Northwest High School s Algebra 2/Honors Algebra 2 Summer Review Packet

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1 Northwest High School s Algebra /Hoors Algebra Summer Review Packet This packet is optioal! It will NOT be collected for a grade et school year! This packet has bee desiged to help you review various mathematical topics. These cocepts are ecessary for you to uderstad i order for you to be successful i Algebra et year. Istructios: DO ALL PROBLEMS WITHOUT USING A CALCULATOR If you have ay questios regardig the summer math packet, please call Aimee Coway at (01) Kha Academy is aother great resource that will show you videos o all the topics listed i this packet ad much more! You ca check it out at the lik below: ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL.

2 Table of Cotets 1. Fractios page 1. Solvig Equatios page. Iteger Facts page. Epoets page. Quadratic Formula page 6. Add, Subtract & Multiply Polyomials page 6 7. Graphig Fuctios page 7

3 Fractios To simplify a fractio, divide umerator ad deomiator by a commo factor E To add or subtract fractios, rewrite the fractios usig a commo deomiator, the add or subtract the umerators E To multiply fractios, multiply umerator times umerator ad deomiator times deomiator. To divide fractios, multiply by the reciprocal of the d fractio. Simplify aswers as eeded E.- E Simplify the followig fractios: SHOW ALL WORK, NOT JUST AN ANSWER!!! =. =. = 1 0 Perform the followig operatios ad simplify if ecessary: SHOW ALL WORK, NOT JUST AN ANSWER!!! =. = 6. = = 8. = 9. = = 11. = 1. = = 1. = 1. = = = = 8 7 p. 1

4 Hits/Guide: Solvig Equatios Equatio Solvig Procedure: 1. Multiply o both sides to clear the equatio of fractios or decimals.. Distribute.. Collect like terms o each side, if ecessary.. Get all terms with variables o oe side ad all costat terms o the other side.. Multiply or divide to solve for the variable. 6. Check all possible solutios i the origial equatio. Eample: 7 1 Distribute Combie like terms. Simplify. Move all terms with variables to oe side. Divide to isolate the variable. Eercises: Solve each equatio. Show all work. 1. r 6 1. t a a a a p.

5 Iteger Facts. KNOW YOUR FACTS No calculator Time yourself. You should do this is 90 secods or less!!! - + = - = (-) = - (-) = = 8 = (-) = (-) = (-8) = - (-6) = (-) = -8 (-1) = (-) = 7 (-) = (6) = - () = (-) = -1 (-1) = 7 7 Be prepared for a timed quick quiz!!! p.

6 Epoets Hits/Guide: Rules of Epoets a 0 1 a 1 a 1 Negative Epoets: a a Product Rule: a m a m m Power Rule: m a Quotiet Rule: a a m a a a a a Quotiet to a Power: b b Product to a Power: ab a b m Eercises: Simplify usig the Rules of Epoets a a y 9. a b y 1. Epress usig a positive epoet y p.

7

8 Quadratic Formula Hits/Guide: Assume that the radical eteds over the whole epressio b ac. Equatio must be i the form a b c = 0 (stadard form) to begi. Try to factor first. If you caot fid factors, the use the quadratic formula. Quadratic Formula b b ac a Eample: Solve 7 Write the equatio i stadard form: 7 0 Idetify a, b, ad c for the formula: a = 1, b = -, c = -7 Substitute ito the formula: Simplify: 16 8 Separate ito two solutios: Solutios:. ad 1. ad Eercises: Solve usig the quadratic formula. Be sure the equatio is i stadard form before usig the quadratic formula. Show all work

9 Additio, Subtractio ad Multiplicatio of Polyomials Hits/Guide: Oly like terms ca be added or subtracted. Like terms have the same variables with the same epoets. Oly the coefficiets (umbers) are added or subtracted. A subtractio sig i frot of the paretheses chages each term i the paretheses to the opposite. Multiply the coefficiets ad use the rules of epoets for the variables. Remember: FOIL: F first, O outers, I iers, L last OR Bo Method Eamples: 1) Add the polyomials. ) Subtract the polyomials ) Multiply the polyomials Eercises: Add, subtract, or multiply the polyomials. Show all work Hit: Thik (+)(+) p. 6

10 Graphig Fuctios NO CALCULATOR. Use slope (m) ad y-itercept (b) to graph the followig liear equatios y = m + b. 1. Plot the y-itercept (b). From the y-itercept, use the slope (m), which is rise over ru, to plot poits across the etire graph. 1. y. 1. y First, solve for y. The graph usig y-itercept ad slope y y y p. 7

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