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Edexcel International AS Maths: Pure 1

Revision Notes

Home / International AS / Maths: Pure 1 / Edexcel / Revision Notes / 1. Algebra & Functions / 1.6 Graphs of Functions / 1.6.3 Solving Equations Graphically


1.6.3 Solving Equations Graphically


Solving Equations Graphically

Solving (simultaneous) equations graphically

Solving Equations Graphically Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

  • This is a way to solve simultaneous equations (see Simultaneous Equations)
  • Coordinates of the intersections are the solutions

 

How do I solve simultaneous equations using a graph?

Solving Equations Graphically Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

 

  • Use graphs and algebra together
  • Sketch a graph if it has not been given
  • Read/interpret a graph if it has been given

 

Solving Equations Graphically Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

  • It can be difficult to tell from a sketch if graphs intersect once, more, or not at all

 

Solving Equations Graphically - Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

Worked Example

Solving Equations Graphically - Example Diagram 1, A Level & AS Level Pure Maths Revision Notes Solving Equations Graphically - Example Diagram 2, A Level & AS Level Pure Maths Revision Notes



  • 1. Algebra & Functions
    • 1.1 Laws of Indices & Surds
      • 1.1.1 Laws of Indices
        • 1.1.2 Manipulating Surds
          • 1.1.3 Surds - Rationalising the Denominator
          • 1.2 Quadratics
            • 1.2.1 Quadratic Graphs
              • 1.2.2 Discriminants
                • 1.2.3 Completing the square
                  • 1.2.4 Solving Quadratic Equations
                    • 1.2.5 Further Solving Quadratic Equations (Hidden Quadratics)
                    • 1.3 Simultaneous Equations
                      • 1.3.1 Linear Simultaneous Equations - Elimination
                        • 1.3.2 Linear Simultaneous Equations - Substitution
                          • 1.3.3 Quadratic Simultaneous Equations
                          • 1.4 Inequalities
                            • 1.4.1 Linear Inequalities
                              • 1.4.2 Quadratic Inequalities
                                • 1.4.3 Inequalities on Graphs
                                • 1.5 Polynomials
                                  • 1.5.1 Expanding Brackets
                                    • 1.5.2 Factorising Expressions
                                    • 1.6 Graphs of Functions
                                      • 1.6.1 Sketching Polynomials
                                        • 1.6.2 Reciprocal Graphs - Sketching
                                          • 1.6.3 Solving Equations Graphically
                                            • 1.6.4 Proportional Relationships
                                              • 1.6.5 Modelling with Functions
                                              • 1.7 Transformations of Functions
                                                • 1.7.1 Translations
                                                  • 1.7.2 Stretches
                                                    • 1.7.3 Reflections
                                                  • 2. Coordinate Geometry
                                                    • 2.1 Equation of a Straight Line
                                                      • 2.1.1 Basic Coordinate Geometry
                                                        • 2.1.2 Parallel & Perpendicular Gradients
                                                          • 2.1.3 Equation of a Straight Line
                                                            • 2.1.4 Modelling with Straight Lines
                                                          • 3. Trigonometry
                                                            • 3.1 Basic Trigonometry
                                                              • 3.1.1 Trigonometry - Definitions
                                                                • 3.1.2 Right-Angled Triangles
                                                                  • 3.1.3 Non-Right-Angled Triangles
                                                                  • 3.2 Radian Measure
                                                                    • 3.2.1 Radian Measure
                                                                      • 3.2.2 Trigonometry Exact Values
                                                                      • 3.3 Trigonometric Functions
                                                                        • 3.3.1 Graphs of Trigonometric Functions
                                                                          • 3.3.2 Transformations of Trigonometric Functions
                                                                        • 4. Differentiation
                                                                          • 4.1 Differentiation
                                                                            • 4.1.1 Definition of Gradient
                                                                              • 4.1.2 Definition of Derivatives
                                                                                • 4.1.3 Differentiating Powers of x
                                                                                  • 4.1.4 Gradients, Tangents & Normals
                                                                                    • 4.1.5 Second Order Derivatives
                                                                                  • 5. Integration
                                                                                    • 5.1 Integration
                                                                                      • 5.1.1 Fundamental Theorem of Calculus
                                                                                        • 5.1.2 Integrating Powers of x


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                                                                                      Author: Lucy

                                                                                      Lucy has been a passionate Maths teacher for over 12 years, helping to engage interest and develop confidence in the subject at all levels. As Head of Department and Director of Maths, Lucy has advised schools across both academy trusts and an entire city, where her role was to support and coach teachers to improve Maths teaching for all.


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