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Common Core math 3

Common Core math 3. Unit 2-Modelling Algebraic Competency Ms. C. Taylor. Warm-Up. Using the data given: 23, 45, 23, 45, 67, 54, 34, 89, 56, 76, 12, 76 Give the Minimum, Lower Quartile, Median, Upper Quartile, Maximum, and standard deviation. (Use Calculator). Rational & Irrational Numbers.

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Common Core math 3

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  1. Common Core math 3 Unit 2-Modelling Algebraic Competency Ms. C. Taylor

  2. Warm-Up • Using the data given: 23, 45, 23, 45, 67, 54, 34, 89, 56, 76, 12, 76 • Give the Minimum, Lower Quartile, Median, Upper Quartile, Maximum, and standard deviation. (Use Calculator)

  3. Rational & Irrational Numbers • Rational Numbers repeated in a pattern, terminate, or can be expressed as a ratio of two integers. • Irrational Numbers don’t repeat in a pattern, never terminate, and cannot be expressed as a ratio of two integers. • Examples of Rational Numbers: 8/9, 2.66666666, 3.0 • Examples of Irrational Numbers: , √2

  4. Exponent Laws And the law about Fractional Exponents:

  5. Polynomial Operations • We can add, subtract, multiply, & divide polynomials. • Polynomials consist of 2 or more terms. • Examples: • When we add or subtract polynomials we DO NOT mess with the exponents! • Add ) + ( • Subtract (

  6. Polynomial Operations • When we multiply or divide polynomials then we have to use Exponent Laws to deal with the exponents! • What do you do when you multiply like bases of exponents? • What do you do when you divide like bases of exponents? • Examples: • Multiply • Multiply • Multiply • Divide • Divide

  7. Warm-Up • What is the probability of driving a Honda or a Nissan, or a Ford. The probability of a Honda is 0.05, probability of a Nissan is 0.35 and the probability of a Ford is 0.67.

  8. Factoring • ALWAYS look for a GCF (Greatest Common Factor) • If a = 1, then find the factors that multiply together to get “c” and add to get “b”. • If a ≠ 1, follow the steps for a = 1, then you have to group the first two and the last two. • Difference of Squares: • Sum & Difference of Cubes: S.O.A.P (Same Opposite Always Positive) • (

  9. Factoring Examples

  10. Factoring Examples

  11. Warm-Up • I want to choose a first, second, and third place winner. I have 25 students to choose from, how many combinations are possible? • Mr. Jones would like to choose 7 students for a history project. There are 89 students that he can choose from, how many combinations are possible?

  12. Long Division • Divide the same way as you would with regular integers.

  13. Synthetic Division • With this division method you only need the coefficients and the only thing to remember is if the divisor is NOT in (x –r) form then you have to use a “–r”.

  14. Warm-Up • Classify the following numbers as irrational or rational: • √2 • 2.4 •  • 5.99999999999999…….

  15. Simplifying Rational Expressions

  16. Warm-Up • Add the polynomials: • (2x2 + 5x – 2) + (-3x2 – 6x + 5) • (-x3 – 2x2 + 3x + 5) + (6x2 – 8x – 9)

  17. Add & Subtract Rational Expressions • More examples in class.

  18. Warm-Up • Add the fractions + . • Subtract the fractions - . • Multiply the fractions * . • NO CALCULATOR!

  19. Multiply & Divide Rational Expressions • More examples in class.

  20. Warm-Up • Simplify the rational expression and state the restrictions:

  21. Inverses of Functions • The relations formed when the independent variable(x) is exchanged with the dependent variable(y) in a given relation. • Given f(x)={(3,4),(1,-2),(5,-1),(0,2)} give the inverse. • To solve algebraically do the following 3 steps: • Set the function equal to y. • Swap the x and y variables. • Solve for y. • Solve the following for its’ inverse f(x)=x – 4 • Solve the following for its’ inverse f(x) =

  22. Warm-Up • Add the following rational expression: . • Subtract the following rational expression:

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