Mathematics

Principal Teacher: Mrs Lewis

In addition to standard S1/S2 courses, the department also offers the following courses:

Standard Grade
Intermediate 1/2
Higher
Advanced Higher

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Standard Grade

Levels: Foundation, general and credit

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AIMS
All Standard Grade Mathematics courses
develop important mathematical skills
which will be useful in everyday life.
Pupils will also develop an appreciation
and awareness of the importance of
mathematics in society.   There is a great
emphasis on mental and non-calculator
skills although technology is used whenever
appropriate.


CONTENT
There are two main elements in all Standard Grade Mathematics courses;  Knowledge and Understanding plus Reasoning and Enquiry.  Work in both these elements is set in context whenever possible.

The Knowledge and Understanding element covers the facts, concepts and skills needed to solve mathematical problems.

The Reasoning and Enquiry element involves the application of mathematical knowledge in problem solving situations.   Pupils must decide how to tackle a particular problem and then use relevant mathematical skills to solve the problem and communicate the solution.   Pupils are encouraged to use their initiative and be resourceful, as there are often different ways of approaching a problem

S3 pupils following a Standard Grade Mathematics course will be placed in a Credit/General section, and will be presented for examination at these two levels. 

Pupils who might previously have studied Standard Grade at General/Foundation Levels will instead follow the Access 3 course in S3 and then the Intermediate 1 course in S4.   The Access 3 course is broadly equivalent to the Standard Grade Foundation course, and the Intermediate 1 course is broadly equivalent to the Standard Grade General Course.

General level is mathematically demanding and introduces pupils to topics such as algebra, Pythagoras and trigonometry.  

Credit level is very mathematically demanding and covers many complex topics in detail.   There is a great emphasis on algebra and on both practical and abstract mathematical thinking.   A pass at Credit level is the recommended entry requirement for a one year Higher Mathematics course in S5.


ASSESSMENT

Pupils will sit an external examination in May of S4. The examination for each level consists of two papers, the first of which is non-calculator.

Intermediate 1/2

Entry requirements: See description below

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ENTRY REQUIREMENTS:

Intermediate1:
Standard Grade Mathematics at grade 3 or 4

Intermediate 2:
Standard Grade Mathematics at grade 5 or 6,
OR a pass in Access 3 Mathematics.


COURSE CONTENT

Students must complete the following two compulsory units.

Mathematics 1:

Basic Calculations; Basic Geometry; Formulae; Calculations in Context.

Mathematics 2:

Graphs, Charts and Tables; Speed, Distance and Time; Pythagoras' Theorem; Integers; Statistics.

In addition, students must complete one additional unit from the two below.

Either
Mathematics 3:Basic Algebra; Graphical Relationships; Basic Trigonometry;
Standard Form.
or
Applications:Calculations in a Social Context; Logic Diagrams; Scale Drawing; Nets; Statistical Assignment.

It is anticipated that the units Mathematics 1, 2 and 3 will be offered in one column of the option choice form and the units Mathematics 1, 2 and Applications in another.   It must be emphasised that in order to progress to follow the Intermediate 2 course in S6, students must complete the units Mathematics 1, 2 and 3 in S5.

ASSESSMENT

Students must pass an internal assessment at the end of each unit. These assessments test minimum competence and students are allowed one re-sit for each assessment. In order to receive an overall course award, students must pass all three unit assessments, although the marks of these assessments are not taken into account in determining the overall course award.

There will be an external examination at the end of the course. The overall course award is based solely on performance in this examination, and each student who passes this examination is awarded a grade A, B or C.

ADDITIONAL INFORMATION
The emphasis is on direct teaching of concepts, facts and skills. Students are expected to assume responsibility for managing their progress. Homework will be issued on a regular basis and study support will be available. Students who are awarded a pass in the Intermediate 1 external examination in the Units Mathematics 1, 2 and 3 may then progress to follow the Intermediate 2 course.

Higher

Entry requirements: See description below

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ENTRY REQUIREMENTS: Standard Grade Mathematics at grade 1 or 2,
OR a pass in Intermediate 2 Mathematics in units Mathematics 1, 2 and 3.


COURSE CONTENT

Students must complete the following two compulsory units.

Mathematics 1:
Straight Line; Functions and Graphs; Basic Differentiation; Recurrence Relations.

Mathematics 2:
Polynomials and Quadratic Theory; Basic Integration; Trigonometric Formulae and Equations; The Circle.

Mathematics 3:
Vectors; Further Differentiation and Integration; Logarithmic and Exponential Functions; Wave Functions.

ASSESSMENT

Students must pass an internal assessment at the end of each unit. These assessments test minimum competence and students are allowed one re-sit for each assessment. In order to receive an overall course award, students must pass all three unit assessments, although the marks of these assessments are not taken into account in determining the overall course award.

There will be an external examination at the end of the course. The overall course award is based solely on performance in this examination, and each student who passes this examination is awarded a grade A, B or C.

ADDITIONAL INFORMATION

The emphasis is on direct teaching of concepts, facts and skills. Students are expected to assume responsibility for managing their progress. Homework will be issued on a regular basis and study support will be available. Students who are awarded a pass in the external examination at Higher may then progress to follow the Advanced Higher course.

Advanced Higher

Entry requirements: See description below

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ENTRY REQUIREMENTS: A pass in Higher  Mathematics  at grade  A, B or C

COURSE CONTENT:

Students must complete the following three compulsory units :

Mathematics 1 :Algebraic Skills; Differentiation; Integration; Functions; Systems of Linear Equations.

Mathematics 2 :Further Differentiation; Further Integration; Complex Numbers; Sequences and Series; Number Theory and Proof.

Mathematics 3:Vectors in 3-D; Matrices; Further Sequences and Series; Ordinary Differential Equations; Further Number Theory and Proof.

ASSESSMENT:

Students must pass an internal assessment at the end of each unit.   These assessments test
minimum competence and students are allowed one resit for each assessment.   In order to
receive a overall course award, students must pass all three unit assessments, although the marks of
these assessments are not take into account in determining the overall course award.

There will be an external examination at the end of the course.   The overall course award is based
solely on performance in this examination and each student who passes this examination is awarded
a grade A, B or C.

ADDITIONAL  INFORMATION:

The emphasis is on direct teaching of concepts, facts and skills.   Students may be able to use the Scholar interactive computer package in association with Heriot Watt University.   Students are expected to assume responsibility for managing their progress.   Homework will be issued on a regular basis and study support will be available.   Students who are awarded a good pass in the external examination may receive exemption from parts of the first year of some university and college courses.