thomas pre-exam

for my pre-exam blog Id like to begin with, although we havn't done it yet. I will have extreme difficulty with it. it is below a 1/20 ratio that i will get over 75% on it. Ive strugled throught entire class, and shown very little sigh of improvement since the first day. There has been no unit ive found easy or relatable to.
There will be a large struggle just to pass this course.
no link posted

thomas chapter 2

Chapter two was made unnessisarily difficult. I found that we did even use the entire first section of this unit with number lines. At no point did we use number lines through the rest of the course. I had many issues with this unit, everything exept expand and simplify to be exact.
In the end, this unit was poorly conceived in the book and should probly have the first setion left out to allow extra time for harder units.
the khan acedemy link wont work again

thomas unit 7

The rational expressions unit was very difficult. when a student frequently goes "I can't do this may I get help?" it usualy means he's having difficulty, and is perhaps having an issue that needs to be tended to. I spent several classes with Studet facilitator trying to get help with this unit with no success. this section will be strugled with on the exam, garrenteed.
The Khanacedemy will not link properly

Statistics in Sports

In most cases when people are watching sports they don't think of all of the math that is used in finding different statistics. The same equation is used in many different sports to calculate many different things. For example:
Batting Average: A batter in baseball has 600 at bats in one season and records 186 base hits. What is his batting average? 186/600= 0.310 the batters average is 310%

Goals Against Average: A goalie in faces 1000 shots in a season he stops 912 of them. What's his goals against average? 912/1000= 0.912 his goals against average is 0.912 GAA

Draft Lottery: There are 30 balls in a bucket and a team has 8 balls in the bucket. What percentage of balls in the bucket are theirs? 8/30= 0.26 they have a 26% chance of winning the draft lottery.

These are just a couple of examples of how math is used in sports. If you look into it farther i'm sure you could find plenty of more.

Pre Exam Blog

Well finally this semester has almost come to the end. We have covered plenty of material over this semester but I had some things that I liked and some I didn't. Some of the things I enjoyed were the trigonometry as I found it quite easy to find the side length and angles of a triangle. My least favorite part of the semester was unit 5. My reasoning for this was because I found solving inequalities and graphing them fairly difficult, but after awhile I started to get the hang of it. Personally I don't mind math so this whole semester was not so bad and I did a lot better than I thought I would coming into it.

Unit 6 Test

I quite enjoyed this unit as I found it quite easy. The things I enjoyed about this unit were using the Sine, and Cosine law to find certain angles and side lengths on triangles. The thing I didn't enjoy about this unit was determining reference angles as I found it boring. Overall I believe this was my favorite unit.

thomas' pretest-sec8

In this test for section 8, I found the work very forgetable. With the added difficulty of remebering what we did over the difficulty of just doing the work made this a very unforgiving unit. However the whole thing was quite no-nonscense, it could have been an easy unit. but it decided to be hard instead.

One final Pre Test Blog

Well i guess its not really a test, but an exam. and i know it is a bit early to be writing about this, but i think it will be okay. I think that i can do fairly well on my exam, as i gain more and more understanding of the things we have learned. If i do my studying, and ask for help on the questions that i am not sure about, it will work out. There are a couple units that in kind of rusty on since we did them so long ago, but im sure that there is plenty i can do to refresh my memory on them. but otherwise, i feel alright about it, and hope i do well on the last test that we get in this course!

Purplemath?

that is certainly a very interesting name to give to a math site. however, despite it's interesting name, i think it is a very good site. the main page is set up very nicely, and it is easy to locate exactly what you need to find help on. I searched something that i have some trouble in, distance and speed word problems. i found a very nice tutorial ( http://www.purplemath.com/modules/distance.htm ) that helped a lot. they way they explain it, and go through a problem was easy to follow, and not difficult to understand what they were doing, and how they did it. the only thing that i didn't like as much was how everything was shown in charts, when I think it would have been a bit easier to understand if they explained it a little different, or did not use so many charts at least. but besides that, i think that how they solved it, and worked through it made sense.

Radians

A Radian is the measure between the length of an arc and its radius. this isa usually represented by the symbol "rad" or a subscript "c". Radian describes the plane angle by a circular arc as the length of the arc is divided by the radius of that arc. more simply put, a measurment for angles using the radius within a circle, instead of the cos, sin, and tan ratios. they are both right, but can be used for different things.
Conversion
1.degrees, is equal to rad * 180 degrees/ Pi.
2. one rad = 1* 180 degrees/ Pi. ~ 57.2958
there are other conversions, but i won't list them all. there are also charts to help with these conversions, you should find a good one by searching "Radian to Degrees conversion chart".

Khan's Academy

I looked up the Khan's Academy website, found an watched a video on something that still gives me a bit of trouble, factoring. I personally found that the video was extremely helpful, and explains what you need to do to solve it very clearly, and in a well organized manner. I may come back to this site at times if i have trouble understanding things, i really like how he teaches. He taught it in a similar way to the way we were taught in class, but more direct, in my opinion. I found it useful, and i think that i will be able to find many more things on the site if i happen to need help.

Rational Expressions

Rational expressions was a topic that i was not sure where it would be applicable in life, and how jobs would use it, or even be based around it. So i looked around, and here is a couple that i found. The first one i found, is Electrical Engineering, which starts with the universal law, that Resistance, (R), equals Voltage (V) over Current (I). Since all of these variables are dependent on time, rational functions need to be set up to figure out how much they will vary, and thus solve your equation! The second one, is Thermodynamics, which is one of the most ideal gas laws. To figure out what is in this case the volume, you need to use your variables, (in this case, pressure, temp, and number of molecules) to be able to solve. But again, to solve you need to make a rational function, and when you solve it, it will give you the answer.

The Art of Trigonometry

We did a project using trig. functions to make a piece of art, as home assignment 7. There are a variety of ways that you can make designs, by changing the different values of the function. Ex. (sinX, 3sinX). for instance, if you could only use sin, you could make an increasing wave of lines. If you use sinX, 2sinX, and 3sinX; you will have lines that go up to 1,2,and 3 and -1,-2,-3, that will show up on your graph. You could also do a similar arrangement with cosine. Sine and cosine are actually very similar, just that they are a translation of one and another, and both form that smooth line between 1 and -1. So to get a sine graph into a cosine graph, you simply translate it!

Unit 8 quiz

We didn't take much time to do this unit but I think I know what I am doing for the most part fairly well. I liked how most of the graphing was sketching and didn't have to be perfect. The part I found difficult was graphing the quadratic functions but I now have a fairly good understanding of it. I found this unit was fairly good.

Final Review

Here is the final exam review guide.

Everything listed below will be covered on the exam.  The exam is 40 multiple choice questions and 21 long answer questions worth 60 marks, for a total of 100.  You should be working through the cummulative exercises at the end of the worktext as well as going back and reviewing each chapter. 

I will be available Monday, Tuesday and Wednesday mornings ( 9 - 12:15) in my classroom.  Please feel free to come and work in there.  Also a reminder that your blog promts and test blogging needs to be finished up.  Deadline is Tuesday, Jan. 31.  If it is not completed by then you will recieve an incomplete as your mark. 

Your exam is Thursday morning, Feb 2, 2012 at 9am.

Pre-Calc 30S Exam Review

Unit 1 – Chapter 1 – Sequences and Series

·    Determine the first term, the common difference, the number of terms or the value of a specific term in a problem involving an arithmetic sequence.

·    Determine the first term, the common difference, the number of terms or the value of the sum of specific numbers of terms in a problem involving an arithmetic series.

·    Determine the first term, the common ratio, the number of terms or the value of a specific term in a problem involving a geometric sequence.

·    Determine the first term, the common ratio, the number of terms or the value of the sum of a specific number of terms in a problem involving a geometric series.

·    Solve a problem that involves a geometric sequence or series.

Unit 2 – Chapter 2 – Absolute Value and Radicals

·         determine the distance between two real numbers.

·         determine the absolute value of a positive or negative real number.

·         Express an entire radical with a numerical radicand as a mixed radical.

·         Express a mixed radical with a numerical radicand as an entire radical.

·         Perform one or more operations (+, -, x, / ) to simplify radical.

·         rationalize the denominator of a rational expression with monomial or binomial denominators.

·         determine any restrictions on values for the variable in a radical equation.

·         determine the roots of a radical equation.

Unit 3 – Chapter 3 – Solving Quadratic Equations

·         Factor polynomial expressions  -  common factoring, trinomial factoring ( by inspection and decomposition), and difference of squares.

·         Solve a quadratic equation of the form ax²+ bx + c = 0  by  determining square roots,  factoring,  completing the square,  applying the quadratic formula, or graphing its corresponding function.

·         Solve a problem by determining or analyzing a quadratic equation. 

Unit 4 – Chapter 4 – Analyzing Quadratic Functions

·         Compare the graphs of a set of functions of the form y = ax² to the graph of y = x² , and generalize, using inductive reasoning, a rule about the effect of a.

·         Determine the coordinates of the vertex for a quadratic function of the form y = a(x-p)²+q

·         Write a quadratic function given in the form ax²+ bx + c = y  as a quadratic function in the form y = a(x-p)² +q by completing the square.

·         Sketch the graph of a quadratic function given in the form ax²+ bx + c = y.

·         Sketch the graph of y = a(x-p)² +q, and identify the vertex, domain and range, direction of opening, axis of symmetry and x - and y -intercepts. 

Unit 5 – Chapter 5 – Graphing Inequalities and Systems of Equations

·         Sketch the graph of a linear or quadratic inequality.

·         Determine the solution of a system of linear-quadratic or quadratic-quadratic equations algebraically.

·         Solve a problem that involves a linear or quadratic inequality.

·         Solve a problem that involves a system of linear-quadratic or quadratic-quadratic equations. 

Unit 6 – Chapter 6 – Trigonometry

·         sketch an angle in standard position, given the measure of the angle.

·         determine the reference angle for an angle in standard position.

·         determine the quadrant in which an angle in standard position terminates.

·         draw an angle in standard position given any point P (x, y ) on the terminal arm of the angle.

·         determine the value of  sin Ɵ, cos Ɵ or tan Ɵ, given any point P (x, y ) on the terminal arm of angle .

·         determine, without the use of technology, the value of sin Ɵ, cos Ɵ or tan Ɵ, given any point P (x, y )       on the terminal arm of angle , where = 0^o, 90^o, 180^o, 270^o or 360^o.

·         determine the sign of a trigonometric ratio for an angle, without the use of technology (CAST Rule).

·         solve an equation of the form sin Ɵ = a, cos Ɵ = a or tan Ɵ = a

·         determine the exact value of the sine, cosine, or tangent of an angle with a reference angle of 30 ^o, 45 ^o, or 60 ^o.

Unit 7 – Chapter 7 – Rational Expressions and Equations

·         determine, in simplified form, the sum or difference of rational expressions

·         determine, in simplified form, the product or quotient of rational expressions.

·         simplify an expression that involves two or more operations on rational expressions

·         determine the solution to a rational equation.

Unit 8 – Chapter 8 – Absolute Value and Reciprocal Functions

·         Sketch the graph of y=|f(x)|; state the intercepts, domain and range; and explain the strategy used.

·         Generalize a rule for writing absolute value functions in piecewise notation.

·         Solve, algebraically, absolute value equations, and verify the solution.

·         Compare the graph of to the graph of y = 1/f(x)   to the graph of y = f(x)

·         Identify, given a function f(x), values of x for which y = 1/f(x)  will have vertical asymptotes; and describe their relationship to the non-permissible values of the related rational expression.

·         Graph, without technology, y = 1/f(x), given  y = f(x) .

Khan Academy Video Solving Rational Equations 1

This video showed us how to solve for X when two equations are set equal to each other but still a fraction. In order to get ride of the denominators, we must cross mutiply by using an lowest common denominator. I thought this was a good video because it laid it out basically and with interesting colour. I'm glad I watched this because it will help me review for the exam. Also I found the skills summary pages in the work text to be the best pages to help me set up a study guide. They show a summary of what we learned through out a unit. Theres like eight of them.

Radians to Degrees

A radian is the angle of an arc formed when the radius is run along the circumference of the circle.

Because pi X radius is equal to half a circle or 180 degrees, we can make this conversion. If you divide radians by pi you get the number of half circles, so if we multiply this by 180 degrees it will tell you the answer in degrees.

Thus the conversion for radians to degrees is:

Degrees= radians(180/pi)

Rational Expressions in Everyday Life

Someone doing a triathlon (bike, run, swim) could calculate what their a possible race time could be for themselves. If they knew how fast they completed the biking aspect of the race, and they knew that they were approximately 3 times faster on bike than running, they could figure out their average running time. They could also figure out their approximate swimming time if they knew what their average speed of swimming downstream was, and also knew what kind of effect the current had on their average speed. Overall this could also help the participant in achieving a faster time as they could see where possible error and time-lost are, and train to prevent any unnecessary time loss.

A baker could also use rational expressions when mixing up new recipes. They could use calculations to see how much flour, oil, chocolate, etc to add to perfect a certain cake. If they wanted to make a healthy cake, in which 75% of the cake was made up of fruit and vegetables, they could figure out the amount of cups, etc. needed to be added.

Rational expressions are used in many more jobs, and I'm sure that some of us will in fact come across them in our lifetime.

Fibonacci Sequence

Fibonacci Sequence has been used in things such as art, architecture, and music. A couple of examples that if found quite interesting are:
1) Chimeny of Turku Engeria, Turku, Finland featuring Fibonacci sequence in 2m high neon lights. By Italian Artist Mario Merez for an environmental project.
2) Rap Group Black Star's song Astronomy (8th light) from the 1988 album Mos Def and Talib Kweli are Black star , features the Fibonacci Sequence in the chorous:
Now everbody hop on the one, the sounds of two
It's the third eye vision, five side dimesion
The 8th light is gonna shine bright tonight

These are a couple of things I found interesting

My Math Song...

So here is my math song that I wrote a while ago, but forgot to post...

It goes to the tune of Feist's "1234"....

1,2,3,4 counting is the first you learn

years go by and

now look what you've got to solve

Oh equations with inequalities

Greater or less than, which is it please?

Oh, oh-no, "poly" factoring

Oh, oh-no, with radicals too!

Start with the squared

Break "ax" and "c" up within

brackets but

double check by FOIL-ing

Oh coordinate planes, with four quadrants

x and y axis, minus and plus

Oh, oh-no, solve for cos, sin, tan?

Oh, oh-no, not sure if I can!

1,2,3,4,5,6, 9 or 10?

Maybe should've paid attention way back then!

(repeat)

Oh, oh-no, there's still more to learn

Oh, oh-no, my head starts to turn

Oh equations! Hurting my brain!

Oh pre-calculus, what a shame!

(repeat)

Hope you like it!

By Rebecca

Here is the original song so you have an idea as to what the music is like:

http://www.youtube.com/watch?v=ABYnqp-bxvg&ob=av2e

Pre-test Post

This unit seemed pretty uncomplicated, which was nice. I found that I grasped most of it easily enough, and got through the unit in about 5 days. It seemed to go by quickly as we really only had to learn simplifying equations with division,multiplication, adding, and subtracting; and then solving equations with those same operations. Hopefully I was actually grasping the concepts and not thinking that I was!! With only the text book as a reference, I only learned how to simplify/ solve rational equations their way. Sometimes the explanations can be confusing more than anything, but I hope in the end I learned how to write & solve the equations in a proper way, with proper notation, etc. One thing I did find confusing were the non-permissable values, but I think for the most part I was over-thinking it. Overall, my hope is that I learned this unit in the right way! Miss you guys!

P.S. Mrs. Frey, my dad is going to send the test probably today or tomorrow.

Unit 7 Pretest Blog

I didn't find this unit too bad actually. i had some trouble with adding and subtracting, but with more practice, it got better. the word problems are also hard to set up, but once i can get the equation, i usually do not have much trouble solving it afterwards. i hope this test goes well, i am feeling sort of confident that i can do okay on it!

Chapter 7 Pre-Test

I found that in this unit we used a lot of the things we have used in previous units including factoring, solving for variables, and solving word problems. I enjoyed simplifying the equations, but when we started solving the equations they became more difficult. The part I found difficult was making the equations for the word problems, though once you figured out what the equation was the math was fairly simple. Overall this unit was fairly straght forward.

Jobs In Which Rational Expressions Are Used

The question asked was "Where would weever use rational expressions?" After doing some research I have found a couple of jobs that do involve using rational expressions:
1) Chemist- A chemist may have to use rational expressions in the case of trying to find out how much solute must go into a solution to make it a certain percentage of each substance (ex. how much bleach should be added to 47 L of water to make a solution that is 6% bleach).
2) Captain of Ship- A captain of a ship may have to use rational expressions in the case of trying to figure out how long it's going to take them to get to a certain location. A rational expression could be used if you have your average speed in still water, the distance travelled upstream/downstream to determine your average speed.
These are just a few examples of jobs that use rational expressions but if you really think about it there are many jobs that use some sort of rational expressions.

Khan Academy

I watched the video from Khan's Academy which is already posted on the blog. It talks about how to solve rational equations. I could see this video being useful if you had never been taught a technique of how to solve a rational equation, but for me since I have already been taught how to solve these equations I found that the video confused me more than it helped me. I found it troubling how he just started factoring, and foiling without giving reason for why he was doing it. Another part I thought that could've been done better is teaching how to find the lowest common factor instead of just jumping into it. So to understand this video at all you had to have complete understanding of how to find your lowest common factor. Personally this video did not help to improve my understanding of the topic, but I think that was due to me already understanding how to solve theseequatons using a different method.

Hello from Australia

Hey Everyone,

Hope you are all doing well!

Just wondering where about you are in terms of unit 7, and how I should pace myself thusly. We have only just settled in, and I am going to try and finish 7.2 today. Hopefully I can try and catch up or at least not fall too far behind.

Thank you,

Rebecca

Solving Rational Equations

Here is a video on solving Rational equations.



For more videos, go to Khan Academy and search Solving Rational Equations and three more should come up. 

Rational Expressions - Blogging Prompt

It was asked today at the end of class - "Where would we ever use rational expression?" 

For this prompt your job is to research and tell me where would you use them.  Come up with at least two jobs that use rational expressions and an example of how they are used in each job. 

Khan’s Academy - Blogging Prompt

Khan’s Academy is a site of numerous videos of various math topics.  Find a topic that you are struggling with and watch a video.  Blog about what you learned from the video and whether you found it helpful or not.

The Art of Trigonometry – Blog Prompt

We did an ‘art’ project using trigonometry as part of home assignment 7.  We used cosine and sine graphs to construct it.  What equations would you use to reproduce it if you can only use the sine function?  Explain how sine and cosine are related.  How do we get from a sine graph to a cosine graph?

Radians – Blog Prompt

In the first lesson of our unit on Trigonometry we briefly discussed radians and how it was another unit for measuring angles.  For this prompt I would like you to give the definition of a radian, state the conversion to degrees and explain how the conversion is determined.

Purplemath

I found the link http://www.purplemath.com/modules/fcntrans.htm very useful in helping me graph quadratics. This website is great in helping you too see what relationship certain quadratics have and how they are graphed. It helps to explain the meaning of numbers and how they are used to change the location of your intercepts and the distance between certain points on your graph. The part I found most useful though is the list of the transformation rules on the top of page 2. It helps to explain how the graph moves when given a certain equation (ex. f(x) + a is f(x) shifted upward a units). This was the part I struggled with the most in this unit so I found this website very useful in helping to better explain this topic. I have only used this website a small amount, but from what I have used it I think it could be helpful in many topics related to math. I plan on using this website more as the year progresses.