Direct proportion to the square

Last updated on Apr 2, 2026

Scaffolded direct proportion to the square worksheet

Direct proportion to the square is when one quantity increases or decreases in proportion to the square of another quantity. This relationship is common in areas like physics, where force and area are connected, or in geometry when calculating areas of shapes. Understanding this concept helps in solving problems where changes aren't linear but grow or shrink more rapidly. Jump to the questions

Practise now

Question

y is directly proportional to p²

y = when p =

Find the equation for y and p

Step 1 - describe the relationship using the correct symbol

y ∝ p²

Step 2 - replace the symbol with the constant of proportionality, k

y = p²

Step 3 - substitute the values from the question into the equation

= k

Step 4 - rearrange the equation to isolate k

÷ = k

Step 5 - determine the value of k

k =

Step 6 - write the final equation linking y and p²

y = p²

Find y when p =

Step 1 - restate the equation

y = p²

Step 2 - substitute the value you know

y = ×

Step 3 - determine the final value of y

y =

Find p when y =

Step 1 - restate the equation

y = p²

Step 2 - substitute the value you know

= × p²

Step 3 - rearrange the equation to isolate p²

÷ = p²

Step 4 - calculate the value of p²

p² =

Step 5 - calculate the value of p

p =