Category: Math 11

Personally, pre calc 11 was more enjoyable to learn than math 10 was. I was not interested in math 10 at all but pre calc was actually fun to learn and felt really good when you fully understood what you were doing. We learned a lot of new things that we did not learn in math 10. My top 5 things I learned in pre calc this year are as follows:

1. Absolute values. I think that the absolute values chapter of pre calc 11 was the hardest to wrap my brain around. There were so many little things I didn’t understand no matter how much I tried to learn them. But I did have a few big takeaways from the chapter. I learned how to reciprocate graphs and draw them with all of the fancy stuff like the asymptotes and 2 opposite functions. I also learned how to put an absolute value into piece wise notation where you have 2 different forms of 1 equation.

2. Quadratic functions. Personally my favourite thing I’ve learned this year in pre calc 11 was how to deal with quadratic functions. They are so complex and have a numerous amount of parts to them. They are fun to graph as parabolas and also fun to factor. I really liked learning about these and think that it will help me in pre calc 12 very well.

3. Factoring. A big part of quadratic functions is being able to factor. Without factoring you aren’t able to go that far with quadratic functions. Factoring gives you the ability to find the X intercepts of a quadratic function. The X intercepts help you graph and better understand the function. Without the X intercepts it would be hard to graph precisely by hand. Factoring also helps us when dealing with quadratic functions in algebra.

4. Updated trigonometry. Trigonometry from math 10 carried over to pre calc 11. All of the basics of trigonometry still stayed true. But the biggest difference was that we learned how to deal with non right triangles and still solve them fully. With using techniques such as the sine law and cosine law, we were able to solve any 180 degree triangle for all of its sides and all of its angles.

5. Arithmetic sequences. Probably the best real life take away from this course. Arithmetic sequences applies to real world problems with money and things growing. Geometric sequences also help too but arithmetic sequences are the most helpful. When dealing with arithmetic sequences you are able to solve for terms within a certain pattern. You can also use the arithmetic series to solve for the total sum of your sequence. Personally this was my favourite all around chapter.

In trig this year we learned what reference angles are. They are determined by the angle that’s closest to the x-axis, this will help decide whether or not you add or subtract from the degree of each quadrant. The rotational angle is determined from 0 to where the arm is

We also learned 2 new formulas, the sine law and the cosine law. These are used to solve non-right angle triangles because Pythagoras can not be used properly. The sine law can only by used when there’s at least one whole fraction in the triangle, while the cosine law is used hweb there is not a full fraction.

There are also special triangles that have a certain pattern to them.

This week we learned how to multiply rational expressions in fraction form. For this question you want to factor as much as possible. Once the equations is factored as much as possible, cross out like terms. 

This week we learned how to simplify rational fractions. These are basically fractions that will involve factoring. A way to make these questions simpler is by crossing out common factors in the denominator and numerator of the fraction because if you divide them they’re just going to equal 1 anyways. We also learned that it is important to know the non-permissible values of x in the denominator. It is important to know because our denominator can never equal 0. therefore the non-permissible values of this expression are -5, -8, and 0.

This week in math he learned how to graph reciprocal quadratic functions. When beginning these questions it is always easiest to start by graphing the original equation, in this example it is x squared minus 3. After graphing this draw a broken vertical line on the zeros or x-intercepts, because this graph has 2 solutions it will have 3 hyperbolas. The 2 “L” shaped hyperbolas hover right above the x-axis and almost touching the broken lines. The hyperbola on the bottom follows the same rules except it’s on the other side of the broken line.

This week in precalc we learned how to solve 2 inequalities by combining the equations. this only works when the equations have 2 variables. An important part of this process is when you send one equation to the other side of the equal sign, that they’re being added or subtracted properly or else the whole process will be ruined as the zeros will not be equal.

This week in pre calc we learned how to solve for quadratic inequalities. When solving for quadratic inequalities, factoring is important as it gives the zero values. I like using the number line as a visual to find whether or not test numbers would give negative or positive results.

Back in unit 3 we learned what a discriminat is. A discriminat is “a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.” It helps us determine how many times the quadratic equation will hit the X axis. If the discriminant is positive there will be 2 roots (the parabola hits X twice), if the discriminant is equal to 0 there will be one root (hits X once), and if the discriminant is negative it will have no real roots (not touch the X axis).

Ex.