CfE Higher Maths




The Higher Course in Mathematics develops learners’ mathematical rigour and the ability to use precise and concise mathematical language assumes a particular importance at this stage.

Candidates who complete a Higher Mathematics course successfully are expected to have a competence and a confidence in applying mathematical techniques, manipulating symbolic expressions and communicating with mathematical correctness in the solution of problems.

The course has obvious relevance for candidates with interests in fields such as commerce, engineering and science where the mathematics learned will be put to direct use.

Entry to the course

This is at the discretion of the school, but you would normally be expected to have attained a pass in
 National 5 Mathematics.

Course Outline





Straight Line

pdf iconStraight Line Summary
pdf iconStraight Line Mind Map
Video-IconVideo – Gradient
Video-IconVideo – Midpoint & Distance Formulae
Video-IconVideo – Equation of a Straight Line
Video-IconVideo – Altitudes, Medians & Perpendicular Bisectors
Video-IconVideo – Intersecting Lines
    HSN Study Notes – Straight Line


pdf icon Quadratics Summary
pdf iconQuadratic Function Mind Map
     HSN Study Notes – Quadratics and Polynomials





August – October


 pdf iconPolynomials Summary
pdf iconPolynomials Mind Map
    HSN Study Notes – Quadratics and Polynomials


pdf iconFunctions Summary
pdf iconFunctions Mind Map
    HSN Study Notes – Functions and Graphs

Differentiation 1

pdf iconDifferentiation 1 Summary
pdf iconDifferentiation Mind Map
    HSN Study Notes – Differentiation

Trigonometric Equations

 pdf iconTrigonometric Equations Summary





October – December


 pdf iconVectors Summary
pdf iconVectors Mind Maps
    HSN Study Notes – Vectors

Differentiation 2

pdf iconDifferentiation2 Summary
pdf iconDifferentiation Mind Map
    HSN Study Notes – Differentiation

Trig –


Angle Formulae

pdf iconAddition & Double Angle Formulae
Video-IconVideo – Proving the Addition Formulae
Video-IconVideo – Easy Proof of Double Angle Formula
pdf iconTrig-Equations & Formulae Mind Map
    HSN Study Notes – Trigonometry

Logs & Exponential

pdf iconExponentia & Logarithmis Functions Summary
pdf iconLog & Exponential Mind Map
    HSN Study Notes – Exponentials and Logarithms





January – March

Integration 1

Integration 1 Summarypdf icon
pdf iconIntegration Mind Map
    HSN Study Notes – Integration


pdf iconThe Circle Summary
pdf iconThe Circle Mind Map
    HSN Study Notes – Circles

Trig – Wave Function

pdf iconThe Wave Function Summary
pdf iconWave Function Mind Map
    HSN Study Notes – Trigonometry

Integration 2

pdf iconIntegration 2 Summary
    HSN Study Notes – Integration

Recurrence Relations

 Recurrence Relations Summarypdf icon
 Recurrence Relations Mind Mappdf icon
    HSN Study Notes – Sequences

Course Summary and Self-Assessment Booklet

Higher Course Summary & Self Assessment Booklet


Homework is an essential part of the course. Homework will often take the form of completion of exercises started in class. Pupils will also be issued with regular homework exercises, these exercises will be marked by the class teacher.

Higher HW Booklet


To gain the overall award students must pass an asessment at the end of each unit as well as an external assessment.

The SQA external exam consists of 2 papers – one calculator, one non-calculator.

In January pupils will sit a prelim exam that coveres units 1 & 2. Pupils will also sit a top-up prelim prelim in April, this will cover a range of topics from units 1, 2 & 3.


Successful completion of this course may lead to further study at Advanced Higher level.

Consolidation Pack

The consolidation pack provides the opportunity to revise some of the keys skills from the Credit or Intermediate 2 courses that are required for Higher Maths.

Higher Consolidation Pack-Key Questions

Higher Maths Consolidation Pack

Past Papers



2017 Higher Exam

2017 Higher Marking

2016 Higher Exam

2016 Higher Marking

2015 Higher Exam

2015 Higher Marking

2014 Higher Exam

2014 Higher Marking

2013 Higher Exam

2013 Higher Marking

2012 Higher Exam

2012 Higher Marking

2011 Higher Exam

2011 Higher Marking

2010 Higher Exam

2010 Higher Marking

2009 Higher Exam

2009 Higher Marking

2008 Higher Exam P1

2008 Higher Exam P2

2008 Higher Marking

2007 Higher Exam P1

2007 Higher Exam P2

2007 Higher Marking P1

2007 Higher Marking P2

2006 Higher Paper 1

2006 Higher Paper 2

2006 Higher Marking P1

2006 Higher Marking P2

2005 Higher Paper 1

2005 Higher Paper 2

2005 Higher Marking

2004 Higher Paper 1

2004 Higher Paper 2

2004 Higher Marking

2003 Higher Paper 1

2003 Higher Paper 2

2003 Higher Marking

2002 Higher Paper 1

2002 Higher Paper 2

2002 Higher Marking

2001 Higher Paper 1

2001 Higher Paper 2

2001 Higher Solutions

2000 Higher Paper 1

2000 Higher Paper 2

2000 Higher Marking

Useful Websites

Mr Graham has produced video tutorials to help with a range of topics. –

Course notes, summary sheets and specimen assesments  –

Course notes, practice exercises and assessments  –

Past papers & marking instructions  –

Revision notes, videos and assessments  –

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