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) 601-61. 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: https://www.khaacademy.org/math/algebra-home ENJOY YOUR SUMMER! WE ARE LOOKING FORWARD TO SEEING YOU IN THE FALL.
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
Fractios To simplify a fractio, divide umerator ad deomiator by a commo factor. 18 6 E.- 1 6 To add or subtract fractios, rewrite the fractios usig a commo deomiator, the add or subtract the umerators. 1 8 11 E.- 1 1 1 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. 1 1 1 1 6 6 E.- E.- 0 10 6 1 Simplify the followig fractios: SHOW ALL WORK, NOT JUST AN ANSWER!!! 8 1 1. =. =. = 1 0 Perform the followig operatios ad simplify if ecessary: SHOW ALL WORK, NOT JUST AN ANSWER!!!. 7 1 6 =. = 6. = 8 7 7. 9 7 1 1 = 8. = 9. = 8 7 10. 8 = 11. = 1. = 8 7 1. 1 1 7 1 = 1. = 1. = 9 8 6 16. 6 = 17. 1 = 18. 1 = 8 7 p. 1
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. 10 7 1 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 9 6. 0 6. a a a a 1. 6 1 6. 7 1 p.
Iteger Facts. KNOW YOUR FACTS No calculator Time yourself. You should do this is 90 secods or less!!! - + = - = 6 - + (-) = - (-) = 6 7-1 + 7 = 8 = 6 8 9-6 + (-) = (-) = 9 8 8 + (-8) = - (-6) = 7 6 6 9-7 + (-) = -8 (-1) = 8 8 + (-) = 7 (-) = 9 - + (6) = - () = 6 6 - + (-) = -1 (-1) = 7 7 Be prepared for a timed quick quiz!!! p.
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. 1... 6. a a 8. 6... 8 6. 7. 8. y 9. a b 10. 11. y 1. Epress usig a positive epoet. 1. 1 y 1. 8 1. p.
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: 1 7 1 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. 1. 1. 6 9. 7 0
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. 9 9 7 ) Multiply the polyomials. 1 8 1 8 Eercises: Add, subtract, or multiply the polyomials. Show all work. 1.. 6. 7 1 6. 9 8. 6. 7. 8. Hit: Thik (+)(+) 9. 10. p. 6
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 1. 1 6. First, solve for y. The graph usig y-itercept ad slope. 7. 1 8. 6 8 9. 8 y y y p. 7