Integrated Math 2 builds upon concepts from previous math courses, focusing on deepening your understanding of geometric principles and connecting them with algebraic ideas. It emphasizes using properties and theorems related to congruent figures to prove and extend your geometric knowledge.
Here's a more detailed look at common topics covered:
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Geometry:
- Congruence and Similarity: Proving triangle congruence using various postulates (SSS, SAS, ASA, AAS) and theorems. Understanding similarity through transformations (dilations).
- Triangle Properties: Exploring properties of special triangles (isosceles, equilateral, right) and related theorems like the Pythagorean Theorem.
- Quadrilaterals: Investigating properties of different quadrilaterals (parallelograms, rectangles, squares, rhombuses, trapezoids, kites) and their relationships.
- Circles: Studying properties of circles, including arcs, chords, tangents, and inscribed angles. Calculating circumference and area of circles and sectors.
- Constructions: Performing geometric constructions using a compass and straightedge.
- Transformations: Understanding and performing transformations (translations, rotations, reflections, dilations) on geometric figures and describing transformations that map one figure onto another.
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Algebra:
- Quadratic Functions: Analyzing and solving quadratic equations, including factoring, completing the square, and using the quadratic formula. Graphing quadratic functions and understanding their key features (vertex, axis of symmetry, intercepts).
- Polynomials: Operations with polynomials (addition, subtraction, multiplication, division). Factoring polynomials.
- Radical Expressions and Equations: Simplifying radical expressions. Solving equations involving radicals.
- Systems of Equations: Solving systems of linear and non-linear equations.
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Connections between Algebra and Geometry:
- Coordinate Geometry: Using coordinate geometry to prove geometric theorems. Finding equations of lines and circles. Calculating distance and midpoint.
- Geometric Modeling: Applying geometric concepts to solve real-world problems.
In summary, Integrated Math 2 aims to solidify your geometric foundations while strengthening your algebraic skills and highlighting the interconnectedness of these mathematical fields. You'll learn to reason deductively, prove geometric relationships, and apply mathematical concepts to solve a variety of problems.
