starting at x=2. IE.. f(2)/f(1), f(3)/f(2)….. What is the value for each? Why?
5. Graph on the website or on your graphing calculator the equation above. Explore exponential graphs
6. What is the effective yield if you invest $10,000 at 4% compounded monthly?
7. A 100 square foot puddle dries in the sun, and shrinks 10% every hour. How long before it is half its size?
8. Make a table, with x values from 1 to 5 for the following: y = 2x, y = x^2, y = 2^x. Describe how each table changes as x increases by 1. Can you describe a rule for linear, polynomial, and exponintial functions?
9. You invest 5,000 at 12 percent for 10 years, compounded continuously. How much do you have after 10 years? How much less would you have if the interest was compounded quarterly instead of continuously after 10 years?
Week 6, Part 1: Email a summary to me before noon on Monday for 10 points. Do not spend more than 1.5 hours on these problems, but try all of them. Skip to the next problem if you get stuck, but first try to figure it out by looking at examples are reviewing notes from class. Prepare questions on problems you are having for your group.
1. Do Chapter 2.5 Exercises (p228 2nd Ed) #3,b
2. Do Chapter 2.6, Exercises 3a-c, 5a-d
3. Do selected problems from Exercises of 2.7. Check answers for ones in book. Try some without answers. Bring to your group and check there.
4. Do Exercise 2.8, #1a-d, #3a-c
5. Do Exercise 2.9 #1a-e, #3a-c, #6a-c
6. Review old quizzes and practice tests. Go over the answers to Tools quiz Week 5
Week 5, Part 1: A summary of the work you did on these problems MUST be emailed to my before noon on Monday, April 26 if you want credit for this work. Include which problems you know, which you struggled with, and which you still do not understand. Do not spend more than 1.5 hours on this work.
Problems to do: If f(x) = 3x – 2 and g(x) = -4x^2 + 5x – 7
1. find (f+g)(x)
2. find (f-g)(x)
3. Simplify: 7x + 2(3x-2(4-5x) ) + 6
4. check above at mathway.com.
5. make your own examples like 3 and check
6. Simplify (x-4)(4-x^2) mathway answer
7. Simplify (x^2-3x+1)(3x^2-5x+2)
8. Use Mathway to experiment with examples
9. express 345,654,765,321 in Scientific Notation
10. What is .000000000321 in Sci Notation
11. Write 3.45 x 10^7
12. Write 5.43 x 10^(-8)
13. Simplify a^(-3)(4a^(-1))(-5a^7) check mathway
14. Experiment with your own examples at mathway
Sam’s Cafe, 3rd edition numbers worked out
Week 4, Part 1: Do these problems before group meeting, and come to your group with questions if you get stuck. Check the answers on the answer link that will be posted Sunday evening.
1. Using the regression calculator on the resources link, do Exercise 1.9 #2 b-g. Note that the graph will be done for you.
2. Do Exercise 1.10 #3 a-d, #7b
3. Do Exercise 1.11 #1 a #5 a,b
4. Do Exercise 1.12 # 1
5. Do Exercise 1.13 #1,3,5,7,15
6. Do Exercise 1.14 #3 a-d (royalties)
7. Do Exercise 1.15 #1 a-c, #4 a,c,e, #5a
8. According to my text edition, you should have the answers to these questions in the back of the textbook. Let me know right away if this is not correct, and substitute a nearby similar problems with and answer you can check in the text. Check them before your group. Find your errors or prepare a question for your group
9. Review the Week 3 exam, found under the Resource link above. Prepare questions for ones you do not understand fully yet.
Week 3, Part 1: Do These problems BEFORE your group meeting for week 3
1. Review Quiz 1 practice problems below
2. Do Exercises 1.3, #1, a-c (Use a regular calculator for a)
3. Do Exercise 1.3, #2b
4. Do Exercise 1.5, #1a, 5b, 6a
5. Is 3+2x-y=.7x-2y+6 a linear graph? why?
6. Ex 1.6, 4a-c
7. Graph y=-2x + 5 using the online graphing calculator at:
http://mathway.com/problem.aspx?p=graphing.. enter the formula y=-2x+5 into the box and press the GRAPH button below the box
8. y=mx+b is the formula for a linear equation. Enter different values for m and b into the graphing calcuator above. What happens when:
m gets big? m gets close to 0 (ie.. .5, .005…)? m gets negative? b changes?
9. What is -8(-2)-(-1)-(-4)/(-2)+(-3) Enter this into the formula box at http://mathway.com/problem.aspx?p=algebra
(the answer should be 12).. Experiment with other formulas you make up so you are sure you can do + - X / for numbers and use the order of opperations. Play with ()s and decimals
Quiz 1 Practice:
Practice the following problems on pages 8-11 in your textbook. The answers are at the end of the textbook:
1.a,c; 5.a,b; 7.a,b; 9.a,c,e 10.a,c,d
In addition, the following are example questions similar to the ones I will ask on Thursday
1. What is a function
2. give an example of a function given as a sentence, but where if you switch the inputs with the outputs it would no longer be a function. Discuss
3. Express the statement: “Monthly payments is a function of the amount borrowed” using function notation
4. Give and example of a function expressed using a table
5. Give an example of a non-function expressed as ordered pairs