Advanced Higher Maths
​What is Advanced Higher Maths? 
Advanced Higher Maths is the most advanced school maths course in Scotland, designed to deepen understanding and prepare pupils for university study, especially in subjects like science, engineering, computing, and economics.
It builds on Higher Maths and focuses on more complex problem-solving, reasoning, and abstract thinking.
​
The course is split into three main areas:
  • Methods of Algebra and Calculus
     Learning advanced techniques in algebra and calculus.
  • Applications of Algebra and Calculus
    Using maths to solve real-world and theoretical problems.
  • Geometry, Proofs and Systems of Equations
     Developing logical thinking, proof skills, and working with equations and shapes.

Throughout the course, pupils will:
·  Tackle challenging mathematical problems
·  Improve logical thinking and reasoning
·  Learn to analyse and interpret information
·  Communicate ideas clearly using maths
·  Develop proof skills

What topics are included?
  • Calculus and algebra (core skills for further study)
  • Complex numbers (used in engineering and electronics)
  • Matrices (used in economics, computing, and games)
  • Number theory (important for things like internet security)

The course is assessed by an SQA Exam. There are 2 exam papers:

  • Paper 1: Non-Calculator, 1 hour, and worth 35 marks.
  • Paper 2: Calculator, 2 hours 30 minutes, and worth 80 marks.
Advanced Higher Course Plan
Course Resources
The principal course resources are the Course Notebooks and Course Textbooks.  Notebooks contain the key learning points, worked examples, and past exam question exercises.  The textbooks provide further examples and practice exercises.​
​Please note that these resources are password-protected; pupils will receive the password from their Maths teacher in class.
​COURSE NOTEBOOKS
The course notebooks include worked examples.

​Course Note 1
​Binomial Theorem, Partial Fractions and Differentiation

Course Note 2
Sequences & Series, Complex Numbers, Systems of Equations and Matrices

Course Note 3
​Vectors, Integration and Differential Equations

Course Note 4
​Functions and Graphs, Applications of Calculus, Mathematical Proof and Number Theory​
COURSE TEXTBOOKS
​The course textbooks are where you will find practice questions.

TEXTBOOK 1
Binomial Theorem, Partial Fractions, Differentiation, Sequences & Series and Complex Numbers

TEXTBOOK 2
Systems of Equations and Matrices
Vectors, Integration and Differential Equations

TEXTBOOK 3
Functions and Graphs, Applications of Calculus, Mathematical Proof and Number Theory
Click here for : Summary Sheet of All Topics
Past Papers & Formulae Sheet
Resources Available:
Resources:
Free Advanced Higher Maths . com has Past and Practice Papers from 2001 avaliable, Past paper Worksheets by Topic, Study Guides, Theory Guides, Mind Maps, and notes for every Advanced Higher Maths topic.
Dynamic Maths offers free worksheets and resources from National 5 to Advanced Higher level. It contains past paper questions and resources for self-study.
The Zeta textbook is avaliable for use at home, your teacher will tell you the access code in class.
YouTube Videos:
App and YouTube account available. Clelland Maths has multiple videos explaining the content of Advanced Higher Maths.
YouTube account available. DLB Maths has multiple videos explaining the content of Advanced Higher Maths.
​YouTube account available. Mr Thomas has multiple videos explaining the content of Advanced Higher Maths.
This website complies with Renfrewshire Council's *Guidelines for the development of school websites *(Lifelong Learning and Work Policy Board, 11 December 2003). 
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