Writing and Using Formulae
A formula is a mathematical rule, written using letters, that shows how one quantity is calculated from one or more others, for example Area = length x width. Writing a formula from a worded description turns words into algebra; using a formula means substituting known values to find an unknown quantity, and rearranging a formula means making a different letter the subject.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the description carefully and identify which quantity is being found; this becomes the subject of the formula, written alone on the left of the equals sign.
- Identify the other quantities involved and choose (or use the given) letter for each.
- Translate the words into algebra, term by term, in the order described.
- To USE a formula, substitute the known values for the letters and evaluate, following the order of operations.
- To REARRANGE a formula and make a different letter the subject, apply the same inverse operation to both sides until the new letter is alone.
- Check a rearranged formula by substituting matching numbers into both the original and rearranged versions - the results should be consistent.
Worked example
A taxi firm charges a fixed fee of 3 pounds plus 2 pounds for every mile travelled. (a) Write a formula for the total cost, C, in pounds, of a journey of m miles. (b) A journey costs 17 pounds. Use your formula to find the number of miles travelled.
- The fixed fee of 3 pounds is added once, and 2 pounds is charged for every mile, m, so the cost from the miles is 2m.
- (a) The formula is C = 2m + 3.
- (b) Substitute C = 17 into the formula: 17 = 2m + 3.
- Subtract 3 from both sides: 14 = 2m.
- Divide both sides by 2: m = 7. The journey was 7 miles.
Practice questions
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Q1Write a formula for the perimeter, P, of a square with side length s.Show answer
Answer: P = 4s
Q2Write a formula for the total cost, C, of n pens costing 2 pounds each.Show answer
Answer: C = 2n
Q3A plumber charges a call-out fee of 40 pounds plus 25 pounds per hour, h. Write a formula for the total charge, T.Show answer
Answer: T = 25h + 40
Q4Using the formula T = 25h + 40, find T when h = 3.Show answer
Answer: T = 115
Q5Using the formula T = 25h + 40, find h when T = 165.Show answer
Answer: h = 5
Q6Make x the subject of the formula y = x + 8.Show answer
Answer: x = y - 8
Q7Make x the subject of the formula y = 5x - 2.Show answer
Answer: x = (y + 2)/5
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A phone plan costs a fixed charge of 12 pounds per month plus 5 pence for every text message sent. (a) Write a formula for the monthly cost, C, in pounds, for sending t text messages, given that 5 pence is 0.05 pounds. (b) Use your formula to find the cost of sending 60 text messages in a month.
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Make x the subject of the formula y = 4x - 7.
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The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Make C the subject of the formula.
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Free printable worksheet
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This topic is chapter 27 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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