The following is a summary of the syllabuses over the last thirty years:

Pre 1970

Five papers - 3 hours; 8 questions from normally10

Mathematics - papers 1, 2 and 4

Pure Mathematics - papers 1, 2 and 3

Applied Mathematics - papers 4 and 5

No Statistics. Vectors only in paper 5. Complex numbers only in paper 3

1970-71

Mathematics - two 3 hour papers; 8 questions from 10.

Further Mathematics - two 3 hour papers; 8 questions from 11

All papers had both Pure and Mechanics. Vectors and complex numbers in ordinary Mathematics.

1972-78

Syllabus A

Mathematics – two 3 hour papers; 8 questions from 10

Further Mathematics – two 3 hour papers; 8 questions from 11

Co-ordinate geometry of circle and parabola in Mathematics. Hyperbola and ellipse in Further Mathematics. Reduction formulae and polar co-ordinates in Further Mathematics.

Syllabus B

Mathematics – two 3 hour papers; paper 1 - 18 from 23, paper 2 – 8 from 10

Further Mathematics – two 3 hour papers; 8 questions from 11

Matrices, groups, functions, binary relations, probability, statistics and normal probability in Mathematics. Boolean Algebra, groups, vector product and geometry, flow diagrams, numerical analysis, system of particles and AC circuit theory in Further Mathematics. No exponential and logarithmic series in Mathematics and very little co-ordinate geometry in either. No reduction formula and polar co-ordinates.

Calculators allowed in 1978 for Mathematics and in 1979 for Further Mathematics

1979-82

Syllabus A as before

Syllabus B

Mathematics split into sections A, B(mechanics) and C(statistics). Candidates could answer from either sections A and B or sections A and C. Section A had some mechanics and probability. The Statistics contained: least squares linear fit, discrete and continuous distributions, Binomial and Normal distributions, Central Limit Theorem.

Further Mathematics became more traditional – less Modern Maths; reintroduction of arc length of a curve and surface area of a volume of revolution, algebraic series, limits, reduction formulae and co-ordinate geometry.

1983-89

In 1985 the syllabus incorporated the 1983 Common Core which consisted of a list of topics. Examination Boards agreed that questions set directly on the core will carry not less than 40% of the total marks.

Syllabus A and B combined.

Mathematics – two 3 hour papers - paper 1 – 16 questions from 18 in section A and 4 in sections B or C; paper 2 – 8 questions from 10 in section A and 2 in sections B or C.

Vectors (up to equn. of line); permutations and combinations; exponential and logarithmic series; complex numbers (up to complex arithmetic and simple loci); co-ordinate geometry (circle and parabola). Functions but no ‘Modern Maths’.

Further Mathematics – 8 questions from 11.

Vectors (vector product and geometry); complex numbers (up to De Moivre’s); theorem); co-ordinate geometry (ellipse and hyperbola); groups; numerical analysis; arc length and surface area by calculus; free motion of a rigid body.

1990-96

The syllabus required a ‘Modelling’ emphasis in the applied papers.

Paper 1 A1 3 hours Pure 10 short and 4 from 5 long qus.

Paper 2 A2 3 hours Further Pure 8 from 10 questions

Paper 3 B1 1½ hours Mechanics 4 short and 2 from 3 long qus.

Paper 4 B2 1½ hours Further Mech. 4 short and 2 from 3 long qus

Paper 5 C1 1½ hours Statistics 4 short and 2 from 3 long qus

Paper 6 C2 1½ hours Further Stat. 4 short and 2 from 3 long qus

AS Mathematics – paper 1

Applied Mathematics – papers 1, 3 and 5

Pure Mathematics and Mechanics – papers 1, 3 and 4

Further Mathematics – papers 2, 4 and 6

Circle and parabola moved to Further Mathematics; No arc length and surface area by calculus; only Binomial theorem in Mathematics; all traditional ‘Further Mechanics’ removed (eg. oblique impact, potential energy test for stability, vertical circular motion and rotational mechanics of a rigid body). Statistics contains simple hypothesis testing in paper 5 and t- test, c ² goodness of fit and 22 contingency tables, correlation and regression in paper 6.

1996-2001

The new 1995 Common Core not only specified topics which were to comprise 50% of the A level content but also assessment objectives. In particular Assessment Objectives:

1. recall, select and use their knowledge of appropriate mathematical facts, concepts and techniques in a variety of contexts;
2. construct rigorous mathematical arguments through appropriate use of precise statements, logical deduction and inference and by the manipulation of mathematical expressions; and
3. evaluate mathematical models, including an appreciation of the assumptions made, and interpret, justify and present the results from a mathematical analysis in a form relevant to the original problem;

Four from ten modules (1½ hours, all questions compulsory) – modules can be retaken as often as candidate wishes in February or June. A Level should assume no more than a grade C at GCSE as entry level of competence.

Modules A1, A2, P1, P2

Mechanics M1, M2, M3, M4

Statistics S1, S2

AS Mathematics – A1, M1 or A1, S1

Mathematics – A1, A2, M1, M2 or A1, A2, M1, S1 or A1, A2, S1, S2

Further Mathematics – P1, P2 and two more from M1, M2, M3, M4, S1, S2 (if not already studied)

Vectors and complex numbers moved to Further Mathematics. Only positive index Binomial theorem in Mathematics. Relative velocity, SHM, centre of mass by calculus and coefficient of restitution moved to M3. Rigid body motion, vertical circular motion, light pin-jointed frameworks, damped oscillations reintroduced in M4.

The influence of hand held computer algebra systems and graphing calculators.

A selection of questions from the 1999 A2 mathematics syllabus are worked using a TI-89 calculator to illustrate the fact that examination questions will have to change.
 
 

Based on a talk given in Belfast Royal Academy to the Irish branch of the IMA, 21st April 1999.