Basic Geometric Concepts and Coordinate Geometry 371 24. Snowhite Paint Co. contracts to paint three houses. Andy can paint a house in 6 days, while Bruce would take 8 days and CarI would take 12 days. After 8 days Andy goes on vacation, and Bruce begins t0 work for a period of 6 days. HOW many days will. it take Carl to complete the contract? (A) 7 (B) 8 (C) 11 (D) 12 (E) 13 Answer Key 4. 25. Mr. Stanley mowed ー of his lawn in ト hours. Mr. SamueIs, who works twice as fast, finished mowing the lawn. How many minutes did Mr. SamueIs work? (A) 12 ー (B) 怡 (C) 25 (D) 38 (E) 50 っ 4 つ」っ 4 つ」っ」 ・ 6- 7 ・ 8 O ・ . 0 一 6 7 ー 8 9- 0 Basic Geometric Concepts and Coordinate Geometry The questions appearing on the SAT that involve geometry make use Of only elementary ideas con- cerning such simple plane figures as angles, lines, circles, and triangles and such simple solid figures as spheres and rectangular solids. A list Of geometric facts is given at the beginning Of each math section Of the SAT, and almost all Of the geometry questions can be worked using these facts as a basis. The more experience you have with the use Of these facts, however, the easier you will find the questions and the quicker you will discover the methods needed tO answer them. The skills you need tO practice involve the following: area, circumference, and arc measures Of circles, angle relationships in triangles; the area Of a trian- gle; the relationship between the sides Of a right tri- angle; the area and perimeter Of a rectangle; and the volumes Of rectangular and spherical solids. TO help you visualize these relationships, we have compiled a summary Of facts and fundamental situa- tions involving common geometric ideas. Be sure tO master these concepts. po 『ね nt Definitions, ReIationships, and Measurements PO 加″ , 2 〃 Planes The building blocks Of geometry are points, lines, and planes. A point indicates a position and has no length, width, or thickness. A line is a continuous set Of points that is straight and infinitely long in tWO opposite directions, but has no width or thick- ness. A plane is a flat surface that extends in all directions but has no thickness. MOSt geometric figures are formed by joining parts Of lines—either line segments or rays. A line seg• ment has tWO points Of a line as endpoints and con- tains all points Of the line that lie between the end- points. A ray has one point of a line as an endpoint and contains all Of the points that lie on a given side of the line. drawings, these figures appear like this: 0 r げ two different rays have the same endpoint, they form an angle The common endpoint is called the vertex, and the rays are called the sides. The angle directly above has rays that are opposite tO each Other and lie along a straight

382 Reviewing Mathematics ■ If ( 3 、一 I) is one endpoint Ofa segment and ( 5 , 0 ) is its midpoint, find the coordinates Of the Other endpoint. Let (. v 、ⅵ be the other endpoint. Practice Exercises coordinates Of point B are ー 5 ). The the coordinates Of point A are ( ー 2. 4. Point P ( 0. ー 4 ) is the midpoint of line AB. where (E) ( 8 、 4 ) (A) ( 2. い (B) ( 4 、 8 ) (C) ( 4 、 4 ) (D) ( 8. 2 ) is at origin ( 0 、 0 ). The coordinates 0f C are Point P ( 4. 2 ) is the midpoint of line OPC. where 0 (A) 0 (B) 5 (C) IO (D) い (E) 凵 What is the distance from point ハ ( 3 、 4 ) to point (E) ( 4. 2 ) (A) い、 3 ) (B) ( 3. 5 ) (C) ( 6 コ 0 ) (D) ( 2. 4 ) midpoint'? point ( 4. 7 ). What are the coordinates 0f the l. A line segment AB is drawn from point ( 2 , 3 ) and 3. (A) obtuse (B) isosceles (C) right and ( ー 3. 2 ). Triangle ABC is 5. The vertices Of triangle ABC are ( ー (A) 2 (B) 4 (C) 8 (D) 12 (E) 16 ( 4. 4 ). ( 8. 4 ). and ( 8. 0 ). The area of ABCD equals 9. The vertices of square ABCD are as follows: ( 4. 0 ). (E) ( 4. 6.5 ) (A) ( 5. 4 ) (B) ( 4. 5 ) (C) ( 6. 4.5 ) (D) ( 4. 6 ) The coordinates of point M are A ( 2. 3 ). B ( 8. 3 ). and C ( 6. 7 ). Median BM is drawn. 8. The vertices of triangle ABC are as follows: (D) AB く BC (E) AC = BC (A) AB = BC (B) AB = AC (C) AB > BC statements iS true? B ( 9. 4 ) 、 and C( l. 7 ). Which of the following 7. Triangle ABC has the following vertices: A い . い . (E) neither isosceles nor right (C) either equilateral or obtuse (D) isosceles (A) equilateral (B) acute and ( ー 3. 2 ). Triangle DEF is 6. The vertices of triangle DEF are い . 2 ). ( (D) equilateral (E) either isosceles or equilateral x 十 3 2 The other endpoint is ( 7 , l). 2 IO. The vertices of triangle ABC are ( 2 , 2 ) , ( 2 , 6 ) , and ( 6 , 2 ). The area of triangle ABC is (A) 8 (B) 10 (C) 12 (D) 凵 (E) 16 What is the area Of a square whose points (corners) are ( 0 、 4 ) , ( 4 , 0 ) , ( 0 , ー 4 ) , and ( ー 4 、 0 ) ? (A) 4 (B) 8 (C) 16 (D) 32 (E) 64 に . The area of a circle whose center is at ( 0 , 0 ) is 9 化 The circle passes through all Of the following points EXCEPT (E) ( 3 、 3 ) い . Quadrilateral ABCD has the following points as its vertices: ( 2. 2 ) 、 ( 6 , 2 ) 、 ( ーエー 2 ) 、 and ( 6 、一 2 ). The area of ABCD is (A) 4 (B) 8 (C) 24 (D) 32 (E) 64 AB is a diameter Of a circle whose ・ center is 0. The coordinates Of point ス are ( ー 2 , 0 ). The coordinates 0f point B are ( 2. 0 ). The circle passes through a point whose coordinates are (B) ( ー 2. 2 ) (C) ( 0 、 4 ) (D) ( 0. ー 2 ) (E) ( 2. 2 ) A circle whose center iS at origin 0 passes through point 尸 ( 4. 3 ). The length 0f the radius 0f this circle ー S (A) 3 (B) 3.5 (C) 4 (D) 4.5 (E) 5 . The coordinates Of a point equally distant from A ( 4. ーコ ) and B ( 4. 6 ) and on the v-axis are (A) ( 0 、 2 ) (B) ( 0. 4 ) (C) ( 0. 8 ) (D) ( 2 、 0 ) (E) ( 2. 2 ) 17. Triangle ABC. is formed by joining point A ( 6 、 5 ). point B ( ー 3. 2 ). and point C ( 9. ー 4 ). If median AM is drawn. the coordinates Of point M are 18. Line segment AB is drawn from point ( ー 3. 4 ) tO point ( ー 3. ー 4 ). Line segment CD is drawn from point ( 3. 3 ) t0 point ( 3 、一 5 ). Which 0f the following is always true? (A) AB > CD (B) AB < CD (C) AB Ⅱ CD (D) AB intersects CD (E) AB 亠 CD ー 4. Ⅱ . い .

16. 17. C. 18. 19. 20. 21. 22. C. A. E. D. D. You can immediately eliminate ど SO ん e , d 〃れⅲなん and 〃行れ i 襯た e , WhiCh make no sense in the context. (Contrast Signal) Just as the 〃ど grows within the 〃 0d , the れ grows within the 朝ど〃 . (Part to WhoIe) A ca 〃襯 may be made 0f 〃 ow ; a s れ化 , 0f わ ro れど . (Part to Whole) A ーん〃れ 0 川どー′ measures temperature or ん a Geiger CO ″′など r measures r dia 行 0 れ . Ch0ice A is incorrect. A filament (the conductor inside a light bulb) gives 0 仕 light; it doesn't measure light. Choice B iS incorrect. A chronometer measures time, not C010r. Choice C iS incorrect. An odometer measures distance, not waves. Choice E iS incorrect. A barometer measures atmospheric pressure, not electricity. (Function) A んれ g の・ is a place for servicing and stormg 召か〃れ e ; a garage iS a place for servicing and storing こ 0 襯 0 わ″ & If your original sentence was 、、 An airplane iS found in a hangar," Ch0ices A, B, C, and E would all have made good ånalogies. If more than one answer appears tO fit your original sentence, you need tO state the relationship more precisely. (Definition) TO g ″ゆ is more extreme than tO ⅵ〃 ; tO g ″ガ 4 ル (laugh loudly and boisterously) is more extreme than tO giggle. (Degree of lntensity) A 〃〃肥 is a sharp-pointed outgrowth on a c c れハ ; a 4 Ⅲ・″ is a sharp-pointed bristle on a (Part to Wh01e) ScoId and 尾わ″んど are synonyms, as are ん″ー e and ルルでた You need tO know the exact meanings Of words in order tO spot the difference between synonyms and degree Of intensity analogies. Choice A is incorrect. Dislike and loathe (hate) are not synonyms. The relationship is one Of Degree Of lntensity. Choice B is incorrect. lmplore (beg; beseech; ask urgently) and request (ask) are not synonyms. Again, the relationship is one 0f Degree 0f lntensity. (Synonyms) 23. 24. 25. 26. 27. 28. 29. A. D. D. E. E. B. B. Test 2/Answer ExpIanations 491 One example Of a 〃ハ″ p / (mammal that carries itS young in a pouch) iS an 0 〃 055 〃川 ; one example Of a rod どれ一 iS a 4 ″レ r /. Answenng some analogy questions requires specialized technical vocabulary typically used in high schOOl science, literature, and SOCial SC1ence classes. (Class to Member) The c 尾立 is a wave's high point; the な 0 ″ g ん , its 10W point. Similarly a 〃た is a high point ofland; a Ⅷ〃 0 , a 10W point. (Spatial Sequence) Titanic (enormous) and ″〃ゆ〃 (tiny or puny) are antonyms. 0 わ (corpulent, excessively fat) and 夜れ ac d (extremely lean, wasted away) are antonyms alSO. (Antonyms) The opening sentence describes the Renaissance artist as an "all-round man. ' ' The passage then develops the idea 0f the Renaissance artist's versatility or adaptability. Remember, when asked to find the main idea, be sure tO check the opening and summary sentences Of each paragraph. (Main Idea/Title) You can arrive at the correct answer by the process Of elimination. Statement I is untrue. The author does not exaggerate facts tO make his point abOlit the Renaissance artist. Therefore, you can eliminate Choices A and D. Statement Ⅱ is true. The author does list examples t0 back up his point. Therefore, you can eliminate Choice C. Statement lll is true. The author cites Edison as an authority on Leonardo. Therefore, you can eliminate Ch0ice B. Only Ch0ice E is left. lt is the correct answer. (Technique) The author admires the diversity Of interest shown by the Renaissance artists. He describes them and their vanous interests in whOlly positive terms. N0te the words great. ' "famous, "well-known, gemus, Remember, when asked tO determine the author's attitude or mood, always 100k for words that convey emotion or paint pictures. (Attitude/Tone) The last paragraph indicates that at least tWO interpretations Of the bOOk are currently in favor. The second paragraph states that critics disagree about what Melville 、、 was trying tO

352 Reviewing Mathematics Multiplication Of decimals by 10 , IOO, 1000 , 0.1 , 0.01 , 0.001 , etc. , can be carried out quickly by changing the position Of the decimal POint. TO multiply by IO, move the decimal point one place tO the right; tO multiply by 100 , move the decimal point two places tO the right; etc. TO multiply by 0.1 , move the deci- mal point one place tO the left; tO multiply by 0.01 , move the decimal point tWO places tO the left; etc. ーワ Examples ・ ( 0.0324 ) ( 0.00D = 0.0000324 ■ ( 324.79 ) ( 0.01) = 3.2479 ■ ( 437.21) ( 0.1) = 43.721 ■ ( 0.003279 ) ( 10 , 000 ) = 32.79 ■ ( 0.27345 ) ( 1000 ) = 273.45 ■ ( 5.9824 ) ( 100 ) = 598.24 ■ ( 72.36 ) ( 10 ) = 723.6 ⅵ S 加 necessary tO carry the division tO one more place decimal places or tO the nearest hundredth," it is When a question is worded ・・ Find correct to two 1 26 3 1 26 3 8 42 4. 邑 . 戸 divisor dividend quotient ■ Divide 9.683 by 4.21. Example dend. tient directly above the decimal point in the divi- places tO the right. Place a decimal point in the quo- mal point Of the dividend the same number Of proper number Of places tO the right. Move the deci- whOle number by moving the decimal point the 旧 dividing decimal nuumbers, make the divisor a 8 ) 0 3.437 ■ Divide correct to two decimal places: 27.5 Example than specified. carried out quickly by changing the position Of the Division Of decimals by 10 , 100 , 1000 , etc. , can be 0.7. ) 0 : öö .314 = ・ Divide 0.22 by 0.7 , correct to two decimal places. Example mal place is less than 5 , drop it. 3.44 コ f the digit just tO the right Of the desired deci- place number.ln the example above, 3.437 becomes place is 5 or greater, add 1 t0 the desired decimal げ the digit just tO the right Of the desired decimal decimal point. TO divide by 10 , move the decimal point one place tO the left; tO divide by 100 , move the decimal point two places tO the left; etc. Examples ■ 72.36 ー 10 = 7.236 ■ 5.9824 ー 100 = 0.059824 ■ 0.27345 ー 1000 = 0.00027345 ■ 0.003279 ー 10 , 000 = 0.0000003279 CO e ⅲ a Fraction tO a DecimaI TO convert a fraction tO a decimal, simply perform the indicated division. The numerator is divided by Examples the denominator. 8 厖面 0 0.875 ■ What is the decimal equivalent of 320 320 448 480 512 560 384 440 2 56 64 ) 新 0 0 0.046875 64 ・ ・ What is the decimal equivalent of 3 49 30 Reduce: 98 60 Divide both sides 0f the equation by 98 : 60 = 98X Subtract ム from b0th sides 0f the equation: ム十 60 = 100X 100 : Multiply each term on b0th sides 0f the equation bY ■ Solve for x: 0.02X 十 0.6 = x. Example on bOth sides Of the equation by 10 , 100 , etc. TO clear an equation Of decimals, multiply each term Decimals SOIving Equations C 側ねⅲ i

lnterpreting Data 383 22. The perpendicular bisector Of AB, where AB is formed by joining point ( 3 , 6 ) and P0int ( 3 , 0 ) , is a line (A) parallel to the y-axis, passing through ( 0 , 0 ) (B) parallel to the x-axis, passing through ( 3 , 3 ) (C) passing through ( 3 , 3 ) and ( 0 , 0 ) (D) intersecting AB at ( 3 , 0 ) (E) intersecting AB at ( 3 , 6 ) 23. point ( ー 2 , 6 ) is the center 0f a circle that is tangent tO the x-axis. The coordinates Of the POint Of tangency are (D) ( 0 , ー 2 ) (E) ( 6 , 0 ) What is the area Of a triangle with vertices at 24. ( 5 , 3 ) , ( Ⅱ , 3 ) , and ( 8 , 8 ) ? (A) 7 (B) い (C) 24 (D) 30 (E) 64 the following line segments, which would be parallel t0 KL? (A) from POint い , 6 ) t0 P0int ( 6 , い ー 6 ) to point ( ー 6 , (B) from point ( ー l) tO point ( ー 6 , (C) from point ( (D) from point ( ー 6 , ー 6 ) tO point ( ー 6 , 6 ) (E) from point い , い to point ( 6 , 6 ) 19. If all points 3 units from ( 0 , 0 ) arejoined, the result will be a (A) square with perimeter 0f 12 units (B) triangle with area of 9V ' 3 (C) circle with diameter 0f 3 units (D) circle with radius of 3 units (E) rectangle with area Of 9 units 20. The locus of points equidistant from a given line is a pair Of lines that are (A) perpendicular (B) equal (C) bisected (D) broken (E) parallel 21. The following points are joined: ( ー 2 , , I), ( 2 , 2 ). AII ofthe following correctly describe the result EXCEPT (A) The line formed is parallel to the x-axis. (B) A straight line is formed. (C) The line formed bisects the right angle formed by the coordinates Of the axes. (D) Any point on the line formed is equidistant from the . v-axis and the v-axis. (E). The line formed passes through the origin. 25. KL is drawn from point ( 1 , 6 ) to point い , ー 6 ). Of Answer Key 4. -6 っ / 8 一 ~ 9. 0 ー 1 ーーっ 4 -6- 7 ′ 8 ′ 0 一 lnterpreting Da ね 3. Use on ツ the information given; dO not add information from your own background knowledge. 4. Be careful tO use the correct units in answering the question. DO not confuse decimals with percentages. 5. Make sure your conclusion iS reasonable. A graph is a pictorial representation Of data that gives an overall view Of facts, omitting minor details. General conclusions can be drawn after examining the data. The ability tO interpret a pictorial representation Of facts and figures is important for success in college- v 引 work. This justifies the inclusion Of this type Of question on the Sch01astic Aptitude Test.ln addi- tion, this type Of question lends itself tO testing the ability tO apply basic principles Of arithmetic, alge- bra, and geometry. Types 0f Graphs Line graphs are used tO show hOW a quantity changes. Very Often the quantity is measured as time changes. げ the line goes up, the quantity is increasing; if the line is horizontal, the quantity is not changing. TO measure the height Of a POint on the graph, it is not necessary tO use a ruler. Use your pencil or a piece Of paper as a straightedge. Graph V in the Practice Exercises is a good illustra- tion. Some graphs deal with two factors (Graph Ⅱ ) , in WhiCh case comparisons are made. HeIpfuI Tips on Coping with Graph Questions 1 . Examine the entire graph. Get the general meaning Of the picture. 2. Avoid lengthy computation. MOSt Of these questions can be answered by estimating or applying the given choices tO the facts presented.

American artists to include in art history textbooks and classes" ・ "lt was in Paris she first felt free to paint" ・ "lndeed, the scope of (her) career so well spans the development of twentieth-century art. " NOte particularly the use of the signal word "indeed" tO call your attention to the author's point. LOis Jones has had a vast range of experiences that have contributed to her work as an artist. The cor- rect answer iS Choice C. Choice A is incorrect. The passage talks of influ- ences on LOiS Jones, not Of LOiS Jones's influence on Others. Choice B is incorrect. The passage men- tions recognition given tO Jones on ツ in passing. Choice D is incorrect. There is nothing in the pas- sage tO support it. Choice E is incorrect. The pas- sage never deals with specific questions Of craft or technique. FamiIiarize YourseIf with the Testing Tactics 131 Certain words occur and reoccur in questions on a passage's purpose or main idea. You probably know most Of these words, but if you're shaky about any Of their meanings, lOOk them up in a good diction- ary and familiarize yourself with how they are used. は would be silly tO miss an answer not because you misunderstood the passage's meaning but because you failed tO recognize a common question WO 「 d. lmportant Words in Questions on Main ldea 0 「 pur- pose bolster (verb) delineate depict discredit document (verb) endorse elaborate (verb) exemplify illustrate refute speculate verify Te ⅲ 0 Terms Used to Describe a Passage's Organization. Another part Of understanding the author's point is understanding how the author organizes what he or she has tO say. TO dO so, often you have to figure out hOW the opening sentence or paragraph is con- nected tO the passage as a whO 厄 . Try this SAT question on the author's technique, based on the previous passage about LOis MaiIou Jones. Which of the following best summarizes the relationship Of the flrst sentence to the rest of the passage? (A) Assertion followed by supporting evidence (B) Challenge followed by debate pro and con (C) Prediction followed by analysis (D) Specific instance followed by general- izations (E) Objective reporting followed by personal remlnlscences The correct answer is Choice A. The author makes an assertion (a positive statement) about Jones's importance and then proceeds tO back it up with specific details from her career. Choice B is incorrect. There is no debate for änd against the author's thesis 0 「 point about Jones; the on ツ details given support that point. Choice C is incorrect. The author does not predict or foretell something that is going tO happen; the author asserts or states positively something that is an accomplished fact. Choice D is incorrect. The author's opening general assertion is followed by specific details tO support it, not the reverse. Choice E iS incorrect. The author shares no personal mem- ories or reminiscences Of Jones; the writing iS objective throughout. lmportant Words in Questions on Technique 0 「 Style abstract analogy antithesis argumentative assertion Cite concrete evidence explanatory expository generalization narrative persuaslve rhetorical thesis When Asked t0 新 oose a TitIe, Watch 0 瞰 for Ch0ices That Are T00 Specific 町 T00 澵 oad. A paragraph has been defined as a group Of sen- tences revolving around a centraltheme. An appro- priate title for a paragraph, therefore, must include this central theme that each Of the sentences in the paragraph is developing.lt should be neither t00 broad nor t00 narrow in its scope; it should be spe- cific and yet comprehensive enough tO include all the essential ideas presented by the sentences. A

692 Seven M 面可 SATs ロ . B. This is a direct proportion. Let x = number Of minutes required tO travel 2 5 2 25 ド 2 4 6 ード ()r 625 % ド ) 2 ()r 100 % ド ) 2 Area Of new square Area Of new square Area Of original square = 525 % of ド lncrease or 6—S ー mile. 2 5 distance ()n miles) 50 time ()n minutes) 60 x 2 ( 60 ) (product of means equals 50X 5 product Of extremes) 50X = 24 24 50 ー 8. A. Minimum number of crates on a trip Minimum weight Of a crate 125 . Minimum weight Of crates on a trip 円 . D. Area of circle = fi(radius)e Area Of circle = ~ ← Area Of rectangle = 第广 (given) Area of rectangle = (Base) (AItitude) Area Of rectangle (altitude) = ( わ ) (altitude) altitude ■ 0 ■ 0 ■・ 0 ■■■第 0 ■函■ 0 00 ■住 0000 ■ 00 ■■・ 00 000 ■・ Z ー■■ 00 ■ 0 ■ 0 ■■■■ 0 ■ . 000 第■■ 0 ■ 00 ■ 000 0000 ・ 00 ■■ 0000 ■■ー or 0.48 = 375 lb. ハー 2 , 0 ) 23. B. Observe that the point of tangency is at Radius OT is 亠 tO the x-axis since a radius is 亠 tO a tangent at the point Of contact. Thus OT is parallel to the y-axis, ånd point T, like point 0 , is 2 units tO the le Of the y-axis. Thus x Since the point T lies on the x-axis, ) ' The coordinates Of the point Of tangency, point T, are ( ー 2 , 0 ). T( ー 2 , 0 ) 0 ( ー 2 , 6 ) (division by の 20. D. To have an average of 90 min. ()r 1 ー hr. ) per day, the tOtal time spent practicing for the week must equal ( 7 ) ト or 10 ー hr. From Monday to Thursday the girl has practiced ト十 2 十 2 十ト or 7 hr. She must therefore spend 3 ー additional hours practicing for the 1 Substitute:@) = ( 2 ) ' 十 24. D. = 4 十一 rest Of the week. 21. D. To raise $ 500 in addition to the expenses of $ 250 the school must receive $ 750 for tickets. $ 750 At 7 per ticket 、 or L000 tickets must $ 0.75 be sold. 3 , the sum of the five 25. A. TO attain an average Of 3 fractions must be 5 3 1 十一十一一十 5 2 29 十一・十一一・十 20 20 20 20 20 The sum of the four fractions The fraction to be added must be 30 29 or 20 ・ 20 20 Section 2 Test of Standard Written EngIish 1 . E. Sentence correct. 2. A. Error in tense. Change has adopted to ad0 〃 d. or 1 2 5 29 20 5 一 2 29 20 1 5 一 2 1 22. D. Let s side Of original square. 、十 150 % or 十ト or 2 ー or ー、 new square = (Side)2 Area Of square Area Of original square side of い ) 2 or -

480 S M 面可 SATS SOlve each 0f the remaimng problems in this section using any available space f0 「 scratchwork. Then decide which is the best 0f the choices given and blacken the corresponding space on the answer sheet. 引 . If the average of the ages Of three men is 44 years, and if no one of them is less than 42 years old, what iS the maximum age, in years, Of any one man? (A) 44 (B) 46 (C) 48 (D) 49 (E) 50 32. Ms. A owes Ms. お $ 70 , and Ms. B owes Ms. A $ 60. IfMs. A gives Ms. お a $ 50 bill, how many dollars in change should Ms. B give Ms. A? (A) 10 (B) 20 (C) 30 (D) 40 (E) 60 33. If a pipe fills a tank in ん hours, what part of the tank does it ⅱⅡ in 2 hours? (C) 2 ん (D) ん + 2 (E) ん一 2 2 34. Base RT of triangle RST is ー of altitude SV. If SV equals c, the area 0f triangle RST 2C2 2 (B) 5 2 28. If 2 〃 painters can paint 2 ん houses in 2 ル weeks, h0W many painters will be needed tO paint 4 ん houses in 4 ル weeks? (A) (B) 2 〃 (C) 4 〃 (D) 8 〃 (E) 16 〃 / ( 0 , 6 ) C B 0 29. ln the diagram above, AOB and 尸 C 召 are right isosceles triangles with equal areas. What are the coordinates Of point P? (A) ( 6 , 0 ) (B) ( 6 , 12 ) (C) ( 12 , 0 ) (D) ( 0 , 12 ) (E) ( 12 , 6 ) 2 2 5 4c 5 (C ) (D) (E) 5 30. If 7 pounds Of vanety 〃 tea is worth 5 pounds 0f vanety 9 tea, and 3 pounds Of variety 〃 tea is worth ズ pounds Of variety 4 tea, then the numerical value Of X iS (E) 4 5 2 (C) 2 ー (D) 3 ー 7 3 35. A man can row down a l()-mile stream in 2 hours and up in 5 hours. What is his average rate, in miles per hour, for the entire tnp? (B) 3 ー (C) 2 ー (D) 3 (E) 7 (A) 1 ー (B) ト IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON THIS SECTION ONLY. DO NOT WORK ON ANY OTHER SECTION IN THE TEST. S T O P

502 Seven M 面可 SATs 30. C. 5 一 5 一 5 ニ 3. B. Convert all fractions tO denominators Of 25 and compare numerators. 旧 3 5 25 ' 5 25 ' 5 25 25 ・ 2 ー 2 ()y division) Therefore: 4 十わ わ十 2 1 引 . C. The average of the ages of the three men is 44 , so the sum of their ages is 44 x 3 or 132 years. If two men are 42 , the sum of their ages is 84 。 The maximum age of the third man is 132 ー 84 or 48 years. 32. D. Ms. A owes Ms. B $ 70 and Ms. B owes Ms. A $ 60 , so Ms. A owes Ms. B $10. If Ms. A gives Ms. B $ 50 ( $ 40 mo 代 than she owes Ms. B), Ms. B must give Ms. A $ 40 in change. Substitute a number for the letter. Let ん 33. A. 2 If the tank fills ⅲ 7 ( ん = 7 ) hr. ー of it fills in 2 1 1 1 1 1 5. B. 30 ー 12 = 2 ー each when purchased by the dozen. ー 2 ー = 2 ー saving per stick. 6. C. 2 ー or 250 % = 62 ー % = 0.04 = 4 % = 9 % -4- - 、一一 8 2 4 hr. Substituting ん for 7 , you find that ー of the tank ⅱ騰ⅲ 2 hr. 34. B. Area Of triangle ー Base x Altitude 2 5 ( 0.2 ) 9 100 L44 = に 0 % 4 % or ( 0.2 ) 2 is smallest. 7. B. ん is the y-coordinate Of point C. POint C is the same distance above the . r-axis, as is point D. The y-coordinate Of point D is 5. Therefore the y-coordinate of point C is 5. Thus ん = 5. 7 ' (Total) distance 35. C. Average rate . The total (T0tal) time distance up and down the stream = 20 miles, and the time = 5 plus 2 or 7 hr. The average or 2 ー m. p. h. rate 000000000 20 C(8 は ) 7 D ( 0 , 5 ) Section 6 月 ( 0 , 0 ) B ( 8 , 0 ) -4 一、・ 4- 工 8. B. ) (subtract 2 ) = 2 ) (add ⅵ 9. D. Since the hundredths unit ( 9 ) is more than 5 , the tenths unit is raised from 9 to 10 so that the digits 69 become 70 , and the number 69.999 becomes 70.0 to the nearest tenth. quantity Of pie number Of people served 9. 0 ノ - ー 1 一 7 工ズ

tively, knowing their general direction, but not find- ・ ing the specific route until they get there. Neither method excels the other, for much depends on the subject matter and intent of the writer. The first method follows a simple, clear-cut formula, which may not win a prize for originality but can help tO turn a muddle of ideas into a model of clar- ity. は has a beginning, a middle, and an end. You can call on it any time you need to set ideas in order. Each step has its place and purpose. The Five-Paragraph Essay FormuIa Title lntroduction BOdy: POint 1 Point 2 Point 3 Conclusion 旧 reality, however, writers rarely follow "The For- mula. " ln fact, you may never see a formula essay in print. Yet a majority of college essays, even those which take circuitous paths between the beginning and end, adhere tO some sort of three-step organi- zation.ln the introduction writers tell readers what they plan tO tell them.ln the bodythey tell them. And in the conclusion they tell them what they to them. Since all writers differ, however, you find end- less variations within each step. 加加面 c 加 G 囮加 the 能 2 s The best essays usually begin with something catchy, something tO lure the readers intO the piece. Basically, it's a hook—a phrase, sentence, or idea that will nab the readers' interest so completely that they'll keep on reading almost in spite of them- selves. Once you've hooked your readers, you can lead them anywhere. 1 . Start with an incident, 「 e or invented, that leads the readers gracefully to the point of your essay. 2. State a provocative idea in an ordinary way or an ordinary idea in a provocative way. Either will spark the readers' interest. 3. Use a quotation—・ not necessarily a famous one. Shakespeare's or your grandmother's will do, as long as the quote relates tO the topic Of your essay. 4. Knock down a commonly held assumption or define a word in a new and surprising way. 5. Ask an interesting question or two which you will answer in your essay. 旧 any collection of good essays you'd no doubt find Other worthy techniques for writing a compelling opening. Even a direct statement that introduces your topic may be appropriate. Whatever your open- Composing Y 側「 Essay 775 ing, though, it must fit your writing style and per- sonality. Work hard at getting it right, but at the same time, not t00 hard. A forced opening may obscure the point Of your essay, or worse, dim the reader's enthusiasm for finding out what you have tO say. Furthermore, an opening that comprises, say, more than a quarter Of your essay is probably t00 long. 釦 : 物円 ge 物 Order is important. What should come first? sec- ond? 、 third? most writing the best order is the clearest order, the arrangement your readers can follow with the least effort. There is no single way tO get from the beginning of a piece Of writing tO the end. The route you take will vary according tO what you want tO dO tO your read- ers. Whether you want tO shock, sadden, inspire, move, or entertain them, each purpose will have its own best order.ln story-telling, the events are often placed in the sequence they occur. But tO explain a childhood memory or define who you are, tO stand up for women's rights or describe a poignant moment—each may take some Other kind Of arrangement. NO one plan iS superior tO another, provided you have a valid reason for using it. The plan that fails is the aimless one, the one in which ideas are arranged solely on the basis Of the order in which they popped into your head. TO guard against aimlessness, rank your ideas in order Of importance either before you start or while you're writing drafts. Although your first idea may turn out tO be your best, you probably should save it forlater in your essay. Giving it away at the start is self- defeating. TO hO your readers' interest, it's better tO work toward your best point, not away from it. げ you have, say, three main points tO make, save the strongest forlast. Launch your essay with your sec- ond-best, and tuck yourleast favorite between the other two. a typical college essay, a body consisting Of three sections will be just about right. Why three? MainIy because three is a number that works. When you can make three statements about a subject, you probably know what you're talking about. One is t00 simple, two is still pretty shallow, three is thought- ful. PsychoIogically, three creates a sense of whole- ness, like the beginning, middle, and end Of a story. Each point doesn't necessarily receive equal treat- ment. You might manage one point with a single paragraph, while the Others get more. But each point has tO be distinctive. Your third point mustn't be a rerun Of the first or second. は shouldn't be difficult to break the main point of most essays intO atleast three secondary points, regardless Of their topic or form. A narrative essay, for example, naturally breaks into a beginning, mid- dle, and end. A process is likely tO have at least three steps, some Of which may be broken intO sub-