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Integrated Algebra Regents Review #3 Operations with Radicals Set Notation Percents Distance, Rate, Time Problems

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When simplifying radicals, create a product using the largest perfect square (4,9,16,25,36,49,64,81,100). Radicals 1)2)

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Radicals When multiplying radicals, multiply coefficients (out · out) and multiply radicands (in · in). Then simplify final answer. 3) 4)

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When dividing radicals, divide coefficients and divide radicands. Radicals 5) A fraction is not simplified if a radical appears in the denominator! 6)

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When adding or subtracting radicals, simplify all radicals. If radicals have “like” radicands, then add or subtract coefficients and keep the radicands the same. Radicals 7)

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Set Notation Universal Set = {10,11,12,13,14,15,16,17,18,19,20,21} A = {14, 21} B = {12,15,18,21} A and B are subsets of the Universal Set (1) Find A B A intersection B (common) (2) Find A B A union B (combine) (3) Find B’ or B c The Complement of B (not B) {21} {12,14,15,18,21} {10,11,13,14,16,17,19,20}

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Percents One week, a pair of gloves cost $15.00. The following week, they are marked down by 25%. What will the gloves cost the following week? Part = % ● Whole Discount = % ● Original Price N = 25% (15) N=.25(15) N = 3.75 The discount is $3.75 How do we find the sale price? Original Price – Discount = Sale Price $15 - $3.75 = $11.25 The gloves will cost $11.25 the following week. OR Sale Price = Original Price ● (1 - rate) = 15 ● (1 -.25) = 15 ●.75 = $11.25

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Percents Ronald bought a DVD that cost $18.99. His total payment including sales tax was $20.51. Find the sales tax rate to the whole percent? Tax = % (Tax Rate) ● Original Price Tax = 20.51 – 18.99 Tax = $1.52 1.52 = N% (18.99) N% = 1.52/18.99 N% = 0.080042…. 8% tax rate

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Word Problems Distance, Rate, Time 1)Finding Distance: 2)Finding Rate: 3)Finding Time: How do you know what to look for? Distance: How far? Rate: How fast? Time: How long? D = RT R = D T T = D R

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Word Problem s Hannah took a trip to her cousin’s house. She drove 120 miles to get there. If it took her 1.2 hours to get halfway to her cousin’s house, what was her average rate of speed? Important Information: Distance traveled: 60 miles (120/2) Time: 1.2 hoursRate: ? If Hannah decided to travel 10 mph faster on the way home, how long would it take her?

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Word Problem s A hiker walked 12.8 miles from 9:00 a.m. to noon. He walked an additional 17.2 miles from 1:00 p.m. to 6:00 p.m. What is his average rate of speed for the entire walk, in miles per hour? Miles WalkedHours 12.83 17.25 30.08

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Test Taking Tips 1) Don't rush through the exam. You have 3 hours…use them! 2) If you get stuck on a problem, move on and come back to it later. 3) After completing the exam once, take a little mental break, then re-do ALL the problems in a different order. Part I (Multiple Choice): o Eliminate choices that don't make sense o If you're not sure how to solve a problem, try testing each choice by substituting o When checking correct choices…make sure you understand why the other choices are incorrect Part II-IV (Open-Ended Response) o Show all work! (a correct answer with no work only receives 1 point) o Read each problem carefully. Read it a couple of times and underline key words and phrases. o Always draw a picture or diagram if one is not provided. o When asked to sketch a graph, always set up a table of values, plot points, and label. o Rounding should never be done until the end of the problem. o Make sure your answer makes sense and ask yourself, "Did I answer the question completely?" o With all written explanations, make sure you are specific and use appropriate mathematical reasoning. Provide mathematical evidence for everything! How do you know when you are completely done with the exam? 1) You have answered every problem at least twice. 2) You have checked that all of your work for Parts II-IV is in ink (except for any graphs). 3) You have made sure that every answer you wrote or bubbled (in ink) is correct.

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Reminders Eat BREAKFAST! Report to the Auditorium at 7:35 am No pencil cases, only clear plastic zip-lock bags with graphing calculator, extra batteries, pens, pencils, eraser and a ruler All cell phones, electronic devices and book bags in lockers Water bottles must be clear plastic (no label) and can only sit under the desk Upon the start of the exam, take time to write down any formulas or main ideas you may forget on the front or back of the reference sheet Upon leaving the exam, you will remove the batteries from your calculator and place the calculator in a box with your teacher’s name on it (the box will be placed in the front of the gym/room) MAKE SURE YOU ARE RETURNING THE CALCULATOR THAT WAS ASSIGNED TO YOU (OR A REPLACEMENT)!

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Now it’s your turn to study! Review all exams in the Green Book and all Regents Review PowerPoints. Older Integrated Algebra Regents Exams with answer keys are available at http://www.nysedregents.org/integratedalgebra. THE REGENTS IS THIS FRIDAY, JUNE 20 th STUDY! STUDY! STUDY! http://www.nysedregents.org/integratedalgebra END OF REGENTS REVIEWS

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