Substitution and Formulae in Words
Substitution means replacing letters in a formula or expression with given numbers and then calculating the result. Many 11+ questions give a formula in words, such as 'cost equals 5 pounds plus 2 pounds per topping', rather than in algebraic notation, so pupils must translate this into a calculation, substitute the given values, and work out the answer, sometimes rearranging to find a missing value.
Before you start
Make sure you're comfortable with these topics first:
Method
- If a formula is given in words, translate it into an algebraic expression or a clear calculation plan first, identifying which words mean add, subtract, multiply and divide.
- Substitute the given number or numbers for each letter in the formula exactly as written, keeping track of which value replaces which letter.
- Follow the correct order of operations, working out brackets first, then multiplication and division, then addition and subtraction, when calculating the substituted expression.
- If the question gives the output and asks for one of the input values, rearrange the formula, or work backwards step by step, similar to a function machine.
- Where a formula involves squaring or another power, such as area = side x side, calculate that part first before combining it with any other terms.
- Check the answer is a sensible size and has the correct units for the context, such as pounds or centimetres squared.
Worked example
The cost, in pounds, of hiring a bike is given by the formula C = 3h + 5, where h is the number of hours hired. Work out the cost of hiring a bike for 4 hours.
- Identify the formula, C = 3h + 5, and the given value, h = 4.
- Substitute h = 4 into the formula: C = 3 x 4 + 5.
- Apply the order of operations, multiplying first: 3 x 4 = 12.
- Add the remaining term: 12 + 5 = 17.
- The cost of hiring the bike for 4 hours is 17 pounds.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Using the formula P = 2l + 2w, find P when l = 8 and w = 5.Show answer
Answer: 26 (2 x 8 + 2 x 5 = 16 + 10)
Q2Using the formula A = s x s, find A when s = 7.Show answer
Answer: 49
Q3A taxi's cost in pounds is described in words as 'a 4 pound fixed charge plus 2 pounds per mile'. Write this as a formula using C for cost and m for miles.Show answer
Answer: C = 4 + 2m
Q4Using the formula C = 4 + 2m from the previous question, work out the cost of a 6-mile taxi journey.Show answer
Answer: 16 pounds (4 + 12)
Q5Using the formula v = u + at, find v when u = 5, a = 2 and t = 3.Show answer
Answer: 11 (5 + 2 x 3 = 5 + 6)
Q6Using the formula C = 3h + 5 from the worked example, a customer is charged 26 pounds. Work out how many hours the bike was hired for.Show answer
Answer: 7 hours (3h = 21, h = 7)
Q7The perimeter of a square is given by P = 4s. If the perimeter is 36 cm, find the side length s.Show answer
Answer: 9 cm
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A plumber's call-out charge, in pounds, is given by the formula C = 25 + 18t, where t is the number of hours worked. (a) Work out the charge for a job taking 3 hours. (b) A customer is charged 97 pounds. Work out how many hours the job took.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
The area of a trapezium is given in words as 'half of the sum of the two parallel sides, multiplied by the height'. (a) Write this as a formula using A for area, a and b for the parallel sides, and h for the height. (b) Use your formula to find the area when a = 6 cm, b = 10 cm and h = 4 cm.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the substitution and formulae in words worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 20 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on substitution and formulae in words, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.