Algebra III
Guiding Principle
A student at the proficient level in Algebra III will be able to demonstrate understanding of
high school mathematics by solving problems, reasoning, communicating, representing,
making connections and solving word problems based on the following indicators:
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Benchmark/Topics |
As a result of studying Algebra III, I will be able to: |
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(1) Matrices · Basic Operations · Determinants · Inverse (2x2) · Solving · Linear Programming |
3.4.1 Demonstrate an understanding of matrices when I can o Perform basic matrix operations o Calculate the determinant of a 2x2 and 3x3 matrix o Determine the inverse of a 2x2 matrix o Solve a system of equations using matrix operations o Solve linear programming problems |
(2) Families of Functions
· Domain and Range · Composition of Functions · Symmetries · Graphs · Inverses · Solve |
7.2.2 Show understanding of families of functions when I can o State the domain and range of a function o Compose two or more functions o Prove symmetry of a function about the x-axis, y-axis, origin, and y = x o Graph functions using the properties of each family of functions (e. g. end behavior, roots, symmetries) o Derive a functions inverse o Solve equations from each of the families of functions covered in this course |
(3) Polynomial and Rational Functions
· Remainder Theorem · Factor Theorem · Rational Root Theorem · Asymptotes and Holes · End Behavior · Inequalities |
7.1.3 Show understanding of polynomial and rational functions when I can o Determine a root using the remainder theorem o Determine a remainder of a polynomial function using the factor theorem o Determine the rational roots of a polynomial function using the rational root theorem o Determine vertical, horizontal and slant asymptotes and holes in the graphs of rational functions o
Determine the end behavior of a polynomial
function and write its behavior using correct notation (e. g. o Solve polynomial and rational function inequalities |
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(4)
Trigonometry
· Identities · Graphing Inverse and Reciprocal Functions · Areas of Triangles · Solving |
7.1.4 Show understanding of trigonometry when I can o Use identities to simplify trigonometric functions o Prove trigonometric identities o Graph the inverse and reciprocal trigonometric functions o Find the area of triangles using Heron’s formulas and using two sides of the triangle and an included angle o Solve trigonometric equations |
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(5) Vectors and Parametrics · Operations · Graphing · Applications |
7.5.5 Demonstrate knowledge of vectors and parametrics when I can o Perform vector operations o Show graphical representations of vectors and parametric equations o Solve problems using vectors and parametric equations
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(6) Polars
and Complex Numbers
· Graphing · Operations · Polar Form · Rectangular Form · Polar Coordinates · Rectangular Coordinates |
7.0.6 Demonstrate understanding of polars and complex numbers when I can o Graph on a polar coordinate system o Perform operations using complex numbers o Convert between polar and rectangular forms o Convert between polar and rectangular coordinates |
(7) Conics
· Recognition · Definitions · Graphing · Critical Points · Systems of Conics |
4.4.7 Demonstrate my understanding of conic sections when I can o Recognize a conic section from its equation o Define each conic section in terms of a locus of points o Graph each conic section and label the distinguishing features of each o Determine the vertex or vertices, focus or foci, equation of the directrix, equations of asymptotes, major and minor axes o Find the points of intersection of a system of two or more conics |
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(8) Series and Sequences · Arithmetic · Geometric |
7.5.8 Demonstrate understanding of series and sequences when I can o Recognize the difference between arithmetic and geometric sequences o Apply the rules of arithmetic and geometric sequences and series in the appropriate situations |
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(9) Introduction to Calculus · Limits · Derivatives · Tangents ·
Critical Points |
7.0.9 Demonstrate a basic understanding of the underpinnings of Calculus when I can o Show the limit of a function as x approaches a given value o Find basic derivatives of polynomial functions o Find the equation of a line tangent to a curve at a given point o Find the relative or absolute maximum(s) or minimum(s) and points of inflection of a curve using derivatives |
*Benchmark Key – State Content Standard . State Benchmark . District Benchmark