About the SAT Math Test

Transcription

1 Capte 18 About te SAT Mat Test Focus on Mat Tat Mattes Most A goup of select matematics skills and abilities contibutes te most to eadiness fo a college education and caee taining. Tese skills and abilities ae used extensively in a wide ange of college majos and caees. Te tee aeas of focus fo mat in te edesigned SAT ae: Heat of Algeba Poblem Solving and Data Analysis Passpot to Advanced Mat Heat of Algeba focuses on linea equations and systems of linea equations tat ae found in many fields of study. You will be asked to ceate equations tat epesent a situation and solve equations and systems of equations as well as to make connections between diffeent epesentations of linea elationsips. Poblem Solving and Data Analysis includes using atios, pecentages, and popotional easoning to solve poblems in eal-wold situations, including science, social science, and caee contexts. It also includes descibing elationsips sown gapically and analyzing statistical data. Tis goup of skills is eally about being quantitatively liteate and demonstating a command of te mat tat esonates tougout college couses, caee taining pogams, and eveyday life. Questions on te SAT Mat Test ae distibuted among tese tee topics wit 19 Heat of Algeba questions, 17 Poblem Solving and Data Analysis questions, and 16 Passpot to Advanced Mat questions. Te emaining six questions test you undestanding of additional topics in mat suc as aea, volume, cicles, tiangles, and tigonomety. Tese two aeas of mat povide a poweful foundation fo te mat you will do in te futue. Passpot to Advanced Mat is te tid aea of focus in te edesigned SAT Mat Test, and once again, it is te mat tat is used in a wide vaiety of caees and college wok. Te poblems in tis aea focus on te mat you will need to pusue fute study in a discipline suc as science and fo caee oppotunities in te STEM fields of science, tecnology, engineeing, and mat. Te Passpot to Advanced Mat section equies familiaity wit 225

2 m at moe-complex equations o functions, wic will pepae you fo calculus and advanced couses in statistics. Tee is also a bief section on Additional Topics in Mat, including geomety, tigonomety, adian measue, and te aitmetic of complex numbes. Te SAT Mat Test equies a stonge and deepe undestanding of a elatively small numbe of mat topics tat ae especially elevant in college and in many caees. Te edesigned SAT Mat Test also contains questions tat focus on seveal ote aeas tat ae impotant fo a wide ange of college couses and caees. Some of tese poblems focus on key concepts fom geomety, including applications of volume, suface aea, aea, and coodinate geomety; similaity, wic is anote instance of popotional easoning; and popeties of lines, angles, tiangles and ote polygons, and cicles. Tee ae also poblems tat focus on te fundamental ideas of tigonomety and adian measue, wic ae essential fo study in STEM fields. Finally, tee ae poblems involving te aitmetic of complex numbes, anote concept needed fo moe-advanced study in mat and te STEM fields. Rigo Tougout te edesigned SAT Mat Test, questions will equie conceptual undestanding, pocedual skill and fluency, and application of matematics in college and caee contexts. Tese tee aspects appea in elatively equal amounts on eac SAT test. Conceptual undestanding and pocedual skill and fluency ae complementay skills. Togete, tey lead to a tooug undestanding of matematical ideas and metods fo solving poblems. Questions on te SAT Mat potions test tese skills in vaious ways because te ability to use matematical ideas and metods flexibly is caacteistic of an undestanding of mat tat can be applied to a wide vaiety of settings. As is mentioned tougout tis guide, te best pepaation fo te SAT is to wok ad in you ig scool classes. Applying you mat skills in you science and social studies classes will pepae you fo many of te questions you ll come acoss on te SAT Mat Test. An essential idea in te elationsip between fluency and conceptual undestanding is obseving stuctue. Recognizing stuctue allows you to undestand matematical elationsips in a coeent manne tat allows you bot to apply tese elationsips moe widely and to extend tese elationsips in useful ways. Many of te examples and sample questions in te following captes ae moe simply and deeply undestood (and moe quickly solved!) if you obseve stuctue in te matematics of te poblem. Poblems Gounded in Real-Wold Contexts Te Mat Test will featue multistep poblems wit applications in science, social science, caee scenaios, and ote eal-life contexts. In some cases, you will be pesented wit a scenaio and ten asked seveal questions about it. You lean specific mat skills in you mat classes, and tese skills ae applied in you science and social studies classes. Wen you use you 226

3 a b o u t te sat mat test matematical skills outside of te mat classoom, you ae pepaing fo te edesigned SAT. Te Makeup of te SAT Mat Test CalCulato and no-calculato Potions Tee will now be calculato and no-calculato potions of te edesigned SAT Mat Test (as is also often tue of Advanced Placement assessments). A calculato is a tool, and te ability to detemine wen to use it is a skill tat you ae expected to ave. In te calculato potion, many questions do not equie a calculato and many questions can be completed faste by and witout using a calculato. In geneal, te questions in te calculato potion ae moe complex tan tose in te no-calculato potion. Questions in te no-calculato potion ae intended to ewad you ability to do poblems effciently and accuately. You sould bing a calculato to use on te mat section of te SAT. A scientific o gaping calculato is ecommended, and familiaity wit you calculato may povide an advantage on some questions. Evey question on te SAT can be solved witout a calculato; oweve, stategically deciding wen to use a calculato will educe te time equied to complete te test. Using a calculato can also elp you avoid missing a question because of computation eos. You ll be pemitted to use a calculato on one potion of te SAT Mat Test, so be sue to bing a calculato wit you to te test. Howeve, many questions don t equie a calculato and can actually be solved moe quickly witout one, so use caeful judgment in deciding wen to use it. Make sue tat you e vey familia wit and comfotable using te calculato you bing wit you on test day. Pactice using te calculato you ll use on te test tougout you test pepaation. MultiPle-CoiCe and Gidded-esPonse Questions About 80% of te questions on te Mat Test ae multiple-coice. Eac multiple-coice question consists of a question followed by fou options. Tee is only one coect, o best, answe and tee is no penalty fo selecting an incoect answe. (Te pe-2016 SAT ad a one-quate-point penalty fo an incoect answe.) Teefoe, you sould povide an answe to evey question on te test. Te ote questions on te Mat Test ae gidded-esponse questions (also called student-poduced esponse questions), and tese questions make up about 20% of te test. Te answe to eac gidded-esponse question is a numbe (faction, decimal, o positive intege) tat you will ente on te answe seet into a gid like te one sown on te next page. Like all questions on te edesigned SAT, tee is no penalty fo answeing a gidded-esponse question incoectly. Examples of filled-in answe gids ae sown on te next page. Note tat you may also ente a faction line o a decimal point. Fute details on ow to gid you answes ae povided in Capte 24. We know we ve stessed tis many times aleady, but it s wot epeating: Tee is no penalty fo selecting an incoect answe on te SAT, so neve leave a question blank! On questions tat you e not sue ow to solve, eliminate as many answe coices as you can, and ten guess fom among te emaining coices. 227

4 m at On gidded-esponse questions, you must fill in te cicles tat coespond to you answe. You won t eceive cedit if you wite you answe only in te boxes at te top of te gid. Wite answe in boxes. Gid in esult. 7 Answe: Answe: / 1 2 / / Faction line 2. 5 / / Decimal point Make sue to get lots of pactice using te facts and fomulas povided in te Refeence section in te Mat Test diections. Pacticing wit tese facts and fomulas will ensue you can use tem accuately and efficiently. MateMatiCs efeence infomation Te Mat Test includes te efeence infomation sown below. You may find tese facts and fomulas elpful as you answe some of te test questions, but make sue you ave plenty of pactice wit tis infomation befoeand. To do well, you ave to be comfotable woking wit tese facts and fomulas. If you ave lots of pactice using tese facts and fomulas befoe te test, you will be a lot moe elaxed wen you use tem duing te test. w c 2x 60 s 45 s 2 b x b a x 3 s A = 2 A = w A = 1 b c 2 = a 2 + b 2 Special Rigt Tiangles 2 C = 2 w w 228 V = w V = V = V = 2 V = Te numbe of degees of acinacicleis 360. Te numbe of adians of acina cicle is 2. Te sum of te measues in degees of te angles of a tiangle is 180. w

5 a b o u t te sat mat test Test Summay Te following table summaizes te key content dimensions of te edesigned SAT Mat Test. SAT Mat Test Content Specifications Time Allotted Calculato Potion (38 questions) 80 minutes 55 minutes No-Calculato Potion (20 questions) 25 minutes Numbe Pecentage of Test Total Questions 58 questions 100% Multiple-Coice (MC, 4 options) 45 questions 78% Student-Poduced Response 13 questions 22% (SPR gid-in) Contibution of Questions to Subscoes Take plenty of time to familiaize youself wit tis table. Knowing exactly wat te Mat Test consists of, including te numbe of questions and time allotted as well as te distibution of question categoies, will elp you to feel confident and pepaed on test day. Heat of Algeba 19 questions 33% Analyzing and fluently solving linea equations and systems of linea equations Ceating linea equations and inequalities to epesent elationsips between quantities and to solve poblems Undestanding and using te elationsip between linea equations and inequalities and tei gaps to solve poblems Poblem Solving and DataAnalysis 17 questions 29% Ceating and analyzing elationsips using atios, popotional elationsips, pecentages, and units Repesenting and analyzing quantitative data Finding and applying pobabilities in context Passpot to Advanced Mat 16 questions 28% Identifying and ceating equivalent algebaic expessions Ceating, analyzing, and fluently solving quadatic and ote nonlinea equations Ceating, using, and gaping exponential, quadatic, and ote nonlinea functions 229

6 m at As you pogess toug you test pactice, assess wic mat skills you e stongest in and wic you ave te geatest oom fo impovement in. Allocate you study time appopiately, and make use of te many esouces available to you on te Kan Academy website (). Additional Topics in Mat* 6 questions 10% Solving poblems elated to aea and volume Applying definitions and teoems elated to lines, angles, tiangles, and cicles Woking wit igt tiangles, te unit cicle, and tigonometic functions Contibution of Questions to Coss-Test Scoes Analysis in Science 8 questions 14% Analysis in Histoy/Social Studies 8 questions 14% *Questions unde Additional Topics in Mat contibute to te total Mat Test scoe but do not contibute to a subscoe witin te Mat Test. As indicated in te content specifications peviously, te Mat Test as two potions. One is a 55-minute potion 38 questions fo wic you ae allowed to use a calculato to solve te poblems. Te ote is a 25-minute potion 20 questions fo wic you ae not allowed to use a calculato. Te bluepint fo eac potion is sown below. Calculato Potion Numbe of Questions % of Test Total Questions % Multiple-Coice (MC) 30 79% Student-Poduced 8 21% Response (SPR gid-in) Content Categoies % Heat of Algeba 11 29% Poblem Solving and 17 45% Data Analysis Passpot to Advanced 7 18% Mat Additional Topics in Mat 3 8% Time Allocated 55 minutes 230

7 a b o u t te sat mat test No-Calculato Potion Numbe of Questions % of Test Total Questions % Multiple-Coice (MC) 15 75% Student-Poduced 5 25% Response (SPR gid-in) Content Categoies % Don t be intimidated by te fact tat you aen t pemitted to use a calculato on one of te SAT Mat potions. Questions in te no-calculato potion ae moe conceptual in natue and don t equie a calculato to be solved. Heat of Algeba 8 40% Passpot to Advanced 9 45% Mat Additional Topics in 3 15% Mat Time Allocated 25 minutes 231