The Higher Mathematics course develops, deepens and extends the mathematical skills necessary at this level and beyond. Throughout this course, pupils acquire and apply operational skills necessary for developing mathematical ideas through symbolic representation and diagrams. They select and apply mathematical techniques and develop their understanding of the interdependencies within mathematics. Pupils will develop mathematical reasoning skills and gain experience in making informed decisions.
Assessment for this course consists of two external exams during the SQA exam diet.
Question paper 1 (non-calculator) worth 55 marks and lasting 1 hour and 15 minutes.
Question paper 2 worth 65 marks and lasting 1 hour and 30 minutes.
The Higher Mathematics course builds upon knowledge previously obtained throughout a pupil's time at school. Any pupil wishing to undertake the course should have already achieved their National 5 Mathematics qualification. It is not possible to advance to Higher Maths from National 5 Applications of Maths.
Pupils who are successful at Higher Mathematics have the opportunity to progress on to Advanced Higher Mathematics.
The Higher Mathematics course consists of four overarching topics:
Algebra
Geometry
Calculus
Trigonometry
Pupils will study the following within these topics:
Composite and inverse functions
Completing the square
Graph transformations
Derivative and inverse graphs
Recurrence relations
Sequences
Quadratic inequalities
Polynomials
Intersections of graphs
Logarithms and exponentials
Function notation
Straight lines
Medians, altitudes and perpendicular bisectors
Circles
Tangency
Intersections of circles
Vectors
Collinearity
Scalar product
Differentiation
Equations of tangents to curves
Increasing/decreasing functions
Curve sketching
Optimisation
Rate of change
Integration
Differential equations
Definite integrals
Area under/between curves
Radians
Trigonometric identities
Addition and double angle formulae
Wave function
Homework is set fortnightly to allow students to recap key ideas in class. This is set online on Google Classroom. There are other useful resources on Google Classroom.
Independent Practise can be found on the Achieve platform linked below. At least an hour of independent work is expected each week using either online resources or textbooks uploaded onto Google Classroom below.
The following websites are helpful to pupils studying Higher Mathematics: