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

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

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

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

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

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}

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

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

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

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?

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