Solve simple problems involving quantities in direct proportion including algebraic proportions.

e.g. Using equality of ratios, if \(y ∝ x\), then

\(\dfrac{y_1}{y_2} = \dfrac{x_1}{x_2}\) or \(\dfrac{y_1}{x_1} = \dfrac{y_2}{x_2}\)

Currency conversion problems.

[see also Similar shapes, 9.04c]

Solve more formal problems involving quantities in direct proportion (i.e. where \(y ∝ x\)).

Recognise that if \(y = kx\), where \(k\) is a constant, then \(y\) is proportional to \(x\).

Formulate equations and solve problems involving a quantity in direct proportion to a power or root of another quantity.

Solve simple word problems involving quantities in inverse proportion or simple algebraic proportions.

e.g. speed-time contexts (if speed is doubled, time is halved).

Solve more formal problems involving quantities in inverse proportion (i.e. where \(y ∝ \dfrac{1}{x}\)).

Recognise that if \(\dfrac{k}{x}\), where \(k\) is a constant, then \(y\) is inversely proportional to \(x\).

Formulate equations and solve problems involving a quantity in inverse proportion to a power or root of another quantity.