Integrated AlgebraRegents Review #3

Operations with RadicalsSet Notation

PercentsDistance, 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) 48 2) 2 50

16 3

4 3

2 25 2

2 5 2

10 2

RadicalsWhen multiplying radicals, multiply coefficients (out · out) and multiply radicands (in · in). Then simplify final answer.

3 2 5 63) 4) 4 5 10 5

15 12

15 2 3

30 3

15 4 3

4 50 20 5

4 25 2 20 5

4 5 2 20 5

20 2 20 5

When dividing radicals, divide coefficients and divide radicands.

Radicals

5) 635

30

2

6

52

306

A fraction is not simplified if a radical appears in the denominator!

6) 3

23

2

3 2

2

multiply by a FOO 2

2

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) 2 32 4 18

2 16 2 4 9 2

2 4 2 4 3 2

8 2 12 2

4 2

Set NotationUniversal 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 Bc The Complement of B (not B)

{21}

{12,14,15,18,21}

{10,11,13,14,16,17,19,20}

PercentsOne 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 = % ● WholeDiscount = % ● Original Price N = 25% (15)N= .25(15)N = 3.75The discount is $3.75

How do we find the sale price?

Original Price – Discount = Sale Price$15 - $3.75 = $11.25The gloves will cost $11.25 the following week.

ORSale 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 – 18.99Tax = $1.52

1.52 = N% (18.99)

N% = 1.52/18.99

N% = 0.080042…. 8% tax rate

Word ProblemsDistance, 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 TT = D R

Word ProblemsHannah 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 hours Rate: ?

miles/hour50R hours

milesR

T

DR

2.1

60

If Hannah decided to travel 10 mph faster on the way home, how long would it take her?

hours2T mph

milesT

R

DT

60

120

Word ProblemsA hiker walked 12.8 miles from 9:00 a.m. to noon. He walkedan additional 17.2 miles from 1:00 p.m. to 6:00 p.m. What ishis average rate of speed for the entire walk, in miles per hour?

Miles Walked Hours

12.8 3

17.2 5

30.0 8

miles/hour3.75R hours

milesR

T

DR

8

30

Test Taking Tips1) 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):oEliminate choices that don't make senseoIf you're not sure how to solve a problem, try testing each choice by substitutingoWhen checking correct choices…make sure you understand why the other choices are incorrect

Part II-IV (Open-Ended Response)oShow all work! (a correct answer with no work only receives 1 point)oRead each problem carefully. Read it a couple of times and underline key words and phrases.oAlways draw a picture or diagram if one is not provided.oWhen asked to sketch a graph, always set up a table of values , plot points, and label.oRounding should never be done until the end of the problem.oMake sure your answer makes sense and ask yourself, "Did I answer the question completely?"oWith 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.

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)!

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 20th

STUDY! STUDY! STUDY!

END OF REGENTS REVIEWS