This semester in math we learned many new important things that were fundemental for my learning. We added on lots from last year, as well as learned some completely new concepts.
- Factoring – we learned factoring last year, however it was this year that it really solidified with me. We used factoring in almost every unit we did, and added on to it from last year. Firstly, I learned the box method and the cross method. Personally, I prefer the cross method as it works best for me and I find it to make more sense visually. We used to solve for X in the quadratics unit, and used it in rational expressions. We used it to simplify expressions when evaluating or solving, and when finding the discrimiants. Without a solid understanding of factoring, completeing the course would of been torture and nearly impossible.
- Completeing the square – With factoring, we learned another concept called ‘completeing the square.’ This is an alternate way of solving a quadratic equation that does not factor. After learning this concept, it continued to be used in other units. We used completing the square when turning an expression in general form, to vertex form, and had the option between factoring, the quadratic formula, and completing the square on tests. This understanding of completeing the square was crucial to my learning, even though at first I found it tricky. Now, I love it and will continue to use it this year.
- Quadratic formula – Out of all the methods to solve/evaluate a quadratic equation/expression, completeing the square was my favourite. I caught onto it right away, and unsuprisingly, we continued to use it throughout the course. I found it to crucial for my learning, as we used it for finding the discriminant and any other quadratic that cannot be factored.
- Rationalizing denominators – With the radicals unit this year, we learned how to rationalize a radical expression. We multiplied by the conjugate and treated the denominator as a complete the square question. This understanding is super important as you cannot leave a radical in the denominator. We rationalized denominators for multiple units, including quadratics that had radicals in their denominator. At first the concept confused me, but now I find it straight forward, which is super important as it is a necessary understanding for pre calc 11.
- Sine Law – This year during the trig unit we learned the sine law and cosine law when solving non-right angle triangles. This understanding is super important because most triangles that you deal with are not perfect right angle triangles. Now that I can comfortably use the sine law, I feel so much more confident about trig than I did last year, and prefer non-right angle triangles to regular right angle ones that we did last year.