Further Mathematics Support Programme
AQA FP4 – Scheme of Work Template - 2016-2017
This template is part of a series designed to assist with planning and delivery of further mathematics courses.
It shows how Integral Resourcesand Live Interactive Lectures can be used to support students and teachers.
/ Teacher-level access to the Integral Resources(integralmaths.org/) for Further Pure and Applied units is available free of charge to all schools/colleges that register with the Further Mathematics Support Programme:/ Student-level access to the Integral Resources andtheLive Interactive Lecturesfor Further Mathematics is available at a moderate cost via:
Integral Resourcesinclude a wide range of resources for both teacher and student use in learning and assessment. A selection of these are suggested in the template below. Sampleresources are available via:
Live Interactive Lectures are available for individual Further Pure and Applied units and take place in the spring and autumn terms.LIL FM is ideal for schools/colleges teaching Further Mathematics with small groups and/or limited time allocation. It is also useful to support less experienced teachers of Further Mathematics. See
Scheduling will depend on circumstances, but the template below breaks the module down into 12 sections which may be allocated approximately equal time. Each section corresponds to one Live Interactive Lecture (LIL) and these take place fortnightly to supplement the teaching and tutorial support in schools/colleges and students' own independent study. FMSP Area Coordinators will be able to offer additional guidance if needed. See
AQA FP4 – Scheme of Work Template - 2016-2017
Topic / Specification statements / Suggested Integral Resources / Assessment(Integral Resources) / Live Interactive Lecture / Other resources
Matrices 1: Matrix algebra /
- Matrix algebra of up to 3 x 3 matrices
- The identity matrix I for 2 x 2 and 3 x 3 matrices.
/ ► Matrices
/ ► Matrices 1: Matrix algebra
- Additional exercise (Q1 & 2)
Matrices 2: Matrix transformations /
- Matrix transformations in two dimensions: shears.
- Rotations, reflections and enlargements in three dimensions, and combinations of these.
/ ► Matrices
/ ► Matrices 1: Matrix algebra
- Additional exercise (Q3, 4, 5)
- Section test M1
Matrices 3: Determinants /
- Second order and third order determinants, and their manipulation.
- Factorisation of determinants.
- Calculation of area and volume scale factors for transformation representing enlargements in two and three dimensions.
/ ► Matrices
/ ► Matrices 2: Determinants
- Determinants teaching activities
- Explore: Determinants (Geogebra)
- Determinant of a 3x3 matrix (Powerpoint)
- Additional exercise
- Section test M2
Matrices 4: Inverse matrices /
- The inverse of a 2 x 2 or 3 x 3 matrix.
/ ► Matrices
/ ► Matrices 3: Inverse matrices
- Walkthrough: Determinants and inverses
- Matrices teaching activities
- Inverse of a 3x3 matrix (PowerPoint)
- Additional exercise
- Section test M3
Vectors 1: The vector product /
- Definition and properties of the vector product.
- Calculation of vector products.
/ ► Vectors
/ ► Vectors 1: The vector product
- Additional exercise
- Section test V1
Vectors 2: The scalar triple product /
- Calculation of scalar triple products.
/ ► Vectors
/ ► Vectors 2: The scalar triple product
- Vector product and scalar triple product teaching activities
- Vectors puzzle
- Additional exercise
- Section test V2
Vectors 3: Equations of lines and planes /
- Applications of vectors to two- and three-dimensional geometry, involving points, lines and planes.
- Cartesian coordinate geometry of lines and planes. Direction ratios and direction cosines.
/ ► Vectors
/ ► Vectors 3: Equations of lines and planes
- Lines and planes teaching activities
- Additional exercise
- Section test V3
Vectors 4: Intersection and angles /
- Applications of vectors to two- and three-dimensional geometry, involving points, lines and planes.
- Cartesian coordinate geometry of lines and planes. Direction ratios and direction cosines.
/ ► Vectors
/ ► Vectors 4: Intersections and angles
- Additional exercise
- Section test V4
► AQA_FP4
/ ► Vectors
- Vectors topic assessment
Matrices 5: Solving linear equations / •Consideration of up to three linear equations in up to three unknowns. Their geometrical interpretation and solution.
- Linear independence and dependence of vectors.
/ ► Matrices
/ ► Matrices 4: Solving linear equations
- Walkthrough: Matrices and simultaneous equations
- Additional exercise
- Section test M4
Matrices 6: Row operations /
- Eigenvalues and eigenvectors of 2x2 and 3x3 matrices.
- Invariant points and invariant lines.
/ ► Matrices
/ ► Matrices 5: Eigenvalues and eigenvectors / Matrices 6: Row operations
Matrices 7: Eigenvalues and eigenvectors /
- Eigenvalues and eigenvectors of 2x2 and 3x3 matrices.
- Invariant points and invariant lines.
/ ► Matrices
/ ► Matrices 5: Eigenvalues and eigenvectors
- Walkthrough: Invariant points
- Matrices teaching activities
- Eigenvalues and eigenvectors matching activity
- Additional exercise
Matrices 8: Diagonalisation /
- Diagonalisation of 2x2 and 3x3 matrices.
/ ► Matrices
/ ► Matrices 5: Eigenvalues and eigenvectors
- Walkthrough: Invariant points
- Matrices teaching activities
- Eigenvalues and eigenvectors matching activity
- Additional exercise
- Section test M5
► AQA_FP4
/ ► Matrices
- Matrices topic assessment
Consolidation and revision / FMSP – Revision Videos
The study plans available on Integral Resources refer to AQA online FP4 textbook.Other textbooks covering this course may be available, and Integral Mathematics Resources does not endorse any particular set of textbooks.