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  • IGCSE Edexcel
  • Further Pure Mathematics
  • 1. Further Pure Mathematics Notes

Further Pure Mathematics

  • IGCSE Edexcel
  • Revision Notes

1. Further Pure Mathematics Notes


1.1 Logarithmic Functions and Indices>1.2 The Quadratic Function>1.3 Identities and Inequalities>1.4 Graphs>1.5 Series>1.6 The Binomial Series>1.7 Scalar and Vector Quantities>1.8 Rectangular Cartesian Coordinates>1.9 Calculus>1.10 Trigonometry>

1.2 The Quadratic Function

1.2.1 The manipulation of quadratic expressions

Type 1: Factorisation

Factorisation involves writing the quadratic expression of x2+ bx + c in the form (x + p)(x + q).

Type 2: Completing the Square

Completing the Square involves writing the expression x2 + bx + c in the form (x + p)2 + q.

1.2.2 The roots of a quadratic equation

Method 1: Solve by Factorisation

Step 1: Factorise the quadratic equation [See 1.2.1].

Step 2: Equate to 0 (Null Factor Law).

Step 3: Find the roots or solution.

Method 2: Solve by Completing the Square

Step 1: Complete the Square [See 1.2.1].

Step 2: Equate to 0 (Null Factor Law).

Step 3: Find the roots or solution.

Method 3: Quadratic Formula

Step 1: Determine a, b and c.

Step 2: Substitute to quadratic formula to find the roots/solution.

 

 

 

The part of the quadratic formula b2 – 4ac is called the discriminant.

The discriminant can be used to identify whether the roots are real or unreal.

1.2.3 Simple examples involving functions of the roots of a quadratic equation

Important notes:

(a+b)2 = a2 + b2 + 2ab → a2 + b2 = (a+b)2 – 2ab

(a+b)3 = a3 + b3 + 3ab(a+b) → a3 + b3 = (a+b)3 – 3ab(a+b)

Previous1.1 Logarithmic Functions and Indices
Next1.3 Identities and Inequalities

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