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Covers zero product property, systems of equations solution types, and key factoring identities such as difference of squares and perfect-square expansions. Includes core line formulas (slope, slope-intercept, standard form), midpoint and distance relations, rate/work/speed templates, and quadratic vertex forms plus the quadratic formula and discriminant interpretation. Also summarizes exponent and radical rules for simplifying expressions.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/sat-math-cheat-sheet-formulas-rules-and-definitions/266409/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/sat-math-cheat-sheet-formulas-rules-and-definitions/266409.png","ImageObject",300,407,{"name":92,"@type":93},"Emma Wilson","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does the zero product property say for SAT math?","Question",{"text":113,"@type":114},"If a product equals 0, then at least one factor must be 0 (a=0 or b=0, or both).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How can you determine whether a system of linear equations has one, zero, or infinite solutions?",{"text":118,"@type":114},"Solve the system and check the final simplified result: a single consistent variable value gives one solution, an impossible statement gives zero solutions, and two equal expressions give infinite solutions. Graphically, this corresponds to one intersection, parallel lines, or identical lines.",{"name":120,"@type":111,"acceptedAnswer":121},"What are the key formulas for quadratics and how is the vertex found?",{"text":122,"@type":114},"The sheet lists vertex form, factored form, and standard form, and explains how the vertex corresponds to the maximum or minimum. It also provides the quadratic formula and explains using the discriminant to decide whether roots are real or not.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},266409,1789407126,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":46},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","SAT MATH SECTION: CHEAT SHEET  \nFORMULAS, RULES, AND DEFINITIONS  \nNote: important formulas included at beginning of every test not included below  \nALGEBRA:  \nZERO PRODUCT PROPERTY: If 􀜽􀜾 = 0, then 􀜽 = 0, 􀜾 = 0, or 􀜽 = 􀜾 = 0 .  \nSYSTEMS OF EQUATIONS:  \nWhen you solve down a system of equations, one of three outcomes is possible as you run the algebra and create a final, simplified equation:  \n\n| One solution | Zero solutions | Infinite solutions |\n| --- | --- | --- |\n| If you get a single x or y value, (i.e. x=5 or y=2) you have one solution. | If you get a statement that is never true (i.e. 5=9 or 0=4), you have no solutions. | If you get two values that always equal each other (i.e. 3x=3x or 5=5), you have infinite solutions. |\n| Comparing equations: You can alternatively put EVERY equation in slope intercept form that is part of your system of linear equations. Then look at each of the y=mx+b forms and compare the two slopes (i.e. the “m’s”) and y-intercepts (the “b’s”) . |  |  |\n| One solution | Zero solutions | Infinite solutions |\n| Different slopes (intercepts don’t matter)\u003Cbr>On a graph this is two lines intersecting at a single point. | Same slopes (parallel lines), different y-intercepts\u003Cbr>On a graph this is two parallel lines. | Same slope, same intercept i.e. identical equations\u003Cbr>On a graph, this is the same line (i.e. both equations you have are actually identical but not “simplified” the same) . |\n\nTIP: Look for shortcuts / use elimination on systems of equations questions to get what the question asks for rather than solve down for each individual variable. I.e. if the question asks for x+y, try to use elimination/adding or subtracting the whole equations to end up with x+y straightaway.  \nFOIL AND FACTORING:  \n• A monomial is a single product such as 4x,7x 3 , or 8n2 .  \n• A binomial has two elements added together such as 4x + 3 or 5n3 + 3n .  \n• A polynomial has multiple elements added together such as 5n3 + 3n2 + 7n + 2 or 5n3 + 3n2 + 7n + 2 or 5x 2 + 2x + 4 5􀝔 2 + 2􀝔 + 4 .  \n• Difference of Squares: The product of the difference (a − b) and the sum ( a + b ) is equal to 􀜽 squared minus 􀜾 squared, (􀜽 − 􀜾)(􀜽 + 􀜾) = 􀜽 2 − 􀜾 2  \n• Square of a Sum: (􀜽 + 􀜾)2 = 􀜽 2 + 2􀜽􀜾 + 􀜾 2  \n• Square of a Difference: (􀜽 − 􀜾)2 = 􀜽 2 − 2􀜽􀜾 + 􀜾 2  \nSLOPE FORMULA: For points ( x1 , y 1) and ( x2 , y 2) , m = ~~ ~~y~~ ~~2x~~ ~~2~~ ~~−~~ ~~y~~ ~~1x~~ ~~1 .  \nSTANDARD FORM SLOPE: If 􀜣􀝔 + 􀜤􀝕 = 􀜥 , slope is equal to – 􀮺􀮻  \nSLOPE-INTERCEPT FORM: 􀝕 = 􀝉􀝔 + 􀜾  \nWhere 􀝉 is the slope of the line, and 􀜾 is the y-intercept of the line at point (0, 􀜾) .  \nMIDPOINT FORMULA: The midpoint of two coordinate points (􀝔1, 􀝕1) and (􀝔2, 􀝕2) is:􀂧􀂨􀂩 ~~ ~~(~~ ~~x1~~ ~~+2~~ ~~x2~~ ~~) , ~~ ~~(~~ ~~y~~ ~~1~~ ~~+2~~ ~~y~~ ~~2~~ ~~) 􀂷􀂹􀂸  \n􁉆~~ ~~(􀝔1~~ ~~+2~~ ~~􀝔2~~ ~~) , ~~ ~~(􀝕1~~ ~~+2~~ ~~􀝕2~~ ~~)􁉇  \nDISTANCE FORMULA: Given two points,(􀝔1, 􀝕1 ) and (􀝔2, 􀝕2 ), the distance between them is: d = ( x2 − x1 )2 + ( y 2 − y 1)2 􀝀 = 􀶥(􀝔2 − 􀝔1 )2 + (􀝕2 − 􀝕1 )2  \nSPEED AND RATES DISTANCE FORMULA: 􀝀 = 􀝎􀝐  \nWORK FORMULA: 􀝓 = 􀝎􀝐  \nCOMBINED WORK FORMULA: 􀝓 = (􀝎1 + 􀝎2 )􀝐  \nQUADRATICS AND POLYNOMIALS: Important-know how to find the vertex of ANY parabola!  \n• VERTEX FORM OF A QUADRATIC: the vertex form of a parabola is: f( x ) = a ( x − h)2 + k  \no The vertex of the parabola in this form is (ℎ, 􀝇)  \no When 􀜽 is positive, the parabola opens upwards, and the minimum is (ℎ, 􀝇) .  \no When 􀜽 is negative, the parabola opens downwards, and the minimum is (ℎ, 􀝇) .  \no Alternate form for parabolas with horizontal axis (RARE, unlikely to appear) 􀝔 =􀜽(􀝕 − 􀝇)2 + ℎ, positive 􀜽 opens right-ward, negative 􀜽 opens leftward  \n• FACTORED FORM: The factored form of a polynomial usually takes the form:  \n􀝂 (􀝔) = 􀜽(􀝔 − 􀝊)(􀝔 − 􀝉)  \no When 􀜽 is positive, the parabola opens upwards.  \no When 􀜽 is negative, the parabola opens downwards.  \no The graph crosses the x-axis at each point when a factored piece equals zero (the zeros) . For example, at x=n, x-n equals 0, so the graph crosses through th","cbCaioHwOAQFWWGC","https://ap.wps.com/l/cbCaioHwOAQFWWGC","pdf",3133009,"English","# Algebra\n## Zero Product Property\n## Systems of Equations\n## FOIL and Factoring\n# Coordinate Geometry and Functions\n## Slope and Line Forms\n## Midpoint and Distance\n## Speed, Rates, and Work\n# Quadratics and Polynomials\n## Vertex, Factored, and Standard Forms\n## Quadratic Formula and Discriminant\n# Radical and Exponent Rules","[{\"question\":\"What does the zero product property say for SAT math?\",\"answer\":\"If a product equals 0, then at least one factor must be 0 (a=0 or b=0, or both).\"},{\"question\":\"How can you determine whether a system of linear equations has one, zero, or infinite solutions?\",\"answer\":\"Solve the system and check the final simplified result: a single consistent variable value gives one solution, an impossible statement gives zero solutions, and two equal expressions give infinite solutions. Graphically, this corresponds to one intersection, parallel lines, or identical lines.\"},{\"question\":\"What are the key formulas for quadratics and how is the vertex found?\",\"answer\":\"The sheet lists vertex form, factored form, and standard form, and explains how the vertex corresponds to the maximum or minimum. It also provides the quadratic formula and explains using the discriminant to decide whether roots are real or not.\"}]","SAT Math - Cheat Sheet - Formulas, Rules, and Definitions | PDF"]