Pre-Calculus * Beta

Getting ready for summer!!!!

For Monday, May 6:

Finish the problem that asks the area of a triangle with sides of 500, 800 and 900 feet. Also, see how far you can get in proving the law of cosines, starting with the diagram I set out.

For Wednesday, May 1:

Harry, you totally misrepresented what I said in the assignment for today (Tuesday). The "if you can" only went to "solve the triangles," not the determination of how many solutions there are.

For Wednesday, do the following three problems (33, 40 and 41):

For Tuesday, April 30:

Three triangles to figure out using the law of sines. You must solve the triangles, if you can, and determine whether there are one possible solution, two or no possible solutions.

1. B = 12˚, b = 27 and c = 19.

2. A = 16˚, c = 9 and a = 3.

3. C = 15˚, a = 26 and c = 29.

For Monday, April 29:

Sketch the triangles in problems 11 - 15 and use the law of sines to solve the triangles. Please list and box the missing values as well as showing them on your sketch. Round sides and angles to whole values. Yes, you may use your calculators. Please show the sine function values that you use to 4 - decimal places in your work. You may get them either from your tables or your calculators.

For Thursday, April 18:

From the first set of problems below (11 - 22) do problems 20 - 22. From the second set of problems (5 - 22), do 10, 14 and 18.

For Tuesday, April 16:

I think we are getting the hang of these!!! From the worksheet below (for Wednesday), let's do 12, 14, 15, 18 and 19. Don't forget to get all solutions, both from 0 to 2π, and with k2π to make it a general solution.

For Wednesday, April 10:

From the problems below, have a go at 1 - 4 and 7 - 10. Don't forget that each proposition such as

sinx = 1/2 will have to solutions between 0 and 2π.

For Wednesday, April 17:

On the first set of problems below, find the specific solutions between 0 (inclusive) and 2π (not inclusive) for problems 15 - 19.

From the second set of problems, find the general solutions, for problems 9, 12, 13 and 17.

For Tuesday, April 9:

From the worksheet (page 367), problems 28, 30 and 33. Also, 36, 28, 39 and 43 below.

For Monday, April 8:

Again, from the trig identities worksheet (page 367), 17 - 20, 23 and 24.

For Thursday, April 4:

Trig Identities: From the sheet we were working on in class, page 367, verify the identities in 6 - 14.

For Wednesday, April 3:

On the same worksheet below. Let's do 11, 12, 19, 20, 22 and 23.

For Tuesday, April 2:

On the following worksheet, do problems 9, 10, 13-18, 20 and 21. For each, using the identities that we know, including the definitions of the co-functions, simplify each expression as much as possible.

For Monday, March 18:

Graph problems 27, 28, 30 and 32 below. The period and amplitude should be straight forward by now, and these have no vertical shift. See if you can incorporate the horizontal shift, applying the principles we learned early in the year. It might help to draw first the curve without the horizontal shift, and then copy the curve only shifted a bit to the right or left.

Also, see if you can do the ferris wheel problem that follows. The period, the amplitude and the vertical shift should all be reasonable easy. See what you can figure out about the horizontal shift. If it eludes you, not to worry.

For Thursday, March 14:

Do problems 31 and 32 below. For 32, don't use a calculator as suggested. Graph the data points and see what kind of sine (or cosine) curve equation you can come up with to model the temperature variation.

For Wednesday, March 13:

Of the following problems, graph 2, 3, 4 and 15. Then, see if you can figure out the equation of the curves in 41, 42, 43, 44 and 46. None of these involve a phase shift and the center line is always the x - axis, so you only need to determine the amplitude and the period.

For Tuesday, March 12:

Find the function values on the following worksheet. You need to have your Latin email address open to be able to get at the document. Only do 1 - 20. You may use your chart or unit circle or whatever will help you. Keep in mind we will have to learn to find these without any outside help.

Trig Funct. Values wrksht.pdf

For Monday, March 11:

Finish the graphing sine and cosine functions worksheet that we were working on in class. If you were not in class, I have posted the worksheet below.

Graphing Sine.pdf

For Tuesday, March 5:

Fill out the chart on the radian worksheet that I handed out in class. If you did not get a copy, it is linked in below. It is not perfectly laid out, but that is the cost of upgrading everything so that formatting gets all wigged out.

Radians.pdf

For Monday, March 4:

Finish the chart of the trig function values up to 360˚. Also, for 1 - 8 (a, b, and c) below, find the reference angle, and on the second set of problems, 11, 12, 16, 18, 20, 22 and 23.

For Thursday, February 28:

Answer the questions on the following worksheet:

Unit Circle definitions.pdf

For Monday, February 25:

We will have an in-class opportunity on the right triangle trig that we have studied. If you want another practice problem or two, do problems 31 and 33 below. For problem 31, you need to use the distance between the two towers, which is given.

For Wednesday, February 20:

Start by doing problem 57 from the problems for Tuesday (below). Then do 65, 66 and 61. For 61, find the height of the tower.

For Tuesday, February 19:

More flagpole problems that are a little more interesting. From the problems below, do 55, 56 and 58.

For Thursday, March 14:

Flagpole problems. Do 47 - 53 below. Remember you must include a diagram. Use trig function values from the trig table I handed out in class. You may use your calculators, but write the function value on you work before you do the calculation. In each problem, solve for the unknown before using a calculator to do the computation.

For Wednesday, February 13:

In a 30 - 60 - 90 right triangle:

1. If the side opposite the 30 ˚ angle is 5, what are the other two sides?

2. If the side opposite the 60˚ angle is 3, what are the other two sides?

3. A playground that is a right triangle with an angle of 30˚, has a shortest side that is 100 yards long. What are the other sides of the playground?

4. Mr Richardson is flying a kite whose string is at a 30˚ angle to the ground. If he has let out 150 yards of string, how high is the kite?

In a 45 - 45 right triangle:

1. The hypotenuse is 50 feet. What is the length of the two sides?

2. What are the sine and cosine of 45˚?

3. You walk 45 paces away from a building until you reach a place where the line of sight to the top of the building is 45˚. How high is the building?

For Tuesday, February 12:

For the following triangles, find the sine, cosine and tangent of the smallest angle, and then the sine, cosine and tangent of the other angle that is not 90 degrees.

1. A triangle with a hypotenuse of 5 and one side of 3.

2. A triangle with two legs that are 7 and 24.

3. A triangle with a hypotenuse of 13 and one leg that is 12.

4. A triangle that has legs of 8 and 15.

For Monday, February 4:

No new homework. I apologize. I apologize for not being there on Thursday.

For Thursday, January 31:

From the following problem set, do problems 8, 11, 14 and 21. These all use some form of exponential function. Part of your job is to figure out the function. Answers that are in exponential form, or logarithmic if the unknown is in the exponent, are fine.

For Wednesday, January 30:

On the following worksheets, problems 43 - 51 odd, and then have a go at 27 and 28. Remember the zero product rule.

For Tuesday, January 29:

Problems 1 - 25 odd from the following worksheet.

Logarithmic Equations.pdf

For Monday, January 28:

Do problems 3 - 14, just part a, below.
Also, do problems 45 - 49.

For Wednesday, January 23:

From the following worksheet, do problems 4, 8 - 12. You may use your calculators to calculate a final answer, but do all work so that I can see how you got to the calculation you make.

For Tuesday, January 22:

On the problem set that I handed out in class, do problems 5 - 8. You may use your calculators to get a final answer, but I want to see the equation you use in simplest form, before you do the calculation. Also do 6 a&b on the other side, and see if you can think through a function for 14, which is a half-life problem, and then answer part b.

For Thursday, January 17:

From the following problem set, do the matching problems 19 - 24. Then find the equations for the functions in problems 39 and 40.

Also, create a table of values and compare the y values for the functions y = 2^x and y = x^2 for x = 1, 2, 3, 4, 5 and 6. How do they compare?

Finally, if I invest $100 for ten years at a simple interest rate of 5%, how much money will I have? If I invest the same $100 for ten years with compounded interest at a rate of 5%, how much will I have? How do those two compare?

Exponential Graphs.pdf

For Wednesday, January 16:

Complete the exponential worksheet that I handed out in class.

For Thursday, January 10:

I am thinking a minor in-class opportunity on graphing rational functions for those who are feeling ready. For those who are not, I will provide you with some specific practice problems that you will work on for class and then for homework.

For Tuesday, January 8:

Graph the two following rational functions:

Rational Functions 1-4.docx

For Wednesday, December 19:

Do problems 38 and 39 below.

For Tuesday, December 18:

MORE RATIONAL FUNCTIONS. These should be pretty straight forward, affirming the basics of what we have learned with no curve balls. Do 33, 34, 37 and 40 below.

For Monday, December 17:

Graph the rational functions in problems 1, 2, 3, 6 and 7 from the following worksheet. Use graph paper. Use the tools we have discussed in class; vertical asymptotes, zeros, y-intercept and horizontal asymptotes. Keep in mind that we are looking for the general flow of each of these curves, but you can always find some function values to guide where the curve will fall.

Graphing Rational Functions.pdf

For Friday, December 7:

Review polynomials. Come with any questions you have.

For Wednesday, December 5:

We will review polynomials in class. We will also talk about the Fundamental Theorem of Algebra. The fundamental theorem takes different forms. See if you can find a statement of the fundamental theorem of algebra.

Review topics will include

® Definition and general form of a polynomial.

® Valuing polynomial functions directly and using synthetic substitution.

® Adding, subtracting and multiplying polynomials.

® Polynomial long division and division by (x - c) using synthetic substitution.

® End behaviour.

® Factor Theorem and Remainder Theorem.

® Zeros of polynomials.

® Factoring quadratics, quadratics in disguise, factoring by grouping.

® Rational Zero Theorem.

® Graphs of polynomial functions.

® Fundamental Theorem of Algebra.

For Tuesday, December 4:

Describe the end behaviour of each of the following polynomial functions. Remember, using arrows, indicate that as x goes to positive or negative infinity, y goes to whatever. (Read carefully each polynomial and copy on to your paper.)

For Monday, December 3:

From the same set of polynomial functions that are below (for Thursday), do problems 27, 29 and 30. For each, find all possible rational zeros, find all actual zeros, write each polynomial in factored form and for 30, using the zeros and the y-intercept, sketch as reasonable a graph of the function as you can. Use graph paper for your sketch.

For Thursday, November 29:

On the following work sheet, do problems 20, 21, 23 and 28. Find all POSSIBLE rational zeros. Then find all actual rational zeros.

For Tuesday, November 27:

Do the following division using synthetic substitution. For 7 and 8, divide the higher degree polynomial by the linear polynomial.

Have a relaxing break and a very HAPPY THANKSGIVING!!!

For Thursday, November 15:

On page 270 of the polynomial work packet that I handed out, do the division in problems13, 14, 16 and 17. On page 271, for the polynomials in problems 38, 40, 44 and 49, value the functions (ignore the directions on the page itself) at -2, -1, 0, 1 and 2.

For Wednesday, November 14:

Find the following powers of i.

For Monday, November 12:

Using the vertex (-b/2a, f(-b/2a)), the axis of symmetry (x = -b/2a) and at least four other points, graph the four quadratic functions, 9, 10, 11, 13.

Remember , label axes, arrows and a proper scale, which for these curves should be 1 per grid line.

For Thursday, November 7:

Sadly, no homework.

For Wednesday, November 6:

We will have a minor in-class opportunity on the various methods for solving quadratics. Then we will move onto looking at the quadratic functions and their graphs.

For Tuesday, November 6:

Using completing the square to solve the four following quadratic equations. Show the steps that I put on the board, meaning establishing the trinomial, showing the binomial squared and then taking square roots.

For Monday, October 29:

Take the weekend off.

For Friday, October 26:

On page 264 of the packet (quadratics), problems 37, 38, 39, 57, 58, 60 and 62.

For Monday, October 15:

Do problems 48 and 50 below.

For Wednesday, October 10:

Do the following three problems using the Bert & Ernie method. Check your solutions in the other two original equations (the equations you did NOT use to solve for the third unknown).

For Tuesday, October 9:

Do the following four problems, 3, 4, 5 and 16.

For Thursday, October 4:

Do problems 14, 15 and 26 above.

For Wednesday, October 3:

Using elimination, do problems 7 - 21 below.

Systems of Equations

For Tuesday, October 2:

Do problem 47 (Buster Brown Shoes). You need to view the wiki from your Latin account to see the problem on the link.
Also do the six system of equation problems that follow, using substitution.

Linear Problems

No homework for Friday. In class, work on the problem that I leave with the substitute.

For Thursday, September 27:

In the packet we were working from in class, do problems 69 and 70. You do not need to graph or sketch a graph, unless you want to or it is helpful.

For Wednesday, September 26:

From the following worksheet, problems 16, 17, 20, 21, 22, 24, 25, 27, 29, 31 and 33.

For Friday, September 21:

On the following problem sets, graph 5 - 8. Graph paper and all of the requirements.

Then do 17 - 20.

For Tuesday, September 18:

From the following problem set, do problems 31, 32, 35, 36, 37, 38, 41 and 45.

No homework for Thursday. I'm sorry!!

For Wednesday, September 11:

On the worksheet that I handed out in class, problems 1, 3, 4 and 11 - 16.

For Thursday, September 6:

For each of the following functions, determine whether the function is odd, even or neither.

For Wednesday, September 5:

Given the two things we know about even functions, see if you can figure out which of the following functions are even. As a reminder, we know that even functions are symmetric around the y-axis, and we know that for even functions f(-x) = f(x). Explain or show work that justifies your conclusion.

For Tuesday, September 3:

Finish the function worksheet that we were working on in class on Thursday.
On page 168 of the problems packet, graph the piece wise functions in problems 38, 41, 43, 44 and 46. Also, do problems 83 and 84 on page 169.

For Thursday, August 30:

On the handout, in section 2.2 (page 167), do problems 23, 24, 25, 26 and 55-60. These all involve reading graphs. You do not have to copy the graphs onto your homework paper.

For Wednesday, August 29:

From the packet that I handed out, on page 156, problems 37, 39, 45-50 and 62.
From the following, do problems 6 - 10.

For Tuesday, August 28:

On the function worksheet that I handed out, page 155, problems 1 - 4, 5, 11, 12, 13, 14, 9 and 20.

For Thursday, January 23:

From the following sets of problems, do 11 - 29 odd, and 33 - 41.

For Monday, January 28:

Do 3 - 14, JUST a, below. Also

Logarithmic Equations.pdf