Maths AA terms: H

Half of a sphere, cut off by a plane through its centre. A solid hemisphere of radius $r$ has volume $\frac{2}{3}\pi r^3$ and total surface area $3\pi r^2$.

A derivative found by differentiating more than once. The $n$th derivative of $f$ is written $f^{(n)}(x)$ or $\frac{d^n y}{dx^n}$.

A diagram for grouped continuous data in which each class is drawn as a bar with no gaps between bars. With equal class widths, the height of each bar is the frequency.

A first-order differential equation that can be written as $\frac{dy}{dx} = f\left(\frac{y}{x}\right)$. The substitution $y = vx$ turns it into a separable equation in $v$ and $x$.

A horizontal line $y = k$ that a graph approaches as $x \to \infty$ or $x \to -\infty$, so that $f(x)$ gets as close to $k$ as you like.

The graph of a function is one-to-one, and so the function has an inverse, when every horizontal line meets it at most once.

The curve formed by the graph of $y = \frac{k}{x}$, or of any function $\frac{ax + b}{cx + d}$ that is not constant: two separate branches, each approaching the same pair of perpendicular asymptotes.

The longest side of a right-angled triangle, opposite the right angle.