The June SAT results have just been released and I am so proud of one student who managed to achieve a perfect score. Needless to say, lots of effort had been invested to make this happen. A critical component to do well in the exam is to have the right guidance from a tutor and have the right discipline to prepare for it. Students will have to read extensively and strive to write as much as possible on a consistent basis. A strong vocabulary and a good understanding of the origin of words is fundamental in achieving a good score in the reading section. As for all other students, although you have not achieved perfect scores, I am still proud and happy of the strong progress that has been made in the scores. All of you guys can now relax and enjoy the summer and remember to start on your college application essays.
Students learning calculus should understand the importance of odd and even functions as it comes out all the time in Calculus AP exams.
The sine series is and odd function series and the cosine function is an even series. Students should remember the alternating signs when writing the sine series. Other notable series include the harmonic series. Looking at the equations and understanding which series it belongs to will help you save a lot of time in solving the problems. Log functions can be further evaluated with understanding of this odd and even series.
Today, I had the opportunity to teach a high school senior in AP Calculus BC. The problem was to integrate powers of natural log x. The natural result was a repetition of the techniques resulting in expressions in terms of ln x. Using this technique ,student was then led to understand the Reduction formula, which is immensely powerful in solving n powers of ln x
Today, I had the opportunity to tutor a graduating senior in advance calculus. Many high school seniors get lost in calculus because of the lack of understanding the usage of the proper techniques of integration. Methods of substitution integration by parts were introduced, followed by trigonometry substitution and partial fraction integration as the last portion. Definite integrals and improper integrals were also introduced. Knowing the right method enables students to save a lot of time in simplifying the solutions. Natural logs were also introduced with half angle formulas. All in all, calculus gets so much easier if the basic concepts are understood and applied accordingly.
Last week, I had to teach my students in Honors Algebra on the topic of permutations, combinations and probability. In today's world of computer science, I decided to teach my students probability and its applications. Topics covered include number theory, expectations and random walks. First, I covered Sample Space, Probability, mutually exclusive events, dependent events and applications in the typical coin toss questions and gambling cards. I also touched on Combinations and Binomial Expansion. Expectations, Random Walks and some theorems were covered to help them expand on some proofs. All in all, it helps solidifies algebraic concepts and it provides them with a glimpse of its applications.
I had the chance to tutor a student for the state contractor's exam. Geometry concepts are essential for builders. Topics covered include circles, triangles, area, perimeter, pythagoras theorem, congruent triangles, cylinders and spheres. Other topics covered include trigonometry questions like sine, cosine and tangent applications. Geometry concepts are also used to apply to roofing. Other topics covered include scaling and calculation of bidding price and percentages. Cost analysis and actors scaling factors are also covered. Topics like Pitch, Rise and Span are also covered. All basic angle topics were also covered, including supplementary angles and angles at a point.