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ACC Module #2 Unit 2.4

ACC Module #2 Unit 2.4

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ACC Module #2 Unit 2.4

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  1. DemingEarly College High SchoolUnit 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions

  2. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Algebraic expressions look similar to equations, but they do not include the equal sign. Algebraic expressions are comprised of numbers, variables, and mathematical operations. Some examples of algebraic expressions are ; ; .Algebraic expressions and equations can be used to represent real-life situations and model the behavior of different variables. For example, 2x + 5 could represent the cost to play games at an arcade. In this case, 5 represents the price of admission to the arcade and 2 represents the cost of each game played.

  3. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate the following expression for g = 6-6.3 + 0.3g Evaluate the following expression for w = 0

  4. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate the following expression for g = 6-6.3 + 0.3g -6.3 + (0.3 * 6) = -6.3 + (1.8) = -4.5 Evaluate the following expression for w = 0

  5. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate the expression for r = -560 and s = 418.|r| + s Evaluate the expression for h = -0.5, j = -4, and k = 15.h*j*k

  6. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate the expression for r = -560 and s = 418.|r| + s |-560| + 418 = 560 + 418 = 978 Evaluate the expression for h = -0.5, j = -4, and k = 15.h*j*k (-0.5)(-4)(15) = 30

  7. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate: Evaluate: 0.88 + 0.6 * (7.5 - 8.2)

  8. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4 Algebraic Expressions Evaluate: Evaluate: 0.88 + 0.6 * (7.5 - 8.2) PEMDAS 0.88 + 0.6 * (-0.7) = 0.88 + (-0.42) = 0.46

  9. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Expression can be rewritten based on their factors. For example, the expression 6x + 4 can be rewritten as 2(3x + 2) because 2 is a factor of both 6x and 4. More complex expressions can also be rewritten based on their factors. The expression can be rewritten as . This is a different type of factoring, where a difference of squares is factored into a sum and difference of the same two terms. With some expressions, the factoring process is simple and only leads to a different way to represent the expression. With others, factoring and rewriting the expression leads to more information about the problem.

  10. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions In the following quadratic equation, factoring the binomial leads to finding the zeros of the function:This equation factors into (x-3)(x-2) = y, where 2 and 3 are found to be the zeros of the function when y is set equal to zero. The zeros of any function are the x-values where the graph of the function on the coordinate plane crosses the x-axis.

  11. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Factoring an equation is a simple way to rewrite the equation and find the zeros, but factoring is not possible for every quadratic.Completing the square is one way to find zeros when factoring is not an option.The following equation can not be factored:

  12. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions The first step in this method is to move the constant to the right side of the equation, making it: .Then, the coefficient of x is divided by 2 and squared ).This number is then added to both sides of the equation, to make the equation still true and we get:

  13. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions This equation can now be factored into . Solving for x then involves taking the square root of both sides and subtracting 5. This leads to two zeros of the function: . Depending on the type of answer the question seeks, a calculator may be used to find the exact numbers.

  14. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Given a quadratic equation in standard form:The sign of a tells us whether the function has a minimum or a maximum value. If a > 0 (or positive), the graph opens upward and has one minimum value. If a < o, the graph opens downward and has one maximum value.Depending on the way the quadratic equation is written, multiplication may need to occur before a min/max value is determined.

  15. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Exponential expressions can also be written, just as quadratic equations. Multiplying two exponential expressions with the same base involves adding the exponents:Dividing two exponential expressions with the same base involves subtracting the exponents:

  16. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Raising an exponential to another exponent includes multiplying the exponents:The zero power always gives a value of 1: Raising a product to a power involves distributing that power:

  17. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting Expressions Raising a fraction to a power involves distributing that power:Finally, raising a number to a negative exponent is equivalent to the reciprocal including the positive exponent.

  18. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Write a variable expression for:8 divided by p Write an expression for: triple q, then raise the result to the 4th power

  19. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Write a variable expression for:8 divided by p Write an expression for: triple q, then raise the result to the 4th power

  20. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Write a variable expression for:raise 3 to the 4th power, then divide g by the result Write an expression for: add 7 and m, divide n by the result, then raise what you have to 6th power.

  21. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Write a variable expression for:raise 3 to the 4th power, then divide g by the result Write an expression for: add 7 and m, divide n by the result, then raise what you have to 6th power.

  22. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Simplify: 2(2s-2) Simplify: -4 + (4 + f)

  23. Unit 2.0 QAS 2.0 Quantitative Reasoning, Algebra, and Statistics (QAS) 2.4.1 Rewriting expressions Simplify: 2(2s-2) 4s – 4 or 4(s-1) Simplify: -4 + (4 + f) -4 + 4 + f = f

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