# Year 13 — Further Maths

### Term 1: Core Pure 2 and Further Mechanics

(The order of delivery over the 2 years may differ from this depending on the needs of the individual teaching group)

Complex numbers: Exponential from of complex numbers, multiplying and dividing complex numbers, De Moivre’s theorem, trigonometric identities, sum of the series, nth root of a complex number, solving geometric problems.

Series: The method of differences, higher derivates, Maclaurin series, series expansions of compound functions

Momentum and impulse: Momentum in one direction, conservation of momentum, momentum as a vector.

Work, energy and power: Work done, kinetic and potential energy, conservation of mechanical energy and the work-energy principle, power.

Each topic is assessed through a 50 minute internal test.

### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

#### Create a supportive community:

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

### Term 2: Core Pure 2 and Further Mechanics

(The order of delivery over the 2 years may differ from this depending on the needs of the individual teaching group)

Methods in calculus: Improper integrals, mean value of a function, differentiating inverse trigonometric functions, integrating with inverse trigonometric functions, integrating using partial fractions.

Volumes of revolution: Volumes of revolution around the x-axis, volumes of revolution around the y-axis, volumes of revolution of parametrically defined curves, modelling with volumes of revolution.

Elastic strings and springs: Hooke’s law and equilibrium problems, Hooke’s law and dynamics problems, elastic energy, problems involving elastic energy.

Each topic is assessed through a 50 minute internal test.

### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

#### Create a supportive community:

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

### Term 3: Core Pure 2 and Further Mechanics

(The order of delivery over the 2 years may differ from this depending on the needs of the individual teaching group)

Polar coordinates: Polar coordinates and equations, sketching curves, area enclosed by polar coordinates, tangents to polar curves.

Hyperbolic functions: Introduction to hyperbolic functions, inverse hyperbolic functions, identities and equations, differentiating hyperbolic functions, integrating hyperbolic functions.

Elastic collisions in one dimension: Direct impact and Newton’s law of restitution, direct collision with a smooth plane, loss of kinetic energy, successive direct impacts.

Each topic is assessed through a 50 minute internal test.

### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

#### Create a supportive community:

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

### Term 4: Core Pure 2 and Further Mechanics

(The order of delivery over the 2 years may differ from this depending on the needs of the individual teaching group)

Methods in differential equations: First-order differential equations, second-order homogeneous differential equations, second-order non-homogeneous differential equations, using boundary conditions.

Modelling with differential equations: Modelling with first-order differential equations, simple harmonic motion, damped and forced harmonic motion, coupled first-order simultaneous differential equations.

Elastic collisions in two dimensions: Oblique impact with a fixed surface, successive oblique impacts, oblique impacts of smooth spheres.

Each topic is assessed through a 50 minute internal test.

### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

#### Create a supportive community:

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

### Term 5: Core Pure 2 and Further Mechanics

Revision and past papers

Internal mock exams

90 minute external exam worth 25% for each of Core Pure 2 and Further Mechanics

.

### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural

#### Develop the individual:

Develop the ability to: construct rigorous mathematical arguments (including proofs) make deductions and inferences assess the validity of mathematical arguments explain their reasoning use mathematical language and notation correctly translate problems in mathematical and non-mathematical contexts into mathematical processes interpret solutions to problems in their original context, and, where appropriate, evaluate their accuracy and limitations translate situations in context into mathematical models use mathematical models evaluate the outcomes of modelling in context recognise the limitations of models and, where appropriate, explain how to refine them.

#### Create a supportive community:

Communication – active listening, oral communication, written communication. Collaborative problem solving – establishing and maintaining shared understanding, taking appropriate action, establishing and maintaining team organisation.

• Spiritual
• Moral
• Social
• Cultural