# Maths Topic 15 - Algebra & equations

Algebra & Equations – including the use of formulae and expressions are maths skills that are commonly tested in 11+ and Selective School exams in the UK.

## Example Questions

### Example Question 1:

Find the value of a if 3a + 2 = 10 – a

Explanation: Move the – a to the left side of the equation and it becomes the inverse operation +a so that 3a + a = 4a. Move the +2 to the right side of the equation and it becomes the inverse operation – 2 so that 10 – 2 = 8. If 4a = 8 then a = 2.

### Example Question 2:

If a piece of ribbon measuring x cm is cut into 6 equal lengths, which of the following is the correct algebraic expression for one cut length?

(a) 6x, (b) 6 ÷ 6x, (c) 1/x, (d) 6x ÷ 6

Explanation: The complete length of x when cut into 6 pieces makes each piece 1/of the whole.

### Example Question 3:

If one side of a cube measures y cm, what is the algebraic expression for its volume?

Explanation: The find the volume of a cube (where all the lengths are the same size) is length × width × height. Using y it would be y × y × y, which is equivalent to y³.