Mathematics at Balboa School

Period 4 Mathematics is comprised of a very special group of students.  Prealgebra students are studying the Pythagorean Theorem to ensure that a rocket is perpendicular to the ground prior to launch.  For example, a private space company, Personal Space, is designing and testing a rocket for tourist trips into low-orbit around the Earth. The test flight engineers specify that a landing can be successful only if the rocket’s direction of flight is perpendicular. Lasers on the ground will measure distances to the rocket, and those distances will be used with the Pythagorean Theorem to ensure that the rocket is perpendicular to the ground when landing.
Algebra-I students are finding that theme park architects use lines and curves to draw their designs. They can model the lines and curves with equations.  
Mathematically speaking, a line may be defined as a linear curve, but in these investigations, lines will be the graphs of linear relationships and curves will represent exponential relationships. The image shown here highlights some of the lines and curves being studied.  Intermediate Algebra students are exploring complex numbers and the imaginary number i.  In math and science the symbol “i” represents the square root of  -1.  The students have found that complex numbers include both real and imaginary numbers and enable the solution of quadratic and higher order equations that have no solution in the domain of real numbers. By performing different operations on complex numbers, the students have discovered that the complex number system is closed.  They are looking again at the discriminantin the quadratic formula to investigate what it can tell them about possible solutions of a quadratic equation, and they are beginning to understand what complex number solutions mean in real-world settings. 
Our geometry students are looking at bridges that come in many different sizes and designs. Have you ever wondered why some bridges are curved and others are straight? What do bridge designers think about when they design a bridge and what role does geometry play?  The answers are all about geometric structures and especially the properties of triangles. 
Precalculus students are learning to find the roots of polynomial equations.  They’ve read that the French mathematician Galois proved there is no general formula for finding roots of polynomial equations of degree 5 or higher. However, they are learning the many methods to solve polynomial functions, including the Rational Zero Theorem, the Fundamental Theorem of Algebra, the Linear Factorization Theorem, and Descartes’s Rule of Signs.   
Students in AP Calculus are completing their study of differential calculus prior to the Holiday Break.  Remaining topics include the study of motion:  for example, the relationship between position, velocity, and acceleration of a particle; and “related rates.”  They are learning to take the derivative of exponential functions, and `log’ and ‘ln’ functions.  For example, they are discovering that functions of the form loga x, ex, and ax= exlnacan be differentiated.  Next semester, they will discover that such functions can also be integrated when they begin study of the integral calculus.

Student of the Month 

Balboa school is happy to have Ruhmit Sahu as our Student of the Month for December. Ruhmit is always such a positive influence to any class he enters. He is hardworking, caring and a great help to teachers and staff as well. Congratulations Ruhmit!