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It covers arithmetic, geometric, and binomial series, key differentiation rules including first principles, integration results, and integration by parts, as well as small-angle approximations and standard trigonometric identities. The booklet also includes numerical methods such as the trapezium rule and Newton-Raphson iteration, probability tools like standard deviation, distributions, hypothesis testing, and normal distribution percentage points, plus kinematics in one and two dimensions.",{"@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/a-level-mathematics-a-h240-formulae-booklet-key-mathematics-formulae/265783/",{"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/a-level-mathematics-a-h240-formulae-booklet-key-mathematics-formulae/265783.png","ImageObject",300,407,{"name":92,"@type":93},"wps_ap_test_251126_0180","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics of calculus are included in the formula booklet?","Question",{"text":113,"@type":114},"It provides differentiation, differentiation from first principles, integration, and integration by parts, along with key rules such as the quotient rule.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which numerical methods are listed?",{"text":118,"@type":114},"It includes the trapezium rule and the Newton-Raphson iteration for solving equations of the form f(x)=0.",{"name":120,"@type":111,"acceptedAnswer":121},"What kinematics formulae are provided?",{"text":122,"@type":114},"It lists motion in a straight line and motion in two dimensions, including relations between velocity, displacement, acceleration, and time.","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},265783,1789400728,{"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":19,"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":52},8796095027276,"https://avatar.qwps.com/avatar/d3BzX2FwX3Rlc3RfMjUxMTI2XzAxODA=","A Level Mathematics A (H240)  \nFormulae Booklet  \nFormulae  \nA Level Mathematics A (H240)  \nArithmetic series  \nSn = 12n^a +lh = 12n\"2a + ^n-1hd,  \nGeometric series  \nS = a^1-rnh  \nn 1-r  \nS3 = ~~ ~~1-a~~ ~~r~~ ~~ for  r  1 1  \nBinomial series  \n^a +bhn = an + nC 1 an-1b+ nC2 an-2b 2 +f+ nCr an-rbr +f+bn ^n ! Nh J N  \nwhere nCr = n Cr = nr = r!~~^~~nn-!~~ ~~r~~h~~!  \n^1+xhn = 1 + nx + n~~^~~n2-!~~ ~~1~~h~~x2 + f + n~~^~~n-1~~h ~~!~~^~~n-r+1~~h~~xr + f ^x 1 1, n ! Rh  \nDifferentiation  \nf^xh f l^xh  \n\n| tankx | k sec2kx |\n| --- | --- |\n| secx | secx tanx |\n| cotx | 2 -cosec x |\n| cosecx | -cosecx cotx |\n\nQuotient rule y = uv , dy~~d~~x = v ~~ d~~u~~d~~x v-2u ~~ dd~~vx  \nDifferentiation from first principles  \nf l^xh = f~~^~~x~~ ~~+~~ ~~~~ ~~-f~~^~~x~~h~~  \nIntegration  \n ~~ ~~ffl~~^~~x~~h^~~x~~h~~ dx = ln f^xh + c  \n;f l^xhaf^xhkn dx = n~~ ~~~~ ~~1~~ ~~ af^xhkn +1 + c Integration by parts ; u ~~ d~~v~~d~~x dx = uv- ;v ~~ d~~u~~d~~x dx  \nSmall angle approximations  \nsin i . i , cosi . 1-12 i 2 , tani . i where i is measured in radians  \nTrigonometric identities  \nsin^A!Bh = sinAcosB! cosA sinBcos^A!Bh = cosA cosB\"sinAsinB  \ntan^A!Bh = ~~ ~~1tAan!tanBAtanB~~ ~~ aA!B ! ^k+ 12hrk  \nNumerical methods  \nTrapezium rule: yaby dx . 12h\"^y0 +ynh +2^y 1 +y2 +f+yn-1h,, where h = b-n~~ ~~a  \nThe Newton-Raphson iteration for solving f^xh = 0: xn +1 = xn-f~~f^~~xl~~^~~xn~~h~~n~~h~~  \nProbability  \nP ^A,Bh = P ^Ah +P^Bh-P^A+Bh  \nP ^A+Bh = P ^AhP ^B  Ah = P ^BhP ^A  Bh or P ^A  Bh = P~~ ^~~AP~~^~~+B~~h~~  \nStandard deviation  \n   /^x-x-h2 =   / x2-x-2 or   / f ^x-x-h2 =    / fx2-x-2  \nn  n  / f  / f  \nThe binomial distribution  \nJ N  \nIf X + B^n, ph then P ^X = xh = nxpx ^1-phn-x , mean of Xis np, variance of Xis np ^1-ph  \nHypothesis test for the mean of a normal distribution  \nIf X + N^n, v2h then X~~ ~~ + N n, ~~ v~~n2 and Xv-nn + N^0, 1h  \nPercentage points of the normal distribution  \nIf Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives the value of z such that P ^Z G zh = p .  \n| p | 0.75 0.90 0.95 | 0.975 0.99 0.995 | 0.9975 0.999 0.9995 |\n| --- | --- | --- | --- |\n| z | 0.674 1.282 1.645 | 1.960 2.326 2.576 | 2.807 3.090 3.291 |\n\nKinematics  \nMotion in a straight line v = u + at  \ns = ut + 12 at2  \ns = 12^u + vhtv2 = u 2 +2as  \n1 2 s = vt-2 at  \nMotion in two dimensions v = u + at  \ns = ut + 12 at2  \ns = 12^u +vht  \n1 2 s = vt-2 at","cbCaip8gvmi6LsWN","https://ap.wps.com/l/cbCaip8gvmi6LsWN","pdf",452223,"English","# Formulae\n## Series and Calculus\n## Trigonometry and Approximations\n## Numerical Methods\n## Probability and Statistics\n## Kinematics","[{\"question\":\"What topics of calculus are included in the formula booklet?\",\"answer\":\"It provides differentiation, differentiation from first principles, integration, and integration by parts, along with key rules such as the quotient rule.\"},{\"question\":\"Which numerical methods are listed?\",\"answer\":\"It includes the trapezium rule and the Newton-Raphson iteration for solving equations of the form f(x)=0.\"},{\"question\":\"What kinematics formulae are provided?\",\"answer\":\"It lists motion in a straight line and motion in two dimensions, including relations between velocity, displacement, acceleration, and time.\"}]","A Level Mathematics A (H240) - Formulae Booklet - Key Mathematics Formulae | PDF"]