Pre-Calculus

Not trying to create little mathematicians, it is the hope of the Grauer School that students discover that satisfying their intellectual curiosity is the easiest path towards learning. Math is just another way at looking at the beauty of the world and trying to understand it a little better. In an effort to develop skills in patient problem solving, responsibility, and the will to face any challenge, Pre-Calculus focuses on broadening conceptual understanding, applying of knowledge, and refining previous skills while learning new material from four broad categories as identified by the California State Standards: mathematical analysis, linear algebra, trigonometry, and probability and statistics. The year is built upon the following essential concepts, all with their own assignments and opportunities for assessment: 

FIRST SEMESTER

LINEAR ALGEBRA

• • Students perform matrix multiplication.

  • Students multiply vectors by scalars and combine vectors in n-dimensions using arithmetic.

  • Students can find the resulting vector of the cross product of two vectors.

  • Students compute the scalar (dot) product of two vectors in n- dimensional space.

  • Students can find the angle between two vectors using the dot product and know that perpendicular vectors have zero dot product.

MATHEMATICAL ANALYSIS

• • Students can identify graphically and numerically different types of functions including transformed functions.

  • Students find the roots and poles of a rational function.

  • Students can graph a rational function and locate its asymptotes.

  • Parametric equations (including graphing)

  • Limits of a sequence as the independent variable approaches a number or infinity

SECOND SEMESTER

PROBABILITY AND STATS

• • Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.

  • Students know the definition of conditional probability.

  • Students solve for probabilities in finite sample spaces.

  • Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes,such as the probability of the occurrence of five heads in 14 coin tosses.

TRIGONOMETRY

• • Understand angles in both degrees and radians.

  • Convert between degrees and radians.

  • Definition of sine and cosine as y- and x- coordinates of points on the unit circle.

  • Know the identity cos^2 (x) + sin^2 (x) = 1.

    • Students prove that cos^2 (x) + sin^2 (x) = 1 is equivalent to the Pythagorean theorem

    • Students prove and simplify other trigonometric identities using this one

  • Graph functions of the form f(t) = A sin ( Bt + C ) or f(t) = A cos ( Bt + C).

    • Students interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.

  • Know the definitions of the six trigonometric function functions.

  • Graph the tangent and cotangent functions.

  • Know that tangent can be interpreted as = delta(y)/delta(x) = slope

  • Students know the definitions of the inverse trigonometric functions.

  • Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

  • Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs

    • Use those formulas to prove and/ or simplify other trigonometric identities.

  • Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines.

    • Use those formulas to prove and/ or simplify other trigonometric identities.

MATHEMATICAL ANALYSIS

• • Know polar coordinates and vectors

    • Convert between polar and rectangular cords

    • Can interpret it all graphically

  • Students are adept at the arithmetic of complex numbers, and can write them in trigonometric form

  • Students understand that a function of a complex variable can be viewed as a function of two real variables.

Teachers are here to ask the questions that get students to learn and discover, not just assess progress along a timeline. We all shine a light into the dark, the job of a good teacher is to encourage students to find the will to go further, to ask the bigger questions. (Sometimes we all could use a little nudge out the door.) 

You can read about the class's Grading Policies HERE.