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Analysis
Guiding Principle
A student at the proficient level in Analysis 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 Analysis, 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 |
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(2) Vectors and Parametrics · Operations · Graphing · Applications |
7.5.2 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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(3) Polars
and Complex Numbers
· Graphing · Operations · Polar Form · Rectangular Form · Polar Coordinates · Rectangular Coordinates |
7.0.3 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 |
(4) Conics
· Recognition · Definitions · Graphing · Critical Points · Systems of Conics |
4.4.4 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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(5) Series and Sequences · Arithmetic · Geometric · Infinite Series · Convergent and Divergent · Sigma Notation · Math Induction |
7.5.5 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 o Determine whether a series is convergent or divergent o Use sigma notation to describe a series o Perform math induction |
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(6) Limits · Calculate Limits · Continuity of Functions ·
· Limits involving infinity · Formal Definition of a Limit |
7.0.6 Demonstrate a basic understanding of limits when I can o Calculate limits o Determine continuity of a function at a point o
Use the o Calculate limits involving infinity o Calculate limits using the formal definition of a limit |
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(7) Derivatives · Notation · Definition of derivative · Numerical derivative · Rules of derivatives · Velocity and Acceleration · Derivatives of Trig Functions · Chain Rule · Implicit Differentiation |
7.0.7 Demonstrate a basic understanding of derivatives when I can o Use and understand appropriate notation o Calculate a derivative by use of the definition o Calculate a derivative by using the numerical derivative o Apply the rules of derivatives o Calculate rates of change o Calculate the derivatives of trig functions o Apply the chain rule o Calculate derivatives using implicit differentiation |
*Benchmark Key – State Content Standard . State Benchmark . District Benchmark