REVISION NOTES

IGCSE Edexcel Further Pure Mathematics

1.3 Identities and Inequalities

1.3.1 Simple algebraic division

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_001_dividing a polynomial.png

1.3.2 The factor and remainder theorems

Part 1: Factor Theorem

If f(x) is a polynomial and f(p) = 0, the (x – p) is a factor of f(x).

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_002_factor theorem.png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_003_factorising a polynomial.png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_004_factorising a polynomial.png

Part 2: Remainder Theorem

If a polynomial f(x) is divided by (ax – b), the remainder is f(b/a).

1.3.3 Simple inequalities, linear and quadratic

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_007_inequalities.png

If two sides of an equation are not equal, use inequalities.

  • > means more than
  • < means less than
  • ≤ means more than equal to
  • ≥ means less than equal to

Type 1: Linear Inequalities

Solving linear inequalities is just like solving linear equations.

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_008_linear inequalities (number line).png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_009_linear inequalities.png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_005_linear simultaneous equation.png

Type 2: Quadratic Inequalities

Step 1: Rearrange the quadratic equation into f(x) > 0 or f(x) < 0

Step 2: Factorise and solve the quadratic equation

Step 3: Sketch a quadratic graph using a number line

Step 4: Solve the quadratic inequalities

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_010_quadratic inequalities.png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_012_quadratic inequalities.png
edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_006_quadratic simultaneous equation.png

1.3.4 The graphical representation of linear inequalities in two variables

Type 1: Linear Inequalities (Graph)

Step 1: Draw the line for each equation

Step 2: Use a coordinate to determine whether the the region is true or not true

Step 3: Shade the region that is true

Step 4: Label the region R

edexcel_igcse_further pure maths_fpm_topic 03_identities and inequalities_011_quadratic inequalities (graph).png
Back
Next

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

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