Joshua and I started by discussing conic sections. We reviewed the equations for a circle, parabola, ellipse, and hyperbola. We identified how to recognize their equations by given their graphs (and vice versa). We recalled how to compute the vertex, axis of symmetry, how to determine if it has a reflection and vertical dilation. Next we pulled problems to practice. Joshua did excellent with this new concept. Next we looked at the ACT website with practice problems. We scanned to find the challenging problems. We were able to review the law of sines and cosines, some matrix problems, and algebraic function problems.
It was great to see Joshua today. We began with answering questions that Joshua had from his practice test. We covered a problem regarding triangles and considering how the sides would be proportional. Josh had the right idea on the setup, but was not correlating the correct numbers together. Once explained, he understood the error. Next, he explained that his loss of points came from the Algebra and Geometry section of the ACT. We looked at the breakdown of content within those sections and Josh said he did not have any understanding of matrices. So we looked at the types of problems that the ACT tests when it comes to matrices. We discussed how to add, subract, and multiply matrices. We discussed how to find a determinant. We worked on how to use matrices to represent systems of equations. Then, we pulled up practice problems on those concepts. Joshua did great. The last concept we need to cover before his next test is conic sections. I will come prepared with material on that subject when we meet next class.
Joshua and I met for an hour today to cover SAT math problems. He came to me with a test booklet he had been working on. We covered a range of topics from solving and graphing quadratic functions, solving systems of equations, special right triangles, and box plots. I provided for Joshua examples with extra practice on problems that he needed it. It was a good review for him.
We first discussed Joshua's final research paper. I congratulated him on his work and noted how he included all of the elements per our class instruction: a thesis, claims, counterargument ,and commentary. We then discussed course selection for Sr. year. We explored the AP Literature reading requirements as Joshua is inclined to take the AP course. I further assigned the summer AP reading.