SGSE

Year 11 Further Maths

Curriculum:

Click to Expand Autumn Content:

Algebra

Functions

Polynomials

Coordinate Geometry

Teaching Content:

Simplify Equations
Solve Linear Equations.
Use the Binomial Expansion.
Understand the Product Rule for Counting.
Manipulate Surds.
Factorise Quadratics and other Expressions.
Rearrange Formulae.
Simplify Algebraic Fractions.
Complete the Square with Quadratic Functions.

Use Function Notation.
Describe the Domain and Range of a Function.
Use Composite Functions.
Utilise Graphs of Functions, including Linear and Quadratic functions.
Understand and Calculate the Inverse of Functions.
Use Exponential Functions.

Solve Quadratic Equations.
Solve Simultaneous Equations in two and three unknowns.
Use the Factor Theorem.
Solve and demonstrate Linear and Quadratic Inequalities.
Calculate and simplify expressions involving Indices.
Work out and use properties of Sequences, including quadratic sequences.
Reproduce and theorise Algebraic Proofs.

Understand and use Parallel and Perpendicular Lines.
Calculate the distance between two points.
Work out the Midpoint of a Line.
Use the Equation of a Straight Line.
Calculate the Intersection of two Lines.
Divide a Line into a given Ratio.
Use the Equation of a Circle.

Click to Expand Spring Content:

Geometry

Calculus

Matrices

Coordinate Geometry

Teaching Content:

Use various Formulae for the Equations of 2D and 3D shapes.
Use Pythagoras’ Theorem.
Know Angle facts, such as with Parallel Lines.
Know and use Circle Theorems.
Understand Geometric Proof.
Use simple Trigonometry, recalling values of specific Angles.
Using Trigonometry outside of Triangles.
Understand and Reproduce the Sine, Cosine and Tangent curves.
Solve Trigonometry Equations.
Learn and utilise Trigonometric Identities.
Learn and Use the Sine Area Rule, the Sine Rule and the Cosine Rule.
Use Trigonometry in Three Dimensions.

Use Differentiation to calculate Gradients of Curves.
Demonstrate Differentiation from First Principals.
Use Differentiation to calculate the Normal of a Curve.
Calculate the Second Derivative.
Calculate Stationary Points.

Understand the use of Matrices.
Calculate Multiplying Matrices.
Use Matrices to apply Transformations.
Combining Matrix Transformations.
Calculate and simplify expressions involving Indices.
Work out and use properties of Sequences, including quadratic sequences
Reproduce and theorise Algebraic Proofs.

Understand and use Parallel and Perpendicular Lines.
Calculate the distance between two points.
Work out the Midpoint of a Line.
Use the Equation of a Straight Line.
Calculate the Intersection of two Lines.
Divide a Line into a given Ratio.
Use the Equation of a Circle.

Click to Expand Summer Content:

By this point in the academic year, we have completed the course content and we are focusing on revision, exam technique and pace.

Subject Overview:

In Further Maths, Year 11 students have 4 lessons each week.

Year 11 students will receive one 30-40 minutes piece of Maths homework each week. In addition, due to the complexity of the course, independent study is considered essential in order to achieve excellent results.

Assessments:

At the end of the course, students will sit 2 papers.
Both papers include a formula sheet.
Paper 1 is Non-Calculator and Paper 2 is a Calculator paper.

Both Papers consider a mix of question styles, from short single-mark questions to multi-step problems. The mathematical demand increases as a student progresses through the papers.

Each papers are written exams: 1 hour and 45 mins each
80 marks Each
Each paper corresponds to 50% of the AQA Level 2 Certificate in Further Mathematics assessment