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DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

1 2 3 4 5 Unit 3 Begins Factoring and Solving The Remainder and Factor The Remainder and Factor The Remainder and Factor Factoring and Solving Polynomial Equations Theorems (Long Division) Theorems (Synthetic Division) Theorems Polynomial Equations  I can explain that an  I can define the  I can explain that identity shows a remainder  I can define the  I can define the an identity shows a relationship between theorem for remainder theorem remainder theorem for relationship two quantities, or polynomial for polynomial division polynomial division and between two expressions, that is division and and divide divide polynomials. quantities, or true for all values of divide polynomials.  Given a polynomial, I will expressions, that the variables, over a polynomials.  Given a polynomial, I p(x) and a number a, is true for all specified set.  Given a will p(x) and a number divide p(x) by (x – a) to values of the  I can prove polynomial, I will a, divide p(x) by (x – find p(a) then apply the variables, over a polynomial identities. p(x) and a a) to find p(a) then remainder theorem and specified set.  I can use polynomial number a, divide apply the remainder conclude that p(x) is  I can prove identities to describe p(x) by (x – a) to theorem and conclude divisible by x – a if and polynomial numerical find p(a) then that p(x) is divisible only if p(a) = 0. identities. relationships apply the by x – a if and only if  I can use inspection to  I can use remainder p(a) = 0. rewrite simple rational polynomial SEC. 6.4 PG 349 59-85 theorem and  I can use inspection expressions in different identities to conclude that to rewrite simple forms; write a(x)/b(x) describe numerical p(x) is divisible rational expressions in the form q(x) + relationships. by x – a if and in different forms; r(x)/b(x), where a(x), only if p(a) = 0. write a(x)/b(x) in the b(x), q(x), and r(x) are SEC. 6.4 PG 349 33-58  I can use form q(x) + r(x)/b(x), polynomials with the inspection to where a(x), b(x), q(x), degree of r(x) less than rewrite simple and r(x) are the degree of b(x). rational polynomials with the  I can use long division expressions in degree of r(x) less to rewrite simple different forms; than the degree of rational expressions in write a(x)/b(x) in b(x). different forms; write the form q(x) +  I can use long division a(x)/b(x) in the form r(x)/b(x), where to rewrite simple q(x) + r(x)/b(x), where DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

a(x), b(x), q(x), rational expressions a(x), b(x), q(x), and r(x) and r(x) are in different forms; are polynomials with the polynomials with write a(x)/b(x) in the degree of r(x) less than the degree of form q(x) + r(x)/b(x), the degree of b(x). r(x) less than the where a(x), b(x), q(x),  I can use a computer degree of b(x). and r(x) are algebra system to  I can use long polynomials with the rewrite complicated division to degree of r(x) less rational expressions in rewrite simple than the degree of different forms; write rational b(x). a(x)/b(x) in the form expressions in  I can use a computer q(x) + r(x)/b(x), where different forms; algebra system to a(x), b(x), q(x), and r(x) write a(x)/b(x) in rewrite complicated are polynomials with the the form q(x) + rational expressions degree of r(x) less than r(x)/b(x), where in different forms; the degree of b(x). a(x), b(x), q(x), write a(x)/b(x) in the and r(x) are form q(x) + r(x)/b(x), SEC. 6.5 PG 356 39-56 polynomials with where a(x), b(x), q(x), the degree of and r(x) are r(x) less than the polynomials with the degree of b(x). degree of r(x) less  I can use a computer than the degree of algebra system to b(x). rewrite complicated rational expressions SEC. 6.5 PG 356 27-38 in different forms; SYNTHETIC DIVISION write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

SEC. 6.5 PG 356 15-26 LONG DIVISION

6 7 8 9 10 Finding Rational Zeros Using the Fundamental Analyzing Graphs of Analyzing Graphs of Review Theorem of Algebra Polynomial Functions Polynomial Functions  I can define the  I can graph polynomial  I can graph polynomial  *I can state the remainder theorem functions, by hand in functions, by hand in Fundamental for polynomial simple cases or using simple cases or using Theorem of Algebra . division and divide technology for more technology for more  *I can verify that polynomials. complicated cases, complicated cases, the Fundamental  Given a polynomial, and show/label and show/label Theorem of Algebra I will p(x) and a maxima and minima of maxima and minima of is true for second number a, divide the graph, identify the graph, identify degree quadratic p(x) by (x – a) to zeros when suitable zeros when suitable polynomials. find p(a) then apply factorizations are factorizations are the remainder available, and show available, and show *SEC 6.7 PG 369 21-46 theorem and end behavior. end behavior. conclude that p(x)  I can determine the  I can determine the is divisible by x – a difference between difference between if and only if p(a) = simple and simple and 0. complicated complicated  I can use polynomial functions, polynomial functions, inspection to and know when the and know when the rewrite simple use of technology is use of technology is rational appropriate. appropriate. expressions in  I can relate the  I can relate the different forms; relationship between relationship between DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

write a(x)/b(x) in zeros of quadratic zeros of quadratic the form q(x) + functions and their functions and their r(x)/b(x), where factored forms to the factored forms to the a(x), b(x), q(x), and relationship between relationship between r(x) are polynomial functions polynomial functions polynomials with of degrees greater of degrees greater the degree of r(x) than two. than two. less than the  I can explain the  I can explain the degree of b(x). connection between connection between  I can use long the completed square the completed square division to rewrite form of a quadratic form of a quadratic simple rational expression and the expression and the expressions in maximum or minimum maximum or minimum different forms; value of the function value of the function write a(x)/b(x) in it defines. it defines. the form q(x) +  I can graph polynomial  I can graph polynomial r(x)/b(x), where functions, by hand in functions, by hand in a(x), b(x), q(x), and simple cases or using simple cases or using r(x) are technology for more technology for more polynomials with complicated cases, complicated cases, the degree of r(x) and show/label and show/label less than the maxima and minima of maxima and minima of degree of b(x). the graph, identify the graph, identify  I can use a zeros when suitable zeros when suitable computer algebra factorizations are factorizations are system to rewrite available, and show available, and show complicated end behavior. end behavior. rational  I can determine the  I can determine the expressions in difference between difference between different forms; simple and simple and write a(x)/b(x) in complicated complicated the form q(x) + polynomial functions, polynomial functions, r(x)/b(x), where and know when the and know when the DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

a(x), b(x), q(x), and use of technology is use of technology is r(x) are appropriate. appropriate. polynomials with  I can relate the  I can relate the the degree of r(x) relationship between relationship between less than the zeros of quadratic zeros of quadratic degree of b(x). functions and their functions and their factored forms to the factored forms to the SEC. 6.6 PG 362 33-44, relationship between relationship between 47-58 polynomial functions polynomial functions of degrees greater of degrees greater than two. than two.  When suitable  When suitable factorizations are factorizations are available, I will factor available, I will factor polynomials using any polynomials using any available methods. available methods.  I can create a sign  I can create a sign chart for a polynomial chart for a polynomial f(x) using the f(x) using the polynomial’s x- polynomial’s x- intercepts and testing intercepts and testing the domain intervals the domain intervals for which f(x) greater for which f(x) greater than and less than than and less than zero. zero.  I can use the x-  I can use the x- intercepts of a intercepts of a polynomial function polynomial function and the sign chart to and the sign chart to construct a rough construct a rough graph of the function. graph of the function. SEC 6.8 13-22, 29-34 A.APR.3 AND F.IF.7 WORKSHEET DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

11 12 13 14 15 Exam Unit4 Exponent Properties Nth Roots & Rational Rational Exponents Exponent Properties  I can simplify Exponents  I can simplify  I can simplify expressions using  I can rewrite an expressions with rational exponents using expressions using Exponent Properties expression using the exponent Exponent Properties Worksheet rational exponent properties. Sec.6.1 Pg.326 16-51 notation  I can rewrite an Sec.7.2 pg.411 22-55 expression using radical notation.  I can evaluate radical and rational exponent expressions with and without a calculator.  I can solve equations with degrees higher than two. Sec.7.1 Pg.404 14-62 DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

16 17 18 19 20 Rational Exponents Rational Exponents Radical Equations Radical Equations Rational Expressions  I can simplify  I can simplify expressions with expressions with  I can solve radical  I can solve radical  I can simplify rational rational exponents rational exponents equations and equations and expressions by using the exponent using the exponent determine if a determine if a factoring. properties. properties. solution is extraneous. solution is extraneous. Sec.9.4 Pg.558 16-27 Sec.7.2 pg.412 56-89 Worksheet Sec.7.6 pg. 441 23-46  I can solve equations with rational exponents.

Sec.7.6 pg. 441 47-62

21 22 23 24 25 Rational Expressions Rational Expressions Rational Expressions Rational Expressions Rational Expressions

 I can simplify  I can simplify rational  I can simplify  I can simplify  I can simplify rational expressions by expressions that are expressions that are expressions that are expressions by factoring. being added or being added or being added or factoring. subtracted by finding subtracted by finding subtracted by finding a  I can simplify rational a common a common common denominator  I can simplify expressions that are denominator denominator rational multiplied and Worksheet expressions that divided. Sec.9.5 Pg.565 12-17,26-37 Worksheet are multiplied and divided. Worksheet

Sec.9.4 Pg.558 28-51 DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

26 27 28 29 30 Complex Fractions Complex Fractions Rational Equations Rational Equations Rational Equations

 I can simplify  I can simplify  I can solve rational  I can solve rational  I can solve rational complex fractions complex fractions equations by equations by equations by multiplying multiplying by the multiplying by the by the common Sec.9.5 Pg.565 38-46 Worksheet common denominator common denominator denominator

Sec9.6 pg.571 21-41 Sec9.6 pg.571 42-50 Worksheet

31 32 33 34 35 Review Exam Remediation Day Remediation Day Remediation Day

***These days can be used to discuss matrices if time allows

36 37 38 39 40 Remediation Day Remediation Day Remediation Day Remediation Day Remediation Day DAILY PACING MAP NLHS Algebra II 2nd 9 Weeks Reviewed 5/15/12

41 42 43 44 45 Review Review Review Finals Finals