AI generatedRatio, proportion and rates of changeGCSE Higher / IGCSE Extended

Finding a constant in an inverse-square model

Inverse proportion to squared means divided by squared, not divided by .

  • Inverse proportion to squared means divided by squared, not divided by .
  • Multiply both sides by squared: = yx squared.
  • Use the known and to find . The model is not defined at .

Example 1

The model is . Find when and .

Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.

Example 2

The model is . Find when and .

Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

The model is . Find when and .

Check answer
Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.
Question 2

The model is . Find when and .

Check answer
Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.
Question 3

The model is . Find when and .

Check answer
Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.
Question 4

The model is . Find when and .

Check answer
Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.
Question 5

The model is . Find when and .

Check answer
Multiply both sides by squared.Substitute the known pair.Simplify the numerical terms and collect like terms.
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