Topic outline

• Useful Files

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    Syllabus Content File
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    Exam Command Words File
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    Announcements Forum

• Past Papers

  Note that there is a new syllabus for exams in 2019 onwards. All the content which was previously on the Additional Mathematics course remains on the syllabus (and will be covered in the past papers below) but there are also two additional topics - Exponentials and Logarithms and Numerical Methods - which won't be covered in any of these past papers.

  You can also find sample textbook chapters on the two new topics: logarithms and exponentials and numerical methods.

  • New Syllabus Specimen (mark scheme at the end): 
  • June 2017: Question Paper | Mark Scheme
  • June 2016: Question Paper | Mark Scheme
  • June 2015: Question Paper | Mark Scheme
  • June 2014: Question Paper | Mark Scheme
  • June 2013: Question Paper | Mark Scheme
  • June 2012: Question Paper | Mark Scheme
  • June 2011: Question Paper | Mark Scheme
  • June 2010: Question Paper | Mark Scheme
  • June 2009: Question Paper | Mark Scheme
  • June 2008: Question Paper | Mark Scheme
  • June 2007: Question Paper | Mark Scheme
  • June 2006: Question Paper | Mark Scheme

• Notes
  • 

    2D Inequalities URL
  • 

    Binomial Expansion URL
  • 

    Binomial Distribution URL
  • 

    Exponentials URL
  • 

    Logarithms URL
  • 

    Fitting Exponential Data URL
  • 

    Trigonometric Equations URL
  • 

    Trapezium Rule URL

• Topic 3

  Co Ordinate Geometry of Straight Lines

  Gradient

  1. Line segment
  2. Parallel lines
  3. Perpendicular lines

  Lines

  1. Equation of a straight line: y=mx+c
  2. Equation of a line given the gradient and point
  3. Distance between two points
  4. Mid-point of a line segment
  5. Equation of a parallel line
  6. Equation of a perpendicular bisector

  Intersection of Graphs

  1. Intersection of two straight lines
  2. Intersection of a straight line and a parabola
  3. Intersection of a straight line and a hyperbola
  4. Nature of the intersection

  Exam Questions – Straight Lines

  1. Exam Questions - Straight lines

  • 

    Practice Questions File

• Topic 4

  Circle Geometry

  • Equation of a circle
  • Finding the centre and radius
  • Equation of a tangent to a circle
  • Equation of a circle through 3 points
  • Circle properties
  • Exam Questions - Circles

  • 

    Practice Questions File

• Quadratics

  Quadratic Functions and Their Graphs

  Quadratic Equations

  1. Solve by factorising
  2. Solve by completing the square
  3. Solve by the quadratic formula
  4. Exam Questions - Solved by the quadratic formula
  5. Solving quadratic equations in some function of x

  Quadratic Equations – Roots and Discriminant

  1. Roots and discriminant of a quadratic equation
  2. Exam Questions - Roots and discriminant

  Quadratic Graphs

  1. Sketching quadratic graphs

• Factors, Remainders and Cubic Graphs

  Factors, Remainders and Cubic Graphs

  Algebraic Long Division

  1. Algebraic long division

  Factor and Remainder Theorems

  1. The factor theorem
  2. How to solve a cubic equation
  3. Exam Questions - Factor theorem
  4. The remainder theorem
  5. Exam Questions - Remainder theorem

• Simultaneous Equations and Quadratic Inequalities

  Simultaneous Equations and Quadratic Inequalities

  Polynomials

  1. Polynomials

  Simultaneous Equations

  1. Elimination method for linear equations
  2. Substitution method for linear and non-linear equations
  3. Exam Questions - Simultaneous equations

  Inequalities

  1. Linear inequalities
  2. Rules for reversing the inequality sign
  3. Solving a linear type
  4. Solving a double inequality
  5. Exam Questions - Solving a double inequality
  6. Quadratic inequalities
  7. Exam Questions - Quadratic inequalities
  8. Exam Questions - Simultaneous inequalities

• Introduction to Differentiation

  Introduction to Differentiation

  • The gradient function dy/dx
  • Differentiation - terms of the form axⁿ
  • The second derivative
  • Exam Questions - Differentiation: introduction

• Applications of Differentiation

  Applications of Differentiation 

  Tangents and Normals

  1. Equations of tangents and normals
  2. Exam Questions - Tangents and normals

  Stationary Points

  1. Stationary points
  2. Nature of a stationary point
  3. Exam Questions - Stationary points
  4. Applications of stationary points
  5. Exam Questions - Applications of stationary points

  Increasing and Decreasing functions

  1. Increasing and decreasing functions
  2. Exam Questions - Increasing and decreasing functions

• Integration

  Integration 

  Integration – Introduction

  1. Integration - Terms of the form axⁿ
  2. Exam Questions - Integration: introduction

  Equations of Curves

  1. Finding the equation of a curve given the gradient function
  2. Exam Questions - Equations of curves

  Definite Integration

  1. Definite integration
  2. Infinite integrals

  Applications of Integration – Area bound by a curve

  1. Area bound by a curve and x-axis
  2. Exam Questions - Area bound by a curve and x-axis

• Trigonometry

  Trigonometry 

  Trigonometric Ratios

  1. Trigonometric ratios for 30°, 45° and 60°
  2. Trig ratios for multiples of 30°, 45° and 60°

  Trigonometric Graphs and Transformations

  1. Trigonometric graphs
  2. Translations of trig graphs
  3. Reflections of trig graphs
  4. Stretches of trig graphs
  5. Combining transformations
  6. Exam Questions - Trigonometric graphs and transformations

  Applications of Trigonometry

  1. Area of a triangle - Given two sides and an included angle
  2. Sine rule
  3. Exam Questions - Sine rule
  4. Cosine rule
  5. Arcs, sectors and segments
  6. Exam Questions - Arcs, sectors and segments

  Trigonometric Equations

  1. Quadrant rule to solve trig equations
  2. Trig equations with different ranges
  3. Trig equations with multiple angles
  4. Trig equations that factorise

  Trigonometric Identities

  1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
  2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
  3. Solving equations using identities
  4. Exam Questions - Trigonometric identities

• Binomial

  Binomial

  Binomial Expansion

  1. Binomial expansion
  2. Binomial expansion formula
  3. Exam Questions - Binomial expansion, basic expansions
  4. Exam Questions - Binomial expansion, comparing coefficients
  5. Exam Questions - Binomial expansion, estimating a value
  6. Exam Questions - Binomial expansion, other

  Binomial Distribution

  1. Binomial distribution