Use formulae

Objective. Substitute into familiar formulae and interpret the result.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

A formula is a mathematical rule written using letters that connects different quantities, allowing you to calculate one value once the others are known. For example, the formula for the area of a rectangle is A=lw, where l is the length and w is the width. To use a formula, substitute the known values for each letter and then carry out the calculation following the order of operations. For instance, if l=6 and w=4, then A=6×4=24. Interpreting the result means stating it with the correct units attached, such as 24 cm².

Worked example

The formula for the perimeter of a rectangle is P = 2l + 2w. Use this formula to find P when l = 9 cm and w = 5 cm.

1 $Substitute the values into the formula: P=2\times9+2\times5.$
2 $Calculate each product: 2\times9=18 and 2\times5=10.$
3 $Add the results: 18+10=28.$
4 $State the answer with units: P=28 cm.$

Answer: 28 cm

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Practice

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Common mistake. Pupils sometimes substitute values into the wrong letters of a formula, swapping length and width incorrectly in a less familiar formula. Always check which letter represents which quantity before substituting.

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