Pre-Calculus B

Scope & Sequence

Schenectady High School Department of Mathematics

J. Brendese

I.      Sets, Numbers, & Systems 

           A.  The Language of Mathematics 

           B.  The Number Line   P.1                                                                            

C.     Linear Equations & Inequalities  P.3  

D.     The Cartesian Coordinate System    P.2                                            

E.      Lines in the Plane   P.4                                                                                 

F.      Solving Equations & Inequalities Graphically, Numerically, & Algebraically    P.5/6

 II.    Functions & Graphs 

            A.  Functions   1.2a

            B.  Functions:  Continuity, Boundedness, Extrema   1.2b

            C.  Functions & Limits   10.3

            D.  Analyzing Functions   1.2c

            E.  Basic Functions   1.3

            F.  Composing Functions   1.4a

            G.  Parametric Functions   1.4b

            H.  Graphical Transformations   1.5

III.    Exponential, Logistic, & Logarithmic Functions 

A.   Properties of Exponents

B.   Exponential & Logistic Functions  

C.   Logarithmic Functions and Graphs  

D.   Properties of Logarithmic Functions  

E.  Logarithmic Equations & Modeling  

IV.    Polynomial & Rational Functions 

             A.  Long Division   2.4a

             B.  Synthetic Division   2.4b

             C.  Complex Numbers   2.5

             D.  The Fundamental Theorem of Algebra   2.6

V.    Trigonometric Functions 

            A.  Angles & Their Measures   4.1

            B.  Right Triangle Trigonometry   4.2

C.  The Circular Functions   4.3

VI.   Analytic Trigonometry 

             A.  Fundamental Identities   5.1

             B.   Proving Trigonometric Identities   5.2

             C.   Sum & Difference Identities   5.3

             D.  Multiple Angle Identities   5.4

VII.   An Introduction to Calculus 

A.  The Tangent Problem   10.1

B.  Basic Rules of Differentiation

            C.  More Rules of Differentiation

            D.  The Chain Rule

VIII.  Systems & Matrices 

A.     Solving Systems of Equations   7.1

B.      Matrix Algebra   7.2

C.     Multivariate Linear Systems & Row Operations   7.3