 A cyclist travels at a constant m miles per hour.

# Level 5-6 Algebra - Formulae

Now you are studying KS3 Maths you'll have come across many formulae. We use them to work out the areas of 2-dimensional shapes, the volumes of 3-dimensional shapes, certain scientific values and plenty more besides. We also find a lot of formulae in algebra.

So, what exactly are formulae? There are many different definitions but the one we like best is: 'two mathematical expressions connected by an equals sign'. Formulae tend to be remembered in one arrangement. For instance, you should recall that the formula for the area of a circle is area = πr2. This is fine if you know r but what if you are given the area and need to find r? You will need to rearrange the formula so that r is the subject. Can you master it?

This quiz allows you to dip your maths toe in the formulae waters! Take your time and read each question carefully before you choose your answers. And don't forget to read the helpful comments after each question. They can shed light on things you might have missed. Good luck!

1.
You are given the formula a = 2b and you are told that the value of b is 4. What is the value of a?
2
4
6
8
2b = 2 x 4. We have been told that a = 2b and therefore a must be 8
2.
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
3.
a2 + b2 = 25. If a = 3 then what is the value of b?
4
5
6
7
If a = 3 then a 2 = 9. 25 - 9 = 16 so b 2 = 16, therefore b must = 4
4.
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!
5.
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'
6.
A cyclist travels at a constant m miles per hour. How far has he travelled in 4 hours?
4m
6m
8m
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
7.
Which sign must be contained in a formula?
+
-
x
=
Remember that all formulae contain an equals sign
8.
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?
26
28
30
32
30 - 2 = c. Sometimes you have to work backwards in order to find the answer
9.
What is the plural of formula?
Formulants
Formulas and formulae
Formulents
Formuleses
Either can be used
10.
If a2 = 6b and a has the value of 6, what is the value of b?
3
6
9
12
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