How To Form And Solve GCSE Maths Equations
Introduction
There will be a number of instances where you will need to form and solve GCSE Maths equation.
What you need to remember is that in many cases you are simply what you would be with numbers, in terms of finding the perimeter of a shape or finding the sum of angles in a triangle, the only difference is that there are letters.
The algebraic technique of being able to collect like terms will be required as well as being able to then solve algebraic equations.
Form And Solve GCSE Maths Equations: Isosceles Triangle
Consider the following question:
You are given the perimeter of the triangle. In questions like this you need to remind yourself that the perimeter of an object is the distance all the way around it.
The two dashes that are shown on the triangle tell you that those lengths in particular are the same so you have an isosceles triangle.
Adding the edges of the triangle gives: 2x+2x+10=4x+10. This gives an expression for the perimeter.
So 4x+10=34. Here you now have a GCSE Maths equation that you must solve.
4x=24 ∴x=6.
Working With A Triangle
Take a look at the following question:
Again you are given the word perimeter – think distance around the outside of an object.
Doing this gives: 3(x-3)+2 x+5+4 x-1=3 x-9+2 x+5+4 x-1=9 x-5
Using the expression just found, a GCSE Maths equation can now be formed:
\begin{aligned} &9 x-5=49\\ &9 x=54 \therefore x=6 \end{aligned}
Example
Take a look at the following question:
The size of the angles of the degrees are shown work out the value of x.
In this instance the question is referring to the degrees in a triangle. You will know that the angles in a triangle add up to 180° so the calculation that needs to be done is that the three angles need to be added just as you would add numbers together.
Doing this gives: 2 x+x+18+2 x+7=5 x+25
This is now an expression and because the angles add up to 180° the following equation can then be written and solved:
\begin{gathered} 5 x+25-180 \\ 5 x=155 \therefore x=31 \end{gathered}Question Practice
Try the following question on your own before looking at the solution:
Question Practice Solution
In this question you have a quadrilateral. In order to start this question you need to be able to determine the sum of interior angles of a four sided shape. This is something that you can either remember or calculate using the formula 180(n-2) which would give 360°.
Next it is a case of taking the interior angles, adding them together in order to obtain an expression.
Doing this will give: 2 x+2 x+x+10+50=5 x+60
Now that an expression has been obtained for the sum of the interior angles of the quadrilateral, this can be set equal to 360 in order to then solve an equation as follows:
\begin{gathered} 5 x+60=360 \\ 5 x=300 \therefore x=60 \end{gathered}When doing GCSE Maths equation questions like the ones shown, you are creating an algebraic expression, collecting like terms and solving an equation. But you need to look carefully at the wording of the question to determine the type of equation that you need to initially create.
So if you see the word “perimeter” this means that you need to add all sides together. If you see “sum of angles in a triangle” you know that these equal 180°
Identifying the type of equation to solve is also a skill in itself as well as being able to collect like terms, simplify and to then solve the equation.
Forming and solving GCSE maths equations is something that you are very likely to see and this especially the case if you are doing the Higher Paper. Such questions might appear towards the back of a paper which means it is more targeted towards those who are aiming to achieve a grade 5.