CHAPTER 20 Sample Math Questions: Multiple-Choice
CHAPTER 20Sample MathQuestions:Multiple-ChoiceIn the previous chapters, you learned about the four areas covered bythe SAT Math Test. On the test, questions from the areas are mixedtogether, requiring you to solve different types of problems as youprogress. In each portion, no-calculator and calculator, you’ll firstsee multiple-choice questions and then student-produced responsequestions. This chapter illustrates sample multiple-choice questions.These sample questions are divided into no-calculator and calculatorportions just as they would be on the actual test.Test-Taking StrategiesWhile taking the SAT Math Test, you may find that some questionsare more difficult than others. Don’t spend too much time on any onequestion. If you can’t answer a question in a reasonable amount oftime, skip it and return to it after completing the rest of the section.It’s important to practice this strategy because you don’t want to wastetime skipping around to find “easy” questions. Mark each questionthat you don’t answer in your booklet so you can easily go back to itlater. In general, questions are ordered by difficulty, with the easierquestions first and the harder questions last within each group ofmultiple-choice questions and again within each group of studentproduced response questions. Don’t let the question position orquestion type deter you from answering questions. Read and attemptto answer every question you can.Read each question carefully, making sure to pay attention to unitsand other keywords and to understand exactly what informationthe question is asking for. You may find it helpful to underline keyREMEMBERIt’s important not to spend toomuch time on any question. You’llhave on average a minute andfifteen seconds per question on theno-calculator portion and a littleless than a minute and a half perquestion on the calculator portion.If you can’t solve a question in areasonable amount of time, skipit (remembering to mark it in yourbooklet) and return to it later.REMEMBERIn general, questions are ordered bydifficulty with the easier questionsfirst and the harder questions lastwithin each group of multiplechoice questions and again withineach group of student-producedresponse questions, so the laterquestions may take more time tosolve than those at the beginning.257
PART 3 MathREMEMBERKnowing when to use a calculator isone of the skills that is assessed bythe SAT Math Test. Keep in mind thatsome questions are actually solvedmore efficiently without the use of acalculator.information in the problem, to draw figures to visualize the informationgiven, or to mark key information on graphs and diagrams provided inthe booklet.When working through the test, remember to check your answersheet to make sure you’re filling in your answer on the correct rowfor the question you’re answering. If your strategy involves skippingquestions, it can be easy to get off track, so pay careful attention toyour answer sheet.On the calculator portion, keep in mind that using a calculator maynot always be an advantage. Some questions are designed to be solvedmore efficiently with mental math strategies, so using a calculatormay take more time. When answering a question, always consider thereasonableness of the answer—this is the best way to catch mistakesthat may have occurred in your calculations.REMEMBERNever leave questions blank on theSAT, as there is no penalty for wronganswers. Even if you’re not sure ofthe correct answer, eliminate asmany answer choices as you canand then guess from among theremaining ones.258Remember, there is no penalty for guessing on the SAT. If you don’tknow the answer to a question, make your best guess for that question.Don’t leave any questions blank on your answer sheet. When you’reunsure of the correct answer, eliminating the answer choices you knoware wrong will give you a better chance of guessing the correct answerfrom the remaining choices.On the no-calculator portion of the test, you have 25 minutes to answer20 questions. This allows you an average of about 1 minute 15 secondsper question. On the calculator portion of the test, you have 55 minutesto answer 38 questions. This allows you an average of about 1 minute26 seconds per question. Keep in mind that you should spend less timeon easier questions so you have more time available to spend on themore difficult ones.
Chapter 20 Sample Math Questions: Multiple-Choice3Directions3The directions below precede the no-calculator portion of the SAT MathTest. The same references provided in the no-calculator portion of theSAT Math Test are also provided in the calculator portion of the test.PRACTICE ATsatpractice.orgFamiliarize yourself with all testdirections now so that you don’thave to waste precious time on testday reading the directions.Math Test – No Calculator2 5 M INU TES, 2 0 QU EST I O NSTurn to Section 3 of your answer sheet to answer the questions in this section.For questions 1-15, solve each problem, choose the best answer from the choicesprovided, and fill in the corresponding bubble on your answer sheet. For questions 16-20,solve the problem and enter your answer in the grid on the answer sheet. Please refer tothe directions before question 16 on how to enter your answers in the grid. You may useany available space in your test booklet for scratch work.1. The use of a calculator is not permitted.2. All variables and expressions used represent real numbers unless otherwise indicated.3. Figures provided in this test are drawn to scale unless otherwise indicated.4. All figures lie in a plane unless otherwise indicated.5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x forwhich f(x) is a real number. rwA pr 2C 2prV whb1A bh2A wh hrwV pr 2hh2xcbac 2 a2 b 2rxs 45 s 230 45 sx 3Special Right Triangleshhr4V pr 3360 1V pr 2h3w V 1 wh3The number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2p.The sum of the measures in degrees of the angles of a triangle is 180.259
PART 3 MathSample Questions:Multiple-Choice – No Calculator1Line ℓ is graphed in the xy-plane below.yℓ5–55x–5If line ℓ is translated up 5 units and right 7 units, then what is the slope ofthe new line?2A)53B) 28C) 911D) 14Content: Heart of AlgebraKey: BPRACTICE ATsatpractice.orgObjective: You must make a connection between the graphical form of arelationship and a numerical description of a key feature.Your first instinct on this questionmay be to identify two coordinateson line ℓ, shift each of them over5 and up 7, and then calculate theslope using the change in y over thechange in x. While this will yield thecorrect answer, realizing that a linethat is translated is simply shiftedon the coordinate plane but retainsits original slope will save time andreduce the chance for error. Alwaysthink critically about a questionbefore diving into your calculations.Explanation: Choice B is correct. The slope of a line can be determinedby finding the difference in the y-coordinates divided by the difference inthe x-coordinates for any two points on the line. Using the points3indicated, the slope of line ℓ is . Translating line ℓ moves all the points2on the line the same distance in the same direction, and the image will be3a line parallel to ℓ. Therefore, the slope of the image is also .2Choice A is incorrect. This value may result from a combination oferrors. You may have erroneously determined the slope of the new lineby adding 5 to the numerator and adding 7 to the denominator in the( 3 5)slope of line ℓ and gotten the result .( 2 7)260
Chapter 20 Sample Math Questions: Multiple-ChoiceChoice C is incorrect. This value may result from a combination oferrors. You may have erroneously determined the slope of the newline by subtracting 5 from the numerator and subtracting 7 from thedenominator in the slope of line ℓ.5Choice D is incorrect and may result from adding 7 to the slope of line ℓ.2The average number of students per classroom, y, at Central High School canbe estimated using the equation y 0.8636x 27.227, where x represents thenumber of years since 2004 and x 10. Which of the following statements isthe best interpretation of the number 0.8636 in the context of this problem?A) The estimated average number of students per classroom in 2004B) The estimated average number of students per classroom in 2014C) The estimated yearly decrease in the average number of students perclassroomD) The estimated yearly increase in the average number of students perclassroomContent: Heart of AlgebraKey: DObjective: You must interpret the slope or y-intercept of the graph of anequation in relation to the real-world situation it models. Also, when themodels are created from data, you must recognize that these models onlyestimate the independent variable, y, for a given value of x.Explanation: Choice D is correct. When an equation is written in theform y mx b, the coefficient of the x-term (in this case 0.8636) is theslope of the graph of this equation in the xy-plane. The slope of the graphof this linear equation gives the amount that the average number ofstudents per classroom (represented by y) changes per year (representedby x). The slope is positive, indicating an increase in the average numberof students per classroom each year.Choice A is incorrect and may result from a misunderstanding of slopeand y-intercept. The y-intercept of the graph of the equation representsthe estimated average number of students per classroom in 2004.Choice B is incorrect and may result from a misunderstanding ofthe limitations of the model. You may have seen that x 10 anderroneously used this statement to determine that the model finds theaverage number of students in 2014.Choice C is incorrect and may result from a misunderstanding of slope.You may have recognized that slope models the rate of change butthought that a slope of less than 1 indicates a decreasing function.261
PART 3 Math34 , and y 0 where a 1, what is y in terms of a?2 Ifa 1 yA) y 2a 2B) y 2a 41C) y 2a 21a 1D) y 2PRACTICE ATsatpractice.orgWhen working with rationalequations, you can multiply bothsides of the equation by the lowestcommon denominator to cleardenominators. In Example 3, therational equation consists of twofractions set equal to each other.In this case, cross multiplicationproduces the same result asmultiplying both sides of theequation by the lowest commondenominator.Content: Passport to Advanced MathKey: AObjective: You must complete operations with multiple terms andmanipulate an equation to isolate the variable of interest.Explanation: Choice A is correct. Multiplying both sides of the equationby the denominators of the rational expressions in the equationgives 2y 4a 4. You should then divide both sides by 2 to isolate they variable, yielding the equation y 2a 2.Choice B is incorrect. This equation may be the result of not dividingboth terms by 2 when isolating y in the equation 2y 4a 4.Choice C is incorrect. This equation may result from not distributingthe 4 when multiplying 4 and (a 1).Choice D is incorrect. This equation may result from solving 2y 4a 41for a, yielding a y 1. A misunderstanding of the meaning of2variables may have resulted in switching the variables to match theanswer choice.4In the complex number system,which of the following is equal to(14 2i)(7 12i)? (Note: i 1) A)B)C)D)PRACTICE ATsatpractice.orgMultiply complex numbers in thesame way you would multiplybinomials (by the “FOIL” method orby using the distributive property).Remember that i 1 and thati 2 1.2627412274 154i122 154iContent: Additional Topics in MathKey: DObjective: You must apply the distributive property on two complexbinomials and then simplify the result.Explanation: Choice D is correct. Applying the distributive propertyto multiply the binomials yields the expression98 168i 14i 24i 2.The note in the question reminds you that i 1 ; therefore,i 2 1. Substituting this value into the expression gives you98 168i 14i ( 24), and combining like terms results in 122 154i.
Chapter 20 Sample Math Questions: Multiple-ChoiceChoice A is incorrect and may result from a combination of errors. Youmay not have correctly distributed when multiplying the binomials,multiplying only the first terms together and the second terms together.You may also have used the incorrect equality i 2 1.Choice B is incorrect and may result from a combination of errors. Youmay not have correctly distributed when multiplying the binomials,multiplying only the first terms together and the second terms together.Choice C is incorrect and results from misapplying the statement i 1 .5The graph of y (2x 4)(x 4) is a parabola in the xy-plane. In which ofthe following equivalent equations do the x- and y-coordinates of thevertex of the parabola appear as constants or coefficients?A)B)C)D)y 2x 2 12x 16y 2x(x 6) 16y 2(x 3)2 ( 2)y (x 2)(2x 8)Content: Passport to Advanced MathKey: CObjective: You must be able to see structure in expressions and equationsand create a new form of an expression that reveals a specific property.Explanation: Choice C is correct. The equation y (2x 4)(x 4) can bewritten in vertex form, y a (x h )2 k, to display the vertex, (h, k ), of theparabola. To put the equation in vertex form, first multiply:(2x 4)(x 4) 2x 2 8x 4x 16. Then, add like terms,2x 2 8x 4x 16 2x 2 12x 16. The next step is completing thesquare.y 2x 2 12x 16y 2(x 2 6x ) 16y 2(x 2 6x 9 9) 16y 2(x 2 6x 9) 18 16y 2(x 3)2 18 16y 2(x 3)2 2Isolate the x 2 term by factoring.Make a perfect square in the parentheses.Move the extra term out of the parentheses.Factor inside the parentheses.Simplify the remaining terms.Therefore, the coordinates of the vertex, (3, 2), are both revealed onlyin choice C. Since you are told that all of the equations are equivalent,simply knowing the form that displays the coordinates of the vertexwill save all of these steps—this is known as “seeing structure in theexpression or equation.”Choice A is incorrect; it is in standard form, displaying the y-coordinateof the y-intercept of the graph (0, 16) as a constant.Choice B is incorrect; it displays the y-coordinate of the y-intercept ofthe graph (0, 16) as a constant.PRACTICE ATsatpractice.orgWhile you may be asked to writethe equation of a parabola in vertexform, sometimes simply knowing theform that displays the coordinatesof the vertex will suffice, saving youprecious time.Choice D is incorrect; it displays the x-coordinate of one of thex-intercepts of the graph (2, 0) as a constant.263
PART 3 Math6If , where a 0 and x 0, which of the following equations gives ain terms of x?1A) a x1B) a x2C) a xD) a x 2Content: Passport to Advanced MathKey: BObjective: You must demonstrate fluency with the properties ofexponents. You must be able to relate fractional exponents to radicals aswell as demonstrate an understanding of negative exponents.PRACTICE ATsatpractice.orgKnow the exponent rules andpractice applying them. Thisquestion tests several of them:11. a b can be written as ba12. a2 is the same as a3. a2 a4. To eliminate a radical from an1 x, square bothequation, as in asides of the equation.Explanation: Choice B is correct. There are multiple ways to approachthis problem, but all require an understanding of the properties of1 x and then proceed toexponents. You may rewrite the equation as a12solve for a, first by squaring both sides, which gives a x , and then bymultiplying both sides by a to find 1 ax 2. Finally, dividing both sides byx 2 isolates the desired variable.Choice A is incorrect and may result from a misunderstanding of theproperties of exponents. You may understand that a negative exponentcan be translated to a fraction but misapply the fractional exponent.Choice C is incorrect and may result from a misunderstanding of the1properties of exponents. You may recognize that an exponent of is the2same as the square root but misapply this information.Choice D is incorrect and may result from a misunderstanding of theproperties of exponents. You may recognize that raising a to the power1of is the same as taking the square root of a and, therefore, that a2can be isolated by squaring both sides. However, you may not haveunderstood how the negative exponent affects the base of the exponent.7If y x 3 2x 5 and z x 2 7x 1, what is 2y z in terms of x?A)B)C)D)3x 3 11x 112x 3 x 2 9x 62x 3 x 2 11x 112x 3 2x 2 18x 12Content: Passport to Advanced MathKey: CObjective: You must substitute polynomials into an expression and thensimplify the resulting expression by combining like terms.264
Chapter 20 Sample Math Questions: Multiple-ChoiceExplanation: Choice C is correct. Substituting the expressions equivalentto y and z into 2y z results in the expression 2(x 3 2x 5) x 2 7x 1.You must apply the distributive property to multiply x 3 2x 5 by 2 andthen combine the like terms in the expression.Choice A is incorrect and may result if you correctly found 2y in terms ofx but did not pay careful attention to exponents when adding theexpression for 2y to the expression for z. As a result, you may havecombined the x 3 and x 2 terms.Choice B is incorrect and may result if you failed to distribute the 2when multiplying 2(x 3 2x 5).Choice D is incorrect and may result from finding 2(y z) instead of2y z.PRACTICE ATsatpractice.orgDon’t worry if you missed thisquestion; there are severalways to make a mistake.Always be methodical whendoing calculations or simplifyingexpressions, and use the space inyour test booklet to perform thesteps in finding your answer.8( )π ? Which of the following is equal to sin5π A) cos5π B) sin53πC) cos 107π D) sin10( )( )( )( )Content: Additional Topics in MathKey: CObjective: You must understand radian measure and have a conceptualunderstanding of trigonometric relationships.Explanation: Choice C is correct. Sine and cosine are cofunctions, or areπ ,π x . Therefore, sin π cos π related by the equation sin(x) cos 522 5 .which reduces to cos 3π10Choice A is incorrect and may result from a misunderstanding abouttrigonometric relationships. You may have thought that cosine is theinverse function of sine and therefore reasoned that the negative of thecosine of an angle is equivalent to the sine of that angle.( )()( )()Choice B is incorrect and may result from a misunderstanding ofthe unit circle and how it relates to trigonometric expressions. Youmay have thought that, on a coordinate grid, the negative sign onlychanges the orientation of the triangle formed, not the value of thetrigonometric expression.Choice D is incorrect. You may have confused the relationship betweenπsine and cosine and erroneously added to the given angle measure2πinstead of subtracting the angle measure from .2265
PART 3 Math9DCABThe semicircle above has a radius of r inches, and chord CD is parallel tothe diameter AB. If the length of CD is of the length of AB, what is thedistance between the chord and the diameter in terms of r ?1 πrA)32 πrB)3C) 2 r2PRACTICE ATsatpractice.orgQuestion 9 is a particularlychallenging question, one that mayrequire additional time to solve. Becareful, however, not to spend toomuch time on a question. If you’reunable to solve a question in areasonable amount of time at first,flag it in your test booklet and returnto it after you’ve attempted the restof the questions in the section.PRACTICE ATsatpractice.orgAdvanced geometry questions mayrequire you to draw shapes, suchas triangles, within a given shape inorder to arrive at the solution. 5D)r3Content: Additional Topics in MathKey: DObjec
257 CHAPTER 20. Sample Math Questions: Multiple-Choice. In the previous chapters, you learned about the four areas covered by the SAT Math Test. On the test, questions from the areas are mixed
Part One: Heir of Ash Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26 Chapter 27 Chapter 28 Chapter 29 Chapter 30 .
TO KILL A MOCKINGBIRD. Contents Dedication Epigraph Part One Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Part Two Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18. Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 Chapter 24 Chapter 25 Chapter 26
DEDICATION PART ONE Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 PART TWO Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22 Chapter 23 .
Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra 1/2 Math 5/4, Math 6/5, Math 7/6, Math 8/7, and Algebra ½ form a series of courses to move students from primary grades to algebra. Each course contains a series of daily lessons covering all areas of general math. Each lesson
18.4 35 18.5 35 I Solutions to Applying the Concepts Questions II Answers to End-of-chapter Conceptual Questions Chapter 1 37 Chapter 2 38 Chapter 3 39 Chapter 4 40 Chapter 5 43 Chapter 6 45 Chapter 7 46 Chapter 8 47 Chapter 9 50 Chapter 10 52 Chapter 11 55 Chapter 12 56 Chapter 13 57 Chapter 14 61 Chapter 15 62 Chapter 16 63 Chapter 17 65 .
New Test Questions Sample multiple-choice math questions are designed to assess CCLS math standards and incorporate both standards and math practices in real-world applications. Math multiple-choice questions assess procedural and conceptual standards. Unlike questions on past math assessments, many require the use of multiple skills and concepts.
MATH 110 College Algebra MATH 100 prepares students for MATH 103, and MATH 103 prepares students for MATH 110. To fulfil undergraduate General Education Core requirements, students must successfully complete either MATH 103 or the higher level MATH 110. Some academic programs, such as the BS in Business Administration, require MATH 110.
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