Integrated math 2

• Course Overview

Geometric Constructions

• Key Concepts:
  • Tools for geometric constructions (compass, straightedge)
  • Constructing basic geometric figures (triangles, bisectors, angles)
  • Applications of constructions in problem-solving

Reasoning in Geometry

• Key Concepts:
  • Introduction to inductive reasoning and patterns
  • Understanding deductive reasoning and its role in proofs
  • Writing logical arguments and constructing geometric proofs

Proving Theorems

• Key Concepts:
  • Theorems related to lines and angles (transversal properties, angle relationships)
  • Proving properties of triangles (triangle congruence criteria)
  • Proving properties of quadrilaterals and other polygons

Properties of Lines

• Key Concepts:
  • Characteristics of parallel and perpendicular lines
  • Angle relationships formed by parallel lines and transversals
  • Applications in geometric proofs and real-world problems

Congruent Triangles

• Key Concepts:
  • Detailed study of congruence criteria (SSS, SAS, ASA, AAS, HL)
  • Using congruent triangles in proofs and problem-solving
  • Applications in various geometric contexts

Properties of Quadrilaterals

• Key Concepts:
  • Classifying quadrilaterals based on properties
  • Exploring the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares)
  • Applications of quadrilateral properties in problem-solving

Coordinate Geometry

• Key Concepts:
  • Understanding the coordinate plane and plotting points
  • Slope, distance, and midpoint formulas
  • Analyzing geometric figures using coordinate geometry

Ratios, Proportions, and Similarity

• Key Concepts:
  • Understanding ratios and proportions
  • Identifying similar figures and their properties
  • Using similarity in geometric problem-solving

Right Triangle Trigonometry

• Key Concepts:
  • Introduction to trigonometric ratios (sine, cosine, tangent)
  • Solving problems involving right triangles
  • Applications of trigonometry in real-world contexts

Circles

• Key Concepts:
  • Properties of circles (radius, diameter, circumference)
  • Angle relationships in circles (central, inscribed, and opposite angles)
  • Arcs, chords, and sectors

Surface Area and Volume

• Key Concepts:
  • Formulas for surface area and volume of geometric solids (prisms, cylinders, cones, spheres)
  • Applications of surface area and volume in real-world contexts
  • Problem-solving using dimensional analysis

Properties of Exponents

• Key Concepts:
  • Laws of exponents (product, quotient, power rules)
  • Understanding rational exponents and their applications
  • Simplifying expressions with exponents

Polynomials and Factoring

• Key Concepts:
  • Introduction to polynomials and their components
  • Operations with polynomials (addition, subtraction, multiplication)
  • Factoring polynomials and solving polynomial equations

Quadratic Functions

• Key Concepts:
  • Graphing quadratic functions and understanding their features (vertex, axis of symmetry)
  • Solving quadratic equations using various methods (factoring, completing the square, quadratic formula)
  • Applications of quadratic functions in modeling real-world scenarios

Course Goals

• Deepen understanding of geometric properties and theorems.
• Strengthen skills in algebra, particularly in working with polynomials and quadratic functions.
• Apply reasoning and problem-solving strategies across mathematical concepts.

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