What is the pKa of methylamine
Both sources are correct. However, they are referring to two different $\mathrm{p}K_\mathrm{a}$ values.

$$\ce{H3C-NH3+ &lt;=&gt;[$K_\mathrm{a1}$] H3C-NH2 + H+ &lt;=&gt;[$K_\mathrm{a2}$] H3C-NH- + 2 H+}$$

The second value is the one that your marking scheme refers to when it asks for the $\mathrm{p}K_\mathrm{a}$ of $\ce{H3C-NH2}$. However, it is of little practical relevance. Most of the time, the question is not how acidic methyl amine is but how basic. And for that, the $\mathrm{p}K_\mathrm{a1}$ value of the conjugate acid, methyl ammonium, is used. $\ce{H3C-NH3+}$ has a $\mathrm{p}K_\mathrm{a1}$ value of approximately $10$, and it is the value you found online.

Formally correct usage would only name $\mathrm{p}K_\mathrm{a2}$ as the value of methyl amine. Colloquial chemists’ usage mainly uses $\mathrm{p}K_\mathrm{a1}$.