Math Test Sections. The College Board: Expanding College Opportunity

Transcription

1 Taking te SAT I: Reasoning Test Mat Test Sections Te materials in tese files are intended for individual use by students getting ready to take an SAT Program test; permission for any oter use must be sougt from te SAT Program. Scools (state-approved and/or accredited diploma-granting secondary scools) may reproduce tem, in wole or in part, in limited quantities, for face-to-face guidance/teacing purposes but may not mass distribute te materials, electronically or oterwise. Tese materials and any copies of tem may not be sold, and te copyrigt notices must be retained as tey appear ere. Tis permission does not apply to any tird-party copyrigts contained erein. No commercial use or furter distribution is permitted. Te College Board: Epanding College Opportunity Te College Board is a national nonprofit member association dedicated to preparing, inspiring, and connecting students to college and opportunity. Founded in, te association is composed of more tan, scools, colleges, universities, and oter educational organizations. Eac year, te College Board serves over tree million students and teir parents,, ig scools, and, colleges troug major programs and services in college admission, guidance, assessment, financial aid, enrollment, and teacing and learning. Among its best-known programs are te SAT, te PSAT/NMSQT, and te Advanced Placement Program (AP ). Te College Board is committed to te principles of equity and ecellence, and tat commitment is embodied in all of its programs, services, activities, and concerns. Copyrigt by College Entrance Eamination Board. All rigts reserved. Advanced Placement, AP, College Board, SAT, and te acorn logo are registered trademarks of te College Entrance Eamination Board. PSAT/NMSQT is a registered trademark of te College Entrance Eamination Board and National Merit Scolarsip Corporation. Tis publication was prepared and produced by Educational Testing Service (ETS), wic develops and administers SAT Program tests for te College Board. Te College Board and Educational Testing Service are dedicated to te principle of equal opportunity, and teir programs, services, and employment policies are guided by tat principle.

2 SECTION Time minutes Questions Directions: In tis section solve eac problem, using any available space on te page for scratcwork. Ten decide wic is te best of te coices given and fill in te corresponding oval on te answer seet. Notes:. Te use of a calculator is permitted. All numbers used are real numbers.. Figures tat accompany problems in tis test are intended to provide information useful in solving te problems. Tey are drawn as accurately as possible EXCEPT wen it is stated in a specific problem tat te figure is not drawn to scale. All figures lie in a plane unless oterwise indicated. Reference Information r r w w b A = πr A = w C = πr A = b V = w V = πr Te number of degrees of arc in a circle is. Te measure in degrees of a straigt angle is. Te sum of te measures in degrees of te angles of a triangle is. c b a c = a + b s s s Special Rigt Triangles. If = (A) (B) (C) (D) (E), wat is te value of? + A B P. In te figure above, point P is on line. Wat is te value of? (A) (B) (C) (D) (E) C D Taking te SAT I: Reasoning Test

3 SID S CHECKING ACCOUNT Cange in Days Account Balance (in dollars) Monday + Tuesday Wednesday Tursday + Friday. Te cart above sows te dollar amounts tat were added to or subtracted from Sid s cecking account on eac of days. According to te cart, te total cange in Sid s account balance for all five days is equal to te cange in te account balance for wic single day? (A) Monday (B) Tuesday (C) Wednesday (D) Tursday (E) Friday. In te y-coordinate plane, te coordinates of tree vertices of a rectangle are (, ),(, ), and (, ). Wat are te coordinates of te fourt verte of te rectangle? (A) (, ) (B) (, ) (C) (, ) (D) (, ) (E) (, ). Francis bougt a stereo for dollars and sold it at a percent profit. Wic of te following gives te amount of Francis profit? (A) $. (B) $. (C) $. (D) $. (E) $. K. In te equation above, K is a digit in te tree-digit number K, and m is a positive integer. Wic of te following could be te digit K? (A) (B) (C) (D) (E). If w < < z and w < y < z, wic of te following statements must be true? I. w < z II. < y III. y < z (A) I only (B) II only (C) III only (D) I and III only (E) I, II, and III = m {,,, }. If k is a number so tat te sum of k and any number in te set above is also in te set, wat is te value of k? (A) (B) (C) (D) (E) Taking te SAT I: Reasoning Test

4 . Te figure above sows a ramp tat etends from level ground to te bed of a truck. Wat is te slope of te ramp? (A) (B) (C) (D) (E) Note: Figure not drawn to scale.,,,,,,,. Te average (aritmetic mean) of te numbers listed above is. Of te following, wic pair of numbers could be removed from te list witout canging te average? (A) and (B) and (C) and (D) and (E) and. Tree percent of, is equal to percent of wat number? (A), (B), (C), (D) (E). Four lines are drawn troug te center of te rectangle sown above. Wat fraction of te area of te rectangle is saded? (A) (B) (C) (D) (E). If n k = and n and k are integers, wic of te following could NOT be a value of n? (A) (B) (C) (D) (E). If is more tan, ten is ow muc more tan? (A) (B) (C) (D) (E) Taking te SAT I: Reasoning Test

5 . Te sum of five consecutive wole numbers is less tan. One of te numbers is. Wic of te following is te greatest of te consecutive numbers? (A) (B) (C) (D) (E). Te pie cart above sows te tree sources for Lana s college tuition. If of te total amount was from scolarsips and was from student loans, wat is te value of? (A) (B) (C) (D) (E) n. If ( + ) ( ) = ( + ) for all values of, wat is te value of n? (A) (B) (C) (D) (E) It cannot be determined from te information given.. If a is greater tan, ten, of te following, wic will always ave te least value? (A) a (B) (C) (D) (E) a a + a a +. A circle of radius and a circle of radius ave eactly one point in common. If P is a point on one circle and Q is a point on te oter circle, wat is te maimum possible lengt of segment PQ? (A) (B) (C) (D) (E). Te coordinates of tree points are given in te figure above. Wic of te following must be true? I. b = c II. f > e III. a + d = (A) None (B) I only (C) I and II only (D) II and III only (E) I, II, and III Taking te SAT I: Reasoning Test

6 . Emerson Scool as s students equally divided among c classes. Te scool wants to order enoug ealt tetbooks so tat eac student will ave a book and eac class will ave etra books. How many ealt tetbooks does te scool need to order? s (A) c + (B) s + (C) s + c (D) c (E) + s cs+ ( ). Wen a coin is tossed in an eperiment, te result is eiter a ead or a tail. A ead is given a point value of and a tail is given a point value of. If te sum of te point values after tosses is, ow many of te tosses must ave resulted in eads? (A) (B) (C) (D) (E). If a triangle as eactly one of its vertices on a circle, wic of te following CANNOT be te number of points tat te triangle and te circle ave in common? (A) Two (B) Tree (C) Four (D) Five (E) Si List I List II. One number is to be selected at random from eac of te lists above. Wat is te probability tat bot of te numbers selected will be less tan? (A) (B) (C) (D) (E). How many positive integers less tan, are divisible by eiter or or bot? (A) (B) (C) (D) (E) STOP If you finis before time is called, you may ceck your work on tis section only. Do not turn to any oter section in te test. Taking te SAT I: Reasoning Test

7 SECTION Time minutes Questions Directions: Tis section contains two types of questions. You ave minutes to complete bot types. You may use any available space for scratcwork. Notes:. Te use of a calculator is permitted. All numbers used are real numbers.. Figures tat accompany problems in tis test are intended to provide information useful in solving te problems. Tey are drawn as accurately as possible EXCEPT wen it is stated in a specific problem tat te figure is not drawn to scale. All figures lie in a plane unless oterwise indicated. Reference Information r r w w b A = πr A = w C = πr A = b V = w V =πr Te number of degrees of arc in a circle is. Te measure in degrees of a straigt angle is. Te sum of te measures in degrees of te angles of a triangle is. c b a c = a + b s s s Special Rigt Triangles Directions for Quantitative Comparison Questions Questions - eac consist of two quantities in boes, one in Column A and one in Column B. You are to compare te two quantities and on te answer seet fill in oval A if te quantity in Column A is greater; B if te quantity in Column B is greater; C if te two quantities are equal; D if te relationsip cannot be determined from te information given. AN E RESPONSE WILL NOT BE SCORED. Notes:. In some questions, information is given about one or bot of te quantities to be compared. In suc cases, te given information is centered above te two columns and is not boed.. In a given question, a symbol tat appears in bot columns represents te same ting in Column A as it does in Column B.. Letters suc as, n, and k stand for real numbers. E E E EXAMPLES Column A Column B Answers r and s are integers. r + s A B C D E A B C D E A B C D E Taking te SAT I: Reasoning Test

8 Answer: SUMMARY DIRECTIONS FOR COMPARISON QUESTIONS A if te quantity in Column A is greater; B if te quantity in Column B is greater; C if te two quantities are equal; D if te relationsip cannot be determined from te information given. Column A Column B Column A Column B is greater tan y.. y + is a positive even integer less tan.. + BC =. Te lengt of segment AD. w + y A stadium contains, seats. At a certain event, percent of te seats remained empty.. Te number of empty seats. < z < z. Te number of different two-letter pairs tat can be formed using te letters C, A, and T Te number of different two-letter pairs tat can be formed using te letters D, O, and G. Te area of a circle wit radius Taking te SAT I: Reasoning Test

9 Answer: SUMMARY DIRECTIONS FOR COMPARISON QUESTIONS A if te quantity in Column A is greater; B if te quantity in Column B is greater; C if te two quantities are equal; D if te relationsip cannot be determined from te information given. Column A Column B Column A Column B. > ( + ) + Sara eiter drives er car to work or walks to work. Sara never drives er car to work on a sunny day. It takes Sara minutes to walk to work and minutes to drive to work.. Te time tat it takes Sara to get to work on a rainy day minutes Lines, m, and n lie in plane P.. Te number of points tat lie on more tan one of te tree lines < <.. n + n + Te retail price of a certain computer at Computer Junction is percent more tan its wolesale price. For a sale, te manager reduces te retail price of tat computer by percent. y =. y y. Te wolesale price of te computer Te price of te computer for te sale Taking te SAT I: Reasoning Test

10 Taking te SAT I: Reasoning Test Unautorized copying or reuse of Directions for Student-Produced Response Questions Eac of te remaining questions requires you to solve te problem and enter your answer by marking te ovals in te special grid, as sown in te eamples below. Decimal Accuracy: If you obtain a decimal answer, enter te most accurate value te grid will accommodate. For eample, if you obtain an answer suc as...., you sould record te result as. or.. Less accurate values suc as. or. are not acceptable. Acceptable ways to grid =.... Note: You may start your answers in any column, space permitting. Columns not needed sould be left blank. Mark no more tan one oval in any column. Because te answer seet will be macinescored, you will receive credit only if te ovals are filled in correctly. Altoug not required, it is suggested tat you write your answer in te boes at te top of te columns to elp you fill in te ovals accurately. Some problems may ave more tan one correct answer. In suc cases, grid only one answer. No question as a negative answer. Mied numbers suc as must be gridded as. or. (If is gridded, it will be interpreted as, not.) Answer:. Fraction line Decimal point Write answer in boes. Grid in result. Answer: Eiter position is correct. or Answer:. If + =, wat is te value of +?. If te ratio of to is equal to te ratio of to, and if te ratio of to g is equal to te ratio of to, wat is te value of g +?

11 . For positive integers a, b, c, and d, is defined as te greater number in te top row minus te lesser number in te bottom row. Wat is te value of? APARTMENT FEATURES Built-in Yes Bookcases No Fireplace Yes No Totals Totals. Te partially completed cart above refers to apartments, of wic ave fireplaces. How many of te apartments ave built-in bookcases?. Te lengts of two sides of an isosceles triangle are and. Wat is one possible lengt of te tird side?. If and y are positive, y =, and y =, wat is te value of y? Taking te SAT I: Reasoning Test

12 . Te average (aritmetic mean) of a set of different numbers is. If te numbers and are removed from te set, wat is te average of te remaining numbers? A B P. In te figure above, te seven small circles, wic ave equal radii, and te large circle sare only tose points on te circles tat are marked. Point P is te center of te large circle and PA and PB are radii. Te area of te saded portion is ow many times te area of one of te small circles?. A rectangle measuring centimeters by centimeters is completely divided into t nonoverlapping triangles, eac wit sides of lengt centimeters, centimeters, and centimeters. Wat is te value of t?. Diana ran a race of meters in two laps of equal distance. Her average speeds for te first and second laps were meters per second and meters per second, respectively. Wat was er average speed for te entire race, in meters per second? STOP If you finis before time is called, you may ceck your work on tis section only. Do not turn to any oter section in te test. Taking te SAT I: Reasoning Test

13 SECTION Time minutes Questions Directions: In tis section solve eac problem, using any available space on te page for scratcwork. Ten decide wic is te best of te coices given and fill in te corresponding oval on te answer seet. Notes:. Te use of a calculator is permitted. All numbers used are real numbers.. Figures tat accompany problems in tis test are intended to provide information useful in solving te problems. Tey are drawn as accurately as possible EXCEPT wen it is stated in a specific problem tat te figure is not drawn to scale. All figures lie in a plane unless oterwise indicated. Reference Information r r c w b w b A = πr a A = w C = πr A = b V = w V = πr c = a + b Te number of degrees of arc in a circle is. Te measure in degrees of a straigt angle is. Te sum of te measures in degrees of te angles of a triangle is. s s s Special Rigt Triangles. A car rental agency carges $ a day plus $. per mile for its rental cars. If tese carges include ta, wat is te total cost of traveling miles in days in a car rented from tis agency? (A) $ (B) $ (C) $ (D) $ (E) $. In te figure above, wat is te value of? (A) (B) (C) (D) (E) Taking te SAT I: Reasoning Test

14 . Te ratio of toggle-bolt prices in year X to toggle-bolt prices in year Y was to. If te ratio of prices in year Y to prices in year Z was to, wat was te ratio of prices in year X to prices in year Z? (A) to (B) to (C) to (D) to (E) to B A. In te cube above, AB =. Wat is te perimeter of rectangle ABCD? (A) (B) (approimately.) (C) + (approimately.) (D) + (approimately.) (E) + (approimately.) C D. A group of people is divided into committees. If eac committee contains at least people, wic of te following statements must be true? (A) Eac committee as at least people. (B) No committees ave te same number of people. (C) No committee as more tan people. (D) At least committee as more tan people. (E) Te largest committee as more people tan te smallest committee. n =.... Te integer n is formed by writing te positive integers in a row, starting wit and ending wit, as sown above. Counting from te left, wat is te t digit of n? (A) (B) (C) (D) (E) Taking te SAT I: Reasoning Test

15 . Wat are all possible values of for wic =? (A) All real numbers ecept (B) only (C) only (D) only (E) No real numbers y. Te figure above sows si rigt triangles. Wat is te value of + y? (A) (B) (C) (D) (approimately.) (E) (approimately.). If + y =, wat is y + in terms of y? (A) (B) (C) (D) (E) y y y y + y. For positive integers, let te symbol represent te sum of te digits of. For eample, = + =. If n is a positive integer and n = +, wic of te following could be te value of n? (A) (B) (C) (D) (E) STOP If you finis before time is called, you may ceck your work on tis section only. Do not turn to any oter section in te test. Taking te SAT I: Reasoning Test