Active Living 11 Final Reflection
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Category Archives: Grade 11
Pre Calc 11 Week 17 – Trigonometry Laws
This week in math we learned about different ratio laws which helped us determine missing sides and angles. Below are the formulas for the laws which will be explained further:
The uncapitalized letters represent angles, and the capital letters represent side lengths. You can use sine law when you have the side and an angle of a triangle and also another value. You then can use the sine law and basic algebra to fill in the triangle. Cosine law is used when you do not have two matching angles and sides. The first cosine law is used to find an angle, and the reverse cosine law is used to find a side length. You have to figure out which one to use based on context clues and from there, insert the numbers into your calculator.
My biggest mistake this week is properly punching in all the numbers with brackets in my calculator. If not done properly, you can receive a different answer or even no answer. A tip for cosine law is to put brackets around (B x C) and (COS A) to ensure they are multiplied before distributed.
Pre calc 11 Week 16 – Perfect Triangles
This week we learned about two different right-angle triangles. One triangle consists of 90, 30, and 60-degree angles. The other one has two 45’s and a 90-degree angle. For the 30,60,90 triangle, the shortest side (across from the 30) is the starting point. This is a multiple of 1x. The 60-degree side is x multiplied by the square root of 3. The 90-degree side is 2x. For the 45, 45, 90, both the 45 sides are 1x and the 90 degree is x multiplied by the square root of 2. Because these triangles of fixed ratios, it is easy to calculate side lengths without using a calculator. These triangles can also help with the unit circle.
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Open in new tab My biggest mistake this week was not remembering where each of the sides go on the triangles. I now have them memorized which will help me for the test.
Pre Calc 11 Week 16 – Trigonometric Ratios
This week in math, we learned about trigonometric ratios and how to determine whether they are positive or negative within the four quadrants. The three ratios are Sine, Cosine, and Tangent. To decide whether or not it’s positive or negative, I used the acronym “All Students Take Calculus” or ASTC. This acronym tells us what quadrant has a positive ratio. In Q1, ALL are positive, Q2, SINE is positive, Q3 TANGENT is positive, Q4 COSINE is positive. An example question could ask in which quadrant is SINE positive. Using ASTC, sine is positive in A and S meaning your answer would be Quadrant 1 and 2.
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Open in new tab My biggest mistake this week is remembering the rules for finding the reference angles in each quadrant. For quadrant 1 it’s 0+ angle, Q2 is 180- angle, Q3 is 180+angle, and Q4 is 360- angle.
Pre Calc 11 Week 15
This week in math we learned about rotations and reference angles. On a graph, there are 4 quadrants starting from the top right being quadrant one and continuing counterclockwise. The standard starting point at 0 degrees is between quadrants 1 and 4 on that line. Something important to know is finding the reference angles by creating an angle on the X-axis. This is dependent on the rotation angle. A rule for finding the reference angle based on the rotation angle is based on which quadrant the terminal line is. To start, find the arm by plotting the coordinates. From there, you can create a right-angle triangle to find the base and width lengths. Finally, you can use basic trigonometry to fill in any missing sides or angles.
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Open in new tab My biggest mistake this week was finding the wrong angle. Each angle has to be connected to the X-axis and sometimes I didn’t do that.
Pre Calc 11 Week #14
This week in math we learned how to solve word problems when applying them to rational equations. First, please make sure you understand the question, then let me know what you are trying to find and any measurements given. Finally, you can write an equation to find your answer. A hint that we were given was to complete a chart with all of the numbers given which makes it easier. Here is an example question:
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Open in new tab My biggest mistake this week is remembering to check my work to find any values that are supposed to work but end up not working because of fractions.
Pre calc 11 week 13 – Factoring Fractions With Variables
This week in math we learned how to add and subtract fractions with variables. For adding and subtracting, you first need to find a common denominator within the fractions. This will allow you to subtract or add the numerators to obtain an answer. To find a common denominator, you multiply all the numbers on the bottom and whatever you multiply on the bottom, you also do to the top. Here is an example:
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Open in new tab My biggest mistake this week was not being careful with the negatives and positives leading to the wrong answer.
Pre calc 11 Week #12 – factoring fractions
This week we learned how to factor fractions when a variable is involved. Here is an example:
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To solve this you first have to factor the top and the bottom. By the method of inspection, you can find that a multiple of -36 and has a sum of -5 is -9 and 4. From there you can find the factor of the top and move on to the bottom. For the bottom, you can take out 2x and be left with x-3. Now you cancel the top and bottom with pairs that match such as x-3 and you are left with your answer. The final step is to determine what “X” cannot be by looking back at the factors before you remove them. You can see that the denominator cannot be zero so you have to find a number that makes it zero which would be “3”.
My biggest mistake this week was being lazy when determining the characteristics of a graph. When finding the X intercepts, I would just write two numbers instead of coordinates (same as for the line of symmetry).
Pre Calc 11 Week 11 – Analyzing word problems
This week in math we learned about analyzing word problems regarding graphing and quadratic functions. To ensure you fully understand the problem, you first have to read it three times. Once just to read it, second to understand it, and third to find what the question is asking for. You also have to locate any numbers or any useful words that will help you find the answer. Here is an Example:
At a water park, it costs $2.5 to rent a mat and $1.25/ride. If you have $20, what is the maximum number of rides you can go on?
(There is no need for a picture because I just typed out the question instead of taking a photo)
To answer this question, first understand what you are trying to find (Maximum # of rides) and locate useful numbers/words like the cost of each ride and the mat price including your budget. From there you can write an equation where $20 is the maximum spending amount (meaning your inequality has to be equal to or less than 20) and the costs. Your inequality should be
20=>1.25x+2.5
This allows you to find “X” which is the number of rides you can go on.
My biggest mistake this week is finding what the questions are asking and how I can relate it to what we are learning in class. This means I need to understand the material better and create connections to certain words or numbers that can be inputted into questions.
Pre calc 11 Week 10 Post – Naming Quadratic Functions
This week in math, we learned how to find the formulas and draw graphs of quadratic functions. To begin with, there are two main forms for an equation (Standard and General). It is recommended that your equation be in standard form to find certain characteristics that are needed to graph. When looking at the equation, you can find the vertex which is needed to start your graph. From there you can find the stretch and the intercepts of the graph. Here are some examples:
To find the vertex, you look at the number in the bracket which states how far left or right the vertex starts, and the number on the end which states how far up or down the vertex is (The number in the bracket is the opposite). If there is a coefficient in front, your graph should either be stretched or squished depending on whether it is a whole number or a fraction. A negative in front means the graph goes down.
My biggest mistake this week was remembering to switch the number in the brackets to the opposite when inputting it on the graph. If the equation shows a positive number, the graph will start on the negative side.