# Integrated Math II Online Credit Recovery

Integrated Mathematics II, a second-year high school math course, introduces students to polynomials, including the factoring of polynomials, before moving onto quadratics equations and quadratic functions. Students expand on their knowledge of sequences in learning about series. The course also covers probability, including conditional probability. There are many geometry topics in the course, including transversals, quadrilaterals, similarity, volume, and circles. Students solve problems using right triangle trigonometry and special right triangles, and use the tools of analytic geometry to describe circles and parabolas in the coordinate plane.

Diagnostic tests assess students’ current knowledge and generate individualized study plans, so students can focus on topics that need review.

Semester 1

Unit 1: Polynomials

As with real numbers, operations can be performed on polynomials. In this unit, students learn how to perform operations on polynomials and explore the closure of polynomials before learning several methods for factoring polynomials. Lastly, students use factoring to find roots of a polynomial equation.

• Semester 1 Introduction

• Foundations for Unit 1

• Overview of Polynomials

• Add and Subtract Polynomials

• Multiply with Monomials

• Multiply Polynomials 1

• Multiply Polynomials 2

• Common Factors of Polynomials

• Factor Perfect Squares

• Factor Differences of Squares

• Factor Quadratic Trinomials

• Find Roots of a Polynomial

Unit 2: Quadratic Equations

In this unit, students learn several methods for solving a quadratic equation and determine which method(s) are best for a given equation. Students then use those skills to transform formulas with quadratics and to solve real-world problems.

• Foundations for Unit 2

• Solve Perfect Square Equations

• Complete the Square

• The Quadratic Formula

• The Discriminant

• Solve Quadratic Equations

• Formulas with Quadratics

• Applications: Quadratic Equations

Unit 3: Quadratic Functions

In this unit, students learn how to graph and transform graphs of quadratic functions. They model situations with quadratic functions and interpret graphs of quadratic functions. Students also learn how to determine the average rate of change for a given interval on a quadratic function and how to solve systems of equations that include one linear and one quadratic equation.

• Foundations for Unit 3

• Standard Form of a Quadratic Function

• Other Forms of a Quadratic Function

• Convert Between Forms

• Transform Quadratic Functions

• Quadratic Rates of Change

• Linear and Quadratic Systems

• Model with Quadratic Functions

• Interpret Quadratic Function Graphs

Unit 4: Sequences and Series

In this unit, students review arithmetic and geometric sequences before learning about series. Students learn sigma notation for series and solve mathematical and real-world problems involving both arithmetic and geometric series.

• Foundations for Unit 4

• Arithmetic Sequences

• Geometric Sequences

• Series and Sigma Notation

• Arithmetic Series and Applications

• Geometric Series and Applications

Unit 5: Counting and Probability

This unit begins with the basics of sample space and outcomes. Students determine probabilities of independent and dependent events and learn about conditional probability. They also determine probabilities of mutually exclusive and non-mutually exclusive events.

• Foundations for Unit 5

• Sample Space and Events

• Probability of Events 1

• Probability of Events 2

• Conditional Probability and Testing for Independence

• The Addition Rule

Unit 6: Transversals and Triangles

Several special angle pairs occur when two lines are intersected by a transversal. Students solve problems with these angle pairs and use special angle pairs to determine if two lines are parallel. Students then prove and use the triangle sum theorem and solve problems involving special segments in triangles.

• Foundations for Unit 6

• 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

• Isosceles and Equilateral Triangles

• Bisectors of a Triangle: Circumcenter

• Bisectors of a Triangle: Incenter

• Medians of a Triangle: Centroid and Orthocenter

• Triangle Midsegment Theorem

Unit 7: Quadrilaterals

This unit is about quadrilaterals. The focus is on parallelograms and their properties. Students use their algebra skills to solve problems involving the side and angle relationships in parallelograms, rectangles, rhombi, and squares. Students also learn about the properties of trapezoids and kites.

• Foundations for Unit 7

• Parallelograms 1

• Parallelograms 2

• Parallelograms 3

• Quadrilaterals and Their Properties

Semester 2

Unit 1: Similarity

Similarity and scale are important geometric ideas. In this unit, students expand on their knowledge of dilations and scale factor, and learn to partition directed line segments. After learning about similar polygons, students discover the ratios for the perimeters and areas of similar figures.

• Course Checkpoints

• Foundations

• Dilations

• Dilations and Scale Factors

• Directed Line Segments

• Similar Polygons 1

• Similar Polygons 2

• Extended Problems: Perimeter and Area Ratios

Unit 2: Triangle Similarity

This unit focuses on similar triangles. Students learn how to prove triangles similar, and then prove and use the triangle proportionality and triangle angle bisector theorems. Students then use similarity to prove the Pythagorean theorem.

• Foundations

• Triangle Similarity 1

• Triangle Similarity 2

• Triangle Proportionality and Triangle Angle Bisector Theorems

• More Triangle Proportionality Theorem

• More Triangle Angle Bisector Theorem

• Similarity and the Pythagorean Theorem

Unit 3: Area and Volume

In this unit, students find the circumference and area of circles, and use that knowledge to solve problems involving composite figures that include a semicircle. Students also learn and apply the volume formulas for prisms, pyramids, cylinders, cones, and spheres before solving problems involving the ratios for the areas and volumes of figures.

• Foundations

• Circumferences and Areas of Circles 1

• Circumferences and Areas of Circles 2

• Composite Figures

• Volumes of Prisms and Cylinders

• Volumes of Pyramids

• Volumes of Cones

• Volumes and Surface Area of Spheres

• Volume Ratios

• Reasoning About Area and Volume

Unit 4: Circles

In this unit, students first learn about and construct inscribed and circumscribed triangles. They then solve problems involving chords and arcs, tangents to circles, and use the relationship between an inscribed angle and its arc. Students also prove circles similar, solve problems with radian measures, and determine areas of sectors of circles.

• Foundations

• 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

• Radian Measure

• Sector Area

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 ratios, and use them to solve mathematical and real-world problems. Students also learn about special right triangles and the laws of sines and cosines.

• Foundations

• Trigonometric Ratios 1

• Trigonometric Ratios 2

• Angles and Trigonometric Ratios

• Sines and Cosines

• Special Right Triangles 1

• Special Right Triangles 2

• Surface Area of a Regular Pyramid

• A New Formula for the Area of a Triangle

• Law of Sines

• Law of Cosines

• Apply the Laws of Sines and Cosines

Unit 6: Conic Sections

This unit introduces students to conic sections. Students learn how write equations of circles and graph circles on the coordinate plane. They also learn to convert between forms of equations for circles. Likewise, students learn how to write equations of parabolas and graph parabolas on the coordinate plane. They will work with parabolas that open both vertically and horizontally. Students will also convert between forms of equations for parabolas.

• Foundations

• Introduction to Conic Sections

• Circles 1

• Circles 2

• Parabolas 1

• Parabolas 2

• Parabolas 3