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Petersons.com/publishing Check out our Web site at www.petersons.com/publishing to see if there is any new information regarding the test and any revisions or corrections to the content of this book We’ve made sure the information in this book is accurate and up-to-date; however, the test format or content may have changed since the time of publication About Thomson Peterson’s Thomson Peterson’s (www.petersons.com) is a leading provider of education information and advice, with books and online resources focusing on education search, test preparation, and financial aid Its Web site offers searchable databases and interactive tools for contacting educational institutions, online practice tests and instruction, and planning tools for securing financial aid Peterson’s serves 110 million education consumers annually For more information, contact Peterson’s, 2000 Lenox Drive, Lawrenceville, NJ 08648; 800-3383282; or find us on the World Wide Web at www.petersons.com/about ® 2005 Thomson Peterson’s, a part of The Thomson Corporation Thomson LearningTM is a trademark used herein under license Editor: Wallie Walker Hammond; Production Editor: Alysha Bullock; Manufacturing Manager: Judy Coleman; Composition Manager: Melissa Ignatowski; Cover Design: Greg Wuttke ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution, or information storage and retrieval systems—without the prior written permission of the publisher For permission to use material from this text or product, submit a request online at www.thomsonrights.com Any additional questions about permissions can be submitted by email to thomsonrights@thomson.com ISBN: 0-7689-1717-4 Printed in the United States of America 10 07 06 05 Contents About the SAT vii Operations with Whole Numbers and Decimals Diagnostic Test • Addition of Whole Numbers • Subtraction of Whole Numbers • Multiplication of Whole Numbers • Division of Whole Numbers • Addition or Subtraction of Decimals • Multiplication of Decimals • Division of Decimals • The Laws of Arithmetic • Estimating Answers • Retest • Solutions to Practice Exercises Operations with Fractions 19 Diagnostic Test • Addition and Subtraction • Multiplication and Division • Simplifying Fractions • Operations with Mixed Numbers • Comparing Fractions • Retest • Solutions to Practice Exercises Verbal Problems Involving Fractions 39 Diagnostic Test • Part of a Whole • Finding Fractions of Fractions • Finding Whole Numbers • Solving with Letters • Retest • Solutions to Practice Exercises Variation 53 Diagnostic Test • Ratio and Proportion • Direct Variation • Inverse Variation • Retest • Solutions to Practice Exercises Percent 69 Diagnostic Test • Fractional and Decimal Equivalents of Percents • Finding a Percent of a Number • Finding a Number When a Percent Is Given • To Find What Percent One Number Is of Another • Percents Greater Than 100 • Retest • Solutions to Practice Exercises Verbal Problems Involving Percent 85 Diagnostic Test • Percent of Increase or Decrease • Discount • Commission • Profit and Loss • Taxes • Retest • Solutions to Practice Exercises Averages 103 Diagnostic Test • Simple Average • To Find a Missing Number When an Average Is Given • Weighted Average • Retest • Solutions to Practice Exercises Concepts of Algebra—Signed Numbers and Equations 115 Diagnostic Test • Signed Numbers • Solution of Linear Equations • Simultaneous Equations in Two Unknowns • Quadratic Equations • Equations Containing Radicals • Retest • Solutions to Practice Exercises Literal Expressions 133 Diagnostic Test • Communication with Letters • Retest • Solutions to Practice Exercises v vi Contents 10 Roots and Radicals 143 Diagnostic Test • Addition and Subtraction of Radicals • Multiplication and Division of Radicals • Simplifying Radicals Containing a Sum or Difference • Finding the Square Root of a Number • Retest • Solutions to Practice Exercises 11 Factoring and Algebraic Fractions 155 Diagnostic Test • Simplifying Fractions • Addition or Subtraction of Fractions • Multiplication or Division of Fractions • Complex Algebraic Fractions • Using Factoring to Find Missing Values • Retest • Solutions to Practice Exercises 12 Problem Solving in Algebra 171 Diagnostic Test • Coin Problems • Consecutive Integer Problems • Age Problems • Investment Problems • Fraction Problems • Mixture Problems • Motion Problems • Work Problems • Retest • Solutions to Practice Exercises 13 Geometry 197 Diagnostic Test • Areas • Perimeter • Right Triangles • Coordinate Geometry • Parallel Lines • Triangles • Polygons • Circles • Volumes • Similar Polygons • Retest • Solutions to Practice Exercises 14 Inequalities 231 Diagnostic Test • Algebraic Inequalities • Geometric Inequalities • Retest • Solutions to Practice Exercises 15 Numbers and Operations, Algebra, and Fractions 243 16 Additional Geometry Topics, Data Analysis, and Probability 273 Practice Test A 313 Practice Test B 319 Practice Test C 327 Solutions to Practice Tests 333 www.petersons.com About the SAT PURPOSE OF THE SAT The SAT is a standardized exam used by many colleges and universities in the United States and Canada to help them make their admissions decisions The test is developed and administered by Educational Testing Service (ETS) for the College Entrance Examination Board The SAT consists of two different types of exams designated SAT and SAT II The SAT tests verbal and mathematical reasoning skills — your ability to understand what you read, to use language effectively, to reason clearly, and to apply fundamental mathematical principles to unfamiliar problems SAT II tests mastery of specific subjects such as Chemistry or French or World History TAKING THE SAT The SAT is offered on one Saturday morning in October, November, December, January, March, May, and June When you apply to a college, find out whether it requires you to take the SAT and if so when scores are due To make sure your scores arrive in time, sign up for a test date that’s at least six weeks before the school’s deadline for test scores Registration forms for the SAT are available in most high school guidance offices You can also get registration forms and any other SAT information from: College Board SAT Program P.O Box 6200 Princeton, NJ 08541-6200 609-771-7600 Monday through Friday, 8:30 a.m to 9:30 p.m Eastern Time www.collegeboard.com Along with your registration form you will receive a current SAT Student Bulletin The bulletin includes all necessary information on procedures, exceptions and special arrangements, times and places, and fees vii viii About the SAT FORMAT OF THE NEW SAT The new SAT is a three-hour, mostly multiple-choice examination divided into sections as shown in the chart below One of the sections is experimental Your score on the six nonexperimental sections is the score colleges use to evaluate your application The critical reading sections of the SAT use Sentence Completions to measure your knowledge of the meanings of words and your understanding of how parts of sentences go together, and Critical Reading questions (short and long passages) to measure your ability to read and think carefully about the information presented in passages The mathematical sections use Standard Multiple-Choice Math, Quantitative Comparisons, and Student-Produced Response Questions to test your knowledge of arithmetic, algebra, and geometry Many of the formulas that you need will be given in the test instructions You are not required to memorize them SAT math questions are designed to test your skill in applying basic math principles you already know to unfamiliar situations The experimental section of SAT may test critical reading or mathematical reasoning, and it can occur at any point during the test This section is used solely by the testmakers to try out questions for use in future tests You won’t know which section it is So you’ll have to your best on all of the sections FORMAT OF A TYPICAL SAT Section #/Content (1) Writing (2) Mathematics Standard Multiple Choice Number of Questions (3)* “Wild Card” an Experimental Section (Varies with test) essay 25 20 25 varies 30 (4) Critical Reading Sentence Completions 16 25 (5) Writing Standard Multiple Choice 35 25 (6) Mathematics Standard Multiple-choice Grid-Ins 10 (7) Critical Reading Sentence Completions 19 (8) Mathematics Standard Multiple Choice 16 Critical Reading Sentence Completions 13 (9) * Can occur in any section www.petersons.com Time 25 25 20 20 About the SAT THE NEW SAT MATH QUESTIONS The mathematical reasoning sections of the SAT test problem solving in numbers and operations, algebra I and II, geometry, statistics, probability, and data analysis using two question types: • Standard multiple-choice questions give you a problem in arithmetic, algebra, or geometry Then you choose the correct answer from the five choices • Grid-Ins not give you answer choices You have to compute the answer and then use the ovals on the answer sheet to fill in your solution Although calculators are not required to answer any SAT math questions, students are encouraged to bring a calculator to the test and to use it wherever it is helpful Mathematics tests your knowledge of arithmetic, algebra, and geometry You are to select the correct solution to the problem from the five choices given Example: If (x + y)2 = 17, and xy = 3, then x2 + y2 = (A) (B) (C) (D) (E) 11 14 17 20 23 Solution: The correct answer is (A) (x + y)2 = 17 (x + y)(x + y) = 17 x2 + 2xy + y2 = 17 Since xy = 3, x2 + 2(3) + y2 = 17 x2 + + y2 = 17 x2 + y2 = 11 Student-Produced Responses test your ability to solve mathematical problems when no choices are offered Example: On a map having a scale of 41 inch = 20 miles, how many inches should there be between towns that are 70 miles apart? Solution: The correct answer is 87 or 875, depending upon whether you choose to solve the problem using fractions or decimals www.petersons.com ix x About the SAT Using fractions Using decimals x 20 70 70 20 x = 70 x= = 20 25 x = 20 70 20 x = 17.5 x = 875 = HOW TO USE THE ANSWER GRID The answer grid for student-produced response (grid-ins) questions is similar to the grid used for your zip code on the personal information section of your answer sheet An example of the answer grid is shown below The open spaces above the grid are for you to write in the numerical value of your answer The first row of ovals has only two ovals in the middle with a “/” These allow you to enter numbers in fractional form Since a fraction must have both a numerator and a denominator, it is not possible that the leftmost or rightmost positions could have a “/” To protect you from yourself, there are no “/s” in those positions The next row has decimal points The horizontal bar separates the fraction lines and decimal points from the digits to Record your answers to grid-in questions according to the rules that follow GRID RULES Write your answer in the boxes at the top of the grid Technically this isn’t required by the SAT Realistically, it gives you something to follow as you fill in the ovals Do it—it will help you Mark the bubbles that correspond to the answer you entered in the boxes Mark one bubble per column The machine that scores the test can only read the bubbles, so if you don’t fill them in, you won’t get credit Just entering your answer in the boxes is not enough www.petersons.com 324 Chapter 17 24 If a classroom contains 20 to 24 students and each corridor contains to 10 classrooms, what is the minimum number of students on one corridor at a given time, if all classrooms are occupied? (A) 200 (B) 192 (C) 160 (D) 240 (E) 210 www.petersons.com 25 If the area of each circle enclosed in rectangle ABCD is 9π, the area of ABCD is (A) (B) (C) (D) (E) 108 27 54 54π 108π Practice Tests Section 25 Questions Time: 30 Minutes Directions: Solve each of the following problems Write the answer in the corresponding grid on the answer sheet and fill in the ovals beneath each answer you write Here are some examples Answer: 3/4 (–.75; show answer either way) Answer : 325 Note: A mixed number such as 1/2 must be gridded as 7/2 or as 3.5 If gridded as “3 1/2,” it will be read as “thirty–one halves.” Simplified as a fraction to simplest form, what part of a dime is a quarter? Marion is paid $24 for hours of work in the school office Janet works hours and makes $10.95 How much more per hour does Marion make than Janet? If the outer diameter of a cylindrical oil tank is 54.28 inches and the inner diameter is 48.7 inches, what is the thickness of the wall of the tank, in inches? What number added to 40% of itself is equal to 84? If r = 25 – s, what is the value of 4r + 4s? Note: Either position is correct A plane flies over Denver at 11:20 A.M It passes over Coolidge, 120 miles from Denver, at 11:32 A.M Find the rate of the plane in miles per hour 53% of the 1000 students at Jackson High are girls How many boys are there in the school? How many digits are there in the square root of a perfect square of 12 digits? In May, Carter’s Appliances sold 40 washing machines In June, because of a special promotion, the store sold 80 washing machines What is the percent of increase in the number of washing machines sold? ( ) 10 Find the value of www.petersons.com 325 Practice Tests PRACTICE TEST C Answer Sheet Directions: For each question, darken the oval that corresponds to your answer choice Mark only one oval for each question If you change your mind, erase your answer completely Section 1 abcde abcde abcde abcde abcde abcde abcde 10 11 12 13 14 abcde abcde abcde abcde abcde abcde abcde 15 16 17 18 19 20 21 abcde abcde abcde abcde abcde abcde abcde 22 23 24 25 abcde abcde abcde abcde Section Note: Only the answers entered on the grid are scored Handwritten answers at the top of the column are not scored www.petersons.com 327 Practice Tests PRACTICE TEST C Section 25 Questions Time: 30 Minutes · = 4x Find x (A) (B) (C) (D) (E) If a > 2, which of the following is the smallest? (A) (B) (C) (D) (E) a a a +1 2 a +1 a −1 If a = b and (A) (B) (C) a –a b (D) a (E) –b (A) (B) (C) (D) (E) (B) (C) (D) (E) (.2)2 (.02)3 If a = , then 12a = b (A) (B) (C) (D) (E) = b , then c = c If a building B feet high casts a shadow F feet long, then, at the same time of day, a tree T feet high will cast a shadow how many feet long? Which of the following has the greatest value? (A) FT B FB T B FT TB F T FB The vertices of a triangle are (3,1) (8,1) and (8,3) The area of this triangle is (A) (B) 10 (C) (D) 20 (E) 14 3b b 9b 12b 16b www.petersons.com 329 330 Chapter 17 Of 60 employees at the Star Manufacturing Company, x employees are female If of the remainder are married, how many unmarried men work for this company? (A) (B) (C) (D) (E) 40 − x 40 − x 40 + x 20 − x 20 − x A circle whose center is at the origin passes through the point whose coordinates are (1,1) The area of the circle is (A) π (B) π (C) 2π (D) 2π (E) π 10 In triangle ABC, AB = BC and AC is extended to D If angle BCD contains 100°, find the number of degrees in angle B 12 Which of the following is greater than ? (A) 33 (B) (C) (D) (E) 1 3 13 What percent of a half dollar is a penny, a nickel, and a dime? (A) 16 (B) (C) 20 (D) 25 (E) 32 14 If 1 + = then c = a b c (A) (B) (C) (D) (E) a+b ab a+b ab ab a+b ab 15 What percent of a is b? (A) (B) (C) (A) (B) (C) (D) (E) 50 80 60 40 20 11 10 (A) (B) (C) (D) (E) 81 15 23 www.petersons.com (D) (E) 100b a a b b 100 a b a 100a b 16 The average of two numbers is A If one of the numbers is x, the other number is (A) A–x (B) A −x (C) 2A – x (D) A+ x (E) x–A Practice Tests 17 If a = 5b, then (A) 5b (B) 3b (C) (D) (E) a= 3b b b 18 A rectangular door measures feet by feet inches The distance from one corner of the door to the diagonally opposite corner is (A) 9'4" (B) 8'4" (C) 8'3" (D) 9'6" (E) 9' 19 Two ships leave from the same port at 11:30 A.M If one sails due east at 20 miles per hour and the other due south at 15 miles per hour, how many miles apart are the ships at 2:30 P.M.? (A) 25 (B) 50 (C) 75 (D) 80 (E) 35 20 If m men can paint a house in d days, how many days will it take m + men to paint the same house? (A) d + (B) d – (C) (D) (E) m+2 md md m+2 md + 2d m 22 There is enough food at a picnic to feed 20 adults or 32 children If there are 15 adults at the picnic, how many children can still be fed? (A) 10 (B) (C) 16 (D) 12 (E) 23 In parallelogram ABCD, angle A contains 60° The sum of angle B and angle D must be (A) 120° (B) 300° (C) 240° (D) 60° (E) 180° 24 The area of circle O is 64π The perimeter of square ABCD is (A) (B) (C) (D) (E) 32 32π 64 16 64π 25 If a train covers 14 miles in 10 minutes, then the rate of the train in miles per hour is (A) 140 (B) 112 (C) 84 (D) 100 (E) 98 21 Ken received grades of 90, 88, and 75 on three tests What grade must he receive on the next test so that his average for these tests is 85? (A) 87 (B) 92 (C) 83 (D) 85 (E) 88 www.petersons.com 331 332 Chapter 17 Section 25 Questions Time: 30 Minutes Directions: Solve each of the following problems Write the answer in the corresponding grid on the answer sheet and fill in the ovals beneath each answer you write Here are some examples Answer: 3/4 (–.75; show answer either way) Answer : 325 Note: A mixed number such as 1/2 must be gridded as 7/2 or as 3.5 If gridded as “3 1/2,” it will be read as “thirty–one halves.” 3 of is added to , what is the result? 8 If If 2n–3 = 32 what is the value of n? In a group of 40 students, 25 applied to Columbia and 30 applied to Cornell If students applied to neither Columbia nor Cornell, how many students applied to both schools? If x2 – y2 = 100 and x – y = 20, what is the value of x + y? A gallon of water is added to quarts of a solution that is 50% acid What percent of the new solution is acid? www.petersons.com Note: Either position is correct full After adding 10 A gasoline tank is gallons of gasoline, the gauge indicates that the tank is full Find the capacity of the tank in gallons If (x – y)2 = 40 and x2 + y2 = 60, what is the value of xy? If 2.5 cm = in and 36 in = yd., how many centimeters are in yard? How much more is 1 1 of than of ? 3 10 If the average of consecutive even integers is 82, what is the largest of these integers? Practice Tests SOLUTIONS TO PRACTICE TESTS PRACTICE TEST A Section 1 (B) x =8 x = 40 Angle C = 40º (Congruent angles.) Angle BAC = 100º (Sum of the angles in a triangle is 180º.) Angle x = 100º (Vertical angles are congruent.) (E) 3 ⋅ = 5 1 10 − − = = = 10 20 20 + =1 5 (C) ⋅ 45 = 36 Used in October = 36 – 15 = 21 (E) Multiples of are apart x is below x + x + is above x + 6x + 18 = 6(x + 3), 2x + = 2(x + 3) 3x + does not have a factor of 3, nor can it be shown to differ front x + by a multiple of (C) 80% = ⋅ 45 = 15 (40) = 10 (A) 10 (E) Angle AOD = 50º Angle COB = 50º Arc CB = 50º Angle CAB is an inscribed angle = 25º 11 (B) a b c d ⋅ ⋅ ⋅ ⋅x =1 b c d e a ⋅x =1 e e x= a 12 (B) Basic toll $1.00 Extra toll $2.25, which is 3($.75) Therefore, the car holds a driver and extra passengers, for a total of persons m+n+ p =q m + n + p = 3q x+y=z m + n + p + x + y = 3q + z 13 (C) Side of square = (C) Divide by y : y = If BE = 2, EA = 1, then by the Pythagorean theorem, BA and AC each equal (C) x=y+1 Perimeter of triangle ABC = + Using the largest negative integers will give the smallest product Let y = –2, x = –1, then xy = 14 (A) (C) Side of square = 12 = diameter of semicircle 15 (C) There are 30º in each of the 12 even spaces between numbers on the clock At 3:30, the minute hand points to and the hour hand is halfway between and The angle between the hands is (30 ) = 75 Remaining sides of triangle add up to 16 Perimeter of semicircle = 1 π d = ⋅ π ⋅ 12 = 6π 2 sides of square in perimeter = 24 Total perimeter of park = 16 + 6π + 24 = 40 + π Multiply every term by a 2a − 2 16 (A) $320 is 125% of his former salary 320 = 1.25 x 32000 = 125 x $256 = x www.petersons.com 333 334 Chapter 17 17 (A) Area of each square = ⋅ 125 = 25 Side of each square = Perimeter is made up of 12 sides 12(5) = 60 18 (C) 3 ⋅ = = 30% 10 19 (D) Circumference is times arc 5(2 π) = 10π = π d d = 10 Section 2 The number must be an even number, as there is no remainder when divided by If division by does give a remainder, it must be 2, since even numbers are apart (answer) ( 8) y 2 = = ⋅ = (answer) x 5 25 r=5 20 (D) The sum of any two sides of a triangle must be greater than the third side Therefore, x must be less than (4 + > x); however, x must be greater than 1, as + x > 4 + = 25 = (answer) = (answer) Illustrate the given facts as follows 21 (E) x can be negative as (–2)2 = 4, which is less than 22 (D) The two children’s tickets equal one adult ticket Mr Prince pays the equivalent of adult tickets 3a = 12.60 a = 4.20 Child’s ticket = This accounts for 23 students, leaving (answer) (4.20) = $2.10 23 (A) ❒ = · + (4 – 2) = + = 10 (answer) It is possible for the first four to be blue, but then the next two must be red Of course it is possible that two red socks could be drawn earlier, but with we are assured of a pair of red socks (answer) 16 (answer) 3x = 12 x=4 3x + = 13 (answer) = 12 − = 5 7 = 30 − = 23 + 23 = 30 24 (C) If the linear ratio is 1:1.5, then the area ratio is (1)2 : (1.5)2 or 1:2.25 The increase is 1.25 or 125% of the original area of will go on to college next year 3 1 ⋅ = = 25% 4 25 (B) 10 ( a + b )2 = a + 2ab + b a + b = 30 2ab = 20 a + 2ab + b = 50 www.petersons.com (aanswer) Practice Tests PRACTICE TEST B Section 1 (A) 20% = ⋅ 1200 = $240 depreciation first year = x 20 325 325 20 x = 325 325 x= ⋅ = =4 =4 20 80 80 16 $1200 – $240 = $960 value after year ⋅ 960 = $192 depreciation second year $960 – $192 = $768 value after years (E) = 2 3 = = 25 = (.9)2 = 81 20 = = 6.6 3 (E) = 25 % = 25% = 0025 1 1 % = ÷ 100 = ⋅ = (D) 4 100 400 (A) 05 (800) = $40 commission (A) Use a proportion comparing inches to miles (D) There are m + f people on the staff Of these, m are men m of the staff is men m+ f 10 (A) The angles are 40°, 60°, and 80°, all acute 11 (C) The linear ratio stays constant, so the perimeter is also multiplied by The area ratio is the square of the linear ratio, so the area is multiplied by 22 or k of the lawn is mowed m k m−k Still undone is 1− or m m 12 (D) In k minutes, 13 (A) 55% of his salary is spent 45% is left There is only one answer among the choices less than of his salary 80:40 = 2:1 (A) Multiply every term by 12 =6 4−3 (D) A + B = 40 B + C = 34 A + C = 42 Represent the angles as 2x, 3x, and 4x x = 180 x = 20 14 (B) Each side of square = Radius circle = Area of square = 82 = 64 Area of circles = 4π r2 = · π · 22 = 16π Shaded area = 64 – 16π 15 (E) Plotting the point shows a 3, 4, triangle Subtract second equation from third A–B=8 Subtract from first equation 2B = 32 B = 16 16 (D) Since times is 54, the product must end in www.petersons.com 335 336 Chapter 17 17 (E) Figure the time elapsed on either side of 12 noon From 7:42 A.M to 12 noon is hrs 18 From 12 noon, to 10:10 P.M is 10 hrs 10 The sum of the two is 14 hrs 28 18 (B) Each side of square AEDC is 10 Each side of square BCFG is Triangle ABC is a 6, 8, 10 triangle, making the perimeter 24 19 (C) There are 90° left for angle since angle BCD is a straight angle Section 25 = (answer) 10 2 Marion’s hourly wage is $24 or $4.80 $10.95 Janet’s hourly wage is or $3.65 $4.80 – $3.65 = $1.15 (answer) The difference of 5.58 must be divided between both ends The thickness on each side is 2.79 (answer) x + 40 x = 84 1.40 x = 84 14 x = 840 x = 60 (answer) 4(r + s) = 4(25) = 100 (answer) 20 (B) Use a proportion comparing pencils to cents Change 2D dollars to 200D cents p x = 200 D c pc =x 200 D 21 (C) Distance of first train = 60x Distance of second train = 70x 60 x + 70 x = 455 130 x = 455 x=3 In hours, the time will be 1:30 P.M 24 (C) The minimum is 20 students in classrooms 25 (A) The radius of each circle is 3, making the dimensions of the rectangle 18 by 6, and the area (18)(6), or 108 www.petersons.com The plane covers 120 miles in 12 minutes or hour In or hour, it covers 5(120), or 600 5 miles 600 (answer) 47% of 1000 are boys (.47)(1000) = 470 boys (answer) For every pair of digits in a number, there will be one digit in the square root (answer) Increase of 40 Percent of Increase = 22 (D) When two negative numbers are multiplied, their product is positive 23 (B) Since times is 42, the product must end in r + s = 25 Amount of increase ⋅ 100% Original 40 ⋅ 100% = 100% 40 (answer) 10 (3 )(3 ) = ⋅ = 18 (answer) Practice Tests PRACTICE TEST C Section 1 (B) 64 = 4x x=3 (4 · · = 64) (D) B and C are greater than A, D, and E all have the same numerator In this case, the one with the largest denominator will be the smallest fraction (A) = 5 (.02)3 = 000008 (C) Cross multiply 4a = 3b Multiply by 12a = 9b (D) a=b= c a= c ac = 1 c= a (A) The ratio of height to shadow is constant B T = F x Bx = FT FT x= B (A) (E) + 12 = r 2 = r2 Area = πr2 = 2π = 45 (.2)2 = 04 (B) Right triangle area = ⋅ ⋅ = 60 – x employees are male of these unmarried (60 − x ) = 20 − 13 x 10 (E) Angle BCA = Angle BAC = 80° There are 20° left for angle B 11 (B) 12 (D) 13 (E) 14 (D) 81 ÷ = ⋅ = 81 10 = =3 3 16 32 = = 32% 50 100 Multiply by abc bc + ac = ab c ( b + a ) = ab c= 15 (A) ab b+a b 100 b ⋅ 100 = a a 16 (C) x+y =A x + y = 2A y = 2A − x ⋅ 5/ b = 3b 17 (B) 5/ 18 (B) feet = 60 inches feet inches = 80 inches This is a 6, 8, 10 triangle, making the diagonal 100 inches, which is feet inches 19 (C) In hours, one ship went 60 miles, the other 45 miles This is a 3, 4, triangle as 45 = 3(15), 60 = 4(15) The hypotenuse will be 5(15), or 75 20 (D) This is inverse variation www.petersons.com 337 338 Chapter 17 m ⋅ d = ( m + 2) ⋅ x Section md =x m+2 21 (A) He must score as many points above 85 as below So far he has above and 10 below He needs another above of the food is 1 gone of the food will feed ⋅ 32 , or 8, 4 22 (B) If 15 adults are fed, 2n–3 = 25 n–3=5 n = (answer) 25 – x + x + 30 – x = 37 55 – x = 37 18 = x 18 (answer) x2 – y2 = (x – y)(x + y) 100 = 20(x + y) = (x + y) (answer) children 23 (C) If angle A = 60°, then angle B = 120° Angle B = Angle D Their sum is 240° 24 (C) Area of circle = 64π = r2 Radius of circle = Side of square = 16 Perimeter of square = 64 25 (C) 10 minutes = hour In one hour, the train will cover 6(14), or 84 miles 3 + = or (answer; both acceptable) 8 = 30% (answer) 10 No of quarts % acid 10 50 Original Added New 10 gallons is = Amount of acid 3 − of the tank 8−3 − = = 12 12 x = 10 12 x = 120 (answer) x = 24 ( x − y )2 = x − xy + y2 40 = 60 − xy xy = 20 xy = 10 (answer) 36(2.5) = 90 (answer) 1 ⋅ = 12 1 ⋅ = 12 (answer) 10 The average is the middle integer If 82 is the third, 86 is the last 86 (answer) www.petersons.com ... any section www.petersons.com Time 25 25 20 20 About the SAT THE NEW SAT MATH QUESTIONS The mathematical reasoning sections of the SAT test problem solving in numbers and operations, algebra... fundamental mathematical principles to unfamiliar problems SAT II tests mastery of specific subjects such as Chemistry or French or World History TAKING THE SAT The SAT is offered on one Saturday... them SAT math questions are designed to test your skill in applying basic math principles you already know to unfamiliar situations The experimental section of SAT may test critical reading or mathematical

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- About the SAT
- PURPOSE OF THE SAT
- TAKING THE SAT
- FORMAT OF THE NEW SAT
- THE NEW SAT MATH QUESTIONS
- HOW TO USE THE ANSWER GRID
- CALCULATORS AND THE SAT
- SCORING THE SAT
- HOW TO USE THIS BOOK
- 1 Operations with Whole Numbers and Decimals
- DIAGNOSTIC TEST
- 1. ADDITION OF WHOLE NUMBERS
- 2. SUBTRACTION OF WHOLE NUMBERS
- 3. MULTIPLICATION OF WHOLE NUMBERS
- 4. DIVISION OF WHOLE NUMBERS
- 5. ADDITION OR SUBTRACTION OF DECIMALS
- 6. MULTIPLICATION OF DECIMALS
- 7. DIVISION OF DECIMALS
- 8. THE LAWS OF ARITHMETIC
- 9. ESTIMATING ANSWERS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 2 Operations with Fractions
- DIAGNOSTIC TEST
- 1. ADDITION AND SUBTRACTION
- 2. MULTIPLICATION AND DIVISION
- 3. SIMPLIFYING FRACTIONS
- 4. OPERATIONS WITH MIXED NUMBERS
- 5. COMPARING FRACTIONS
- 6. COMPLEX FRACTIONS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 3 Verbal Problems Involving Fractions
- DIAGNOSTIC TEST
- 1. PART OF A WHOLE
- 2. FINDING FRACTIONS OF FRACTIONS
- 3. FINDING WHOLE NUMBERS
- 4. SOLVING WITH LETTERS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 4 Variation
- DIAGNOSTIC TEST
- 1. RATIO AND PROPORTION
- 2. DIRECT VARIATION
- 3. INVERSE VARIATION
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 5 Percent
- DIAGNOSTIC TEST
- 1. FRACTIONAL AND DECIMAL EQUIVALENTS OF PERCENTS
- 2. FINDING A PERCENT OF A NUMBER
- 3. FINDING A NUMBER WHEN A PERCENT OF IT IS GIVEN
- 4. TO FIND WHAT PERCENT ONE NUMBER IS OF ANOTHER
- 5. PERCENTS GREATER THAN 100
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 6 Verbal Problems Involving Percent
- DIAGNOSTIC TEST
- 1. PERCENT OF INCREASE OR DECREASE
- 2. DISCOUNT
- 3. COMMISSION
- 4. PROFIT AND LOSS
- 5. TAXES
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 7 Averages
- DIAGNOSTIC TEST
- 1. SIMPLE AVERAGE
- 2. TO FIND A MISSING NUMBER WHEN AN AVERAGE IS GIVEN
- 3. WEIGHTED AVERAGE
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 8 Concepts of Algebra—Signed Numbers and Equations
- DIAGNOSTIC TEST
- 1. SIGNED NUMBERS
- 2. SOLUTION OF LINEAR EQUATIONS
- 3. SIMULTANEOUS EQUATIONS IN TWO UNKNOWNS
- 4. QUADRATIC EQUATIONS
- 5. EQUATIONS CONTAINING RADICALS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 9 Literal Expressions
- DIAGNOSTIC TEST
- 1. COMMUNICATING WITH LETTERS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 10 Roots and Radicals
- DIAGNOSTIC TEST
- 1. ADDITION AND SUBTRACTION OF RADICALS
- 2. MULTIPLICATION AND DIVISION OF RADICALS
- 3. SIMPLIFYING RADICALS CONTAINING A SUM OR DIFFERENCE
- 4. FINDING THE SQUARE ROOT OF A NUMBER
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 11 Factoring and Algebraic Fractions •
- DIAGNOSTIC TEST
- 1. SIMPLIFYING FRACTIONS
- 2. ADDITION OR SUBTRACTION OF FRACTIONS
- 3. MULTIPLICATION OR DIVISION OF FRACTIONS
- 4. COMPLEX ALGEBRAIC FRACTIONS
- 5. USING FACTORING TO FIND MISSING VALUES
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 12 Problem Solving in Algebra
- DIAGNOSTIC TEST
- 1. COIN PROBLEMS
- 2. CONSECUTIVE INTEGER PROBLEMS
- 3. AGE PROBLEMS
- 4. INVESTMENT PROBLEMS
- 5. FRACTION PROBLEMS
- 6. MIXTURE PROBLEMS
- 7. MOTION PROBLEMS
- 8. WORK PROBLEMS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 13 Geometry
- DIAGNOSTIC TEST
- 1. AREAS
- 2. PERIMETER
- 3. RIGHT TRIANGLES
- 4. COORDINATE GEOMETRY
- 5. PARALLEL LINES
- 6. TRIANGLES
- 7. POLYGONS
- 8. CIRCLES
- 9. VOLUMES
- 10. SIMILAR POLYGONS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 14 Inequalities
- DIAGNOSTIC TEST
- 1. ALGEBRAIC INEQUALITIES
- 2. GEOMETRIC INEQUALITIES
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 15 Numbers and Operations, Algebra, and Functions
- DIAGNOSTIC TEST
- 1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)
- 2. SETS (UNION, INTERSECTION, ELEMENTS)
- 3. ABSOLUTE VALUE
- 4. EXPONENTS (POWERS)
- 5. FUNCTION NOTATION
- 6. FUNCTIONS—DOMAIN AND RANGE
- 7. LINEAR FUNCTIONS—EQUATIONS AND GRAPHS
- 8. QUADRATIC FUNCTIONS—EQUATIONS AND GRAPHS
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 16 Additional Geometry Topics, Data Analysis, and Probability
- DIAGNOSTIC TEST
- 1. RIGHT TRIANGLES AND TRIGONOMETRIC FUNCTIONS
- 2. TANGENT LINES AND INSCRIBED CIRCLES
- 3. EQUATIONS AND GRAPHS OF LINES IN THE XYPLANE
- 4. GRAPHS OF FUNCTIONS AND OTHER EQUATIONS—FEATURES AND TRANSFORMATIONS
- 5. DATA ANALYSIS
- 6. PROBABILITY
- RETEST
- SOLUTIONS TO PRACTICE EXERCISES
- 17 Practice Tests
- PRACTICE TEST A
- PRACTICE TEST B
- PRACTICE TEST C

- New SAT math workbook
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- New SAT Math workbook
- 354
- 505
- 5