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Arithmetic

Note Taking Guide 1.5

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1.05 Descriptive Modeling and Accuracy Essential Questions After completing this lesson, you will be able to answer the following questions: How do you define the appropriate quantities to model a situation or description? How do you choose the level of accuracy given the limitations of a situation? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Precision Versus Accuracy Precision: _________________ Accuracy: _________________ Significant Figures Counting the amount of digits: How many significant figures would each have? 5.01 ___ significant figures 11 ____ 1.2 ____ 5.00____ Find the area of the rectangle with the following measurements: length= 8.2cm width= 10.4cm What would you need to round to based on the number of significant figures? ____

Significan Figures Worksheet

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Name: Block: Significant Figures & Rounding 1. For each of the following, ? Underline the significant figures in the number. ? Write the uncertainty as ? the appropriate quantity. (a) 57,300? 100 ?? Sample problem with correct answer. (b) 13,500 (c) 26.0012 (d) 02452 (e) 0.000 000 025 (f) 320. (g) 6.0? 10?7 (h) 150.00 (i) 10 (j) 0.005 310 0 2. Round off each of the following numbers as indicated. (a) 13,500 to the nearest 1,000 (b) 26.0012 to the nearest 0.1 (c) 02452 to the nearest 10,000 (d) 0.000 025 to the nearest 0.000 01 (e) 320. to the nearest 10 (f) 6.0? 10?7 to the nearest 10?6 (g) 150.00 to the nearest 100 (h) 10 to the nearest 100 3. Solve the following math problems and express the answer to the correct number of significant

Steps for Factoring Polynomials

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1. Pull out greatest common factor or GCF [This is a very important step that is often skipped] Ex: or 2. Look at number of terms a. 2 Terms: If there are two terms (binomial), then check to see if it is i. A difference of squares: Ex: ii. A difference of cubes Ex: iii. A sum of cubes Ex: If there are two terms and the expression is none of the above, it is prime! b. 3 Terms: If there are three terms (trinomial), then factor into two binomials thinking of the FOIL method in reverse. Find factors of c that add up to b. Start by identifying the factors of c. The sign before c determines whether signs are the same or different in the 2 binomials that are produced, .

Factoring Polynomials of Degree 3

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Factoring Polynomials of Degree 3 Factoring a 3 - b 3 An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2) : (a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3 For example, the factored form of 27x 3 - 8 ( a = 3x, b = 2 ) is (3x - 2)(9x 2 + 6x + 4) . Similarly, the factored form of 125x 3 -27y 3 ( a = 5x, b = 3y ) is (5x - 3y)(25x 2 +15xy + 9y 2) . To factor a difference of cubes, find a and b and plug them into (a - b)(a 2 + ab + b 2) . Factoring a 3 + b 3 An expression of the form a 3 + b 3 is called a sum of cubes. The factored form of a 3 + b 3 is (a + b)(a 2 - ab + b 2) : (a + b)(a 2 - ab + b 2) = a 3 + a 2 b - a 2 b - ab 2 + ab 2 + b 3 = a 3 - b 3 .
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