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CQ27 Rational Operations INTENSE Clearing Practice
 * NEW PRACTICE PROBLEMS** * Added 6/1/13
 * CQ27 Rational Operations Clearing Practice**

Rational Operations Practice Problems** #29 Rational Operations #31 Rational Operations #32 Rational Operations #33 Factoring British Method

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Graphing Parabolas in Standard Form Graphing Parabolas in Vertex Form || n/a || Solve by taking the Square Root Complete the Square 1 Quadratic Formula || Complete the Square 2 || Simplifying Radicals Multiplying Radicals || Adding & Subtracting Radicals || Simplifying Expressions with Exponents Exponent Rules Fractional Exponents Negative Fractional Exponents ||  ||
 * Concept || First Four Work || Clearing Work ||
 * 18. Finding & Applying Quadratics || Vertex of a Parabola
 * 19. Solving Quadratics || Solve by factoring
 * 20. Radical & Complex Operations || Square Roots
 * 21. Advanced Radicals || Radical Equations ||  ||
 * 22. Rational Exponents || Negative Exponents
 * 23. Composite Functions || Composite Functions ||  ||

Graphing Stories

Graphing systems of equations || No calculator Solutions to Systems of Equations || Systems of equations with elimination || These will both be completed without a calculator. Convert multi-digit repeating decimals to fractions Convert 1-digit repeating decimals to fractions || Intersections || Graphs of Inequalities Graphing Linear Inequalities Graphing & Solving Linear Inequalities || Graphing System of Inequalities Graphing & Solving System of Inequalities || Factoring Polynomials 1 Factoring Polynomials 2 || Factoring Polynomials with 2 Variables Factoring Polynomials by Grouping || Dependent Probability || Probability with Permutations & Combinations || =Probability Notes= =INDEPENDENT VS. DEPENDENT (2+ events)= When looking at a probability of 2 or more events, we must first decide whether the events are dependent on one another. If the probability of the second event changes based on the first event, the events are dependent. We must account for how the 1st event changes the probability of the 2nd event. Example1 - 5 quarters and 3 dimes - What is the probability of selecting a quarter and then a dime with out replacement? Since removing the quarter will reduce the number of coins, the original probability of a dime(3/8) will change to 3/7 after the coin is removed. p(quarter then dime) = p(quarter) • p(dime after quarter) p(quarter then dime) = 5/8 • 3/7 <- notice there is 1 less coin which changes the probability p(quarter then dime) = 15/56
 * Concept || First Four Practice || Clearing Practice ||
 * 9.Graphing || Converting between slope-intercept and standard form
 * 10.Elimination || Systems of equations with simple elimination
 * 11.Substitution || Systems of equations with substitution || Age word problems ||
 * 12.Applications || Systems of Equations || Systems of equations word problems ||
 * 13.Inequality
 * 14.Factoring || Factoring Linear Binomials
 * 15. Probability || Independent Probability
 * Dependent Probability p(a and b) = p(a) • p(b after a)**

If the probability of the second dones not change based on the first event, the events are independent and much easier to calculate. Example2 - Flip a "fair" coin 2 times and get heads 2 times. The probability of the coin coming up heads on the second flip is unaffected by the first flip. p(heads then heads) = p(heads) • p(heads) p(heads then heads) = 1/2 • 1/2 = 1/4
 * Independent Probability p(a and b) = p(a) • p(b)**

=EXCLUSIVE VS. INCLUSIVE (OR)= The next part of probability, which I **TRIED** to explain yesterday, is figuring out if events can occur at the same time. If two events cannot occur at the same time, they are said to be mutually exclusive. Exclusive looks like exclude... hmmm. I'm going to use the current US Senate for these examples.

Here is the current make up of the US Senate Senators
 * || Male || Female || Total ||
 * Democrat || 39 || 12 || 51 ||
 * Republican || 42 || 5 || 47 ||
 * Independent || 2 || 0 || 2 ||

Example3 - If I go to the link above, and randomly select a senator, what is the probability the senator is a republican or an independent?

When trying to decide if an event is mutually exclusive, ask yourself if the events can happen at the same time. Is it possible in this example to select a senator that is a republican and an independent? The answer is no. Being an independent excludes you from being an republican. So for mutually exclusive events, we follow... p(a or b) = p(a) + p(b) - we can tell it is exclusive if p(a and b) = 0 or impossible.
 * Mutually Exclusive**

Example3 answer p(republican or independent) = p(republican) + p(independent) p(republican or independent) = 42/100 + 2/100 = 44/100 < before we reduce, the probability tells us how many senators there are total. p(republican or independent) = 42/100 + 2/100 = 11/25

Example4 - I randomly select a senator, what is the probability they are female or a democrat? Again, ask yourself if these events can happen at the same time? Is it possible to be a female and a democrat. The answer is yes. So the event is considered to be inclusive. Inclusive looks like include... hmmm.For mutually exclusive events, we find the total probability of both events, and then remove the overlap. For this problem we add the probability of the senator being female (17/100) to the probability of being Democratic (51/100) and then remove the double counting. Since some 51 democrats we counted must be women, we remove all parties that satisfy both events. Notice how cool this is...

P(female or democrat) = P(female) + p(democrat) - p(democrat and female) P(female or democrat) = 17/100 + 51/100 - 12/100 = 56/100 56/100 make sense since there are 51 democrats and 5 women who are republicans.

p(a or b) = p(a) + p(b) - p(a and b)
 * Mutually Inclusive**

Birthday Problem

Will be required at some point.... Multiplying Polynomials Equations from Tables

=Extra Practice= ==== **SAT** Symbols & Functions Symbols & Functions 2 ====

**NEAT** Views of Function
=Old Stuff=

1st Marking Period Concepts
=**@ABOVE AND BEYOND**= Crazy Survey