# HS Math 2 : Module 1

In Module 1, students will work with a new type of function - Quadratic functions. Contextual problems familiarize students with how quadratics grow and how they compare to linear or exponential functions from HS Math 1.

By the end of this module, students should be able to do the following:

• Identify whether a table, equation, or graph is linear, exponential, or quadratic.
• Write an explicit equation for a quadratic relationship.
• Write a recursive equation for a quadratic relationship.
• Evaluate function values for a quadratic function.

Module 1 Resources:

• # Structures of Expressions

In Module 2, students will continue to work with Quadratic functions. They will explore different ways of writing quadratics (Standard Form, Vertex Form, and Factored Form) as well as identify the features of quadratics illuminated by each form.

By the end of this module, students should be able to do the following:

• Transform (move and change) the graph of the original parabola y=x^2 by shifting left, right, up, down, stretching, or flipping.
• Identify the vertex and the axis-of-symmetry for the graph of a parabola.
• Write the Vertex Form (or Graphing Form) for the graph of a quadratic.
• Quickly make an accurate graph by hand of a quadratic function written in Vertex Form (or Graphing Form).
• Take a quadratic in Standard Form and turn it into Vertex Form (or Graphing Form) by Completing the Square.
• Factor a quadratic function given in Standard Form to create the Factored Form.
• Identify the x-intercept(s), y-intercept, and vertex of a quadratic function.

Module 2 Resources:

• # Solving Quadratics & Other Equations

In Module 3, students will develop a number of techniques to solve quadratic equations and other complex equations. They will also further explore ideas of exponents initially learned in 8th grade, but now extend concepts to rational numbers. During this module, students will encounter situations that require a new type of number set, the Complex Numbers, and perform arithmetic with these new numbers.

By the end of this module, students should be able to do the following:

• Use rules of exponents on both integer and rational number exponents.
• User rational exponents to solve radicals and visa-versa.
• Solve a quadratic equation by completing the square and taking a square root.
• Use Complex Numbers to solve quadratic equations.
• Perform arithmetic (add, subtract, multiply, divide) with Complex Numbers.
• Simplify imaginary numbers.

Module 3 Resources:

• # More Functions, More Features

In Module 4, students will begin working with piecewise functions and absolute value functions. Function features from last year's High School Math 1 class are revisited while describing these new functions. Students will work with the piecewise functions and absolute value functions within multiple representations (graphs, equations, tables, and context). Module 4 also introduces the idea of inverse and determining if the inverse is a function.

By the end of this module, students should be able to do the following:

• Write a piecewise equation for the graph of a piecewise function.
• Evaluate piecewise functions (both from graphs and equations).
• Identify features of functions including: domain, range, intervals of increasing, intervals of decreasing, rate of change, etc.
• Graph absolute value functions.
• Write the equation for the graph of an absolute value.
• Solve absolute value equations.
• Find the inverse of a function from various representations (tables, equations, graphs, situations).
• Identify if the inverse is a function or not.

Module 4 Resources:

• # Geometric Figures

In Module 5, students develop their logic and reasoning skills by creating geometric proofs. Students will use flow diagrams and two-column proof formats to prove things about angles, lines, triangles, and quadrilaterals. Students will review and use geometric constructions and triangle congruence properties (AAS, SAS, SSS, ASA) from HS Math 1.

By the end of this module, students should be able to do the following:

• Construct a logical sequence of statements that flow from beginning assumptions to correct justified conclusions.
• Construct proofs in a variety of formats, including flow diagrams and two-column proofs.
• Use the triangle congruence properties (AAS, SAS, SSS, ASA) to formally prove other conjectures.
• Prove theorems about triangles, including the sum of the interior angles of a triangle is 180 degrees.
• Prove theorems about triangles, including base angles of isosceles triangles are congruent.
• Prove theorems about lines and angles, including properties of perpendicular bisectors of a line.
• Know what an altitude of a triangle is.
• Know what a median of a triangle is.
• Know what an angle bisector of a triangle is.
• Know what a perpendicular bisector is.

Module 5 Resources:

• # Similarity & Right Triangle Trigonometry

In Module 6, students use the concepts of similarity and dilation from 8th grade to develop new properties of similar shapes, especially triangles. Most importantly, students use similarity to create the world of Trigonometry and establish the definition of the three main trig ratios - sine, cosine, and tangent. After memorizing the trig ratios, students will also learn to use the inverse of the trig ratios as well as develop some properties/identities of the trig ratios.

By the end of this module, students should be able to do the following:

• Determine if two shapes are similar.
• Determine the scale factor (or zoom factor or ratio) between two similar shapes.
• Find missing side lengths and angles of similar shapes.
• Write a sine equation for a given right triangle (both with numeric values and with symbolic values).
• Write a cosine equation for a given right triangle (both with numeric values and with symbolic values).
• Write a tangent equation for a given right triangle (both with numeric values and with symbolic values).
• Use the inverse sine, inverse cosine, and inverse tangent to find missing angles in right triangles.
• Use trig and trig inverse to solve right triangles.
• Solve application problems (word problems) involving right triangles using trigonometry.

Module 6 Resources:

• # Circles - A Geometric Perspective

In Module 7, students explore properties and shapes found within circles. This includes similarity, chords, secant lines, tangent lines, central angles, inscribed angles, circumscribed angles, inscribed polygons, areas of sectors and much more!

By the end of this module, students should be able to do the following:

• Solve problems involving central anglesinscribed angles, and circumscribed angles in circles.
• Solve problems involving chords, secant lines, and tangent lines within circles.
• Find the area of circles and smaller areas of sectors.
• Find the circumference of circles and smaller arc lengths.
• Define a radian angle measure using circles.

Module 7 Resources:

• # Circles and Other Conics

In Module 8, students...

By the end of this module, students should be able to do the following:

• TBA.

Module 8 Resources:

• # Probability

In Module 9, students examine probabilities in many different situations. They will use Tree Diagrams, Venn Diagrams, and Two-Way Tables to determine probabilites, conditional probabilities, and compound probabilities.

By the end of this module, students should be able to do the following:

• Find a probability from data given in either a Tree Diagram, a Venn Diagram, or a Two-Way Table.
• Find a conditional probability from data given in either a Tree Diagram, a Venn Diagram, or a Two-Way Table.
• Find a compound probability from data given in either a Tree Diagram, a Venn Diagram, or a Two-Way Table.
• Construct a Tree Diagram, a Venn Diagram, or a Two-Way Table for a given situation.

Module 9 Resources: