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Content MathML, like any language, is difficult to "learn" completely. Becoming comfortable with the semantics and structure of Content MathML is a lot easier than memorizing every possible element
This MathML "cookbook" provides you with the "ingredients" (or helpful examples) to begin writing your own MathML expressions. Namespaces are not included, so please be sure to include an appropriate namespace if combining these snippets with other XML languages.
<math><apply><eq/><apply><plus/><cn>2</cn><cn>2</cn></apply><cn>4</cn></apply></math>
<math><apply><eq/><apply><plus/><apply><power/><ci>x</ci><cn>2</cn></apply><apply><times/><cn>2</cn><ci>x</ci></apply><cn>3</cn></apply><apply><times/><apply><minus/><ci>x</ci><cn>1</cn></apply><apply><plus/><ci>x</ci><cn>3</cn></apply></apply></apply></math>
<math><apply><eq/><ci>x</ci><apply><divide/><apply><minus/><ci>c</ci><ci>b</ci></apply><ci>a</ci></apply></apply></math>
<math><apply><eq/><apply><root/><degree><cn>3</cn></degree><ci>b</ci></apply><apply><log/><logbase><cn>2</cn></logbase><ci>a</ci></apply></apply></math>
<math><apply><eq/><apply><plus/><apply><power/><apply><sin/><ci>?</ci></apply><cn>2</cn></apply><apply><power/><apply><cos/><ci>?</ci></apply><cn>2</cn></apply></apply><cn>1</cn></apply></math>
<math><apply><limit/><bvar><ci>h</ci></bvar><lowlimit><cn>0</cn></lowlimit><apply><divide/><apply><minus/><apply><ci>f</ci><apply><plus/><ci>x</ci><ci>h</ci></apply></apply><apply><ci>f</ci><ci>x</ci></apply></apply><ci>h</ci></apply></apply></math>
<math><apply><eq/><apply><ci>F</ci><ci>x</ci></apply><apply><int/><bvar><ci>t</ci></bvar><lowlimit><ci>a</ci></lowlimit><uplimit><ci>x</ci></uplimit><apply><ci>f</ci><ci>t</ci></apply></apply></apply></math>
<math><apply><diff/><bvar><ci>x</ci></bvar><apply><ci>f</ci><ci>y</ci></apply></apply></math>
<math><apply><partialdiff/><bvar><ci>x</ci></bvar><bvar><ci>y</ci></bvar><apply><ci type="function">f</ci><ci>x</ci><ci>y</ci></apply></apply></math>
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