[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-266368-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-266368-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","sat-math-must-know-facts-formulas-core-math-review","SAT Math Must-Know Facts & Formulas - Core Math Review","","SAT Math must-know facts and formulas organized by key topic areas: numbers and algebraic sequences, factors and multiples, percents, averages and central tendency, fundamental counting and probability, and exponent/radical rules. It also consolidates core equation-solving and factoring identities, function and proportion relationships, absolute value, distance and midpoint, slope and line equations including parallel and perpendicular conditions, and essential geometry results such as special right triangles, the Pythagorean Theorem, and triangle area and angle facts.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/sat-math-must-know-facts-formulas-core-math-review/266368/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/sat-math-must-know-facts-formulas-core-math-review/266368.png","ImageObject",300,407,{"name":42,"@type":43},"Cart","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",19,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the basic number sets covered (integers, rationals, and reals)?","Question",{"text":63,"@type":64},"Integers are whole-number negatives to positives. Rationals are fractions that can be expressed as ratios of integers. Reals include integers, rationals, and special numbers such as √2, √3, and π.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do you find a percent of a whole using the given formula?",{"text":68,"@type":64},"Use percent = part/whole × 100, equivalently part = (percent/100) × whole. Examples show converting 75% of 300 to 225 and solving for x in equations like 45 = (x/100) × 60.",{"name":70,"@type":61,"acceptedAnswer":71},"What geometric facts are included for lines and triangles?",{"text":72,"@type":64},"For lines, the slope-intercept form y = mx + b is given, along with conditions for parallel lines (equal slopes) and perpendicular lines (negative reciprocal slopes). For triangles, the Pythagorean Theorem a² + b² = c² and the special right-triangle relationships are highlighted, plus area = 1/2 · b · h and the fact that interior angles sum to 180°.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},266368,1789406833,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":101,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":80,"read_time":143},18829141979164,"https://eur-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","SAT Math Must-Know Facts & Formulas Numbers, Sequences, Factors  \nIntegers: . . . , -3, -2, -1, 0, 1, 2, 3, . . .  \nRationals: fractions, that is, anything expressable as a ratio of integers  \nReals: integers plus rationals plus special numbers such as √2 , √3 and π  \nOrder Of Operations: PEMDAS  \n(Parentheses / Exponents / Multiply / Divide / Add / Subtract)  \nArithmetic Sequences: each term is equal to the previous term plus d  \nSequence: t 1 , t 1 + d, t 1 + 2d, . . .  \nExample: d = 4 and t 1 = 3 gives the sequence 3, 7, 11, 15, . . .  \nGeometric Sequences: each term is equal to the previous term times r  \nSequence: t 1 , t 1 · r , t 1 · r 2 , . . .  \nExample: r = 2 and t 1 = 3 gives the sequence 3, 6, 12, 24, . . .  \nFactors: the factors of a number divide into that number  \nwithout a remainder  \nExample: the factors of 52 are 1, 2, 4, 13, 26, and 52  \nMultiples: the multiples of a number are divisible by that number  \nwithout a remainder  \nExample: the positive multiples of 20 are 20, 40, 60, 80, . . .  \nPercents: use the following formula to find part, whole, or percent  \npercent  \npart = × whole  \n100  \nExample: 75% of 300 is what?  \nSolve x = (75/100) × 300 to get 225  \nExample: 45 is what percent of 60?  \nSolve 45 = (x/100) × 60 to get 75%  \nExample: 30 is 20% of what?  \nSolve 30 = (20/100) × x to get 150  \n[www.erikthered.com/tutor](www.erikthered.com/tutor) pg. 1  \nSAT Math Must-Know Facts & Formulas Averages, Counting, Statistics, Probability  \naverage = nsuum~~ ~~omberfotfermsterms  \ntotal distance average speed =  \ntotal time  \nsum = average × (number of terms)  \nmode = value in the list that appears most often  \nmedian = middle value in the list (which must be sorted)  \nExample: median of {3, 10 , 9 , 27 , 50} = 10  \nExample: median of {3, 9 , 10 , 27} = (9 + 10)/2 = 9 .5  \nFundamental Counting Principle:  \nIf an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N × M ways.  \nProbability:  \nnumber of desired outcomes  \nprobability =  \nnumber of total outcomes  \nExample: each SAT math multiple choice question has  \nfive possible answers, one of which is the correct answer.  \nIf you guess the answer to a question completely at ran  \ndom, your probability of getting it right is 1/5 = 20% .  \nThe probability of two different events A and B both happening is P (A and B) = P(A) · P(B), as long as the events are independent (not mutually exclusive) .  \nPowers, Exponents, Roots  \nxa · xb = xa+b  \n(xa )b = xa·bx0 = 1  \nxa /xb = xa−b  \n(xy)a = xa · ya √xy = √x · √y  \n1/xb = x −b (−1)n = 􀀚 11,,  \nif n is even;  \nif n is odd.  \n[www.erikthered.com/tutor](www.erikthered.com/tutor) pg. 2  \nSAT Math Must-Know Facts & Formulas  \nFactoring, Solving  \n(x + a)(x + b) = x2 + (b + a)x + aba2 − b2 = (a + b)(a − b)  \na2 + 2ab + b2 = (a + b)(a + b)  \na2 − 2ab + b2 = (a − b)(a − b)  \n“FOIL”  \n“Difference Of Squares”  \nTo solve a quadratic such as x2 +bx+c = 0, first factor the left side to get (x+a1 )(x+a2 ) = 0, then set each part in parentheses equal to zero. E.g. , x2 + 4x + 3 = (x + 3)(x + 1) = 0 so that x = −3 or x = −1.  \nTo solve two linear equations in x and y: use the first equation to substitute for a variable in the second. E.g., suppose x + y = 3 and 4x − y = 2 . The first equation gives y = 3 − x, so the second equation becomes 4x − (3 − x) = 2 ⇒ 5x − 3 = 2 ⇒ x = 1, y = 2 .  \nFunctions  \nA function is a rule to go from one number (x) to another number (y), usually written  \ny = f (x) .  \nFor any given value of x, there can only be one corresponding value y. If y = kx for some number k (example: f (x) = 0 .5 · x), then y is said to be directly proportional to x. If y = k/x (example: f (x) = 5/x), then y is said to be inversely proportional to x.  \nAbsolute value:  \n|x| = 􀀚 xx,, if xif x  0;  \n0.  \nLines (Linear Functions)  \nConsider the line that goes through points A (x1 , y 1 ) and B (x2 , y2 ) .  \nDistance from A to B: p (x2 − x1 )2 + (y2 − y1 )2  \nMid-point ","cbCaitv4ikLjHDLT","https://ap.wps.com/l/cbCaitv4ikLjHDLT","pdf",67973,"English","# Numbers and Operations\n## Integers, rationals, and reals\n## Order of operations (PEMDAS)\n## Arithmetic and geometric sequences\n## Factors, multiples, and percents\n# Averages, Counting, and Probability\n## Average, mode, median\n## Fundamental counting principle\n## Probability and independence\n# Powers, Exponents, and Roots\n## Exponent rules and reciprocal powers\n# Factoring and Solving\n## Quadratic factoring and FOIL\n## Solving quadratic and linear systems\n# Functions and Linear Equations\n## Direct/inverse proportionality\n## Absolute value\n## Distance, midpoint, and slope\n## Parallel and perpendicular lines\n# Geometry\n## Special right triangles and Pythagorean Theorem\n## Triangle area and angle sums","[{\"question\":\"What are the basic number sets covered (integers, rationals, and reals)?\",\"answer\":\"Integers are whole-number negatives to positives. Rationals are fractions that can be expressed as ratios of integers. Reals include integers, rationals, and special numbers such as √2, √3, and π.\"},{\"question\":\"How do you find a percent of a whole using the given formula?\",\"answer\":\"Use percent = part/whole × 100, equivalently part = (percent/100) × whole. Examples show converting 75% of 300 to 225 and solving for x in equations like 45 = (x/100) × 60.\"},{\"question\":\"What geometric facts are included for lines and triangles?\",\"answer\":\"For lines, the slope-intercept form y = mx + b is given, along with conditions for parallel lines (equal slopes) and perpendicular lines (negative reciprocal slopes). For triangles, the Pythagorean Theorem a² + b² = c² and the special right-triangle relationships are highlighted, plus area = 1/2 · b · h and the fact that interior angles sum to 180°.\"}]","SAT Math Must-Know Facts & Formulas - Core Math Review | PDF",15]