Departmental Course Outline for Lv2 Algebra 2
Courses: 241 Lv2 Algebra 2Note: This working document describes our coverage
plans, but may be revised somewhat during the year.
We hope you will find it useful as an overview of the course
and as an approximation of what topics will be covered.
Minimum Topic Coverage
- Function concepts
- Definition as a set
of ordered pairs, as a rule, compared with relations
- Function notation
- Independent and dependent
variable; domain and range
- Graphs of functions
and relations
- Arithmetic
operations on functions
- Inverse of a
function (Option to explore only graphically)
- Inverse functions
- Graphical meaning
in terms of ordered pairs
- Whether an inverse
exists
- Applications and
modeling
- Linear functions
and relations
- Slope-intercept and
point-slope form
- Graphs and use of a
coordinate system
- Geometric
interpretation of slope and slope as a rate
- Solving linear
equations
- Linear regression
- Linear inequalities
in one and two variables
- Absolute value
equations and inequalities - solved by graphing
- Applications and
modeling
- Systems of linear
equations and inequalities
- Solving
algebraically using substitution and by graphing
- Use graphing
calculators to solve arbitrary systems (not necessarily linear)
- (Optional) Linear programming
- Applications and
modeling
- (Optional) Matrix algebra
- Matrix concepts
- Terminology: row,
column, identity, inverse
- Graphing calculator
techniques
- Operations
- Addition, subtraction
and scalar multiplication.
- Multiplication by
graphing calculator
- Multiplication by
hand
- Identity and inverse
matrices
- Finding inverses by
calculator
- Finding inverses
using formulas and/or by hand
- Solve systems of
equations
- Using inverses (to
solve AX = B)
- Selected
applications and modeling, e.g., inventory, cost and profit, area of a
triangle, equation of line, cryptography, transformations of the
coordinate plane (dilation, reflection, rotation).
- Quadratics
- Terminology:
intercept, root, zero, solution.
- Graphing: roots,
y-intercept, vertex, symmetric points, axis of symmetry
- Vertex form
- Solving
- Ways to find the
vertex: vertex form, -b/2a, symmetry, graphing calculator
- The quadratic
formula
- Relationship
between discriminant and roots
- (Optional) Complex numbers
- The imaginary unit i
- Solving quadratics
with complex roots
- Finding a parabola from three points
- Applications and
modeling e.g. motion, gravitational constant
- (Optional) Polynomials
- Vocabulary: Degree,
coefficient, leading coefficient, term, nth degree, term, constant term,
root=solution=zero=x-intercept, complete factoring
- Multiplying,
binomial theorem
- Factoring
- Common factor
- Difference of
squares, perfect squares
- Finding roots
- The
factor/remainder theorem
- When complete
factoring is possible
- Use of graphing
calculator to solve
- Graphs and curve
sketching
- End behavior
- Number of
roots/changes in sign
- Turning points
- Finding a function
from a graph
- Applications and modeling
- Powers, roots and
radicals
- nth roots
- Solving radical
equations by graphing
- Applications and
modeling
- (Optional) Rational equations and functions
- Inverse, joint and
direct variation
- Solving rational
equations by graphing
- Add, subtract,
multiply and divide rational expressions
- Vertical asymptotes
- Applications and modeling
- Exponential
Functions
- Basic laws of
exponents, negative and rational exponents, roots
- Solve exponential
equations using graphing calculator
- Find an exponential
equation from two points
- Graphs of
exponential functions
- Applications and
modeling e.g. growth and decay, bank interest and depreciation, Ph,
Richter scales
- (Optional)
Logarithms
- Counting principles
and probability
- Counting problems
- Factorials,
permutations and combinations, nCr and nPr formulas
- With repeated
values
- Circular
arrangements
- (Optional) Binomial
theorem, Pascal's triangle
- Simple probability:
cards, dice
- Rules of probability
- Conditional
probability
- Independent Events
- Applications and
modeling
- Statistics
- Measures of center
(mean, median, mode)
- Boxplots, Histograms, Stem-and-Leaf
- (Optional) Sequences and series
- Arithmetic and
geometric sequences
- Applications and
modeling
- Right Triangle Trig
/ Geometry Review
- Pythagorean Theorem
- Geometric ratio definition
of SIN, COS, TAN
- Using Trig to solve
right triangles for sides and angles.
- Area and perimeter
problems
- Applications and
modeling
Calculator Skills
- Graph and analyze more advanced functions
- Find zeros of functions using tables and graphs
- (Optional) Perform matrix operations (add, subtract, multiply, find inverses)
- !, nCr, nPr
- sin, cos, tan, and inverses
- Statplots, regression