Further Pure Mathematics

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>

Part 1: Factor Theorem

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

Part 2: Remainder Theorem

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

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

Type 1: Linear Inequalities

Solving linear inequalities is just like solving linear equations.

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

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