Algebra Final Exam Review Packet

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1 Algebra 1 00 Final Eam Review Packet UNIT 1 EXPONENTS / RADICALS Eponents Degree of a monomial: Add the degrees of all the in the monomial together. o Eample - Find the degree of 5 7 yz Degree of a polynomial: Is equal to the with the highest degree. o Eample Find the degree of the polynomial: y y 7 5 Adding / Subtracting Monomials: You can only add or subtract monomials that have the bases AND eponents. o You add / subtract the, the bases & eponents stay the! o Eample Simplify y y + 5y Multiplying Monomials: When you multiply like bases, the eponents! o Eample - 5 ( y z )( y z) Powers of Monomials: When you raise a monomial to a power the eponents! o Eample 7 ( y z ) Dividing Monomials: When you divide like bases, the eponents! o Eample 1 6y z 5 9 y z Distributing Monomials: Eample 5 y (5 y y ) Multiplying Polynomials: Double - Distribute or! o Eample ( 5)( )

2 Algebra 1 00 Final Eam Review Packet Eponents Practice: Write each epression in eponential form p p p p. m n n m n Find the degree of the monomial.. d bc a 7 15 Find the degree of the polynomial.. ab b a ab b a 5 Simplify the following epressions Simplify and show your work. All fractions must be simplified. 8. y y b a ab ab b a

3 Algebra 1 00 Final Eam Review Packet y y y 6 y y 15. y y 16. a m a p 6 7 9a b 0. ( y )( y ) + (y )( y ) 1. 6 a b ( 9 ) 0. (5 ) 5. m

4 Algebra 1 00 Final Eam Review Packet Radicals Simplifying Radicals: Always look for the perfect square. o Eample 16 Multiplying Radicals: You can multiply the coefficients in front of the radicals and everything under the radicals together. o Eample 1 80 Dividing Radicals: You can not have a radical in the denominator so you must rationalize it by multiplying the whole fraction by the radical in the denominator. o Eample Adding and Subtracting Radicals: After simplifying, you can combine like radicals" which means that the epressions have the same number under the radical. o Eample 7 8 Distributing Radicals: Use the distributive property with all of the rules of radicals. o Eample 6 Solving Radical Equations: Follow these steps o 1. Isolate the square root quantity. o. both sides of the equation. o. Simplify and solve. o.! Eample 7 8

5 Algebra 1 00 Final Eam Review Packet Radicals Practice: Simplify the following radicals: 1.).).) 5.) 6.) 7.) 9.) 10.) 11.) 1.) 1.) 1.) 15.) 16.)

6 Algebra 1 00 Final Eam Review Packet 17.) 18.) ) 0.) ( )( 5) 1.) 5.) 6 Solve for :.).) 5.) 6.) 7.) 8.)

7 Algebra 1 00 Final Eam Review Packet UNIT QUADRATICS Methods for solving quadratics: 1. Factoring factor then solve using Zero Product Property Methods of factoring: a. Difference of Two Squares Binomials only ( A ) ( B ) = ( A B ) ( A + B ) Must Have : 1. Binomial. Subtraction. Perfect Squares. Even Eponents b. Sum Product Factoring ( when a 1 so that + b + c) - Trinomials What two numbers multiply to give you c and also add up to give you b? ( +?)( +?) or ( -?)( -?), c > 0 ( +?)( +?), c > 0 c. Splitting the Middle Term ( when a 1 so that 1. Find product of ac. Find factors of ac that add up to b. Rewrite the trinomial with new factors. Group and factor! a b c ) - Trinomials. Solve by Taking Square Root of both sides 1. Isolate the squared quantity. Square root each side. T it off and make one side positive and one side negative. Check your solutions in the original equation. Solve by Quadratic Formula - If a b c 0, then 1. Arrange the terms into the standard form.. State the value of a, b, c. Use the quadratic formula to solve for b b ac. a

8 Algebra 1 00 Final Eam Review Packet Graphing Quadratics (Parabolas) Direction it faces - depends on sign of a, +a = upward, - a = downward Ais of Symmetry (AOS) - If the symmetrical sides of a parabola graph are folded, this is the line on b which the fold occurs formula a Verte the maimum or minimum point of the parabola (AOS determines, plug into original equations to determine y coordinate y-intercept The point where the parabola crosses the y-ais (set =0) -intercepts the point(s) where the parabola crosses the -ais (set y =0) Factor the following polynomials (you do NOT have to find solutions for ). GCF FIRST! 1. 1 y y

9 Algebra 1 00 Final Eam Review Packet Solve the following equations by factoring. Solve by factoring (difference of perfect squares, sum product, or splitting the middle term.) Be sure to pull out GCF if possible! = = 6 7. ( + + 0) + ( ) = = 5 Solve by taking the square root of both sides. No decimals (i.e., simplify all radicals) ( ) 6 = 11. ¼( + 5) + 9 = = 0

10 Algebra 1 00 Final Eam Review Packet Solve by the quadratic formula. No decimals (i.e., simplify all radicals) = = 0 Solve by any method you choose. No decimals (i.e., simplify all radicals). You do not need to check your answers (y +6) (y - 7) =

11 Algebra 1 00 Final Eam Review Packet For the following word problems, use any method of solving that is applicable. 1. The length of a rectangle is 5 cm greater than its width. Find the dimensions of the rectangle if its area is 16 cm.. Find three consecutive odd integers such that the sums of the squares of the first and third is eight more than two times the second. Find the set of integers.

12 Algebra 1 00 Final Eam Review Packet. y a.) Verte b.) Ais of Symmetry c.) -intercept(s) d.) y-intercept

13 Algebra 1 00 Final Eam Review Packet. y a.) Verte b.) Ais of Symmetry c.) -intercept(s) d.) y-intercept

14 Algebra 1 00 Final Eam Review Packet 5. y 16 a.) Verte b.) Ais of Symmetry c.) -intercept(s) d.) y-intercept

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