The Diagnostic

If $\alpha ,\beta$ are the roots of $x^2-5x+3=0$, find ${\alpha }^2+{\beta }^2$.

Which are the vertical asymptotes of $y={\displaystyle \frac{x+1}{x^2-4}}$?

The standard result for ${\displaystyle \sum _{r=1}^n{r}^2}$ is:

The determinant of $\left(\begin{array}{cc}2& 1\\ 3& 4\end{array}\right)$ is:

The area of a sector bounded by a polar curve $r=f(\theta )$ is:

For vectors $𝐚,𝐛$, the magnitude $|𝐚\times 𝐛|$ equals:

Having assumed a statement is true for $n=k$, the inductive step requires you to prove it true for:

The identity ${\cosh }^{2}x-{\sinh }^{2}x$ equals:

An eigenvalue $\lambda$ of a matrix $𝐀$ satisfies:

${\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}}(\sinh x)$ equals:

${\displaystyle \int \frac{1}{\sqrt{a^2-x^2}}\mathrm{d}x}$ equals:

By de Moivre's theorem, $(\cos \theta +i\sin \theta {)}^4$ equals:

The integrating factor for ${\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}}+P(x)y=Q(x)$ is: