This week in Pre-Calc we learnd trigonometry. Trigonometry this year was quite different than last year, because we were working with non-right angle triangles. The reference angle in this years trigonometry is very important, because it helps us relate it to grade 10 trig, and because it can help us use our special triangles. The notes I took for this unit were very heavy, because we learned so many new math laws, like the sine and cosine law. When doing the review I was able to create a whole paper of notes, with the most importnat stuff put together.

This sheet is what I think the most important concepts to know are.

This week in Pre-Calc 11 we learned about a cncept that is very hard for me, called “Rational Expressions. A rational expression is the quoient of two polynomials. This unit requires a lot of factoring, and also a lot of self control. By that I mean, you have to realyy stop yourself from simplifying any further, otherwise your answer will be completely wrong. This unit is especially hard when you are adding and subtracting rational expressions, because you have to find a common denominator with polynomials that have nothing in common. This unit requires a lot of thinking and practicing. The main thing to remember in this unit is that once you’ve done the necessary steps, don’t try to simplify any further. Also if you’re subtracting, always remember to disttibute your negative and change the correct signs to their opposites.

Here are some examples of rational expressions

This week in Pre-Calc 11 we worked with very weird looking graphs. We focused on absolute value functions and reciprocal functions. The weirdest ones we worked with were the quadratic reciprocal functions with 4 invariant points.

With absolute value functions you have to graph your equation, and then flip whatever is negative to it’s positive form. ex. (-2,-3) will flip to (-2,3), you only flip the y-value, not the x.

The most crazy thing we learned this week was the reciprocal functions. That’s where you put your equation under 1 and graph that. The most important points for this are the x-intercepts. The x-intercepts become your asymptotes. Asymptotes are the points on the graph that you can not touch or cross. The asymptotes can be represented as an electric fence. You can get as close as you want to it without getting shocked, but as soon as you touch it you get zapped. Asymptotes don’t just make one single point untouchable though. For example if the assymptote is y=2, you can not go below 2.

This is an example of a reciprocal function

This week in Pre-Calc we learned about Absolute Value Equations.  The main thing to know is that if it is an absolute value equation it can never be negative. Since it can never ever be negative you have to flip up the negative points when you graph it. Meaning when you graph the original equation (without thinking about absolute values), you need to mirror the negative points to make them positive for the absolute value equation. Another thing to know about Absolute Value Equations is piece-wise notation. Piece wise notation is when you make to equations that are the exact same, but for one of the equations you change the numbers in the absolute value braces to their opposites. To solve absolute value equations you should always isolate the numbers in the braces, and move all the numbers outside of it to the other side of the equation. After you’ve isolated it, you can get rid of the braces. Then solve the equation. To check plug your solution back into the equation.

This week in Pre-Calc we learned about Solving Quadratic Inequalities in One Variable, Graphing Linear Inequalities in Two Variables, and Solving Quadratic Systems of Equations.

When solving in one variable you first factor the expression, then Determine the zeros, and then using a sign chart (number line) determine your restrictions etc.

When graphing linear inequalities in two variables it is represented by a boundary line and a shading on one side. The boundary line can be a solid line/broken line. If solid it means it is greater than or equal to, and if it’s broken that means it is either less than or greater than. To graph an inequality first graph the equation, then determine whether you have a solid or broken line. Next choose a test point not directly on the line. When you can use (0,0), if the statement at the end is true, shade that side of the line, if not  shade the other side. Always isolate y

When solving Quadratic Systems of Equations you would solve algebraically, either with substitution, or elimination. You could also graph, but if your point of intersection is not on a “pretty” point, you will not be able to be completely accurate. To solve get everything equal to zero.

Systems: What is a system? A system is when 2 or more equations are needed to find a solution. Their point of intersection is the solution. If 2 lines are parallel they will never have a solution. If the lines are the exact same and are right on top of each other there is an infinite number of solutions. The 3 types of solving systems is graphing, elimination, and substitution.

This week in pre- calc was mainly just review for our mid-term. We didn’t learn any new skills but we spent the week strengthening old ones. We did a lot of practice worksheets to help us memorize what we did. When it came to taking the midterm, I feel I did well on the stuff we did earlier on in the year, but I definetely steuggled when it came to graphing quadratics.

This week in pre-calc we learned about modelling quadratics. We also went further into detail about quadratics. This unit is quite difficult, because you need to find certain points by doing a lot of algebra. The most important point to find is the vertex and once you have it you can find the line of symmetry. You can also determine whether you move 1 down over 1, 3 down over 1 etc. If not you multiply those numbers by your “a” to get the other points. I feel I can help myself in this unit by watching youtube videos and asking others to help me when I don’t understand something. Modelling quadratics is definetely a tough part of this unit.

This week in pre-calc we expanded on “Analyzing the Quadratic Equation”. We learned about 3 different forms. We learned about standard form, general form, and factored form. All 3 forms are connected to each other and tell us different things. Standard form + q gives us the vertex, general form gives us the y-intercept, and factored form gives us roots, zeros, and x-intercepts. Each letter in all the equations gives us different parts of the graph. For standard form “A” tells us which way it opens and the width of the parabola the smaller the number, the wider the parabola. “P” gives us the x-intercept. If “p” is negative it moves to the left, and if its positive it moves to the right. The “q” is the y-intercept, if its gets larger the parabola moves up, if it gets smaller the parabola moves down. For general form the “c” is the y intercept.

This week we started on graphing quadratic equations. We learned about finding the vertex, y and x axis, lines of symmetry etc. Our last lesson was warming us up for graphing. We learned about parbolas as well. Desmos.com is a really cool website to help you graph the quadratic.

This is the main equation for graphing a quadtraic, things are added to this.