Starting Pre-calculus

After the intense practice for the SAT exam, now we are focusing on pre-calculus. We flew through the few chapters since we knew most of the stuffs in it. As I’ve mentioned in my previous posts, we use a lot of Khan Academy as our source to further our learning.


One of the part that interest me the most is learning to sketch a polynomial graph. Before I was introduced to pre-calculus I only use to see a parabola graph-shape looking graph but now graphing a polynomial is a much cooler graph(in my opinion). To draw sketch a polynomial functions graph, you need to follow a few steps.


Step 1: Find all of the x-intercepts of graph.

Step 2: Make a table of values for the polynomial. Include test points to know whether the graph of the polynomial lies above or below the x-axis on the intervals determined by the zeros. Include the y-intercept in the table.

Step 3: Determine the end behavior of the polynomial.

Step 4: Plot all the intercept and other points you found in the table. Then sketch the graph.


Using Desmos, this is the difference between a quadratic and a polynomial graph(bigger power).

This is the graph of : x^3+5

This is the graph of: x^2+5

We spent almost two months practicing for the upcoming SAT in math class. Since we have already know most of its contents, we prioritize those time to finding strategies to beat the test. One of the tricks is to try limiting our time on easier questions so that we could save up more times for the harder ones.

Moreover, as I had gone through many practice tests, I realized that sometimes skipping questions isn’t always bad. So if there are questions that are tricky and would take much time, I would skip the question and move on to the easier ones.

Even Though, everyone is telling me that the result of this test will not depict who I really am, but the result of the test is essential for me, to find awesome opportunities that would brighten up my future, since I would need full scholarship offering from universities.  





We used Khan Academy as our main resource in practicing math problems for the SAT.