Students in SVGS Advanced Calculus wrestled with extending what they learned in calculus last year to three dimensional space. Along the way, they are mastering the use of software tools which (in addition to being powerful problem solving assistants) help us visualize the difficult new concepts of vector calculus. Here’s a link to a webpage containing a student created plot illustrating the fundamental truth underlying the technique of Lagrange optimization: http://www.svgs.k12.va.us/web/math/LagrangePlot.html
You are welcome to track our day to day progress by visiting the class webpage on Moodle: http://www.svgs.k12.va.us/moodle/course/view.php?id=137
Just click “Login as a guest”.
AP CALCULUS BC
Our AP Calculus BC class began the year with a study of limits and continuity. We then explored the tangent line problem which led into a unit on differential calculus. We applied differentiation techniques to a wide variety of functions represented analytically, graphically, and numerically. We then turned our attention to integral calculus where we studied antiderivatives and Riemann sums as a lead-in to the Fundamental Theorems of Calculus. We applied the Theorems extensively to physical situations and are now expanding our repertoire of integration and additional types of functions. In the second semester we will also investigate differential equations, infinite series, and applications of calculus to find areas and volumes. The AP Calculus BC exam will be given on Wednesday, May 7.
Last weeks of the first semester, students in AP Statistic class were studying about experimental design and sampling distribution, preparing all the tools they need in approaching inference, next semester. They practice randomization techniques using random digits charts, or graphing calculator or Excel spreadsheet. They used Java applets to illustrate sampling distribution and they focus on understanding and effectively formulate and communicate strategies for statistical research. Second semester will be dedicated to the Inference unit, the most important part of the AP Statistics Exam.
In SVGS Dual Enrollment Calculus, we worked hard the first semester extending ideas from algebra, geometry, and trigonometry into a world of change. Students are learning to use software tools like Maple to help visualize tough new concepts, like the limit definition of the definite integral, illustrated by the student lab to the below. (http://www.svgs.k12.va.us/web/math/DefiniteIntegrals.pdf. You are welcome to track our day to day progress by visiting the class webpage on Moodle: http://www.svgs.k12.va.us/moodle/course/view.php?id=101. Just click “Login as a guest”. The site has links to online homework, labs, classwork handouts, lecture notes, and test reviews.
We have covered a number of topics about functions, from basic properties to real –world problems solving. Those included basic trigonometry, vector analysis, polynomial (and rational) functions, logarithmic and exponential functions. Efforts were made to incorporate science especially physics concepts such as forces, velocities, momentum, work and periodic motion etc. into our studies. New labs / projects were designed and conducted. Maple –powerful mathematics software package with symbolic computation capability – was introduced for visualizing math concepts and demonstrating the properties of those functions and their transformations.
Congratualtions to Ailec Wu! Ailec won the regional AMC12 at VMI and has qualified for the American Invitational Mathematics Examination. Michael Laterza and Daniel Brooks also participated with a strong showing.
Moody’s Mega Math Challenge is a mathematical modeling contest for high school students sponsored by The Moody’s Foundation and organized by SIAM. The M3 Challenge spotlights applied mathematics as a powerful problem-solving tool, as a viable and exciting profession, and as a vital contributor to advances in an increasingly technical society. The contest introduces high school students to applied mathematics by giving them an opportunity to work in teams to tackle a real-world problem under time and resource constraints akin to those faced by industrial applied mathematicians.
SVGS students(left to right as shown below), Tori Prevette, Ailec Wu, Cady Van Asseldelft, Alex Maneval, Olivia Heeb, Gus Holberg and Jared Samuelson worked for seven hours to solve a real life problem.