This course is designed for Scottish learners preparing for Higher Mathematics who need structured teaching, reliable revision, and practical support for SQA-style assessment. It covers the full progression from core algebra and functions through calculus, trigonometry, geometry, sequences, vectors, and proof, with a strong focus on applying methods accurately under exam conditions.
Students begin with a diagnostic process that identifies strengths and gaps across the course. They then work through carefully sequenced modules that teach the underlying mathematics, not just shortcuts. Each topic includes concrete method development, common error correction, and practice in presenting working clearly enough to secure marks.
The course is especially useful for learners who want to improve both mathematical understanding and assessment performance. It supports students who need to strengthen weak topics, consolidate classroom learning, or prepare systematically for prelims and the final exam.
- Algebra and equations: simplification, factorisation, algebraic fractions, surds, indices, linear and quadratic equations, polynomial methods, inequalities, and modelling from context
- Functions and graphs: function notation, domain and range, inverse and composite functions, straight lines, quadratics, polynomials, graph transformations, and graphical solving
- Coordinate geometry and geometry: gradients, equations of lines, circles, midpoint and section problems, and coordinate-based geometric proof
- Trigonometry: right-angled trigonometry, exact values, trig graphs, solving trig equations, identities, double-angle formulae, and proof
- Calculus: differentiation, stationary points, optimisation, tangent problems, integration, definite integrals, and area under or between curves
- Sequences, recurrence, and vectors: arithmetic and geometric sequences, summation, recurrence relations, vector operations, vector geometry, and formal proof
- Assessment skills: command words, marking logic, calculator and non-calculator strategy, timing, error analysis, and full timed practice with review
Throughout the programme, students learn to use subject-specific vocabulary accurately, interpret question wording, choose efficient methods, and structure solutions in a way that matches how Higher Mathematics marks are awarded. The course also emphasises retrieval practice, cumulative review, and mistake-log work so progress is measurable rather than guesswork.
- Diagnose current performance by topic and identify priority gaps
- Rebuild and extend Higher Mathematics knowledge in a logical sequence
- Practise original exam-style questions with clear, fully explained solutions
- Improve accuracy, notation, and method selection across mixed-topic problems
- Develop confidence with timed work, paper strategy, and final target-grade planning
By the end of the course, students should be able to solve Higher Mathematics problems with greater fluency, explain their reasoning clearly, handle SQA-style questions more confidently, and complete practice assessments with informed review of what to improve next.