### Utah Mathematics Core

#### Secondary Mathematics II

Students in Secondary Mathematics II will focus on quadratic expressions, equations, and functions, extend the set of rational numbers to the set of complex numbers, link probability and data through conditional probability and counting methods, study similarity and right triangle trigonometry, and study circles with their quadratic algebraic representations.

Honors students will also represent complex numbers and their operations on the complex plane, solve systems of equations, prove and apply trigonometric identities, express conic sections algebraically, and solve problems using volume measurements.

All Secondary II Core Curriculum should be included in the Secondary II Honors Curriculum.

Secondary II Possible Sequence

#### Curriculum Guide

#### Unit 1 Extending the Number System

Extend the Properties of Exponents to Rational Exponents

Use Properties of Rational and Irrational Numbers

Perform Arithmetic Operations with Complex Numbers

Perform Arithmetic Operations on Polynomials

#### Unit 2 Quadratic Functions and Modeling

Interpret Functions that Arise in Applications in Terms of a Context

Analyze Functions Using Different Representations

Build a Function that Models a Relationship Between Two Quantities

Build New Functions From Existing Functions

Construct and Compare Linear, Quadratic, and Exponential Models and Solve Problems

#### Unit 3 Expressions and Equations

Interpret the Structure of Expressions

Write Expressions in Equivalent Forms to Solve Problems

Create Equations that Describe Numbers or Relationships

Solve Equations and Inequalities in One Variable

Use Complex Numbers in Polynomial Identities and Equations

#### Unit 4 Applications of Probability

Understand Independence and Conditional Probability and Use Them to Interpret Data

Use Probability to Evaluate Outcomes of Decisions

#### Unit 5 Similarity, Right Triangle Trigonometry and Proof

Understand Similarity in Terms of Similarity Transformations

Prove Theorems Involving Similarity

Use Coordinates to Prove Simple Geometric Theorems Algebraically

Define Trigonometric Ratios and Solve Problems Involving Right Triangles

Prove and Apply Trigonometric Identities

#### Unit 6 Circles With and Without Coordinates

Understand and Apply Theorems About Circles

Find Arc Lengths and Areas of Sectors of Circles

Translate Between the Geometric Description and the Equation for a Conic Section

Use Coordinates to Prove Simple Geometric Theorems Algebraically

Explain Volume Formulas and Use Them to Solve Problems

#### Honors

Perform Arithmetic Operations with Complex Numbers

Prove and Apply Trigonometric Identities

Translate Between the Geometric Description and the Equation for a Conic Section

Explain Volume Formulas and Use Them to Solve Problems

#### Resources