Pure Mathematics with FP1 and FP2

Pure Mathematics with FP1 and FP2

1. Core 1

   • Factor/Remainder Theorem
     • If, when you factorise a quadratic equation, the remainder is 0 then this is the Factor Theorem.
       • Use the factor theorem to factorise the polynomial 2x³ - 7x² - 28x - 12
         • Factor Theorem answer
     • The Remainder Theorem is when the remainder from factorising is not 0
       • When x³ + ax² - x - 2 is divided by x - 4, the remainder of 74. Find the value of a
         • Remainder Theorem answer
   • Binomial Expansion
   • Surds
   • Simultaneous Equations
   • Coordinate Geometry
   • Completing the Square
   • Differentiation from First Principles
   • Rules of Differentiation
   • Stationary/Turning Points
   • Normals and Tangents
   • Inequalities
   • Transformations
   • Lines and Curves
   • Roots of Equations

2. Core 2

   • Logarithms
   • Arithmetic Progressions
   • Geometric Progressions
   • Circles
   • Trigonometry - Sine and Cosine Rule
   • Trigonometry Equations
   • Trigonometry Identities
   • Radian Measure
   • Integration
   • Area Under a Curve
   • The Trapezium Rule

3. Core 3

   • Secx, Cosecx and Cotx
   • Pythagorean Identities
   • Exponential and Log Functions
   • Differentiating a Bracket
   • The Quotient Rule
   • Differentiation of Inverse Trigonometry Functions
   • Implicit Differentiation
   • Parametric Differentiation
   • Disproof by Counter Example
   • Simpson's Rule
   • Functions
   • The Modulus Function
   • Integration
   • Approximate Solutions
   • Multistep Transformations
   • Intersecting Lines and Curves
   • The Product Rule
   • Trigonometry Differentiation

4. FP1

   • Matrices
     • Matrices
     • Row Reduction
       • Row Reduction
   • Roots of Equations
     • Quadratic Equations
       • Roots of Equations - Quadratic
     • Cubic Equations
       • Roots of Equations - Cubic
   • Complex Numbers
     • Complex Numbers
   • Number Systems
     • Number Systems
   • Differentiation
     • Differentiation
   • Isometry in the Plane
     • Isometry in the Plane
   • Mathematical Induction
     • Mathematical Induction
   • Triangular Numbers
     • Triangular Numbers
     • Triangular Numbers

5. FP2

   • Further Partial Fractions
     • Further Partial Fractions
   • Complex Numbers
     • Complex Numbers
   • Factor Formulae
     • A+B=x        A-B=y To write a product as a sum/difference; - Write in descending order - A=sum     B=difference If cos2x+cos3x+cos4x, use factor formulae on 2 extreme angles and then factorise result with the middle
     • Factor Formulae
   • The t Formulae
     • The t Formulae
   • Further Integration
     • Further Integration
   • General Solutions
     • General Solutions
   • Functions
     • Functions
   • Conics
     • Conic Sections
       • Properties of Conic Sections