Direct and inverse proportion

Multiplying by $x^2$ instead of dividing by it — the single most common error on this topic.

When the relationship involves $d^2$, students use $d$ instead of $d^2$.

Writing $y \propto \tfrac{1}{x}$ and stopping — a formula needs an equals sign and a value for $k$.

You cannot answer without finding $k$: substitute the given pair, solve, then rewrite the full equation. For $y = kx$ with $x = 4$, $y = 20$: $k = 5$, so $y = 5x$. Scaling directly without $k$ can work for simple direct cases but fails for squares and inverses.

When a squared term is the unknown, remember the final root. If $F = \dfrac{200}{d^2}$ and $F = 2$, then $d^2 = 100$, so $d = 10$ — stopping at $d^2 = 100$, or not square-rooting, drops the last mark.