Pure Year 1

Ch1: Algebraic Expressions

Ch2: Quadratics

Ch3: Equations and Inequalities

Ch4: Graphs & Transformations

Ch5: Straight Line Graphs

Ch6: Circles

Pure Year 1

 Ch7: Algebraic Methods

 Ch8: Binomial Expansion

 Ch9: Trig Ratios

 Ch10: Trig Identities &

 Ch11: Vectors

 Ch12: Differentiation

Pure Year 1

 Ch13: Integration

 Ch14: Exponentials 

 Statistic

Ch1: Data Collection

 Ch2: Location & Spread

 Mechanics

Ch8: Modelling

 Ch9: Const Acceleration

Year 10 and 11 GCSE Higher Content

Year 10 and 11 GCSE Higher Content

Pure Year 1

Ch1: Algebraic Expressions

• Expanding Brackets
• Factorising
• Indices
• Surds

Ch2: Quadratics

• Solving Quadratics
• Completing the square
• Functions
• Quadratic Graphs
• Discriminant

Ch3: Equations and Inequalities

• Simultaneous Eqn’s
• Quadratic Sim Eqn’s
• Linear & Quadratic ineqs
• Inequalities on graphs
• Regions

Ch4: Graphs & Transformations

• Cubic graphs
• Quartic graphs
• Reciprocal graphs
• Points of intersection Translations

Ch5: Straight Line Graphs

• y = mx + c
• Eqns of straight lines
• Parallel & perpendicular lines
• Lengths & areas
• Problem solving

Ch6: Circles

• Midpoint & perp bisectors

• Eqn of a circle
• Straight lines & circles
• Tangents & chords
• Circles & triangles

Pure Year 1

Ch7: Algebraic Methods

• Algebraic Fractions
• Polynomial Division
• The Factor Theorem
• Mathematical proof
• Methods of proof

Ch8: Binomial Expansion

• Pascal’s Triangle
• Factorial Notation
• The Binomial Expansion

Ch9: Trig Ratios

• Cosine Rule, Sine Rule
• Area = ½abSinC
• Solving problems
• Trig Graphs
• Transformations

Ch10: Trig Identities &

• Equations
• Angles in 4 quadrants
• Trig identities & equations
• Equations & Identities

Ch11: Vectors

• Magnitude & direction
• Position Vectors
• Geometrical Problems

Ch12: Differentiation

• Gradient of curves
• Diff’ating xⁿ & quadratics
• Diff’ating two+ terms
• Tangents & Normals
• Increasing/ decreasing fns
• 2nd derivatives
• Stationary points

Pure Year 1

Ch13: Integration

• Integrating x^n
• Indefinite integrals
• Finding functions
• Definite integrals
• Area under a curve
• Area under x-axis
• Area between curve & a line

Ch14: Exponentials &

• Logarithms
• Exponential fns
• Y=e^x & Ln(x)
• Exponential modelling
• Laws of logs
• Equations with logs
• Logs/non-linear data

Statistic

Ch1: Data Collection

• Populations & Samples
• Sampling
• Non-random sampling
• Types of data
• The Large Dataset

Ch2: Location & Spread

• Central tendency
• Measures of location
• Measures of spread
• Variance & Standard deviation
• Coding

Mechanics

Ch8: Modelling

• Constructing a model
• Assumptions
• Quantities & units
• Vectors

Ch9: Const Acceleration

• D-time graphs
• Velocity-time graphs
• Const accel 1
• Const accel 2

Statistics

 Ch3: Representing Data

 Ch4: Correlation

 Ch5: Probability

 Mechanics

Ch10: Forces & Motion

 Ch11: Variable Accel

Statistics

Ch6: Binomial Distr.

Ch7: Hypothesis Testing

Pure year 2

Ch1: Algebraic Methods

 Ch2: Functions & Graphs

Pure year 2

 Ch3: Sequences & Series

 Ch4: Binomial Expansion

 Ch5: Radians

 Ch6: Trig Functions

Year 10 and 11 GCSE Higher Content

Year 10 and 11 GCSE Higher Content

+ Half Term 1,2,3

Year 10 and 11 GCSE Higher Content

+ Half Term 1,2,3

Statistics

Ch3: Representing Data

• Outliers
• Box plots
• Cumulative
• frequency

• Histograms
• Comparing data

Ch4: Correlation

• Correlation
• Linear Regression

Ch5: Probability

• Calculating probability
• Venn diagrams
• Mutually exclusive & independent events
• Tree Diagrams

 Mechanics

Ch10: Forces & Motion

• Force diagrams
• Forces as vectors
• Forces & acceleration
• Motion in 2D
• Connected particles

 Ch11: Variable Accel

• Functions of time
• Using differentiation
• Maxima/minima
• Using integration

Const acceleration

Statistics

Ch6: Binomial Distr.

• Probability distributions
• Binomial distributions
• Cumulative probabilities

Ch7: Hypothesis Testing

• Hypothesis testing
• Critical values
• One-tailed tests
• Two-tailed tests

*Finish Mech/Stats topics or revise using past papers

Pure year 2

Ch1: Algebraic Methods

• Proof by Contradiction
• Algebraic Fractions
• Partial Fractions
• Repeated Factors
• Algebraic Division

Ch2: Functions & Graphs

• Modulus Function
• Functions & Mappings
• Composite Functions
• Inverse Functions
• |f(x)| & f(|x|)
• Combining transformations

• Solving modulus functions

Pure Year 1

Ch3: Sequences & Series

• Arithmetic Sequences
• Arithmetic Series
• Geometric sequences
• Geometric Series
• Sum to infinity
• Sigma notation
• Recurrence relations
• Modelling with series

Ch4: Binomial Expansion

• Expanding (1+x)ⁿ
• Expanding (a+bx)ⁿ
• Using Partial Fractions

Ch5: Radians

• Radian Measure
• Arc length
• Sectors & segments
• Trig equations
• Small angle approximations

Ch6: Trig Functions

• sec, cosec, cot
• graphs sec, cosec, cot
• using sec, cosec, cot
• Trig identities

Inverse trig functions

Trigonometry

Ch. 7 Trigonometry and Modelling

Ch. 8 Parametric Equations

Ch. 9 Differentiation

Ch. 10 Numerical Methods

Ch. 12 Vectors

Ch. 11 Integration

Stats Ch.1 Regression

Mechanics Ch. 4 Moments

• Y1 A-level Trigonometry
• Y12 A-level Differentiation

Y1 A-level Integration

Y1 Stats and Mechanics

• Addition formulae
• Angle addition formula
• Double angle formulae
• Solving trig equations
• Simplifying acosx ± bsinx
• Proving trig identities
• Modelling with trig identities

• Parametric equations
• Using trig identities
• Curve sketching
• Points of intersection
• Modelling with parametric equations.
• Diff’ating sinx & cosx Diff’ating ex, ax, lnx Chain rule
• Product rule Quotient rule
• Diff’ating trig functions Diff’ating parametrics

• Implicit diff’ation 2nd derivatives Rates of change

• Locating roots Iteration
• Newton-Raphson Application
• 3D coordinates
• Vectors in 3D Vector problems
• Applications to mechanics
• Integrating Standard functions Integrating f(ax + b)
• Using trig identities Reverse chain rule Substitution
• By parts
• Partial fractions
• Finding areas
• Trapezium rule
• Differential equations

• Modelling with Diff Eqns

• Exponential models
• Correlation
• Hypothesis testing
•  
• Moments
•  
• Resultant moments
• Equilibrium
• Centres of mass
• Tilting

Statistics and Mechanics

 Stats Ch. 2 Conditional Probability

Ch.3 Normal Distribution

 Mechanics Ch.5 Forces and Friction

Ch.6 Projectiles

Ch.7 Applications of Forces

Mechanics Ch.8 Further Kinematics

 Revision and Exams

Y1 Stats and Mechanics

Y1 Mechanics

• Set notation
• Conditional probability
• Venn diagrams
• Formulae
• Tree diagrams
• The normal distribution
• Finding probabilities
• Inverse normal dist.
• Standard normal dist.
• Finding µ Ѳ
• Approx. binomial dist.
• Hypothesis test for the normal distribution
• Resolving forces
• Inclined planes
• Friction
• Horizontal projection
• Horiz/vert projection
• Projection at angle
• Projectile motion
• Formulae
• Static particles
• Modelling with statics
• Friction and static particles
• Static rigid bodies
• Dynamics & inclined planes
• Connected articles

• Vectors in kinematics
• Vector methods with projectiles
• Variable acceleration in 1 dimension
• Differentiating vectors

• Integrating vectors

Series

Polynomials

Trigonometry

Ch. 1 Complex Numbers

Ch. 2 Argand Diagrams

 Ch. 6 Matrices

Ch.7 Linear Transformations

Ch. 3 Series

Ch. 4 Roots of Polynomials

Ch. 8 Proof by induction

Ch. 9 Vectors

Ch. 5 Volumes of Revolution

Pure Book Y2:

Ch. 6 Trigonometric Functions

Ch. 7 Trigonometry and modelling

Decision Maths:

Ch. 3 Algorithms on Graphs

Ch. 2 Graphs and Networks

Ch.4 Route Inspection

Ch. 1 Algorithms

Solving quadratic equations

Y1 A-level trigonometry

• Imaginary & complex numbers
• Multiplying complex numbers
• Complex conjugation
• Roots of quadratics
• Solving cubics & quartics
• Argand diagrams
• Modulus argument
• Modulus argument form
• Loci
• Regions
• Multiplication
• Determinants
• Inverting 2x2’s
• Inverting 3x3’s
• Solving equations
• Transformations in 2D
• Reflections & rotations
• Enlargements & stretches
• Successive transformations

• Transformations in 3D

• Sum of natural numbers
• Sum of squares & cubes
• Roots of quadratics
• Roots of cubics
• Roots of quartics
• Roots of a polynomial Transformations
• Introduction Divisibility
• Matrices
• Eqn of a straight line in 3D
• Eqn of a plane in 3D
• Dot product
• Angles between lines & planes
• Points of intersection
• Perpendiculars
• Spin around the x-axis
• Spin around the y-axis
• Adding & subtracting volumes
• Modelling

• sec, cosec, cot
• graphs sec, cosec, cot
• using sec, cosec, cot
• Trig identities
• Inverse trig functions

• Addition formulae
• Double angle formulae
• Solving trig equations
• Simplifying acosx ± bsinx

• Kruskal’s Prims
• Prims & Matrix
• Dijkstra’s
• Modelling with graphs Graph Theory
• Types of graphs
• Graphs & networks & Matrices

• Eulerian Graphs
• Route inspection algorithm
• Algorithms
• Flow charts
• Sorting algorithms
• Bin-packing
• Order of an algorithm

Complex Numbers

Pure Book Y2:

Ch. 9 Differentiation

 Decision Maths:

Ch. 6 Linear Programming

Ch. 8 Critical Path Analysis

Pure Book Y2:

Ch. 11 Integration

 Decision Maths:

Ch. 5 Travelling Salesman

 Ch 9. Simplex Algorithm

Pure Y2 Book:

Ensure all prerequisites for Y2 are covered

 Y2 Core FM Book:

Ch. 1 Complex Numbers

Ch. 2 Method of Differences

GCSE algebraic manipulation including indices

Y12 A-level integration

Y1 A-level FM Complex Numbers

• Differentiating sinx & cosx
• Differentiating ex and lnx
• The chain rule
• The product rule
• The quotient rule
• Differentiating trig functions
•  Implicit Differentiation

• Linear programming problems

• Graphical methods
• Locating the optimal point
• Solutions with integer values
• Modelling a project
• Dummy activities
• Early and late event times
• Critical activities
• The float of an activity
• Gantt charts

• Integrating Standard functions
• Integrating f(ax + b)
• Using trig identities
• Reverse chain rule
• Substitution
• By parts
• Partial fractions
• Differential equations

• *Classical & practical TSM problems
• *Min spanning tree for upper bound
• *Min spanning tree for lower bound
• *Nearest Neighbour for upper bound

• *Formulating problems
• *Simplex method
• *Integer solutions
• *2-stage simplex method

• *The Big-M

• Exponential form
• Multiplying and dividing complex numbers
• De Moivres Theorem
• Trigonometric Identities
• Sums of series
• Nth roots of a complex number
• Solving geometric problems

• The method of differences
• Higher derivatives
• Maclaurin series
• Series expansion of compound functions

Differential Equations

Conic Sections

Ch3. Methods in Calculus

Ch.4 Volumes of Revolution

Ch. 5 Polar Coordinates

Ch. 6 Hyperbolics

Ch.7 Differential Equations

Ch. 8 Modelling with DEs

FP1 Ch. 1 Vectors

Ch. 2 Conic Sections 1

Ch. 3 Conic Sections 2

Ch. 4 Inequalities

Ch. 5 t-formulae

Ch 6. Taylor Series

Y1 FM Calculus

Y1 and 2 A-level calculus

Y1 A-level vectors

A-level Y1 and 2 Trigonometry

Modulus function

• Improper integrals
• The Mean Value Theorem
• Diff’ating inverse trig functions
• Integrating inverse trig functions
• Integrating with partial fractions
• Rotating around the x-axis
• Rotating around the y-axis
• Parametric curves
• Modelling
• Polar coordinates and equations
• Sketching curves
• Area enclosed by a polar curve
• Tangents to polar curves
• Introduction
• Inverse hyperbolic functions
• Identities & equations
• Diff’ating hyperbolic functions
• Integrating hyperbolic functions

• 1st order ODE’s
• 2nd order homogeneous ODE’s
• 2nd order non-homogeneous ODE’s
• Using boundary conditions
• Modelling with 1st order ODE’s
• Simple harmonic motion
• Damped & forced harmonic motion
• Coupled first order simultaneous eqns]
• Cross product
• Areas
• Scalar triple product
• Straight lines
• Geometrical problems

• Parametric equations Parabolas
• Rectangular hyperbolas Tangents & normals Loci
• Ellipses Hyperbolas Eccentricity
• Tangents & normal (ellipses) Tangents & normal (hyperbola) Loci
• Algebraic Methods Using Graphs to solve inequalities
• Modulus inequalities
• The t-formulae
• Applying t-formulae
• Solving trig equations Modelling
• Taylor series
• Limits
• Diff’ntl equations

Revision of all topics

 Ch. 7 Methods in Calculus

Ch.8 Numerical Methods

Ch.9 Reducible Differential Equations

Previous work on Differential Equations

• Leibnitz Thm
• L’Hospital’s Rule
• Weierstrass substitution
• 1st order ODE’s
• 2nd order ODE’s
• Simpson’s rule
• 1st order RDE’s
• 2nd order RDE’s
• Modelling