Category Archives: Math 11

Pre-Calculus 11 Core Competency Self-Assessment

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Core Competency Reflection

This semester I think that something I did well was using vocabulary and terminology to answer questions in both tests, and assignments. Using vocabulary helped me understand concepts and use my words to explain them effectively. This was helpful for me due to the fact that I learn concepts better when I can use terms or vocabulary to help me get a better idea of it, even if I’m not the best at solving the questions in that specific unit. Fully understanding the terms and concepts I was taught helped me understand and connect concepts I actually understood together in a way where I could express my learning effectively. Knowing the vocabulary was also more efficient for me because if I was struggling to solve a question, I could connect it to the terms I had used and it occasionally helped guide me on where to start or finish with certain questions. For example, using terms and vocabulary also made it easy for me to memorize formulas which help when solving questions in a variety of units.

Another thing that went well for me this semester was working collaboratively alongside others. In this course we did a lot of group work where we would solve questions together and communicate with each other so that everyone understood what was happening. I think group work was very helpful for me because if I didn’t understand something I could ask my peers and they could help me out. Group work was also beneficial because one of my group members could bring up something they use that helps them and it caused the rest of us to think about it and it could help us all. During group work it was also nice to see how others use techniques they have to solve questions and use them as well which broadens my own knowledge on how to answer certain questions as well as tech us new techniques we could potentially use in the future. In the beginning of the course we had to work in groups with people we didn’t really know so it was important to have effective communication to make sure everyone was on the same page and was following along with what was being done. I feel that those skills were transferred over when we got to pick our own groups due to the fact that my group was really good at making sure everyone was on the right track and even supported each other by offering assistance when anyone needed it, and helping each other when we were either struggling or doing a question wrong.

Next I want to reflect on how I was able to treat both myself and others with respect. This kind of builds off of the communication point I had made when talking about communication within group work as well. Within our group whenever a mistake was made, nobody was ever rude or mean to the person who made it. Mistakes occur in math and many other subjects as well, so it is important to be respectful and kind when correcting someone or helping them solve a mistake they made in the equation, question, formula etc. Lastly, this semester I learned a lot about growth in my life. I found out both areas I’ve grown in, as well as areas I want to see growth in, and I can act on them or create a plan accordingly.

Advice for Future Students

My biggest piece of advice for future students in math would be to not let work pile up. It’s really easy for you to fall behind and miss certain units or not understand them but once you are behind it’s easier to let it continue rather than put in the extra effort and get back on track. Other pieces of advice would be to 1) do the assigned workbook questions on time, 2) don’t be afraid to ask for help whenever you find yourself struggling with concepts, 3) pay attention to vocabulary just as much as solving because it can help with questions, 4) Make sure that you use class time effectively to give you more time to study and prevent you from falling behind.

Transforming Parabolas

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my given equation
parent function of parabola

Desmos Graph of Equation and Parent Function

Parent Function and Given Parabola

Significance of a, h, and k Within the Equation

In my equation, a was represented as ½. Due to the fact that the coefficient on the x² value (a) is a positive number the parabola created by my equation opened upwards rather than downwards which is what would’ve occurred had the coefficient been a negative number instead. The coefficient of the equation also determines what the parabola will look like in terms of width, shape and direction. The coefficient of my equation is ½, and because the coefficient is in between 0 and 1 it means that my parabola will be wider, which can be seen on the graph, rather than compressed had the coefficient been greater than 1. The value of h in the equation I was given is 6, it is a positive number due to the fact that when it is plugged into the equation y = a(x – h)2 – k, the 6 becomes a negative number. This means that the parabola’s vertex will be shifted 6 spots to the right of the parent function which in this case is 0. Lastly, in my equation the value of k is -7. This value gives us the upward or downward shift of the parabola meaning that the vertex moves up or down whatever value k represents. In this case my parabola’s vertex was shifted down by 7 places.

Self-Assessment

During this assignment I was able to show my mathematical learning by using the material learned in order to further my understanding of parabola’s and make assumptions regarding how they’d look without the need of a graph. I demonstrated this throughout my explanations of each different variable and how it influences the parabola’s appearance and equation. In order to both show my mathematical understanding I had to use mathematical vocabulary to fully explain the points needed and my thoughts behind them. For example, I used words like coefficient, compressed, vertex, and parabola to have better descriptions of what exactly I was trying to say in a precise and accurate way. Lastly, in this assignment I used formatting to provide a clear and visually appealing way to present my learning so that others could comprehend it better. In my assignment I specifically used the formatting to apply headings and subheadings to represent changes in topics, colours to coordinate images and words, as well as labelling all images and equations to avoid confusion on what is being described and shown to provide more clarity.

Facing a Challenge

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Section 1.5 Question #6 m

The first time I tried this problem I found it challenging because at that point I wasn’t used to seeing an expression within a radical, so it was difficult for me to start solving the question. However, once I recognized the mistakes that I had made along the way it made the question a lot easier to understand.

The reason I had some difficulty while answering this question was because in my first attempt at solving this question I had forgotten to remove the GCF of the first radical the first time, but once I noticed my mistake the question was a lot easier to complete. Although it was quite a simple step, I overlooked it and that had an impact on how I ended up answering the question as well as the way that I got there. After that I noticed that I had forgot to separate the radical to be able to continue solving the question. The reason I had forgot to do so is because radicals are still fairly new to me so I sometimes tend to forget the rules of radicals and when they are applicable. After fixing my mistakes the question was easy to solve. I had to start with removing the GCF of the radical which was 9, leaving behind (x – 1), and because √9 is separated from the starting expression you can remove it. √9 is also a perfect square so the answer to that would just be 3. The last step of the question would just be to collect the like terms which leaves you with the answer 4√x-1 .

In order to figure out my mistake I used strategies including things like looking back at the notes provided to help determine where I had messed up and how I can move myself into to correct path from my mistake. I also asked a peer or friend if I needed extra support or to see mistakes that I overlooked when doing the question.

In order to correctly complete this question, I had to remember to identify a GCF if there is one present, and to simplify the question to make it easier to solve. I also had to remember to simplify within the radical (radicand) whenever possible in order to complete the expression and answer the question.

Next time I encounter a difficult problem, I might try to use other resources provided for me such as the videos and work contained in the school math departments website or using the textbook and working backwards from the answer given. Despite there being other resources I could’ve used the ones I did use were helpful in helping me understand the question, how to solve it, and the reasoning behind the explanation of the answer.