[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143673-105":59,"doc-detail-143673-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","sat-math-cheat-sheet-exponents-proportions-equations-and-geometry-formulas","SAT Math Cheat Sheet - Exponents, Proportions, Equations and Geometry Formulas","","A compact SAT math reference sheet compiling core algebra, functions, and geometry formulas with quick-rule guidance. It covers exponent and radical laws, proportions, rates, percent change, and simple/compound interest, then extends to exponential growth and decay models, linear equations, absolute value rules, and coordinate geometry essentials like distance and midpoint. It also summarizes slope concepts, line forms, function transformations and symmetry, factor and remainder theorems, quadratic equation tools, plus angle conversions and key polygon/sector measurements for fast problem solving.",{"@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-exponents-proportions-equations-and-geometry-formulas/143673/",{"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-exponents-proportions-equations-and-geometry-formulas/143673.png","ImageObject",300,407,{"name":92,"@type":93},"Theodore","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",33,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What are the main exponent rules included in the cheat sheet?","Question",{"text":113,"@type":114},"It lists product, quotient, power of a power, power of a product, and zero/negative exponent rules, emphasizing careful handling of signs and fractional forms.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do proportions and rates relate in the sheet?",{"text":118,"@type":114},"It provides a proportion formula with cross-multiplication ad = bc, and a rate formula expressed as Rate = Quantity / Time.",{"name":120,"@type":111,"acceptedAnswer":121},"Which quadratic equation tools are summarized?",{"text":122,"@type":114},"It includes standard form, the quadratic formula with the discriminant, and vertex-related formulas such as x-coordinate of the vertex and vertex form y = a(x - h)^2 + k.","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},143673,1787696301,{"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":52,"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":144},7971461740886,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","SAT Math Cheat Sheet  \nMade with :) by SAT GURUS  \nExponents and Radicals Rules  \n1. Exponent Rules  \n• Product of Powers: am · an = am+n  \n• Quotient of Powers: ~~a~~am~~n~~ = am−n  \n• Power of a Power: (am )n = am·n  \n• Power of a Product: (ab)n = an · bn  \n• Power of a Quotient: 􀀀 ~~a~~b􀀁 n = ~~a~~bn~~n~~  \n• Zero Exponent: a0 = 1 (for a  0)  \n• Negative Exponent: a −n = a~~1n~~  \n2. Radicals Rules  \n• Product of Radicals: √a · √b = √a · b  \n• Quotient of Radicals: ab = p ~~a~~b  \n• Power of a Radical: ( a)m = am    \n• Simplifying Radicals: √a · b = √a · √b  \n• Rationalizing the Denominator: To rationalize a , multiply by a~~a~~  \n3. Common Tricks  \n• Misleading Exponent Rules: Be cautious with negative exponents and zero exponents, especially in fractional forms.  \n• Radicals in Denominators: Remember to rationalize denominators when needed.  \n• Nested Radicals: Simplify inner radicals first before applying operations to the outer ones.  \n• Special Values: Recognize and simplify radicals of perfect squares, cubes, etc., quickly.  \nProportions and Rates  \nProportion Formula:  \na  c  \n=  \nb d  \nCross-multiplication yields ad = bc.  \nRate Formula:  \nRate = Quantity  \nTime  \nPercentages  \nPercent Change Formula:  \nPercent Change = New~~ ~~Value~~ ~~−Old~~ ~~VaOlulde~~ ~~Value × 100%  \nInterest Formulas  \nSimple Interest  \n• Formula: I = P · r · t  \n• Total Amount: A = P + I Compound Interest  \n• Formula: A = P 􀀀1 + ~~r~~n􀀁 nt  \n• Interest: I = A − P  \n• Where:  \n– P = Principal  \n– r = Annual interest rate (decimal)  \n– n = Number of compounding periods per year  \n– t = Time (years)  \nExponential Growth/Decay  \nExponential Growth Formula:   \nf (t) = A(1 + r)t  \nwhere f (t) is the value of the quantity at time t, A is the initial value, and r is the growth rate.  \nExponential Decay Formula:  \nf (t) = A(1 − r)t  \nwhere f (t) is the value of the quantity at time t, A is the initial value, and r is the decay rate.  \nLinear Equations  \nSlope-Intercept Formula:  \ny = mx + b  \nwhere m is the slope and b is the y-intercept.  \nPoint-Slope Formula:  \ny − y 1 = m (x − x1 )  \nwhere (x1 , y 1 ) is a point on the line.  \nSystems of Equations Solving by Substitution:  \n• Solve one equation for one variable.  \n• Substitute this expression into the other equation and solve. Solving by Elimination:  \n• Add or subtract equations to eliminate one variable.  \n• Solve for the remaining variable.  \nAbsolute Value  \nAbsolute Value Definition:  \n|x| = (x  \nSolving Absolute Value Equations:  \nif x ≥ 0  \nif x \u003C 0  \n|x| = a ⇒ x = a or x = −a  \nSolving Absolute Value Inequalities:  \n|x| \u003C a ⇒ −a \u003C x \u003C a  \n|x| > a ⇒ x \u003C −a or x > a  \nCoordinate Geometry   \nDistance Between Two Points:  \nd = p (x2 − x1 )2 + (y2 − y1 )2  \nMidpoint Formula:  \n􀀒 x~~ ~~1~~ ~~+2~~ ~~x2 , y~~ ~~1~~ ~~+2~~ ~~y2 􀀓  \nSlope Formula:  \nm = y2 − y 1 x2 − x 1  \nEquation of a Line (Slope-Intercept Form) :  \ny = mx + b  \nwhere m is the slope and b is the y-intercept.  \nEquation of a Line (Point-Slope Form) :  \ny − y 1 = m (x − x1 )  \nSlope Concepts  \nSlope  \n• Definition: The slope of a line measures its steepness and direction. It is calculated as the ratio of the change in y (rise) to the change in x (run) .  \n• Formula: m = yx Positive Slope  \n• Description: The line rises as it moves from left to right.  \n• Example: m > 0 Negative Slope  \n• Description: The line falls as it moves from left to right.  \n• Example: m \u003C 0  \nParallel Lines  \n• Description: Lines that never intersect and have the same slope.  \n• Condition: m 1 = m2 Perpendicular Lines  \n• Description: Lines that intersect at a right angle.  \n• Condition: The product of their slopes is −1 . If m 1 and m2 are the slopes of the lines, then m 1 · m2 = −1.   \nFunction Transformations  \nVertical Shift:  \ny = f (x) + k  \nShifts the graph up if k > 0 and down if k \u003C 0.  \nHorizontal Shift:  \ny = f (x − h)  \nShifts the graph right if h > 0 and left if h \u003C 0.  \nVertical Stretch/Compression:  \ny = af (x)  \nStretches the graph verticall","cbCaipR1eTrGqFL3","https://ap.wps.com/l/cbCaipR1eTrGqFL3","pdf",4747489,"English","# Exponents and Radicals Rules\n# Proportions and Rates\n# Percentages\n# Interest Formulas\n## Simple Interest\n## Compound Interest\n# Exponential Growth/Decay\n# Linear Equations\n# Absolute Value\n# Coordinate Geometry\n## Distance and Midpoint\n## Slope and Line Equations\n# Slope Concepts and Line Relationships\n# Function Transformations and Symmetry\n# Factor and Remainder Theorems\n# Quadratic Equations\n# Angles and Polygon Measures","[{\"question\":\"What are the main exponent rules included in the cheat sheet?\",\"answer\":\"It lists product, quotient, power of a power, power of a product, and zero/negative exponent rules, emphasizing careful handling of signs and fractional forms.\"},{\"question\":\"How do proportions and rates relate in the sheet?\",\"answer\":\"It provides a proportion formula with cross-multiplication ad = bc, and a rate formula expressed as Rate = Quantity / Time.\"},{\"question\":\"Which quadratic equation tools are summarized?\",\"answer\":\"It includes standard form, the quadratic formula with the discriminant, and vertex-related formulas such as x-coordinate of the vertex and vertex form y = a(x - h)^2 + k.\"}]","SAT Math Cheat Sheet - Exponents, Proportions, Equations and Geometry Formulas | PDF",25]