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Arithmetic and Algebra - Geometry - Trigonometry","","ACT Formula Sheet汇总了算术与代数、指数与根式性质、通用方程与概率/百分比变化、等差与等比数列（含通项与求和）、组合与排列、对数的运算规则。内容还覆盖圆的面积与周长、弧长与扇形面积、坐标圆方程、平行四边形与梯形等常见几何面积、立体体积与线段距离/中点等解析几何公式，并包含三角函数关系与直角三角形基本恒等式，适合快速复习与考前查阅。",{"@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/act-formula-sheet-arithmetic-and-algebra-geometry-trigonometry/266413/",{"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/act-formula-sheet-arithmetic-and-algebra-geometry-trigonometry/266413.png","ImageObject",300,407,{"name":92,"@type":93},"Eliana","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"ACT Formula Sheet包含哪些主要知识模块？","Question",{"text":113,"@type":114},"主要包括算术与代数、指数与根式性质、通用公式（含二次方程、概率与百分比变化）、等差/等比数列与对数规则，以及几何中的圆、面积/体积、直线与距离和三角函数。","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"等差数列与等比数列如何求第n项和前n项和？",{"text":118,"@type":114},"等差数列用通项公式a_n=a_1+(n-1)d，并可用求和公式S_n=(a_1+ a_n)的对应形式；等比数列用a_n=a_1 r^{n-1}，并给出前n项和S_n=a_1(… )的表达。",{"name":120,"@type":111,"acceptedAnswer":121},"圆和几何部分有哪些常用公式？",{"text":122,"@type":114},"圆的面积A=πr^2、周长C=2πr、圆弧长与扇形面积的表达，以及圆心在(h,k)且半径为r时的方程(x-h)^2+(y-k)^2=r^2；此外还给出平行四边形、梯形、三角形等面积公式和常见立体体积公式。","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},266413,1790359032,{"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":81,"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":144,"read_time":39},4398048949847,"https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267","ACT FORMULA SHEET  \nArithmetic and Algebra  \nProperties of Exponents and Radicals  \nan ∙ am = an+m ()n =  n√ = a  \n = an-m  \na-n =  n√_b = n√ ∙ n√__b  \n(an)m = anm - = an  \n√n __ab =   \n(ab)n = anbn ()-n = ()n  \nn __  m  \n√ am = a n  \nGeneric Formulas  \nQuadratic Formula: For ax2 + bx + c = 0, x = _-  \nEvent Probability: oesssiireblde   \nPercent Growth/Decay: Original(1 ± r1)(1 ± r2) ...  \nIn Percent Growth or Decay, r1, r2, ... are the percents an amount is being changed by each year, month, etc.  \nArithmetic Mean: Sum of Terms  Number of Terms  \nDistance: Distance = Rate ∙ Time  \nPercent Change: l-l ∙ 100%  \nArithmetic Sequence/Series Geometric Sequence/Series  \nCommon Difference: d = an+1-an  \nFind the nth term: an = a1 + (n-1)d  \nSum the first n terms: Sn =  (a1 + an)  \nCombination (Order Doesn’t Matter): nCr = (_-! ! Permutation (Order Does Matter): nPr = _n-_!_r)_!  \nRemember, n is the number of choices you have, and r is how many you are going to choose.  \na Common Ratio: r = _  \nFind the nth term: an = a1rn-1  \nSum the first n terms: Sn = a1 ( -_-)  \nloga ax = xxlogay = logay x  \nlogax + logay = loga (xy)  \nlogax-logay = loga ()  \nCounting and Ordering Properties of Logarithms   \nGeometry  \nThe Circle  \nArea: A = πr2  \nCircumference: C = 2πr  \nArc length: L(A,B) = _3_0 ∙ 2πr  \nSector Area: AOB = _3_0 ∙ πr 2  \nEquation for circle with center (h, k) and radius r: (x-h)2 + (y-k)2 = r2  \nAreas  \nParallelogram: A = bh  \nTrapezoid: A =  (b1 + b2)h  \nTriangle: A =  bh  \nCube: A = 6s 2  \nAngles  \nSum of Interior Angles: = 180(n-2)˚  \nEach Interior Angle: = _(_- )_˚  \nSum of Exterior Angles: = 360˚  \nEach Exterior Angles: =   \nPythagorean’s Theorem in 3D  \nVolumes  \nCube: V = s3  \nRectangular Prism: V = lwh  \nCylinder: V = πr2 h  \nSphere: V = πr 3  \nLines  \nSlope of a Line: m = --   \nMidpoint: M = ( , 2 )  \nDistance: d =√(x2-x1)2 + (y2-y1)2  \n_____________  \nd2 = a2 + b2 + c2  \n2  \nTrigonometry  \nPythagorean Theorem  \nPythagorean Theorem d2 = a2 + b2 + c2  \nTrigonometric Ratios  \nsin A = opposite leg hypotenuse adjacent leg  \ncos A = _________  \nhypotenuse  \nopposite leg tan A = _________  \nadjacent leg  \ncsc A =  \nsec A =  \ncot A =  \nhypotenuse opposite leg  \nhypotenuse adjacent leg  \nadjacent leg opposite leg  \nA  \nb  \nC a B","cbCaigGGtYEytb9I","https://ap.wps.com/l/cbCaigGGtYEytb9I","pdf",211148,"English","# Arithmetic and Algebra\n## Properties of Exponents and Radicals\n## Generic Formulas\n## Arithmetic Sequence/Series and Geometric Sequence/Series\n## Logarithms\n# Geometry\n## The Circle\n## Areas and Volumes\n## Lines and Distance\n# Trigonometry","[{\"question\":\"ACT Formula Sheet包含哪些主要知识模块？\",\"answer\":\"主要包括算术与代数、指数与根式性质、通用公式（含二次方程、概率与百分比变化）、等差/等比数列与对数规则，以及几何中的圆、面积/体积、直线与距离和三角函数。\"},{\"question\":\"等差数列与等比数列如何求第n项和前n项和？\",\"answer\":\"等差数列用通项公式a_n=a_1+(n-1)d，并可用求和公式S_n=(a_1+ a_n)的对应形式；等比数列用a_n=a_1 r^{n-1}，并给出前n项和S_n=a_1(… )的表达。\"},{\"question\":\"圆和几何部分有哪些常用公式？\",\"answer\":\"圆的面积A=πr^2、周长C=2πr、圆弧长与扇形面积的表达，以及圆心在(h,k)且半径为r时的方程(x-h)^2+(y-k)^2=r^2；此外还给出平行四边形、梯形、三角形等面积公式和常见立体体积公式。\"}]","ACT FORMULA SHEET - Arithmetic and Algebra - Geometry - Trigonometry | PDF",1789407135]