Advanced Higher

Mathematics at Advanced Higher provides the foundation for many developments in the sciences and in technology as well as having its own intrinsic value. This Course is designed to enthuse, motivate, and challenge learners by enabling them to:

  • select and apply complex mathematical techniques in a variety of mathematical situations, both practical and abstract
  • extend and apply skills in problem solving and logical thinking
  • extend skills in interpreting, analysing, communicating and managing information in mathematical form, while exploring more advanced techniques
  • clarify their thinking through the process of rigorous proof

The Course develops and expands a range of mathematical skills. It allows the learner to develop further skills in calculus and algebra. Areas such as number theory (which helps keep the internet secure), complex numbers (the uses of which are ubiquitous, ranging from the solution of equations to the description of electronic circuits) and matrices (used in game theory and economics) are introduced. The learner’s mathematical thinking will also benefit from examples of rigorous proof.

Notes and exercises

These pages contain notes, exercises and practice materials for each block of work;

Block A      Block B      Block C      Block D


As a matter of routine, you should be working independently through the exercises from the topics covered in class. Additional, formal homework exercises will be posted here;

Exam Homework 10 – 2011 Q15, 2012 Q6          (Solutions)
Exam Homework 10 – Extension 2014 Q16
Exam Homework 9 – 2011 Q4 and 2011 Q15    (Solutions)
Exam Homework 9 – Extension 2015 Q11
Exam Homework 8 – 2015 Q5 and 2014 Q5       (Solutions)
Exam Homework 8 – Extension 2015 Q18
Exam Homework 7 – 2011 Q9 and 2012 Q4       (Solutions)
Exam Homework 6 – 2010 Q2 and 2010 Q3       (Solutions)
Exam homework 5 – 2013 Q10 and 2002 A7      (Solutions)
Exam homework 4 – 2008 Q4 and 2012 Q3         (Solutions)
Exam homework 3 – 2008 Q7 and 2010 Q15      (Solutions)
Exam homework 2 – 2010 Q1 and 2009 Q13      (Solutions)
Exam homework 1 – 2006 Q4 and 2008 Q15      (Solutions)

Weekly HW4      (Solutions)
Weekly HW3      (Solutions)
Weekly HW2      (Solutions)
Weekly HW1      (Solutions)

Exam Revision

Specimen Papers from 2020
Paper 1      Paper 2

Past Papers & Marking schemes
2019 Paper      Marking scheme
2018 Paper      Marking Scheme
2017 Paper      Marking Scheme
2016 Paper      Marking scheme
2015 Paper      Marking scheme
2014 Paper      Marking scheme
2013 Paper      Marking scheme
2012 Paper      Marking scheme
2011 Paper      Marking scheme
2010 Paper      Marking scheme
2007 Marking scheme      2008 Marking scheme      2009 Marking scheme
2004 Marking scheme      2005 Marking scheme      2006 Marking scheme
2001 Marking scheme      2002 Marking scheme      2003 Marking scheme

Exam Materials for new AH
Specimen Question Paper      Exemplar Question Paper

Revision Materials
Formulae list      Standard derivatives      Differentiation and Integration Rules      Trig formulae

Useful links


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Block D

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