Tensile is how far something can go before snapping

Compressive Strenght is how far something can go when flexing

**Post-Activity Assesment **

- The beam to weight ration is important to engineers because if the ratio is incorrect the design may encounter many flaws.
- I beams are very common now if industrial building such as schools. Some building such as airplane hangars, Airports and stadiums may use other types of beams to adjust to their designs and purpose.
- In a playground, you would not use concrete because it decays and chips over time. On the other hand, aluminum or steel takes way longer to decay, is very water-resistant and can be replaced much faster than concrete. Material such as steel or titanium would be good for making bridges but materials such as wood and steel would make good beams for homes.

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- Math was never my best subject at any point in my lifetime, I always struggled to grasp the concepts and the biggest mistake a made was not asking the teacher for help when I needed it. But Pre Calculus 11 changed this, I started asking more and more question thus improving my understanding of concepts I also started completing my homework more often and realising how important it was to complete all the problem is the homework no matter the difficulty of how long it takes you to finish the problem because once you finish you will understand the concept more than ever, because you worked hard to get to the answer. And have realised if you understand the concept math actually becomes fun.
- Working with other students was the best idea Ms. Burton could have came up with. With this freedom I got to share my ideas with other, if I had the question wrong we could work together as a team to solve this question. As the saying goes “Two heads are better than one” I truly agree with this statement because working alone is fine to a certain point but after a while it gets boring and you start to doze out. On the other hand working with a partner keeps you awake and wanting to learn more as well as collaborating ideas to create one bug one
- The unit that I found the most fun and interesting was the trigonometry unit. Last year in grade 10 I really struggled with this topic because I could not grasp how to find the angles and when to use the inverse sine. But now thanks to Pre Calculus 11 I have expanded on trigonometry I have gained a much bigger knowledge of this topic. Since trig is a very common topic in Pre Calculus 12 having this expanded knowledge on this topic will launch me forward into grade 12 with a head start. For once in my life I felt smart when I was solving these trigonometric question with ease.
- Using tools such as Desmos helped me allot to expand my understanding of quadratics and inequalities because I could see what I was doing. Using websites such as thatquiz, quizziz and quizlet. Though the questions could sometimes be challenging, it helped us to remember certain things and made it easier to do other questions like them in the future. The websites made the questions look like a game less like practice which helped me just enjoy math and not worry about it.
- Finally the best thing about Pre Calculus 11 is the experience of helping out with a district wide video. On the first day we where taught by another teacher who went over solving and graphing quadratic equations. They started off with some writing and drawing, then we moved on to do some Parabola yoga. Doing this got me to learn in an interactive way and this drilling the concept into my head. In general helping with a district wide video was a great experience because there are many new teacher coming into the industry and helping them was a great idea and doing this it also helped me learn more about quadratic formulas and study for my final exam. Overall this class was very fun and interactive I think all the things that s. Burton implemented into the course really helped me out. Although I am not thrilled with my results in math this year I have gained the knowledge to but everything aside and take math seriously and not a joke. Very stoked for next year!

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This is going to be the second to last post of the year and in this post I will be explaining sine law.

To make Sin law work you must figure out which side is which so angle A is opposite side a, angle B is opposite side b and angle C is opposite side c. Remember that angles are always labelled with capital letters and sides are with lowercase

Now you must write out the formula and figure out what goes where. Dont worry if one or two fractions are missing numerical values as long as you have one complete fraction then you will be fine.

You then make sure that your variable is one top. If it’s on the bottom, you are allowed to flip the equation to have the angles on the top and the sides on the bottom.

Once you finish this step cross multiply and solve fo the undknown using basic algebra.

If you are finding an angle you must use the inverse Sin otherwise you will not be able to find the angle propperly.

Once you do this many times you will start the get the hang of it.

Enjoy!

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In this unit we where introducted to triangles that go past 90 degrees even though it this may seem a little strangle it is quite simple. As we where taught in grade 10 we ended only using the Soh Cah Toa method and pythagorous to find our solutions.

But we have two types of angle. The rotation angle and reference angle. You can find these by drawing your line throught the angle that was given then draw a vertical line to the x-axis. The triangle created makes you reference angle and the rotation angle is the angle to your line. That’s why you can have a triangle with an angle of 200 degrees now.

Instead of using Soh Cah Toa

sin = y/r , cos = x/r, tan = y/x

]]>To solve rational equations we must cancel out the denominators. To do this we must multiply by each denominator, this will cancel them out but because we have to do the same for everything in the equation, we will have then multiply the numerators by the values that were not canceled out. Before we do anything we must find the non-permissible values so we do not forget in the end. If any of the solutions for x is a non-permissible value, it is extraneous and is not a real solution. To explain this we must show an example. The goal of the equation is to isolate and find x. We may have to solve a quadratic or linear equation to get x.

Here are the steps to solving a Rational Equation

- Factor any quadratic functions you see in your equations
- Multiply by the Denominator
- Write down your non-permissible values
- Solve

Example:

Now the division looks as follows:

To divide two rational expressions, we “flip and multiply” and simplify

=

Next, Multiply across

=

The next step is to cancel out. When done you will be left with…

]]>Below you will see an example of a division question:

since this is a division question you need to flip the second fraction to its reciprocal value

Now turn it into a simple multiplication question

$latex frac (x+2)(x-8)/(x-3)(x-7)*frac(x-3)(

now since everything is factored you want to get rid of the factors that are the same so the (x+2) and the (x-3) is something that you would get rid of. this will turn the equation into

$latex frac (x-8)(x-5)/(x+7)(x+7)

And now you solve for x you can find your nonpermissible values.

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Both have similarities but also many differences.

Both an absolute value graph and reciprocal function graph can either be linear or quadratic.

An absolute value graph looks either like a V or W if quadratic and the graph is never in quadrants 3 or 4 due to the fact it is an absolute value meaning there can be no negatives. Critical points are the X-intercepts and where the graph starts to reflect. Below are the different types of what an absolute value graph may look like.

Linear:

Quadratic:

While a reciprocal function has two invariant points. and one vertical asymptote. An asymptote is an invisible barrier that separates the two values apart. Both a linear and quadratic reciprocal function graph hyperbolas are created which follow the asymptotes before hitting the invariant points and then follow back to the asymptote. Below are the different types of what a reciprocal function graph can look like.

Linear:

Quadratic:

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So far in this unit, I have had only one thing that is troubling me and that is writing the equations on piecewise notation. I understand how to write the equation by the thing that is confusing for me is writing what is greater than or less than or equal to.

Down below you will see an example of Piecewise notation:

Graph y=|-2x+5| and write in piecewise notation

To find how this graph looks in piecewise notation we must first find the reciprocal of the equation. To find that I must multiply everything by -1.

f(x)= {-2x+5 { 2x-5

Now we must find if it is greater than or less than or equal to a number. To find this we need to look at the graph, first out x intercept or critical point is on 2.5 so our first so our first value will be x>=2.5. And for the bottom one we will get x < 2.5

So our final piecewise notaion will look something like this:

f(x)= {-2x+5 , x>=2.5 { 2x-5 , x < 2.5

]]>$latex x^2=y – 2x – 8

The first step is to choose a system that will be your base for the equations. I Chose y=2x+5

Next, organize the other equation to the y=mx +b format

Next, you must put it into your base equations

Then you let algebra take over and solve for x

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Linear inequalities will give us a straight line on a graph. When we are given inequalities we are usually given a y value that is greater than or equal to another value, that consists of an x variable. We can also be given a greater than/less than or equal to symbol. This greater than or less than help us decide which side of the line contains the real answers, which we shade in. We also need to determine if the line is broken or solid. The way we can determine that it is greater/less than (>,<) then it is a broken line. If it is greater/less than or equal to .

If we are given the equation of 3x + 7 < y. Just from looking at this equation we can determine the y-intercept which is 7. We can also determine the slope which is 3/1, which means it goes up 3 and over 1 each time.

(Insert Picture Here)

To know whether or not which side of the line contains the real answer, we must perform a test. We will insert the point (0,0) into the equation if it comes out there (left side equals to the right side). If we insert 0 then we will get that 7<0 which is false so we would shade in the right side of the line.

(Insert Picture Here)

The last and final thing that I need to mention is that you need to remember that one must remember to switch the signs if the coefficient of x is negative.

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