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(Math Program of Studies 10-12 (Number (20-3 (Analyze puzzles and games…
Math Program of Studies 10-12
Algebra
10C
Factor and multiply polynomials
#
10-3
Solve problems related to the formulas for perimeter, area, Pythag Thrm, Trig ratios, incomes
20-3
Solve problems related to volume & capacity, surface area, slope and R.O.C., simple interest, finance charges
Apply proportional reasoning & unit analysis
Slope
20-1
Solve and perform operations on rational expressions & equations
Determine equivalence in radical expressions
Solve and perform operations on radical expressions and equations
30-3
Demonstrate an understanding of linear relations: recognize patterns &trends, graphing, tables of values, writing equations, interpolating and extrapolating, solving problems.
Relations and Functions
10C
Slope
Linear Relations (& graphs)
Relationships vs. Functions
Linear Functions/Function Notation
Relationships among data, graphs, & situations
Systems of Linear Equations
20-1
Systems of Linear-Quadratic & Quadratic-Quadratic Equations (2 Variables)
Linear-Quadratic Inequalities (2 Variables)
Quadratic Functions & Equations
Quadratic Inequalities (1 Variable)
Absolute Value Functions & Graphs
Arithmetic Sequences
Factor Polynomial Expressions
Geometric Sequences
Reciprocal Functions (Linear & Quadratic) & Graphs
20-2
Understand Quadratic Functions
Solve quadratic equations
30-1
Reflections
Inverses of Relations
Horizontal/Vertical Translations & Stretches and their Graphs
Logarithms & Laws
Compositions & Operations of Functions
Exponential & Logarithmic Functions and Equations
Factoring Polynomials (deg < or = 5) and Graphs
Radical Functions and Graphs
Rational Functions and Graphs
30-2
Operations on rational expressions
Determine equivalent forms of rational expressions
Solve rational equations
Logarithms and Laws
Solve exponential equations
Exponential and logarithmic functions
Polynomial functions to solve problems
Sinusoidal functions to solve problems
Permutations, Combinations, & Binomial Theorem
30-1:
Permutations
Combinations
Fundamental Counting Principle (number of choices)
Binomial Theorem (expand powers)
Number
20-1
Absolute Value of Real Numbers
#
10C
Powers: integrals and rationals
Factoring Whole Numbers
Irrational numbers
20-3
Analyze puzzles and games that involve numerical reasoning, using problem solving strategies.
Solve Budget Problems
Compound interest
Demonstrate an understanding of financial institution services
Demonstrate an understanding of Credit options
10-3
Solve problems that involve unit pricing currency exchange using proportional reasoning
Wages, salary, contracts, commissions,piecework to calculate gross & net
pay
20-2
Analyze and prove conjectures, using inductive and deductive reasoning to solve problems
Analyze puzzles and games that involve spatial reasoning
Solve problems that involve operations on radicals and radical expressions w/ numerical and variable radicands
Solve radical equations (limited to SqRt or Cube root)
30-3
Solve problems involving the acquisition of a vehicle
Analyze puzzles and games that involve logical reasoning
Critique the viability of small business options
Probability
30-2:
2 Events
Fundamental Counting Principle
Mutually Exclusive & Non-mutually Exclusive
Permutations
Odds & Probability Statements
Combinations
30-3:
Fractions, Decimals, Percents
Odds vs. Probability
Theoretical vs. Experimental
Statistics
20-3:
Create/Interpret Graphs (Bar, Line, Circle, Histogram)
30-3:
Central Tendency (mean, median, mode)
Percentiles
Trigonometry
20-1
Understand angles in standard position
Solve Problems using Trig Ratios
Cosine Law, Sine Law Problems (Include Ambiguous Case)
30-1
Understanding Angles in Standard Position (Degrees and Radians)
Develop Equation of Unit Circle
Solve Problems using Trig Ratios
Graph and analyze Trig Functions
Solve First, Second and Third Degree Equations
Prove Trig Identities
Geometry
20-2
Derive Proofs Involving Angle Properties
Solve Problems involving properties of angles
Solve Problems using Sine law / Cosine Law (Excluding Ambiguous Case)
10-3
Analyze Puzzles and Games using Spatial Reasoning
Pythagorean Theorem
Understand Similarity of Regular and Irregular Polygons
Use Primary Trig Ratios
Angles involving Perpendicular, Parallel, Transverse Lines
Problems involving Acute, Obtuse, Straight and Reflex Angles
20-3
Solve Problems Involving 2 and 3 Right Angle Triangles
Solve Problems involving scale
Model and Draw 3D objects and views
Draw and Describe Exploded Views, Component Parts
30-3
Solve Problems using Sine and Cosine Laws (Excluding Ambiguous Case)
Solve Problems involving Triangles, Quadrilaterals and Regular Polygons
Demonstrate Transformations on 2D or 3D objects
Measurement
10C
Estimation and Measurement Strategies
Surface Area and Volume
Conversions between Imperial and SI Units (and Proportional Reasoning)
Trigonometric Ratios/Right Triangles (
LINK HERE RELATION TO TRIG)
20-2
Rates
Scale diagrams/Proportional Reasoning
Relationships between scale factors, areas, surface areas, volumes
10-3
Understand SI and Imperial Systems (conversions between them)
Linear measurements (including fractions and decimals
Area Problems
20-3
SI and Imperial problems: Surface Area, Volume, Capacity
30-3
Limitations of measurement (precision, accuracy, uncertainty, tolerance)
Logical Reasoning
30-2
Analyze puzzles and games and use problem solving strategies
Set Theory
Mathematics Research Project
20-2
Historical event of mathematics
30-2
Current event of mathematics
Factoring polynomials progressively builds upon the skill of factoring whole numbers
Understanding the concept of absolute value helps build toward their graphs