Mathematics Advanced Higher
Course Structure
This course has three units as follows:
Methods in Algebra and Calculus (AH) 8 SCQF credits (40 hours)
Applications of Algebra and Calculus 8 SCQF credits (40 hours)
Geometry, Proof and Systems of Equations 8 SCQF credits (40 hours)
In common with all mathematics courses, this course includes 40 hours over and above the 120 hours for the component units. This may be used for induction, extending the range of learning and teaching approaches, support, consolidation, integration of learning and preparation for external assessment.
Recommended Entry
While entry is at the discretion of the centre, candidates will normally be expected to have attained the following:
- Higher Grade Mathematics at an A
It is advisable that only candidates with a strong interest in mathematics and/or a desire to study the subject further at university should embark on the course. Pupils should display a high level of responsibility for their own learning and should only consider this course if they are well motivated.
Course Content
| Methods in Algebra and Calculus (AH) | Applications of Algebra and Calculus (AH) | Geometry, Proof and Systems of Equations (AH) |
| Partial Fractions | The Binomial Theorem | Systems of Equations |
| Differentiation | Complex Numbers | Matrices |
| Further Differentiation | Sequences and Series | Vectors |
| Integral Calculus | Further Methods of Proof and Number Theory | Further Complex Numbers |
| Further Integration | Differential Calculus and Applications of Differential Calculus | Proof and Elementary Number Theory |
| Differential Equations |
Assessment
Learners following the Advanced Higher Mathematics course will complete the three units and an Added Value Unit. The Added Value Unit takes the form of a written assessment. The assessment paper is externally assessed at Advanced Higher.
Mathematics Higher
Course Structure
This course has three units as follows:
Expressions and Functions (H) 8 SCQF credits (40 hours)
Relationships and Calculus (H) 8 SCQF credits (40 hours)
Applications (H) 8 SCQF credits (40 hours)
In common with all courses, this course includes 40 hours over and above the 120 hours for the component units. This may be used for induction, extending the range of learning and teaching approaches, support, consolidation, integration of learning and preparation for external assessment.
Recommended Entry
While entry is at the discretion of the department, candidates will normally be expected to have attained one of the following:
- National 5 Mathematics, at an A/B
Course Content
| Expressions and Functions (H) | Relationships and Calculus (H) | Applications (H) |
| The Straight Line | Quadratic Theory | Differential Calculus 2 – Applications |
| Algebraic Fractions | Polynomials | Integral Calculus |
| Trigonometry 1 & 2 | Differential Calculus 1 | Lines and Circles |
| Vectors | Trigonometry 3 | Recurrence Relations |
| Logs and Exponential Functions |
Assessment
Learners following the Higher Mathematics course will complete the three units and an Added Value Unit. The Added Value Unit takes the form of a two part written assessment. The assessment papers are externally assessed at Higher.
Mathematics National 4 and 5
National 5 and National 4 Courses aim to help pupils to learn how to describe, tackle and solve problems that require the use of mathematical knowledge and techniques. Pupils are encouraged to see Mathematics as arising out of solving problems, often in the real world, and not just as a collection of knowledge, skills and techniques to be remembered and then applied.
As a rule, all pupils are required to do Mathematics. In S5/6, pupils working towards National 4 and 5 are taught in one class but follow different courses. The choice of course is dependent upon progress and attainment demonstrated in S4.
Course Structure
Each course consists of three units, namely:
| National 4 | Expressions and Formulae | Relationships | Numeracy |
| National 5 | Expressions and Formulae | Relationships | Applications |
Recommended Entry
Learners wishing to study National 5 Mathematics should have a pass at National 4 Mathematics.
Learners wishing to study National 4 Mathematics should have a pass at National 3 Applications of Mathematics.
Assessment
Learners following the National 4 course will complete the three units, which are internally assessed, and an Added Value Unit. The Added Value Unit takes the form of a two part written assessment. The assessment papers are internally assessed at National 4. To achieve the award, learners must pass the three unit assessments and the Added Value Unit.
Learners following the National 5 course will complete the three units and an Added Value Unit. The Added Value Unit takes the form of a two part written assessment. The assessment papers are externally assessed at National 5.
National 4 Applications of Mathematics
The purpose of the National 4 Applications of Mathematics Course is to motivate and challenge learners by enabling them to think through real-life situations involving mathematics and to form a plan of action based on logic.
The Course develops confidence and independence in being able to handle mathematical processes and information in a range of real-life contexts. The Course also enables learners to draw conclusions, assess risk and make informed decisions based on data presented in a variety of forms.
The mathematical skills within this Course are underpinned by numeracy, and are designed to develop learners’ mathematical reasoning skills relevant to learning, life and work in an engaging and enjoyable way.
As a rule, all pupils are required to do Mathematics. In S5/6, pupils working towards National 4 and 5 are taught in one class but follow different courses. The choice of course is dependent upon progress and attainment demonstrated in S4.
Course Structure
Each course consists of three units, namely:
Managing Finance and Statistics (40 hours)
Geometry and Measures (40 hours)
Numeracy (40 hours)
In common with all courses, this course includes 40 hours over and above the 120 hours for the component units. This may be used for induction, extending the range of learning and teaching approaches, support, consolidation, integration of learning and preparation for external assessment.
Recommended Entry
Learners wishing to study National 4 Applications of Mathematics should have a pass at National 3 Applications of Mathematics or equivalent.
It is also worth noting that National 5 Applications of Mathematics is not a prerequisite for Higher Maths. Any pupil wishing to study Higher Mathematics should opt for National 5 Mathematics.
Assessment
Learners following the National 4 Applications of Mathematics course will complete the three units, which are internally assessed, and an Added Value Unit. The Added Value Unit takes the form of a two part written assessment. The assessment papers are internally assessed at National 4. To achieve the award, learners must pass the three unit assessments and the Added Value Unit.
National 5 Applications of Mathematics
The purpose of the National 5 Applications of Mathematics Course is to motivate and challenge learners by enabling them to think through real-life situations involving mathematics and to form a plan of action based on logic.
The Course develops confidence and independence in being able to handle mathematical processes and information in a range of real-life contexts. The Course also enables learners to draw conclusions, assess risk and make informed decisions based on data presented in a variety of forms.
The mathematical skills within this Course are underpinned by numeracy, and are designed to develop learners’ mathematical reasoning skills relevant to learning, life and work in an engaging and enjoyable way.
As a rule, all pupils are required to do Mathematics. In S5/6, pupils working towards National 4 and 5 are taught in one class but follow different courses. The choice of course is dependent upon progress and attainment demonstrated in S4.
Course Structure
Each course consists of three units, namely:
Managing Finance and Statistics 6 SCQF credits (40 hours)
Geometry and Measures 6 SCQF credits (40 hours)
Numeracy 6 SCQF credits (40 hours)
In common with all courses, this course includes 40 hours over and above the 120 hours for the component units. This may be used for induction, extending the range of learning and teaching approaches, support, consolidation, integration of learning and preparation for external assessment.
Recommended Entry
Learners wishing to study National 5 Applications of Mathematics should have a pass at National 4 Applications of Mathematics or National 4 Maths.
It is also worth noting that National 5 Applications of Mathematics is not a prerequisite for Higher Maths. Any pupil wishing to study Higher Mathematics should opt for National 5 Mathematics.
Assessment
Learners following the National 5 Applications of Mathematics course will complete the three units and an Added Value Unit. The Added Value Unit takes the form of a two part written assessment. The assessment papers are externally assessed at National 5.