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A cyclist travels at a constant m miles per hour.

# Level 5-6 Algebra - Formulae

Now that you're diving into KS3 Maths, you've encountered loads of formulae. They help us figure out areas, volumes, scientific stuff, and much more. Algebra comes in handy if we need to re-arrange formulae - so don't say algebra is useless!

What exactly is a formula? It's like a pair of maths expressions joined by an equals sign. Usually, we remember them in one setup, like the area formula for a circle: area = πr2. Easy if you know 'r', but what if you're given the area and need to find 'r'? You have to rearrange the formula. Do you know how?

1.
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
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?
2
4
6
8
2b = 2 x 4. We have been told that a = 2b and therefore a must be 8
3.
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
4.
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
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.
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
9.
What is the plural of formula?
Formulants
Formulas and formulae
Formulents
Formuleses
Either can be used
10.
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!