MTH248: Integrated Mathematics II

This list is representative of the materials provided or used in this course. Keep in mind that the actual materials used may vary, depending on the school in which you are enrolled, and whether you are taking the course as Independent Study.

For a complete list of the materials to be used in this course by your enrolled student, please visit MyInfo. All lists are subject to change at any time.

Scope & Sequence : Scope & Sequence documents describe what is covered in a course (the scope) and also the order in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K12 Scope & Sequence documents for each course include:

Course Overview

Integrated Mathematics II, a second-year high school math course,  focuses on extending the number system to include irrational and complex numbers, as well as computation with quadratic polynomials. The course continues with quadratic expressions, equations, and functions, including making comparisons to their linear and exponential counterparts, covered in MTH147: Integrated Mathematics I. The course also introduces conditional probability as a way to make better decisions when given limited information. Geometry topics include similarity, right triangle trigonometry, and volume. Students use the tools of analytic geometry, synthesizing algebra and geometry concepts, to describe circles and parabolas in the coordinate plane.

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Course Length

Two Semesters

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Prerequisites

MTH147: Integrated Mathematics I (or equivalent)

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Course Outline

SEMESTER 1

Semester A, Unit 1: Extending the Number System

In this unit, students take an in-depth look at radicals. In addition to simplifying radical expressions, students discover the relationship between radical expressions, rational exponents, and complex numbers.

  • Semester 1 Introduction
  • Foundations for Unit 1
  • Rational Numbers
  • Square Roots
  • Irrational Numbers
  • Simplifying Radical Expressions
  • Fractional Exponents and Higher Roots
  • Applying Roots and Powers
  • Imaginary Numbers
  • Real and Complex Numbers
  • Operations with Complex Numbers
  • Core Focus: Number Systems and Closure
  • Unit Review
  • Unit Test

Semester A, Unit 2: Quadratic Polynomials

Like real numbers, polynomials can be added, subtracted, multiplied, and divided. In this unit, students learn how to perform operations with polynomials.

  • Foundations for Unit 2
  • Overview of Polynomials
  • Adding and Subtracting Polynomials
  • Multiplying Monomials
  • Multiplying Polynomials by Monomials
  • Multiplying Polynomials
  • The FOIL Method
  • Discuss: Polynomials and Closure
  • Dividing Monomials
  • Common Factors of Monomials
  • Dividing Polynomials by Monomials
  • Core Focus: Polynomials and Algebra Tiles
  • Unit Review
  • Unit Test

Semester A, Unit 3: Factoring and Solving Quadratic Equations

In this unit, students expand on their knowledge of polynomials to solving equations. Through factoring, graphing, and other techniques, students learn how to manipulate polynomial equations to find solutions.

  • Foundations for Unit 3
  • Common Factors of Polynomials
  • Factoring Perfect Squares
  • Factoring Differences of Squares
  • Factoring Quadratic Trinomials
  • Finding Roots of a Polynomial
  • Solving Perfect Square Equations
  • Completing the Square
  • Core Focus: Formulas with Quadratics
  • Unit Review
  • Unit Test

Semester A, Unit 4: Working with Functions

In this unit, students learn how to identify functional relationship that they see in their daily lives. Students learn multiple ways to represent functions and how to use function notation. This chapter also focuses on special functions such as absolute value functions, piecewise functions, step functions, and function inverses.

  • Foundations for Unit 4
  • Function Basics
  • Function Equations
  • Absolute Value Functions
  • Piecewise Functions
  • Step Functions
  • Discuss: Domain and Range
  • Function Operations, Part 1
  • Function Operations, Part 2
  • Function Inverses
  • Core Focus: Multiple Representations
  • Unit Review
  • Unit Test

Semester A, Unit 5: Quadratic Functions and Models

In this unit, students learn how to graph, analyze, and apply quadratic functions. Students also learn how to solve systems of equations that include one linear and one quadratic equation.

  • Foundations for Unit 5
  • Graphing Quadratic Functions
  • Properties of Quadratic Functions
  • Applications: Quadratic Functions
  • Linear/Quadratic Systems
  • Core Focus: Properties of Quadratic Functions
  • Unit Review
  • Unit Test

Semester A, Unit 6: Conditional Probability

In this unit, students explore conditional probability by first developing a solid understanding of the basics of counting and simple probability. Students then extend these concepts to interpreting two-way tables and solving real-world problems, including independent events and conditional probability.

  • Foundations for Unit 6
  • Counting Principles
  • Basic Probability
  • Probability With and Without Replacement
  • Independent and Dependent Events
  • Discuss: Probability
  • Interpret Two-Way Tables
  • Conditional Probability
  • Core Focus: Conditional Probability
  • Unit Review
  • Unit Test

Semester A, Unit 7: Semester Review and Test

  • Semester Review
  • Semester Test

SEMESTER 2

Semester B, Unit 1: Geometric Reasoning

In this unit, students prove and use many geometric theorems. These theorems are about parallel lines, quadrilaterals, and triangles. The main goal of this chapter is to learn more about geometric reasoning.

  • Semester 2 Introduction
  • Foundations for Unit 1
  • Reasoning Part 1
  • Reasoning Part 2
  • Quadrilaterals and Their Properties 1
  • Quadrilaterals and Their Properties 2
  • Parallel Lines and Transversals 1
  • Parallel Lines and Transversals 2
  • Converses of Parallel Line Properties 1
  • Converses of Parallel Line Properties 2
  • The Triangle Sum Theorem 1
  • The Triangle Sum Theorem 2
  • Core Focus: Styles of Proofs
  • Unit Review
  • Unit Test

Semester B, Unit 2: Similarity

Similarity and scale are important geometric ideas. In this chapter, students use them to solve problems involving similar shapes. Students also learn and use some interesting theorems about lengths and relationships within a shape that has similar parts.

  • Dilations and Scale Factors 1
  • Dilations and Scale Factors 2
  • Similar Polygons 1
  • Similar Polygons 2
  • Discuss: Similarity
  • Triangle Similarity 1
  • Triangle Similarity 2
  • Side-Splitting Theorem 1
  • Side-Splitting Theorem 2
  • Core Focus: Similarity
  • Unit Review
  • Unit Test

Semester B, Unit 3: Area and Volume

In this unit, students learn how to find the circumference and area of circles. They also learn and apply the volume formulas for pyramids, cylinders, cones, and spheres.

  • Foundations for Unit 3
  • Circumferences and Areas of Circles 1
  • Circumferences and Areas of Circles 2
  • Volumes of Pyramids
  • Volumes of Cylinders
  • Volumes of Cones
  • Volumes of Spheres
  • Volume Ratios
  • Core Focus: Reasoning About Area and Volume
  • Unit Review
  • Unit Test

Semester B, Unit 4: Circles

When you combine angles, triangles, or segments with circles, you get some interesting results. In this unit, students learn about inscribed and circumscribed triangles as well as how to find the lengths of chords and arcs. Students also learn what similarity has to do with circles and what radian measure is.

  • Foundations for Unit 4
  • Relationships Between Triangles and Circles 1
  • Relationships Between Triangles and Circles 2
  • Chords and Arcs 1
  • Chords and Arcs 2
  • Tangents to Circles 1
  • Tangents to Circles 2
  • Inscribed Angles and Arcs 1
  • Inscribed Angles and Arcs 2
  • Similarity in Circles
  • Core Focus: Radian Measure and Sector Areas
  • Unit Review
  • Unit Test

Semester B, Unit 5: Right Triangle Trigonometry

The relationships between sides and angles in a right triangle are at the heart of trigonometry. In this unit, students learn the sine, cosine, and tangent trigonometric ratios and use them to solve various problems with right triangles.

  • Foundations for Unit 5
  • Tangents 1
  • Tangents 2
  • Sines and Cosines 1
  • Sines and Cosines 2
  • Discuss: Applications of Trigonometry
  • Special Right Triangles 1
  • Special Right Triangles 2
  • Core Focus: Trigonometric Identities
  • Unit Review
  • Unit Test

Semester B, Unit 6: Conic Sections

In this unit, students learn how to write the equation of a circle or parabola when given its graph, and how to graph a circle or parabola when given its equation. Students also learn how to use the distance formula to derive the equation of a circle or parabola.

  • Foundations for Unit 6
  • Introduction to Conic Sections
  • Circles
  • Parabolas
  • Core Focus: Deriving Conic Equations
  • Unit Review
  • Unit Test

Semester B, Unit 7: Project

  • Project Day 1
  • Project Day 2
  • Project Day 3
  • Project Day 4
  • Project Day 5

Semester B, Unit 8: Semester Review and Test

  • Semester Review
  • Semester Test
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Lesson Scheduling

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K12 Scope & Sequence documents for each course include:

  • Course Overview (as seen above)
  • Course Outline
  • Lesson Time and Scheduling