Magnet students take Magnet Precalculus or, by invitation, Magnet
Functions either in the ninth grade, if they have already taken a
geometry course before entering the Magnet, or in tenth grade, after
the Magnet
Geometry course. The curriculum is very similar between the two
courses, but while Functions is an intense, two-semester course, Precalculus
is taught over three semesters. Upon completion of either
course, Magnet students go on to Magnet
Analysis I.
The courses start with a discussion of functions and their properties,
such as boundedness, periodicity, even/odd, increasing/decreasing,
etc. Graphing, operations on functions, transformations and inverses
of functions, and the concepts of domain and range are then discussed.
The courses include trigonometry, starting with basic circular functions
and terms: the unit circle, reference angles, radian/degree measure,
arc length, amplitude, displacement, period, etc. Parametric form,
harmonic and circular motion, and trigonometric proofs and identities
are then discussed.
Another aspect is solving equations and inequalities. Students learn
to solve linear, rational, quadratic, absolute value, and trigonometric
equations and inequalities. Simplifying and solving radical equations
comes next, followed by a unit on logarithms.
Students also learn about the law of sines, the law of cosines, and
other topics concerning triangles.
Another unit focuses on complex numbers and polar coordinates follows.
Students start with basic arithmetic on complex numbers (addition,
subtraction, multiplication, and division). Conversions from polar
to rectangular forms and graphing in polar form follows, including
a discussion on DeMoirve's theorem.
In the vectors unit, students learn dot products, cross products,
scalar and vector projections, direction cosines, etc. The classes
then move through parametric equations, and on to matrices, topics
including Cramer's rule and the Gauss-Jordan elimination method.
The sequence continues with polynomial functions. The rational root,
factor, remainder, and complex zero theorems are all covered, followed
by work on polynomial function graphing, and determining all roots
of a given function. Rational functions are then discussed, with a
look at asymptotes, limits, and simplifying rational algebraic expressions
and complex fractions.
Conics are also included, with the discussion of the types of conics
and their properties, followed by a discussion of their graphs (including
degenerate and rotated conics). Eccentricity and discriminants of
conics are then taught, followed by solving systems with combinations
of equations of conics, and the polar forms of conic equations.
Finally, there is a unit on series and sequences. Arithmetic, geometric,
and infinite series are discussed, as are binomial expansion, recursion,
mathematical induction, and limits.
Whew! That is a lot of ground to cover in two or three semesters.
A Magnet student may get any of the Magnet's mathematics teachers,
Mr. Walstein, Ms. Escatell, Ms. Dyas, or Ms. Bishop, when they take
Precalculus or Functions; each one teaches at least one section. Mr.
Pham also crosses over from chemistry and teaches a section of Precalculus.