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High School Integrated Mathematics II

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Suggested Prerequisites

Integrated Mathematics I

Description

Algebra and geometry are everywhere! Engineers use them to build highways and bridges. Artists use them to create perspective in their paintings, and mapmakers help travelers find things using the points located on grids. Throughout this course, you will travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem solving.

Module One: Review of Algebra

-Review algebraic concepts

-Identify functions, solve inverses, and compose functions

-Graph linear equations and inequalities

-Write the equation of a line given different information

-Identify and compare key features of functions


Module Two: Rational, Complex, and Polynomials 

-Rewrite expressions with rational exponents

-Apply properties of rational exponents to simplify expressions

-Solve radical equations

-Simplify imaginary and complex numbers

-Use algebraic properties to simplify complex numbers

-Define and determine the characteristics of polynomials

-Add, subtract, multiply, and divide polynomial expressions


Module Three: Factoring and Quadratics

-Determine greatest common factors and special products

-Factor a polynomial by grouping

-Factor using the sum and difference of cubes

-Graph quadratic functions

-Solve quadratic equations by completing the square

-Solving quadratic equations using different methods

-Solve quadratic equations with complex solutions

-Derive equations for parabolas


Module Four: Systems of Equations and Inequalities 

-Solve systems of equations algebraically

-Solve systems of nonlinear equations using different methods

-Solve systems of nonlinear equations graphically

-Solve systems of nonlinear equations graphically

-Create exponential functions and solve equations

-Create logarithmic functions and solve equations


Module Five: Statistics 

-Determine outcomes of events in sample spaces

-Determine the independence of two events

-Construct and interpret two-way frequency tables

-Calculate and interpret conditional probability

-Prove equations using the Pythagorean Identity

-Simplify expressions using the Pythagorean Identity

Module Six: Proofs of Theorems 

-Write proofs regarding lines and angles

-Write proofs about triangles

-Write proofs about quadrilaterals


Module Seven: Dilations and Similarity 

-Perform and represent dilations

-Prove that two polygons are similar

-Prove that two triangles are similar


Module Eight: Triangle Similarity Proofs 

-Using triangles to prove theorems

-Using distance and slope to classify polygons

-Calculate perimeter and area of polygons using coordinates

-Use coordinates to divide segments into ratios

-Derive formulas for circumference and area of circles

-Derive volume formulas for cylinders, pyramids, and cones

-Use Cavalieri's Principle to compare volumes


Module Nine: Right Triangles and Trigonometry

-Use similar triangles to define trigonometric ratios

-Find trigonometric ratios for right triangles

-Solve real-world problems using trigonometric ratios


Module Ten: Circles

-Identify and describe properties of circles

-Construct inscribed circles of a triangle

-Construct circumscribed circles of a triangle

-Create equations of circles

-Identify key features of circles