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26 Free Simultaneous Equations Worksheets and Lesson Plans for KS3 and KS4 Maths

Whether you're introducing this mathematical concept to KS3 students or stretching GCSE ones, working on linear equations or quadratic, using graphical methods or elimination, these resources have you covered...

  • 26 Free Simultaneous Equations Worksheets and Lesson Plans for KS3 and KS4 Maths

1 | Simultaneous equations with McDonald’s food


Author: Andy Lutwyche

Use simultaneous equations to calculate how much each person must pay based on their orders at McDonald’s.

Get this resource here.


2 | Introduction to simultaneous equations with picture-based puzzles


Author: Owen134866

This lesson is intended as an introduction to simultaneous equations, where students solve picture-based puzzles without using formal algebra.

The idea is that the following lesson they can look at equations given algebraically and see how it is effectively the same thing.

Get this resource here.


3 | Solve equations graphically with the cover-up method


Author: Ben Cooper

This PowerPoint shows the graphical methods for solving simultaneous equations using the cover-up method.

Get this resource here.


4 | Solving equations graphically KS3 worksheet


Author: Andy Lutwyche

This is a worksheet with some questions on solving simultaneous equation in three sections.

Section one is two linear equations, section two is a quadratic and y=n, and section three is the extension which is a quadratic and y=mx+c.

There is a RAG table for students to mark their progress and this can be amended depending on how far you want to go. Students will need to plot graphs and estimate solutions as not all are integers.

Get this resource here.


5 | Solving simultaneous equations KS4 lesson


Author: Manoj Mistry

This is a three-part lesson with grade B questions.

The starter includes questions to recap and consolidate previous learning in accordance with the route map (scheme of work) I have uploaded.

Get this resource here.


6 | Introduce simultaneous equations using area


Author: Zeb Friedman

This lesson uses area to introduce simultaneous equations. Students move from informal to formal solutions effortlessly.

This was inspired by the NCETM departmental workshops, and two of their documents are included in the download with worksheets and lesson plan.

Get this resource here.


7 | Exploding linear and non-linear equations for KS4


Author: Andy Lutwyche

This is a set of six sheets of increasingly difficult simultaneous equations designed to make students think and discuss how to work through their solutions by giving them different parts of the process.

They include simultaneous equations that involve a linear and a non-linear equation.

This is also designed to stretch at GCSE or could be used at the start of A level.

Get this resource here.


8 | How to solve simultaneous equations graphically


Author: Ben Cooper

This KS3 or GCSE PowerPoint activity has a couple of simple slides showing what we mean by solving simultaneous equations, and how to solve them graphically.

There are some questions and answers at the end. It assumes students can plot y=mx + c style equations.

Get this resource here.


9 | Simultaneous equations GCSE topic review


Author: David Morse

Ideal for students who are revising simultaneous equations, these revision sheets have exam-type questions which gradually increase in difficulty.

The last questions have an extra twist.

Get this resource here.


10 | Simultaneous equations graphically


Author: Owen134866

This lesson will show students how plotting two linear equations in x and y allows them to solve simultaneous equations.

The PowerPoint has a full explanation as the starter and there is a sheet of questions for students to practice.

Before doing this task they should have covered algebraic versions of simultaneous equations, as well as linear graph plotting.

Get this resource here.


11 | Real-world simultaneous equation example worksheet


Author: Andy Lutwyche

Trying to find a real-life example of where we might solve simultaneous equations graphically I came up with this. Students have to plot to linear graphs and find the point of impact.

You could bring in Pythagoras and find out if the two bodies were travelling at the same speed would they actually collide, but I wanted to keep the worksheet to one side of A4.

Get this resource here.


12 | Simultaneous equations tarsia puzzle


Author: Clea Rodgers

Solve pairs of linear simultaneous equations to put Tarsia puzzle together – good for group work.

Get this resource here.


13 | How to solve quadratic simultaneous equations


Author: Ben Cooper

This is a walk-through of how to solve simultaneous equations where one is linear and the other is quadratic. There is also a starter activity that gets students to practise factorising.

Get this resource here.


14 | Simultaneous equations GCSE worksheets


Author: Claire Mooney

This worksheet features GCSE questions for simultaneous equations, and comes with an answer sheet.

Get this resource here.


15 | Streaker at the cricket KS4 worksheet activity


Author: Andy Lutwyche

Find the equation of the line and the circle, then calculate the points where the streaker crosses the boundary.

Get this resource here.


16 | Solving quadratic simultaneous equations KS4 lesson


Author: Manoj Mistry

This is a three-part lesson on solving quadratic simultaneous equations at grade A* level. The starter recaps solving grade B simultaneous equations. There is a mini-plenary and exam question plenary embedded. And answers are provided throughout.

Get this resource here.


17 | Solving simultaneous equations graphically


Author: Owen134866

This lesson shows students how plotting two linear equations in x and y allows them to solve simultaneous equations.

The PowerPoint has a full explanation as the starter and there is a sheet of questions for students to practice.

Before doing this task they should have covered algebraic versions of simultaneous equations, as well as linear graph plotting.

Get this resource here.


18 | Simultaneous equations KS4 worksheet


Author: Ben Cooper

The objective of these KS4 maths algebra worksheets is to be able to solve simultaneous equations. It’s a simple simultaneous equations worksheet, with starter, main and extension.

The starter has negative number questions and solving simple linear equations. The difficulty is staggered in the main bit. The extension is a worded simultaneous equation.

Get this resource here.


19 | Simultaneous equations graded worksheet


Author: Andy Lutwyche

This resource has three sections with differing levels of difficulty on solving simultaneous equations by elimination. It’s nothing fancy, just a load of questions (and answers).

Get this resource here.


20 | Linear simultaneous equations GCSE 9-1 exam question practice


Author: David Morse

This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, saving valuable time in class.

Get this resource here.


21 | Quadratic simultaneous equations GCSE 9-1 exam question practice


Author: David Morse

This carefully selected compilation of exam questions also has fully-worked solutions designed for students to go through at home. Only this one is for quadratic equations.

Get this resource here.


22 | Solving simultaneous equations with the elimination method in KS4


Author: Aaron Needham

This PowerPoint for simultaneous equations is specifically for the elimination method, but also briefly covers the substitution method.

Get this resource here.


23 | Correcting errors in linear simultaneous equations worksheet


Author: Andy Lutwyche

Clumsy Clive is tackling simultaneous equations homework but as per usual is making errors. There are three sets of linear simultaneous equations for students to correct and a linear/quadratic to look at.

Get this resource here.


24 | Using graphical solutions worksheet


Author: Tumshy

This worksheet features 12 simultaneous equation questions for students to solve graphically. Answers are included.

Get this resource here.


25 | KS4 introductory lesson to solving simultaneous equations


Author: Manoj Mistry

This is a three-part lesson on solving simultaneous equations where the coefficients of one variable is the same.

The starter recaps work on solving equations. The main and extension are grade B questions. There is a mini-plenary and plenary embedded, and answers are provided throughout.

Get this resource here.


26 | Simultaneous equations and graphs lesson


Author: Nyima Drayang

This full lesson introduces solving simultaneous equations using graphical methods.

The starter is a kinaesthetic activity where pupils order themselves according to the value of the expressions they are holding (answers and values to substitute are shown on the board).

For the main activity they pick out graphs to find pairs of solutions to (at first by trial and error) – which later they draw and solve graphically.

Get this resource here.

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