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A cyclist travels at a constant m miles per hour.

Level 5-6 Algebra - Formulae

Understand and use formulae in KS3 algebra. Substitute values, rearrange to change the subject, and check results with sensible units in real-life contexts.

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Fascinating Fact:

Fuel economy links distance and fuel: litres per 100 km equals 100 × litres ÷ km. Example: 5 litres over 80 km is 6.25 litres per 100 km.

In KS3 Maths, formulae describe relationships between quantities, such as area A = l×w or speed v = d÷t. You will substitute numbers, use correct units, and rearrange a formula to make a chosen variable the subject.

Key Terms

Formula: A rule written using letters and numbers, e.g., v = d÷t.
Subject of a formula: The variable that is on its own, e.g., making t the subject gives t = d÷v.
Substitution: Replacing letters with given numbers to calculate a result.

Frequently Asked Questions (Click to see answers)

How do I rearrange a formula to make a different letter the subject?

Use inverse operations on both sides. For v = d÷t, multiply by t then divide by v to get t = d÷v.

What is the difference between an expression, an equation, and a formula?

An expression has no equals sign. An equation states two sides are equal. A formula is an equation showing a rule between variables.

How do I substitute values correctly in a formula?

Put numbers in place of letters with brackets where needed, use the correct order of operations, and include units in your final answer.

Try These Related Quizzes

1 .

You are given the formula x - 2 = c and you are told that the value of c is 28. What is the value of x?

30 - 2 = c. Sometimes you have to work backwards in order to find the answer

2 .

You are given the formula a = 2b and you are told that the value of b is 4. What is the value of a?

2b = 2 x 4. We have been told that a = 2b and therefore a must be 8

3 .

The perimeter of a rectangle is twice its length plus twice its width; this can be represented as p = 2l + 2w. What is the perimeter if l = 12cm and w = 6cm?

18 cm

24 cm

36 cm

48 cm

Perimeter means 'all the way around the outside'

4 .

A cyclist travels at a constant m miles per hour. How far has he travelled in 4 hours?

10m

If m is the number of miles travelled in one hour then the miles covered in 4 hours would be 4 x m or 4m

5 .

What is a 'variable'?

A division sign

A letter or symbol representing a varying quantity

A multiplication sign

An equals sign

We call them variables because their values vary

6 .

If a = 2 and b = 5, which of the following formula is correct?

2a + 6b = 31

3a + b² = 31

4a + 6b - 2b = 31

5a x 2b = 31

Don't worry, you will NOT normally be presented with formulae that don't add up!

7 .

a² + b² = 25. If a = 3 then what is the value of b?

If a = 3 then a ² = 9. 25 - 9 = 16 so b ² = 16, therefore b must = 4

8 .

What is the plural of formula?

Formulants

Formulas and formulae

Formulents

Formuleses

Either can be used

9 .

Which sign must be contained in a formula?

Remember that all formulae contain an equals sign

10 .

If a² = 6b and a has the value of 6, what is the value of b?

In this case you have two variables (a and b) and there is no reason why they cannot both have the same value - in this case 6

You can find more about this topic by visiting BBC Bitesize - Expressions and formulae

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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