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Understanding Formulas, Models, and Geometry: A Comprehensive Guide

This guide covers essential mathematical concepts including types of formulas, solving and rearranging them, and exploring mathematical models. You will learn about crucial formulas such as Distance (D = R·T), Total Cost (C = A·U), and Simple Interest (I = P·r·t). The guide also includes geometry basics, calculating perimeters and areas for shapes like squares, rectangles, and circles, as well as volumes for cubes and spheres. Finally, discover how to apply these concepts to real-world situations with examples.

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Understanding Formulas, Models, and Geometry: A Comprehensive Guide

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  1. Sect. 1.5Formulas, Models & Geometry (Lite!) • Types of Formulas • Solving Formulas • (Rearranging) • Mathematical Models 1.5

  2. You already know the Rules 1.5

  3. Types of Formulas • D = R·T Distance = Rate x Time • Economics: • C = A·Utotal_Cost= Amount x Unit_cost • I = P·r·tsimple_Interest = Principal x Rate x Time • A = P + P·r·tAccumulated_value = Principal + interest • S = C + C·mSelling_price = wholesale_Cost + Markup • Geometry: Squares Rectangles Circles • Perimeters P=4s P=2w+2l C=πd (circumference) • Areas A=s2 A=w·l A= π r2 • Cubes Blocks Spheres • VolumesV=s3 V=w·l·h V= (4/3)π r3 • Angles In a triangle 180° = a + b + c 1.5

  4. General Approach to Solving Formulas 1.5

  5. Solving Formulas – 3 Variables • Pick one of the variables and rearrange the formula (using algebraic properties) to isolate it 1.5

  6. Simple Interest – 4 variables • Only two terms in this formula 1.5

  7. Formulas with Complex Terms • When a factor is a sum … 1.5

  8. Isolating a Common Factor • The Law of Distribution works both ways:a(b + c) = ab + ac and ab + ac = a(b + c) 1.5

  9. Mathematical Models • To represent or approximate real-world situations • Use the Body Mass Index formula to find someone’s approximate weight. Her BMI is 42.2 and height is 5’9” • First, solve the formula for W, then substitute, simplify and solve. (board) 1.5

  10. Next? • Now on to 1.6 Properties of Exponents 1.5

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