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Covers FOIL and factoring, key quadratic forms and how to identify vertex information, plus slope-intercept, midpoint, distance, speed/rates, and work formulas. Includes quadratic solution methods using the quadratic formula and the discriminant, along with exponent and radical rules, logarithm definitions and change-of-base, and essential circle theorem relationships for angles, arc length, and sector area.",{"@graph":69,"@context":122},[70,84,105],{"@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-2020-important-formulas-rules-and-definitions/266557/",{"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-2020-important-formulas-rules-and-definitions/266557.png","ImageObject",300,407,{"name":92,"@type":93},"Valentina","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-20","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you determine the number of solutions for a system of equations?","Question",{"text":112,"@type":113},"After solving, one solution corresponds to a single x or y value, zero solutions corresponds to a statement that is never true, and infinite solutions corresponds to two expressions that are always equal (e.g., 3x=3x or 5=5).","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the key forms of a quadratic and how do they help find the vertex?",{"text":117,"@type":113},"Use vertex form f(x)=a(x-b)²+k to read the vertex as (h,k) and use standard form f(x)=ax²+bx+c by first computing the x-value that locates the vertex, then substituting to get the y-value. Factored form f(x)=a(x-n)(x-m) helps interpret x-intercepts and supports finding the vertex x as the midpoint of the two zeros.",{"name":119,"@type":110,"acceptedAnswer":120},"Which rules are most important for exponents, radicals, and logarithms?",{"text":121,"@type":113},"Exponent rules include zero power a⁰=1, negative exponents, and power/product/quotient combinations. Radical rules relate radicals to fractional exponents, and logarithms use log_a=b meaning a=b’s power with common logs log x=log10 x and natural logs ln x=log_e x, plus change-of-base for positive a,b,c with b≠1 and c≠1.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},266557,1789408888,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":46},13056703020460,"https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923","# SAT MATH SECTION:CHEAT SHEETFORMULAS,RULES,AND DEFINITIONS\n\nNote:important formulas included at beginning of every test not included below  \nALGEBRA:  \n   \nZERO PRODUCT PROPERTY:If ab=0,then a=0,b=0,or a=b=0.  \nSYSTEMS OF EQUATIONS:  \nWhen you solve down a system of equations,one of three outcomes is possible as you run the  \nalgebra and create a final,simplified equation:  \n\n| One solution   | Zero solutions   | Infinite solutions   |\n| --- | --- | --- |\n| If you get a single x or y  \u003Cbr>value,(i.e.x=5 or y=2)you  \u003Cbr>have one solution   | If you get a statement that is  \u003Cbr>never true(i.e.5=9 or0=4),  \u003Cbr>you have no solutions.   | If you get two values that  \u003Cbr>always equal each other(i.e.  \u003Cbr>3x=3x or 5=5),you have  \u003Cbr>infinite solutions.   |\n| Comparing equations:You can alternatively put EVERY equation in slope intercept form that  \u003Cbr>is part of your system of linear equations.Then look at each of the y=mx+b forms and  \u003Cbr>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  \u003Cbr>don't matter)   | Same slopes(parallel lines),  \u003Cbr>different y-intercepts   | Same slope,same intercept  \u003Cbr>i.e.identical equations   |\n\n## FOIL AND FACTORING:\n\n·Amonomial is a single product such as 4x,7x³,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 or5n³+3n²+7n+2or 5x²+2x+45x²+2x+4.  \n·Difference of Squares:The product of the difference (a-b)and the sum(a+b)is equal  \nto a squared minus b squared,(a-b)(a+b)=a²-b²  \n·Square of a Sum:(a+b)²=a²+2ab+b²  \n·Square of a Difference:(a-b)²=a²-2ab+b²  \nSLOPE-INTERCEPT FORM:y=mx+b  \nWhere m is the slope of the line,and b is the y-intercept of the line at point(0,b).  \nMIDPOINT FORMULA:The midpoint of two coordinate points(x₁,y₁)and(x₂,y₂)is:  \nSupertutorTV SAT Math Formula Cheat Sheet  \nDISTANCE FORMULA:Given two points,(x₁,y₁)and(x₂,y₂),the distance between them is:  \nSPEED AND RATES DISTANCE FORMULA:d=rt  \nWORK FORMULA:w=rt  \nCOMBINED WORK FORMULA:w=(r₁+r2)t  \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-b)²+ko The vertex of the parabola in this form is(h,k)  \no When a is positive,the parabola opens upwards,and the minimum is(h,k).o When a is negative,the parabola opens downwards,and the minimum is(h,k).o Alternate form for parabolas with horizontal axis(RARE,unlikely to appear)x =a(y-k)²+h,positive a opens right-ward,negative a opens leftward  \n·FACTORED FORM:The factored form of a polynomial usually takes the form:f(x)=a(x-n)(x-m)  \no When a is positive,the parabola opens upwards.  \no When a is negative,the parabola opens downwards.  \no The graph crosses the x-axis at each point when a factored piece equals zero (the  \nzeros).For example,at x=n,x-n equals 0,so the graph crosses through the point  \n(n,0)on the x-axis.  \nIn the case of a quadratic,which will typically have two roots(i.e.two factored piecesthat include an x),the midpoint of 2 zeros is the x-value of the vertex.In the exampleabove,the zeros are at x=n and x=m.So the x value of its vertex is the average of n and  \nm.  \n·STANDARD FORM:the standard form of the parabola has the general form:f(x)=ax²+bx+cf(x)=ax²+bx+c  \nis the x-value of the vertex.The y-value of the vertex can be found byplugging in this value for x and solving for y(or f(x)).Memorize this!  \no Assuming a vertically oriented parabola,the vertex is always either themaximum or the minimum of the graph.(remember max/min is always the y-value!)  \no When a is positive,the parabola opens upwards.  \nSupertutorTV SAT Math Formula Cheat Sheet  \no When a is negative,the parabola opens downwards.  \no The sum of the two roots is(not necessary to know,but occasionally helpful)  \n(not necessry to know,but occasionallyo The product of the two roots ihelpful","cbCaiuye5hmmsSPp","https://ap.wps.com/l/cbCaiuye5hmmsSPp","pdf",381814,"English","# Algebra\n## Systems of equations outcomes\n## FOIL and factoring\n## Slope-intercept form\n## Midpoint and distance\n## Speed, work, and combined work\n# Quadratics and polynomial formulas\n## Vertex, factored, and standard forms\n## Quadratic formula and discriminant\n# Exponent, radical, and logarithm rules\n# Circle theorems","[{\"question\":\"How do you determine the number of solutions for a system of equations?\",\"answer\":\"After solving, one solution corresponds to a single x or y value, zero solutions corresponds to a statement that is never true, and infinite solutions corresponds to two expressions that are always equal (e.g., 3x=3x or 5=5).\"},{\"question\":\"What are the key forms of a quadratic and how do they help find the vertex?\",\"answer\":\"Use vertex form f(x)=a(x-b)²+k to read the vertex as (h,k) and use standard form f(x)=ax²+bx+c by first computing the x-value that locates the vertex, then substituting to get the y-value. Factored form f(x)=a(x-n)(x-m) helps interpret x-intercepts and supports finding the vertex x as the midpoint of the two zeros.\"},{\"question\":\"Which rules are most important for exponents, radicals, and logarithms?\",\"answer\":\"Exponent rules include zero power a⁰=1, negative exponents, and power/product/quotient combinations. Radical rules relate radicals to fractional exponents, and logarithms use log_a=b meaning a=b’s power with common logs log x=log10 x and natural logs ln x=log_e x, plus change-of-base for positive a,b,c with b≠1 and c≠1.\"}]","SAT Math Cheat Sheet 2020 - Important formulas, rules, and definitions | PDF"]