# Year 12 — Further Maths

### Term 1: Y12 Further Maths Term 1 Core Pure

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

An introduction to Complex Numbers

Further complex numbers, Loci and the Argand Diagram

Matrices;

Add, subtract and multiply conformable matrices.

Multiply a matrix by a scalar.

Understand and use zero and identity matrices.

Use matrices to represent linear transformations in 2-D.

Successive transformations.

Single transformations in 3-D.

Find invariant points and lines for a linear transformation.

Topic assessments on Complex Numbers and Matrices

### 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: Y12 Further Maths Term 2 - Decision 1

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

Algorithms; Graphs and Networks; Algorithms on Graphs; Route Inspection; Travelling Salesman Problem;

Each topic will be tested through a 50 minute assessment

### 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: Y12 Further Maths Term 3 - Core Pure

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

Roots of equations

Understand and use the relationships between the roots and coefficients of polynomial equations up to quartic equations.

Form a polynomial equation whose roots are a linear transformation of the roots of a given polynomial equation (of at least cubic degree).

Know that non-real roots of polynomial equations with real coefficients occur in conjugate pairs.

Solve cubic or quartic equations with real coefficients.

Sequences and series 1:

Summing series

Understand and use formulae for the sums of integers, squares and cubes and use these to sum other series.

Sequences and series 2:

Induction

Construct proofs using mathematical induction.

Contexts include sums of series, divisibility and powers of matrices.

Each topic is assessed through a 50 minute formal assessment task.

### 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: Y12 Further Maths Term 4 - Decision 1

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

Linear Programming; Simplex Algorithm; Critical Path Analysis

Each topic will be tested through a 50 minute assessment

### 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: Y12 Further Maths Term 5 - Core Pure

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

Complex Numbers

Hyperbolic functions

Polar coordinates

Each topic is assessed through a 50 minute formal test in class.

### 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 6: Y12 Further Maths Term 6

Revision and end of year module examinations

90 minute mock papers for each of Core Pure Maths 1 and Decision Maths 1

### 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.