{"id":469,"date":"2023-01-24T19:37:50","date_gmt":"2023-01-24T14:07:50","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=469"},"modified":"2023-01-24T19:37:52","modified_gmt":"2023-01-24T14:07:52","slug":"mathematics-revision-sheet","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/","title":{"rendered":"Mathematics revision sheet for class 11 and class 12 physics"},"content":{"rendered":"

[latexpage]<\/p>\n\n\n\n

Here are\u00a0the Mathematics revision sheets for class 11 and class 12 physics<\/p>\n\n\n\n

Differentiation<\/span><\/strong><\/h2>\n\n\n\n

We have two quantities x and y such that $y=f(x)$ where $f(x)$ is some function of x. We may be interested in finding the followings things<\/p>\n\n\n\n

    \n
  1. $\\frac{dy}{dx}$\n

     <\/p>\n<\/li>\n\n\n\n

  2. Maximum and Minimum values of y.It can be found with the method of Maxima and Minima<\/span> <\/li>\n<\/ol>\n\n\n\n

    $\\frac{dy}{dx}$ is the called the derivative of y w.r.t to x<\/p>\n\n\n\n

    It is defined as<\/p>\n\n\n\n

    $\\frac{dy}{dx}=\\lim_{\\Delta x \\to 0}\\left ( \\frac{\\Delta y}{\\Delta x} \\right )$<\/p>\n\n\n\n

    Some commonly known functions and their derivatives are:-<\/p>\n\n\n\n

    $y=x^n$<\/td>$\\frac{dy}{dx}=nx^{n-1}$<\/td><\/tr>
    $y=sinx$<\/td>$\\frac{dy}{dx}=cosx$<\/td><\/tr>
    $y=cosx$<\/td>$\\frac{dy}{dx}=-sinx$<\/td><\/tr>
    $y=tanx$<\/td>$\\frac{dy}{dx}=sec^{2}$<\/td><\/tr>
    $y=cotx$<\/td>$\\frac{dy}{dx}=-cosec^{2}$<\/td><\/tr>
    $y=secx$<\/td>$\\frac{dy}{dx}=secx tanx$<\/td><\/tr>
    $y=ln x$<\/td>$\\frac{dy}{dx}=\\frac{1}{x}$<\/td><\/tr>
    $y=e^{x}$<\/td>$\\frac{dy}{dx}=e^{x}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    Some important and useful rules for finding derivatives of composite functions<\/p>\n\n\n\n

      \n
    1. $\\frac{d}{dx}(cy)=c\\frac{dy}{dx}$ where c is constant <\/li>\n\n\n\n
    2. $\\frac{d}{dx}(a+b)=\\frac{da}{dx} + \\frac{da}{dx} $ where a and b are function of x<\/span> <\/li>\n\n\n\n
    3. $\\frac{d}{dx}(ab)=a\\frac{db}{dx}+b\\frac{da}{dx}$<\/span> <\/li>\n\n\n\n
    4. $\\frac{d}{dx}(\\frac{a}{b})=\\frac{[b\\frac{da}{dx}-a\\frac{db}{dx}]}{b^{2}}$<\/span> <\/li>\n\n\n\n
    5. $\\frac{dy}{dx}=(\\frac{dy}{da})(\\frac{da}{dx})$<\/span> <\/li>\n\n\n\n
    6. $\\frac{d^{2}y}{dx^{2}}=(\\frac{d}{dx})(\\frac{dy}{dx})$<\/li>\n<\/ol>\n\n\n\n

      Maximum and Minimum values of y<\/strong><\/span><\/p>\n\n\n\n

      Step 1:<\/strong>
      fine the derivative of y w.r.t x<\/p>\n\n\n\n

      $(\\frac{dy}{dx})$<\/p>\n\n\n\n

      Step2:<\/strong>
      Equate<\/p>\n\n\n\n

      $\\frac{dy}{dx}=0$<\/p>\n\n\n\n

      Solve the equation to find out the values of x<\/p>\n\n\n\n

      Step3:<\/strong>
      find the second derivative of y w.r.t x and calculate the values of<\/p>\n\n\n\n

      $\\frac{d^{2}y}{dx^{2}}$<\/p>\n\n\n\n

      for the values of x from step2<\/p>\n\n\n\n

      if $\\frac{d^{2}y}{dx^{2}}>0$ then the value of x corresponds to mimina of y then $y_{min}$ can be find out by putting this value of x<\/p>\n\n\n\n

      if $\\frac{d^{2}y}{dx^{2}}<0$ then the value of x corresponds to maxima of y then $y_{max}$ can be find out by putting this value of x<\/p>\n\n\n\n

      Integration<\/span><\/strong><\/h2>\n\n\n\n

      $I=\\int_{a}^{b}f(x)dx$<\/p>\n\n\n\n

      It reads as integration of function f(x) w.r.t. x within the limits from x=a to x=b.<\/p>\n\n\n\n

      Integration of some important functions are<\/p>\n\n\n\n

      $\\int sinx dx=-cosx$<\/p>\n\n\n\n

      $\\int cosx dx=sinx$<\/p>\n\n\n\n

      $\\int sec^{x}dx=tanx$<\/p>\n\n\n\n

      $\\int cosec^{x}dx=-cotx$<\/p>\n\n\n\n

      $\\int \\frac{1}{x}dx=lnx$<\/p>\n\n\n\n

      $\\int x^{n}dx=\\frac{x^{n+1}}{n+1}$<\/p>\n\n\n\n

      $\\int e^x dx=e^x$<\/p>\n\n\n\n

      Useful rules for integration are<\/p>\n\n\n\n

      $\\int cf(x)dx=c\\int f(x)dx$<\/p>\n\n\n\n

      $\\int[f(x)+h(x)]=\\int f(x)dx+\\int h(x)dx$<\/p>\n\n\n\n

      $\\int f(x)g(x)dx=f(x)\\int g(x)dx -\\int\\left ( f'(x)\\int g(x)dx \\right ) dx$<\/p>\n\n\n\n

      Trigonometry<\/strong><\/span><\/h2>\n\n\n\n


      Properties of trigonometric functions<\/p>\n\n\n\n

      1. Pythagorean identity<\/span><\/strong><\/em><\/p>\n\n\n\n

      $sin^2 A +cos^2 A=1$<\/p>\n\n\n\n

      $1+tan^ A=sec^2 A$<\/p>\n\n\n\n

      $1+cot^2 A=cosec^2 A$<\/p>\n\n\n\n

      2. Periodic function<\/span><\/strong><\/em><\/p>\n\n\n\n

      $sin(A+2\\pi)=sinA$<\/p>\n\n\n\n

      $cos(A+2\\pi)=cosA$<\/p>\n\n\n\n

      3.Even-Odd Identities<\/strong><\/em><\/span><\/p>\n\n\n\n

      $cos(-A)=cos(A)$<\/p>\n\n\n\n

      $sin(-A)=-sin(A)$<\/p>\n\n\n\n

      $tan(-A)=-tan(A)$<\/p>\n\n\n\n

      $cosec(-A)=-cosec(A)$<\/p>\n\n\n\n

      $sec(-A)=sec(A)$<\/p>\n\n\n\n

      $cot(-A)=-cot(A)$<\/p>\n\n\n\n

      4. Quotient identities<\/span><\/strong><\/em><\/p>\n\n\n\n

      $tan(A)=\\frac {sin A}{cos A}$
      $cot(A)=\\frac{cos A}{sin A}$<\/p>\n\n\n\n

      5. Co-function identities<\/span><\/strong><\/em>
      $sin\\left ( \\frac{\\pi}{2}-A \\right )=cos(A)$<\/p>\n\n\n\n

      $cos\\left ( \\frac{\\pi}{2}-A \\right )=sin(A)$<\/p>\n\n\n\n

      $tan \\left ( \\frac{\\pi}{2}-A \\right )=cot(A)$<\/p>\n\n\n\n

      $cosec \\left( \\frac{\\pi}{2}-A \\right )=sec(A)$<\/p>\n\n\n\n

      $sec\\left ( \\frac{\\pi}{2}-A \\right )=cosec(A)$<\/p>\n\n\n\n

      $cot\\left ( \\frac{\\pi}{2}-A \\right )=tan(A)$<\/p>\n\n\n\n

      6. Sum difference formulas<\/span><\/strong><\/em>
      $sin(A\\pm B)=sin(A)cos(B) \\pm sin(B)cos(A)$<\/p>\n\n\n\n

      $cos(A \\pm B)=cos(A)cos(B) \\mp sin(A)sin(B)$<\/p>\n\n\n\n

      $tan(A \\pm B)=\\frac {tan(A) \\pm tan(B)}{1 \\mp tan(A) tan (B)}$<\/p>\n\n\n\n

      7. Double angle formulas<\/span><\/strong><\/em>
      $cos(2A)=cos^2(A)-sin^2(A)=2cos^2 (A)-1=1-2sin^2(A)$<\/p>\n\n\n\n

      $sin(2A)=2sin(A)cos(A)$
      $tan(2A)=\\frac{2tan(A)}{1-tan^2(A)}$<\/p>\n\n\n\n

      8. Product to sum formulas<\/span><\/strong><\/em><\/p>\n\n\n\n

      $sin(A)cos(B)=\\frac {1}{2}[cos(A-B)-cos[A+B]$<\/p>\n\n\n\n

      $cos(A)cos(B)=\\frac {1}{2}[cos(A-B)+cos[A+B]$<\/p>\n\n\n\n

      $sin(A)cos(B)=\\frac {1}{2}[sin(A+B)+sin[A-B]$<\/p>\n\n\n\n

      $cos(A)sin(B)=\\frac {1}{2}[sin(A+B)-sin[A-B]$<\/p>\n\n\n\n

      9. Power reducing formulas<\/span><\/strong><\/em>
      $sin^2 A=\\frac{1-cos(2A)}{2}$<\/p>\n\n\n\n

      $cos^2 A=\\frac{1+cos(2A)}{2}$<\/p>\n\n\n\n

      $tan^2 A=\\frac{1-cos(2A)}{1+cos(2A)}$<\/p>\n\n\n\n

      10. reciprocal identities<\/span><\/em><\/strong><\/p>\n\n\n\n

      $Sin(A)=\\frac{1}{cosec(A)}$<\/p>\n\n\n\n

      $cos(A)=\\frac{1}{sec(A)}$<\/p>\n\n\n\n

      $tan(A)=\\frac{1}{cot(A)}$<\/p>\n\n\n\n

      $ cosec(A)=\\frac{1}{sin(A)}$<\/p>\n\n\n\n

      $Sec(A)=\\frac{1}{cos(A)}$<\/p>\n\n\n\n

      $cot(A)=\\frac{1}{tan(A)}$<\/p>\n\n\n\n

      Binomial Theorem<\/strong><\/h2>\n\n\n\n

      $(a+b)^n=C_{0}^{n}a^{n}+C_{1}^{n}a^{n-1}b+C_{2}^{n}a^{n-2}b^2+………+C_{n}^{n}b^{n}$
      From the binomial formula, if we let a = 1 and b = x, we can also obtain the binomial series which is valid for any real number n if |x| < 1.
      (1+x)^n=1+nx+\\frac{n(n-1)}{2!}x^2+\\frac{n(n-1)(n-2)}{3!}x^3+………..<\/p>\n\n\n\n

      Geometric Series<\/strong><\/h2>\n\n\n\n

      $a,aq,aq^2,aq^3,aq^4………..aq^{n-1}$ where q is not equal to 0, q is the common ratio and a is a scale factor.The formula for the sum of the first n numbers of geometric progression
      $S_{n}=\\frac{a(1-q^n)}{(1-q)}$
      Infinite geometric series where |q| < 1
      If |q| < 1 then $a_{n} \\to 0$, when n -> infinity So the sum S of such an infinite geometric progression is:
      $S=\\frac{1}{(1-x)}$ which is valid only for |x|<\/p>\n\n\n\n

      Arithmetic Progression<\/strong><\/h2>\n\n\n\n

      $a,a+d,a+2d,a+3d……….a+(n-1)d$<\/p>\n\n\n\n

      The sum S of the first n values of a finite sequence is given by the formula:<\/p>\n\n\n\n

      $S=\\frac{n}{2}[(2a + d(n-1)]$<\/p>\n\n\n\n

      Quadratic Formul<\/strong>a<\/h2>\n\n\n\n


      $ax^2+bx+c=0$
      then
      $x=-\\frac{b\\pm?(b2-4ac)}{2a}$<\/p>\n\n\n\n

      Download this post as pdf<\/span><\/span><\/em><\/strong><\/p>\n\n\n\"Icon Mathematics revision sheet for class 11 and class 12 physics pt 1<\/a> (40.5 KiB)\n\n\n\"Icon Mathematics revision sheet for class 11 and class 12 physics part 2<\/a> (48.0 KiB)\n","protected":false},"excerpt":{"rendered":"

      This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.<\/p>\n","protected":false},"author":8,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[14,37],"tags":[],"class_list":["post-469","post","type-post","status-publish","format-standard","hentry","category-physics","category-tips-and-tricks"],"yoast_head":"\nMathematics revision sheet for class 11 and class 12 physics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematics revision sheet for class 11 and class 12 physics\" \/>\n<meta property=\"og:description\" content=\"This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/\" \/>\n<meta property=\"og:site_name\" content=\"physicscatalyst's Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/PhysicsCatalyst\" \/>\n<meta property=\"article:published_time\" content=\"2023-01-24T14:07:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-01-24T14:07:52+00:00\" \/>\n<meta name=\"author\" content=\"physicscatalyst\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"physicscatalyst\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Mathematics revision sheet for class 11 and class 12 physics","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/","og_locale":"en_US","og_type":"article","og_title":"Mathematics revision sheet for class 11 and class 12 physics","og_description":"This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.","og_url":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/","og_site_name":"physicscatalyst's Blog","article_publisher":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_author":"https:\/\/www.facebook.com\/PhysicsCatalyst","article_published_time":"2023-01-24T14:07:50+00:00","article_modified_time":"2023-01-24T14:07:52+00:00","author":"physicscatalyst","twitter_misc":{"Written by":"physicscatalyst","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/#article","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/"},"author":{"name":"physicscatalyst","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f"},"headline":"Mathematics revision sheet for class 11 and class 12 physics","datePublished":"2023-01-24T14:07:50+00:00","dateModified":"2023-01-24T14:07:52+00:00","mainEntityOfPage":{"@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/"},"wordCount":1003,"commentCount":2,"publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"articleSection":["Physics","Tips and tricks"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/","url":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/","name":"Mathematics revision sheet for class 11 and class 12 physics","isPartOf":{"@id":"https:\/\/physicscatalyst.com\/article\/#website"},"datePublished":"2023-01-24T14:07:50+00:00","dateModified":"2023-01-24T14:07:52+00:00","breadcrumb":{"@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/physicscatalyst.com\/article\/mathematics-revision-sheet\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/physicscatalyst.com\/article\/"},{"@type":"ListItem","position":2,"name":"Physics","item":"https:\/\/physicscatalyst.com\/article\/physics\/"},{"@type":"ListItem","position":3,"name":"Mathematics revision sheet for class 11 and class 12 physics"}]},{"@type":"WebSite","@id":"https:\/\/physicscatalyst.com\/article\/#website","url":"https:\/\/physicscatalyst.com\/article\/","name":"physicscatalyst's Blog","description":"Learn free for class 9th, 10th science\/maths , 12th and IIT-JEE Physics and maths.","publisher":{"@id":"https:\/\/physicscatalyst.com\/article\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/physicscatalyst.com\/article\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/physicscatalyst.com\/article\/#organization","name":"physicscatalyst","url":"https:\/\/physicscatalyst.com\/article\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/","url":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","contentUrl":"https:\/\/physicscatalyst.com\/article\/wp-content\/uploads\/2024\/08\/cropped-logo-1.jpg","width":96,"height":96,"caption":"physicscatalyst"},"image":{"@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst","https:\/\/www.youtube.com\/user\/thephysicscatalyst","https:\/\/www.instagram.com\/physicscatalyst\/"]},{"@type":"Person","@id":"https:\/\/physicscatalyst.com\/article\/#\/schema\/person\/9b302efdc9b32e459cb1e61ab7506d3f","name":"physicscatalyst","sameAs":["https:\/\/physicscatalyst.com","https:\/\/www.facebook.com\/PhysicsCatalyst","https:\/\/x.com\/physicscatalyst"]}]}},"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"shareaholic-thumbnail":false},"uagb_author_info":{"display_name":"physicscatalyst","author_link":"https:\/\/physicscatalyst.com\/article\/author\/physicscatalyst\/"},"uagb_comment_info":0,"uagb_excerpt":"This mathematics sheet would be helpful for quick revision of most of maths formulas needed before class 11 and 12 physics examination. It covers quick and much needed formulas on differentiation , integration, trigonometry, AP, GP etc.","_links":{"self":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/469","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/users\/8"}],"replies":[{"embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/comments?post=469"}],"version-history":[{"count":2,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/469\/revisions"}],"predecessor-version":[{"id":7614,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/posts\/469\/revisions\/7614"}],"wp:attachment":[{"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/media?parent=469"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/categories?post=469"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicscatalyst.com\/article\/wp-json\/wp\/v2\/tags?post=469"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}