Inverse proportion to the square

Last updated on Apr 3, 2026

Inverse proportion to the square worksheet

Inverse proportion to the square occurs when one quantity decreases in proportion to the square of another. This is commonly seen in physics, such as in gravitational force or light intensity, where distance affects the strength of the force or brightness. Understanding this concept helps in solving problems where small changes in one value lead to much larger changes in another. Jump to the questions

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Question

y is inversely proportional to p²

y is when p is

Find the equation for y and p

Step 1 - describe the relationship using the correct symbol

y ∝ 1 / 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

= ÷

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 - determine the value of p²

p² =

Step 5 - calculate p

p =