SGSE

Year 11 Higher Maths

Curriculum:

Click to Expand Autumn Content:

Circle Theorems

More Algebra

Vectors and Geometric Proof

Proportion and Graphs

Prior Knowledge:

Know properties of isosceles triangles.
Define the chord of a circle.
Know that a line from the centre of a circle to the midpoint of a chord is perpendicular to the chord.
Know that angles round a point add to 360^°.
Recall the sum of angles of a quadrilateral.
Use correct mathematical vocabulary for parts of a circle.
Understand that x² + y² = r² is the equation of a circle with centre at the origin.
Find the gradient of a line from its equation and know the gradient of a line perpendicular to it.

Substitute into a linear formula.
Simplifying numerical and simple algebraic fractions.
Factorise simple expressions by identifying the common factor.
Identify rational and irrational numbers.
Find the LCM of two simple algebraic expressions.
Find the output of a function machine, given the input.
Identify an odd number and an even number written algebraically.

Understand translation vectors.
Identify parallel lines/vectors.
Understand the relationship between ratio and fractional parts.

Recognise direct proportion.
Use inverse proportion.
Evaluate indices.
Find the area of a trapezium.
Translate coordinates.
Understand the concept of ‘stretching’.

Teaching Content:

Solve problems involving angles, triangles and circles.
Understand and use facts about chords and their distance from the centre of a circle.
Solve problems involving chords and radii.
Understand and use facts about tangents at a point and from a point.
Give reasons for angle and length calculations involving tangents.
Understand, prove and use facts about angles subtended at the centre and the circumference of circles.
Understand, prove and use facts about the angle in a semicircle being a right angle.
Find missing angles using these theorems and give reasons for answers.
Understand, prove and use facts about angles subtended at the circumference of a circle.
Understand, prove and use facts about cyclic quadrilaterals.
Prove the alternate segment theorem.
Solve angle problems using circle theorems.
Give reasons for angle sizes using mathematical language.
Find the equation of the tangent to a circle at a given point.

Change the subject of a formula where the power of the subject appears.
Change the subject of a formula where the subject appears twice.
Add and subtract algebraic fractions.
Multiply and divide algebraic fractions.
Change the subject of a formula involving fractions where all the variables are in the denominators.
Simplify algebraic fractions.
Add and subtract more complex algebraic fractions.
Multiply and divide more complex algebraic fractions.
Simplify expressions involving surds.
Expand expressions involving surds.
Rationalise the denominator of a fraction.
Solve equations that involve algebraic fractions.
Use function notation.
Find composite functions.
Find inverse functions.
Prove a result using algebra.

Understand and use vector notation.
Work out the magnitude of a vector.
Understand the components of a vector.
Calculate using vectors and represent the solutions graphically.
Calculate the resultant of two vectors.
Solve problems using vectors.
Use the resultant of two vectors to solve vector problems.
Express points as position vectors.
Prove lines are parallel.
Prove points are collinear.
Solve geometric problems in two dimensions using vector methods.
Apply vector methods for simple geometric proofs.

Write and use equations to solve problems involving direct proportion.
Write and use equations to solve problems involving indirect proportion.
Solve problems involving square and cubic proportionality.
Write and use equations to solve problems involving inverse proportion.
Use and recognise graphs showing inverse proportion.
Recognise graphs of exponential functions.
Sketch graphs of exponential functions.
Calculate the gradient of a tangent at a point.
Estimate the area under a non-linear graph.
Understand the relationship between translating a graph and the change in its function notation.
Understand the effect stretching a curve parallel to one of the axes has on its function form.
Understand the effect reflecting a curve in one of the axes has on its function form.

Keywords:

Theorem, chord, Tangent, Subtended, Cyclic polygon, cyclic quadrilateral, alternate segment

Proof, counter-example, other key words are introduced in previous units

Vector, magnitude, displacement, equal vectors, scalar, triangle law for vector addition, parallelogram law for vector addition, resultant vector, position vectors, collinear, geometric proof

Constant of proportionality, inversely proportional, exponential functions, exponential growth, exponential decay, tangent, chord, asymptote

Click to Expand Spring Content:

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

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:

Year 11 is primarily spent preparing for pupils to sit the Higher GCSE again at the end of the year. The first term will be spent teaching the reminder of the GCSE course at a slower pace than in Year 10, while lesson time after Christmas will be dedicated to revising different topics in preparation for the Summer exams.

Assessments:

Pupils are typically given less topics tests in Year 11, but they sit a Mock Examination in November. Pupils may be given practice assessments during lessons, which may be asked to be sat under exam conditions as practice.