INTEGRATED MATH 2, PART 2
Price: $125 | Credits: One Semester | Dept: Math | Course ID# 232-2
Integrated Math 2, Part 2 is the second semester of Integrated Math 2 and develops geometric reasoning through similarity, right-triangle trigonometry, polygons, circles, and probability. Students use ratios, dilations, and similarity theorems; apply the Pythagorean Theorem and trigonometric relationships; analyze properties of polygons and quadrilaterals; and solve problems involving circles and conic sections. Students conclude by using sample spaces, counting methods, probability rules, two-way tables, and conditional and geometric probability. Integrated Math 2 is approved by the University of California A-G as mathematics (category C).
Upon completion of this course, the student is awarded 5 credits. Each credit corresponds to 15 hours of study. Of course, some students work more quickly than others, and some can devote more hours to study, so some students are able to complete the course at an accelerated rate.
LEARNING OBJECTIVES
In this module, students gain a comprehension of the following:
- How to use ratios, proportions, scale factors, and dilations to analyze similar figures.
- How to prove triangles similar and apply proportional relationships within triangles.
- How to use the Pythagorean Theorem and properties of special right triangles.
- How to apply sine, cosine, tangent, the Laws of Sines and Cosines, and other methods to solve triangles.
- Properties of polygons and special quadrilaterals.
- How coordinate geometry can be used to classify and analyze quadrilaterals.
- Properties and theorems involving circles, arcs, chords, tangents, secants, and inscribed angles.
- How to calculate circumference, area, arc length, and sector area and write equations of circles.
- Basic properties of conic sections.
- How to calculate probabilities using sample spaces, counting methods, probability rules, two-way tables, permutations, combinations, and geometric probability.
TOPICS COVERED
This course covers the following topics:
- Ratios and Proportions
- Similar Polygons and Scale Factor
- Dilations
- Proving Triangles are Similar
- Geometric Mean and Parts of Similar Triangles
- Parallel Lines and Proportional Parts
- Pythagorean Theorem and Its Converse
- Special Right Triangles
- Basic Trigonometric Functions
- Angles of Elevation and Depression
- Area of a Triangle
- Law of Sines and Law of Cosines
- Classifying Polygons
- Polygon Theorems
- Parallelograms
- Rectangles, Rhombuses, and Squares
- Trapezoids and Kites
- Quadrilaterals on a Coordinate Plane
- Constructing Regular Polygons
- Central Angles, Chords, and Arcs
- Inscribed Angles and Inscribed Polygons
- Tangent Lines and Circumscribed Polygons
- Chords, Secants, and Tangents
- Area and Circumference of a Circle
- Arc Length and Areas of Circle Sectors and Segments
- Equations of Circles
- Introduction to Conic Sections
- Sample Spaces
- Probability and Counting
- Geometric Probability
- Two-Way Frequency Tables
- Probability and the Addition Rule
- Probability and the Multiplication Rule
- Conditional Probability
- Probability with Permutations and Combinations
