High School Integrated Mathematics III

Module One: Basics of Geometry

-Define points, lines, and planes

-Perform geometric constructions using a compass

-Perform geometric constructions using technology

-Introduction to different types of proofs

Module Two: Transformations and Congruence 

-Perform and represent translations

-Perform and represent reflections

-Perform and represent rotations

-Prove two figures are congruent

Module Three: Coordinate Geometry

-Classify polygons using coordinate geometry

-Solve problems using slope

-Use coordinates to find perimeter and area of polygons

-Use coordinates to divide segments into ratios

Module Four: Volume and Figures 

-Derive formulas for circumference and area of circles

-Derive volume formulas for cylinders, pyramids, and cones

-Use Cavalieri's Principle to compare volumes

-Solve real-world applications involving density

-Identify shapes of cross-sections of 3-D objects

-Identify 3-D objects generated by 2-D objects

-Find the surface area of 3-D figures

Module Five: Trigonometry

-Identify and describe properties of circles

-Apply trigonometric functions using the unit circle

-Graph trigonometric functions with periodic

-Analyze transformations

-Fit functions to data to solve problems

-Prove equations using the Pythagorean Identity

-Simplify expressions using the Pythagorean Identity

Module Six: Dividing and Solving Polynomials 

-Dividing polynomials using long division

-Dividing polynomials using synthetic division

-Determining key features of polynomials using Theorems

-Determine zeros using Rational Root Theorem and Descartes' Rule of Signs

-Use zeros and end behavior to graph polynomial functions

-Solve polynomial equations

-Graph polynomial functions to determine key features and solutions

-Prove polynomial identities

Module Seven: Rational Expressions 

-Simplify rational expressions

-Multiply and divide rational expressions

-Add and subtract rational expressions

-Simplify complex fractions

-Identify discontinuities of rational expressions

-Identify asymptotes of rational functions

-Solve rational equations and justify solutions

-Apply rational equations to real-world scenarios

Module Eight: Exponential and Logarithmic Functions 

-Create exponential equations to model real-world situations

-Create logarithmic functions and solve equations

-Use properties of logarithms to solve equations

-Solve exponential equations with unequal bases

-Graph exponential functions

-Graph logarithmic functions

-Determine effects of combining different types of functions

Module Nine: Sequences and Series

-Identify and use arithmetic sequences to solve problems

-Identify and use arithmetic series to solve problems

-Identify and use geometric sequences to solve problems

-Identify and use geometric series to solve problems

-Use sigma notation to evaluate a series

-Identify and find infinite, convergent, and divergent series

-Graph sequences and series

Module Ten: Statistics

-Use measures of center and spread to fit normal distribution

-Estimate population percentages

-Population inferences using statistics, models, surveys, and experiments

-Use surveys to estimate population parameters

-Determine margin of error and evaluate data reports

-Use experiments to compare treatments, assess significance, evaluate data reports