Pre-Calculus - 2004
Strand
Analysis
Unit: Algebraic Concepts
Mathematics
Binomial
Expansion
Binomial Theorem identify and apply the binomial theorem.
Pre-Calculus
Binomial Expansion: Finding Terms find
an nth term within a binomial expansion.
Exponents
Exponential Equations solve equations involving exponents.
Pre-Calculus
Logarithms/Exponents: Simplifying use
relationships between logarithms and exponents to simplify expressions.
Factoring
Remainder/Factor Theorems apply the remainder and factor
theorems.
Formulas
Fundamental Theorem of Algebra identify and use the Fundamental Theorem of
Algebra.
Logarithms
Logarithms: Simplifying use logarithmic properties to
simplify expressions.
Pre-Calculus
Logarithmic Equations solve
equations involving logarithms.
Quadratic
Equations/Formula
Quadratic Equation: Standard Form state a quadratic equation in standard
form.
Systems
of Equations
Systems of Equations: Determinants solve systems of equations by
applying determinants.
Strand Analysis
Unit: Calculus and Pre-Calculus
Mathematics
Pre-Calculus - 2004
Complex
Numbers
Complex Numbers: Polar Form write complex numbers in polar form.
Pre-Calculus
Complex Numbers in Trigonometric Form show
complex numbers in trigonometric form.
Pre-Calculus
Complex Numbers: DeMoivre's
Theorem determine powers and roots of complex
numbers by using DeMoivre's theorem.
Pre-Calculus
Complex Numbers: Degenerate/Imaginary identify degenerate and imaginary cases.
Conic
Sections
Conic Section: Determining Equation find the equation of a locus given
the description.
Pre-Calculus
Conic Sections: Using Discriminant distinguish
conics by using the discriminant.
Curve
Sketching
Curves: Equations of Tangents/Slopes find the equation of tangents to the
graphs of curves using the slope formula.
Derivatives/Antiderivatives
Derivatives: Derived Function find a derived function given the
definition.
Limits
Limits: Neighborhoods of Domain/Range find a neighborhood of the range for
the neighborhood of a given domain.
Matrices
Matrices: Invert a Square Matrix invert a square matrix.
Parametric
Equations
Parametric Equations: Cartesian Forms identify and apply parametric forms
of functions and convert between their parametric and Cartesian form.
Pre-Calculus
Parametric Equations: Graph sketch the graph of a set of parametric equations.
Vectors
Vectors: Components resolve a given vector into its component vectors.
Pre-Calculus
Vectors: Magnitude/Direction find the magnitude and direction of a given vector.
Pre-Calculus
Vectors: Angle Between find the
measure of an angle between two given vectors.
Pre-Calculus
Vectors: Perpendicular/Parallel recognize
both perpendicular and parallel vectors.
Pre-Calculus
Vectors: Standard Position determine the equivalent vector in standard position to a given
vector.
Pre-Calculus
Vectors: Operations with Scalars perform
basic operations (addition, subtraction, and multiplication) on a vector by a
scalar.
Pre-Calculus
Vectors: Dot Product determine the dot product of two vectors.
Pre-Calculus
Vectors: Real World Problems solve
real world problems using vectors.
Strand Analysis
Unit: Functions
Mathematics
Pre-Calculus - 2004
Circular
Functions
Circular Functions: Rotation list the values of the 6 circular
functions for a specific rotation.
Pre-Calculus
Circular Functions: Properties graph
a circular function and identify its amplitude, period, phase shift, and
vertical shift.
Pre-Calculus
Circular Functions: Graph/Equation identify the equation of any of the 6 circular functions given
its graph.
Pre-Calculus
Circular Functions: Model Real World see circular functions as models for periodic, real world functions.
Exponential
Functions
Exponential Functions: Graph exponential functions.
Pre-Calculus
Exponential Functions: Real World solve real world problems involving exponential functions.
Exponential/Logarithmic
Functions
Exponential/Logarithmic: Domain/Range analyze exponential and logarithmic
functions and compare their domains and ranges.
Pre-Calculus
Exponential/Logarithmic: Relationships
identify a logarithmic as the inverse of an exponential function.
Functions
Trigonometric/Circular: Domain/Range state the domain and range of a given
function.
Functions/Relations
Functions: Intercepts find the intercepts of both
polynomial and rational functions.
Pre-Calculus
Functions: Properties find the
following characteristics of a given function: continuous, bounded, monotonic,
or symmetric with the x-axis or origin.
Graphing
Functions
Graphing:
Asymptotes/Discontinuity Point find both asymptotes and points of discontinuity.
Pre-Calculus
Graphing: Continuous Points/Intervals find
and graph functions which are continuous at a point and/or continuous over an
interval.
Inverses
Inverses find the inverse of a given function and determine whether
that is a function.
Limits
Limits: Using Theorems determine the limits of functions
using limit theorems.
Pre-Calculus
Limits: Determine Graph graph and determine limits, should they exist, of a function
for which x increases without bound.
Pre-Calculus
Limits: Point of Discontinuity determine the limit, should it exist, of a rational function
at a point of discontinuity.
Logarithmic
Functions
Logarithmic Functions: Real World solve real world problems involving
logarithmic functions.
Pre-Calculus
Logarithmic Functions: Base 10 and e evaluate
a logarithmic function with base 10 and e and represent it on a graph.
Operations
Operations: Algebra/Compositions perform algebra and compositions on
two given functions.
Polynomial
Functions
Polynomial Functions: Evaluate/Graph graph and analyze the polynomial
functions such as linear and quadratic.
Pre-Calculus
Polynomial Functions: Roots find
both real and complex roots of polynomial functions.
Pre-Calculus
Polynomial Functions: Application solve real world problems using polynomial functions.
Problem
Solving
Problem Solving: Functions/Inverses use the inverse of a trigonometric
or circular function to solve a problem.
Trigonometric
Functions
Trigonometric Functions/Polar/Complex see the relationship between
trigonometric functions, polar coordinates, and complex numbers.
Trigonometric/Circular
Functions
Trigonometric/Circular Functions: Graph and analyze the 6 circular and
trigonometric functions.
Pre-Calculus
Trigonometric/Circular Functions find
similarities and differences between trigonometric and circular functions.
Pre-Calculus
Trigonometric/Circular Functions:
Inverse analyze and graph inverse of both
circular and trigonometric functions.
Strand Analysis
Unit: Geometry
Mathematics
Pre-Calculus - 2004
Proofs
Proofs: Inequalities/Induction prove inequality formulas through the use
of mathematical induction.
Symmetry
Symmetry: Axis of Symmetry analyze graphs and discuss an axis of
symmetry.
Translations
Translation/Rotation: New Equations find new equations that result from
a translation or rotation of axes.
Triangles
Triangles: Oblique solve a problem involving an oblique triangle.
Pre-Calculus
Triangles: Estimate with Oblique/Right
estimate the solution to a problem which involves oblique or right
triangles.
Strand Analysis
Unit: Measurement
Mathematics
Pre-Calculus - 2004
Area of a
Triangle
Area of a Triangle: Oblique compute the area of an oblique
triangle.
Strand Analysis
Unit: Number Theory
Mathematics
Pre-Calculus - 2004
Exponential
Notation
Exponential Notation: Simplify expressions, find the missing term
in a simplified expression, simplify terms with zero and integer exponents, and
evaluate a sample student's work for errors.
Strand Analysis
Unit: Numeration
Mathematics
Pre-Calculus - 2004
Sequences/Series
Series: Sigma Notation show a series in correct sigma notation.
Pre-Calculus
Series: Arithmetic/Finding Sums determine
the sum of an arithmetic series.
Pre-Calculus
Sequence: Finding Terms find
any term in a sequence given an expression or rule for the nth term.
Pre-Calculus
Sequence: Finding Formula determine a formula for the nth term given any sequence.
Pre-Calculus
Series: Finite/Infinite Geometric determine
the sum of a finite and infinite geometric series should it exist.
Pre-Calculus
Sequence/Series: Convergent/Divergent identify
convergent and divergent sequences and series and their limits should they
exist.
Pre-Calculus
Sequence: Increasing/Decreasing find
whether a given sequence is increasing or decreasing.
Pre-Calculus
Sequence: Least/Greatest Upper Bound determine the least and greatest upper bounds of a sequence
should they exist.
Pre-Calculus
Series: Proving with Induction prove
series formulas through the use of mathematical induction.
Pre-Calculus
Series: Infinite/Natural Log express
as an infinite series the number e and the expression e to the power x.
Strand Analysis
Unit: Real Numbers and the Coordinate Plane
Mathematics
Pre-Calculus - 2004
Graphing
Graphing: 2nd Degree
Equations/Identify recognize
the graph of a second degree equation.
Linear
Equations
Equations of the Line find the slope or coordinate points,
solve equations of the line, identify the equation of a line for a
corresponding graph, and write an equation of a line when given coordinate
points, the slope, and y-intercept.
Strand Analysis
Unit: Trigonometry
Mathematics
Pre-Calculus - 2004
Polar
Forms/Equations/Graphs
Polar Form: Transfer from Cartesian transform points from Cartesian to
polar coordinates.
Pre-Calculus
Polar Form: Transfer to Cartesian transform
points from polar to Cartesian coordinates.
Pre-Calculus
Polar Coordinates: Graph graph different points in the polar coordinate system.
Pre-Calculus
Polar Graphs: Symmetry/Shifts identify
shifts in polar graphs when working with sine and cosine and discuss symmetry
in polar graphs.
Pre-Calculus
Polar Equations: Identify identify different polar equations such as conics, spirals,
roses, cardioids, and limacons.
Pre-Calculus
Polar Equations: Graph represent polar equations in graphical form.
Radians/Angles
Angle Measure: Converting convert between angle and radian
measure.
Triangles
Triangles: Solving Right find the measure of each unknown
side (to the nearest tenth or hundredth) or angle (to the nearest degree),
solve real-world trigonometry problems, and include the angle of depression or
elevation in calculations.
Pre-Calculus
Triangles: SSA Case discern whether 0, 1, or 2 triangles exist, and what they are
in an SSA (side, side, angle) case.
Trigonometric
Equations
Trig. Equations: Solutions determine possible solutions for
trigonometric equations.
Pre-Calculus Trig.
Equations: Domain determine exact solutions for a trigonometric function given a
particular domain.
Trigonometric
Identities
Trig. Identities identify and use the trigonometric identities.
Trigonometric
Ratios
Trig. Ratios: Angles list the values of the 6 trigonometric ratios for the
acute angles in a specific right triangle.
Pre-Calculus Trig. Ratios:
Problem Solving use the
trigonometric ratios of angle measure to solve problems.
Pre-Calculus Trig. Ratios:
Law of Sines/Cosines use the Law of Sines
and Cosines to solve problems.