Mathematics

Our aim as a department is to provide our pupils with a soundly based mathematical education in which high academic standards are emphasised so that pupils can achieve their potential.  

We try our best to prepare the pupils for the outside world so that they can use Mathematics confidently in real situations and in their studies at university and beyond.

Extra-curricular

Maths Challenges and Olympiads

Every year we enter a large number of pupils for the Senior and Intermediate Maths challenges.  Those who do well then go on to compete in the British Mathematical Olympiad or the Intermediate Olympiad.  The whole of second form is entered for the Junior Maths challenge.

The Glenalmond Mathematical Society

The Mathematical Society is aimed at our gifted and talented mathematicians in forms 3-5.  We meet once a week and look at problems well beyond the GCSE course including numerous Senior Maths Challenge problems.

Head of Department - Mr Gareth O'Neill

Mr Gareth O'Neill, BSc, PGCE 
Mr Martin Orviss, MA, MMath, PGCE
Mr Mike Jeffers, BSc, PGCE 
Mrs Sarah Sinclair, BSc, PGCE 
Mr Patrick Erdal, BSc, PGCE, DipAcc 
Mrs Sylvia Smith, BSc, PGCE
Miss Rachel Mullan, BSC, PGCE (Numeracy Coordinator)

Second Form

A number of pupils enter the school aged 12 and the aim is to cover topics similar to pupils who will be studying for Common Entrance. They are taught together in a mixed ability group with differentiated content. We put an emphasis on gaining a solid foundation in numerical and algebraic skills with investigations and puzzles to make mathematics interesting and fun. Extension work is provided for gifted mathematicians and extra support is available for those who find mathematics difficult.

Third Form

All pupils begin the GCSE syllabus in Third Form, which provides continuity and plenty of time to prepare thoroughly for obtaining a good grade in GCSE Mathematics by the time they sit the examination in Fifth Form. The Third Form year is spent making sure that the Foundation level GCSE topics are securely understood and that the pupil's algebra is well enough developed to cope with the algebraic content in higher tier GCSE in Fourth and Fifth Forms.

All pupils will study the new Edexcel Linear A GCSE 1MA1 course and will be entered for the Higher Tier which awards grades 9-1.  The new GCSE Mathematics has three written papers and will be sat at the end of the Fifth Form by most pupils. One paper is non-calculator and two papers are calculator and there is no coursework.  Set 1 follow an accelerated programme and finish the GCSE course in Fourth Form.  In Fifth Form they then study the CCEA GCSE Further Mathematics Course.  They sit two examinations in this at the end of Fifth Form, both of which are two hours long.  This course covers Pure Maths, Mechanics and Statistics and is excellent preparation for A Level Mathematics and Further Mathematics.

Each year group is divided into five sets who are keen to achieve the best results according to their abilities. There are regular topic tests and pupil progress is carefully tracked. Pupils are encouraged to employ Assessment for Learning techniques in all their studies and teachers encourage an active learning approach. Prep is set regularly to reinforce concepts and give more opportunity for practicing mathematical skills. Pupils have access to an online Mathematics tutorial site called Mymaths.

Independent thinking skills are promoted by the use of puzzles, quizzes and extension problems which are available for all classes. In addition pupils in the Third, Fourth and Fifth Forms are entered for the Intermediate and Senior Mathematics Challenges.

Mathematics is a popular A Level subject with almost half of Lower Sixth currently studying Mathematics and three classes continuing to Upper Sixth. In addition, Further Mathematics classes run every year and its popularity is increasing year on year.  We teach the new specification offered by Edexcel as it allows some flexibility in the topics we can offer.

 

Course Description

The new A Level Mathematics specification has a compulsory content which is studied by all pupils. It is approximately two thirds Pure Mathematics based and one third applied.

The Pure Mathematics sections cover topics such as

Algebra and Functions The Binomial Expansion
Quadratic Functions Algebraic Fractions
Equations and Inequalities Partial Fractions
Sketching Curves  Exponential and Logarithm functions 
Coordinate Geometry   Numerical Methods
Sequences and Series Transforming graphs of functions
Differentiation Differentiating functions formed by combining
Integration  Trigonometrical, exponential, logarithmic and polynomial functions
Trigonometry Vectors
Radian Measure  

                                        

The applied papers cover topics such as                                                                                               

Statistics Mechanics 
Background Statistics  Modelling
Mathematical Models   Kinematics   
Representing and analysing data Vectors
Probability   Forces  
Correlation  Newton’s Laws
Regression Impulse and Momentum
Discrete Random Variables   Moments
The Normal Distribution  

 

Further Mathematics

In Lower Sixth the Further Mathematics class complete all of the topics above and also extend into some Further Pure Mathematics

Further Pure 1                                                      

Solving polynomial equations   Tangents and Normals        
Complex Numbers    Matrices
Numerical solution of equations Summation of finite series
The parabola Proof by induction
Cartesian and parametric equations    

                                       

In Upper Sixth, Further Mathematicians then study more Further Pure topics which are a compulsory part of the course. We then teach a wide variety of Applied Mathematics topics which can be chosen from Mechanics, Statistics and Decision Mathematics.  This allows pupils to choose topics they have more of an interest in and that are likely to be more beneficial for their degree course.

 

Assessment Methods

The new A Level Mathematics course is assessed at the end of the two years by three 2 hour papers.  Paper 1 and Paper 2 are Pure Mathematics and Paper 3 is half Mechanics and half Statistics.  Calculators are allowed in all papers.

Further Mathematics is assessed at the end of the two year course by four 1.5 hours papers.  Paper 1 and Paper 2 are Further Pure Mathematics papers.  Papers 3 and 4 can be chosen by pupils from a list of Mechanics, Statistics, Decision Mathematics or another Further Pure paper.

 

Recommended Entry Requirements

A grade 9,8 or high 7 at GCSE Mathematics following a linear route is essential preparation for A Level Mathematics with emphasis on good algebraic skills. Equal success in other Scottish or International examinations of equivalent level is also a good entry qualification. A 9 at GCSE is essential for A Level Further Mathematics and in addition pupils must be able to demonstrate that they have studied topics well above and beyond the level required at GCSE.  There will also be some holiday work to complete in the last few weeks before starting the Sixth Form to make sure pupils have the necessary algebraic skills to successfully start Sixth Form studies.

 

Subject combinations

Mathematics combines well with a wide variety of other subject but in particular Physics, Chemistry, Biology, Economics, Business Studies, Design and Technology, Art and Geography.

 

Careers and Higher Education

A Level Mathematics is a challenging course which suits those thinking of studying Mathematics, Engineering, Physics, Economics, Business, Finance, Statistics, Accountancy, Architecture or Computer Science at University.  It is also a desirable qualification for those wishing to study Medicine, Veterinary, Dentistry, Biochemistry, Psychology, PPE and many more.

 

STEP mathematics and scholarship mathematics

Those interested in Oxbridge entry are encouraged to explore wider topics in the world of mathematics beyond A Level by extensive further reading which should start in Lower Sixth. Extra tutorials are run to help pupils prepare for STEP papers which are the examinations often demanded by Cambridge University, Bath and Warwick.  We also enter a number of our more able mathematicians for the British Mathematical Olympiad.

Purpose of the Course

The purpose of this course is to develop the learner’s understanding of Algebra, Trigonometry, Geometry and Calculus.  There is an emphasis on mathematical reasoning and modelling and how these branches of Mathematics can be used in the world around us.

 

SQA Higher Assessment Structure

SQA Higher Mathematics is assessed by two terminal examinations.  Paper 1 is 1hr 10mins, non-calculator and worth 60 marks.  Paper 2 is 1hr 30mins, calculator and worth 70 marks.

 

Breakdown of the Course

Algebra and Trigonometry:  Manipulating algebraic and trigonometric expressions including the use of factorising and completing the square. Composite, inverse and transformations of functions.  Logarithms.  Solving logarithmic and trigonometric equations.

Algebraic and Geometric Skills: Vectors and scalar products, equations of straight lines and Circles  and other straight line and circle properties.  Sequences and recurrence relationships.

Calculus:  Differentiation and Integration of simple polynomials, trigonometric and log functions including differentiation by the Chain, Product and Quotient rules.  Maximum and Minimum values of a function.  Finding areas by Integration.  Solving differential equations.

 

Comparison with A Level Mathematics

The new A Level course is assessed by 3 terminal papers all two hours long and worth 100 marks.  Two of the papers are Pure Mathematics and have similar topics to that in the Higher Course mentioned above but there a few more topics in the A Level course and they are covered in greater depth.  The third paper at A Level covers Mechanics and Statistics which is not part of the Higher Course. 

The Higher Course is close in content and level of difficulty to that of the modules C1,C2 and C3 under the current A Level Mathematics specification which finishes next year.