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  1. Revision notes
  2. A Level
  3. Maths
  4. Edexcel
  5. Second Order Derivatives

Second Order Derivatives

Maths: Edexcel A Level Pure Maths, topic 7.1.6

Test yourself on Second Order Derivatives

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Previous topic7.1.5 Finding derivativesNext topic7.2.1 Stationary Points

Maths: Edexcel A Level Pure Maths contents

  1. 1 Proof

    • 1.1 Types of Numbers

      • 1.1.1 Whole Numbers
      • 1.1.2 The Four Rules for Positive Numbers
      • 1.1.3 Negative Numbers
      • 1.1.4 Integers
      • 1.1.5 The Four Rules for Negative Numbers
      • 1.1.6 Real Numbers
      • 1.1.7 Rational vs Irrational
    • 1.2 Notation

      • 1.2.1 Sets
      • 1.2.2 Subsets
      • 1.2.3 Venn Diagrams
      • 1.2.4 Sets Numbers
      • 1.2.5 Notation in Mathematical Arguments
    • 1.3 Proof

      • 1.3.1 Mathematical Proof
      • 1.3.2 Proof by Deduction
      • 1.3.3 Proving an Identity
      • 1.3.4 Polynomial Identities
      • 1.3.5 Proof by Exhaustion
      • 1.3.6 Disproof by Counter Example
      • 1.3.7 Proof by Contradiction (A2 Only)
  2. 2 Algebra & Functions

    • 2.1 Powers & Roots

      • 2.1.1 Exponential Rules
      • 2.1.2 Rational Exponents
      • 2.1.3 Surds
      • 2.1.4 Simplify Surds
      • 2.1.5 Rationalise Denominator
    • 2.2 Quadratic Equations

      • 2.2.1 Quadratic +/-
      • 2.2.2 Factorise Quadratics
      • 2.2.3 Quadratic Formula
      • 2.2.4 Complete the Square
      • 2.2.5 Solve Quadratics Graphically
      • 2.2.6 Simultaneous Equations
      • 2.2.7 Simultaneous Quadratic Equations
      • 2.2.8 Simultaneous Equations Graphs
      • 2.2.9 Simultaneous Equations Word Problems
      • 2.2.10 Quadratic Equations of Powers
    • 2.3 Inequalities

      • 2.3.1 Solving Inequalities
      • 2.3.2 Solving Double Inequalities
      • 2.3.3 Solving Quadratic Inequalities
      • 2.3.4 Representing Inequalities
      • 2.3.5 Graphing Inequalities
      • 2.3.6 Set Notation
      • 2.3.7 Set Notation & Inequalities
    • 2.4 Polynomials

      • 2.4.1 Polynomials
      • 2.4.2 Adding & Subtracting Polynomials
      • 2.4.3 Remainder Theorem
      • 2.4.4 Algebraic Long Division
      • 2.4.5 Rewriting Rational Expressions
    • 2.5 Graphs

      • 2.5.1 Graphs of Polynomials
      • 2.5.2 Simultaneous Equations Graphs
      • 2.5.3 Simultaneous Quadratic Equations
      • 2.5.4 Graphs of Proportion
      • 2.5.5 Graphs of Common Functions 1
      • 2.5.6 Graphs of Common Functions 2
      • 2.5.7 Graphs of Common Functions 3
      • 2.5.8 Proportion
      • 2.5.9 Direct Proportion
      • 2.5.10 Inverse Proportion
    • 2.6 Functions

      • 2.6.1 Properties of Functions
      • 2.6.2 Inverse Functions
      • 2.6.3 Composite Functions
    • 2.7 Transformation of Graphs

      • 2.7.1 Reflections
      • 2.7.2 Rotation
      • 2.7.3 Translation
      • 2.7.4 Stretches & Compressions
      • 2.7.5 Effects of Transformations
      • 2.7.6 Combinations of Transformations
    • 2.8 Partial Fractions (A2 Only)

      • 2.8.1 Partial Fractions
      • 2.8.2 Partial Fractions with Three Linear Factors
      • 2.8.3 Partial Fractions with Three Linear Factors 2
      • 2.8.4 Partial Fractions with Repeated Factors
      • 2.8.5 Partial Fractions - Practice
  3. 3 Coordinate Geometry

    • 3.1 Straight Lines

      • 3.1.1 y = mx +c
      • 3.1.2 Gradient & Y-intercept
      • 3.1.3 Distance-Time Graph
      • 3.1.4 Velocity-Time Graph
      • 3.1.5 Conversion Graph
    • 3.2 Circles

      • 3.2.1 Equations of Circles centred at Origin
      • 3.2.2 Finding the Centre & Radius
      • 3.2.3 Equation of a Tangent
      • 3.2.4 Circle Theorems - Perpendicular Bisector
      • 3.2.5 Circle Theorems - Angle at the Centre
      • 3.2.6 Circle Theorems - Angle at a Semi-Circle
      • 3.2.7 Equation of a Perpendicular Bisector
      • 3.2.8 Equation of a Circumcircle
      • 3.2.9 Circumcircle of a Right-angled Triangle
    • 3.3 Parametric Equations (A2 only)

      • 3.3.1 Parametric Equations
      • 3.3.2 Modelling with Parametric Equations
  4. 4 Sequences & Series

    • 4.1 Binomial Expansion

      • 4.1.1 Pascal's Triangle
      • 4.1.2 Factorials
      • 4.1.3 Binomial Expansion
      • 4.1.4 Binomial Expansion & Rational Powers (A2 only)
      • 4.1.5 Binomial Expansion & Rational Powers 2 (A2 only)
    • 4.2 Sequences (A2 only)

      • 4.2.1 Nth term Rules
      • 4.2.2 Recurring Rules
      • 4.2.3 Types of Sequences
      • 4.2.4 Arithmetic Sequences
      • 4.2.5 Geometric Sequences
      • 4.2.6 Sigma Notation
      • 4.2.7 Arithmetic Series
      • 4.2.8 Geometric Series
      • 4.2.9 Sum to Infinity of a Geometric Series
      • 4.2.10 Modelling with Sequences & Series
  5. 5 Trigonometry

    • 5.1 Using Angles

      • 5.1.1 Radians
      • 5.1.2 Arc length
      • 5.1.3 Area of Sectors
      • 5.1.4 Area of Segments
    • 5.2 Trigonometric Functions

      • 5.2.1 Unit Circle
      • 5.2.2 Properties of Trig Functions
      • 5.2.3 Trigonometry
      • 5.2.4 Exact values
      • 5.2.5 Graphs of Trigonometric Functions
      • 5.2.6 Small Angle Approximation
    • 5.3 Triangle Rules

      • 5.3.1 Sine Rules
      • 5.3.2 Cosine Rules
      • 5.3.3 Area of a Triangle
    • 5.4 Trigonometric Identities

      • 5.4.1 Secant, Cosecant & Cotangent
      • 5.4.2 Pythagorean Identities
      • 5.4.3 Angle Addition Formulae
      • 5.4.4 Manipulating the Angle Addition Formulae
      • 5.4.5 Double Angle Formula
  6. 6 Exponentials & Logarithms

    • 6.1 Exponentials & Logarithms

      • 6.1.1 Exponential Function
      • 6.1.2 Logarithms
      • 6.1.3 Properties of Logarithms
      • 6.1.4 Natural Logarithm
      • 6.1.5 Graphs of Exponents & Logarithms
    • 6.2 Exponential Growth Decay

      • 6.2.1 Population Growth
      • 6.2.2 Depreciation
      • 6.2.3 Graphing Linear and Exponential Growth
      • 6.2.4 Interpreting Exponential Growth and Decay Graphs
      • 6.2.5 Compound Growth & Decay
      • 6.2.6 Compund Interest
  7. 7 Differentiation

    • 7.1 Derivatives

      • 7.1.1 Gradient of a Curve
      • 7.1.2 Differentiation from First Principles
      • 7.1.3 Differentiation from First Principles - Practice
      • 7.1.4 Differentiation
      • 7.1.5 Finding derivatives
      • 7.1.6 Second Order Derivatives
    • 7.2 Graphs & Differentiation

      • 7.2.1 Stationary Points
      • 7.2.2 Maxima & Minima
      • 7.2.3 Modelling with Differentiation
      • 7.2.4 Using Second Derivatives (A2 only)
      • 7.2.5 Rate of Change (A2 only)
    • 7.3 Differentiation With Trigonometry and Exponentials

      • 7.3.1 Differentiation with Sin & Cos
      • 7.3.2 Diff. of Exponential Functions
      • 7.3.3 Differentiation of Trig. Functions 1 (A2 only)
      • 7.3.4 Differentiation of Trig. Functions 2 (A2 only)
    • 7.4 Rules of Differetiation (A2 only)

      • 7.4.1 Chain Rule
      • 7.4.2 Product Rule
      • 7.4.3 Quotient Rule
    • 7.5 Parametric & Implicit Differentiation

      • 7.5.1 Parametric Differentiation
      • 7.5.2 Implicit Differentiation
  8. 8 Integration

    • 8.1 Integration

      • 8.1.1 Integration - Basics
      • 8.1.2 Integration - Definite Integrals
      • 8.1.3 Finding Functions
      • 8.1.4 Area under curves
      • 8.1.5 Area under x-axis
      • 8.1.6 Area between curves and lines
    • 8.2 Integration (A2 Only)

      • 8.2.1 Integration - Standard Functions
      • 8.2.2 Integration - Reverse Chain Rule
      • 8.2.3 Integration by Substitution
      • 8.2.4 Integration by Parts
      • 8.2.5 Integration by Parts - Practice
      • 8.2.6 Integration by Partial Fraction
      • 8.2.7 Modelling with Differential Equations
  9. 9 Numerical Methods

    • 9.1 Finding Solutions

      • 9.1.1 Number Iterations
      • 9.1.2 Iterations to 1 Decimal Places
      • 9.1.3 Iteration Formula
      • 9.1.4 Locating Roots
      • 9.1.5 Newton Raphson Method
    • 9.2 Finding the Area

      • 9.2.1 Trapezium Rule
  10. 10 Vectors

    • 10.1 2D Vectors

      • 10.1.1 Vectors - Magnitude & Direction
      • 10.1.2 Unit Vectors
      • 10.1.3 Vectors - Algebraic Operations
      • 10.1.4 Position Vectors
      • 10.1.5 Vector Proofs
      • 10.1.6 Vectors Word Questions
    • 10.2 3D Vectors

      • 10.2.1 3D Vector Magnitude
      • 10.2.2 3D Vectors - Algebraic Operations
      • 10.2.3 Position Vectors 3D
      • 10.2.4 3D Vectors Word Questions
    • 10.3 Vector Proofs

      • 10.3.1 Coming Soon

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