Other Pages: Lower 6th Mathematics; Text Book Pages; Replies to Requests
MATHEMATICS (9164)
GCE ADVANCED LEVEL
Introduction
In developing the scheme, attention was paid to the
following considerations:
(i)
|
the need to produce a Mathematics syllabus which provides
continuity from O-Level or ZGCE, through to the tertiary education;
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(ii)
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the desire to produce examination papers which will enable
candidates to demonstrate positive evidence of their attainment, and which at
the same time will eliminate any adverse effects of question choice;
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(iii)
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the desire to preserve those topics from the Mathematics
syllabus (9202) which have proved to be of value and which are likely in the
future to be of value;
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(iv)
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the desire to allow centres to choose from three different
routes to 'A' Level Mathematics, depending on the choice of Pure Mathematics
and/or Mechanics or Statistics or both in the broad area of 'applications';
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(v)
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the desire to expose all candidates to some application in
both fields, Mechanics and Statistics.
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Syllabus Aims
The syllabus is intended to provide a framework for 'A'
Level courses that will enable students to:
(a)
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develop further the understanding of mathematical concepts
and processes in a way that encourages confidence and enjoyment;
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(b)
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develop a positive attitude to learning and applying
mathematics;
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(c)
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acquire and become familiar with appropriate mathematical
skills and techniques;
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(d)
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appreciate mathematics as a logical and coherent subject;
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(e)
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develop their ability to' think clearly, work carefully
and communicate mathematical ideas successfully;
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(f)
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develop their ability to formulate problems
mathematically, interpret a mathematical solution in the context of the
original problem, and understand the limitations of mathematical models;
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(g)
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appreciate how mathematical ideas can be applied in the
everyday world;
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(h)
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acquire a suitable foundation for the study of mathematics
and related disciplines.
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Assessment Objectives
The assessment will test candidates' abilities to:
(a)
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recall, select and use their knowledge of appropriate
mathematical facts, concepts and techniques in variety of context;
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(b)
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construct rigorous mathematical arguments through
appropriate use of precise statements, logical deduction and inference and by
the manipulation of mathematical expressions;
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(c)
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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.
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It is expected that Assessment Objectives (a) and (b) will
apply to all components and that Assessment Objective (c) will apply mainly to
Papers 2,3 and 4 of mathematics.
In addition to the above Objectives, other objectives of
more specialised relevance are listed at the start of the appropriate sections
in the list of curriculum objectives.
Scheme of Assessment
All papers will contain questions of various lengths with no
restriction on the number of questions which may be attempted. On each paper,
the total of the question marks will be 120. The length of each paper will be
such that most able candidates may complete the paper and the structure of each
paper will be such that less able candidates will be able to demonstrate
positive achievement. Questions in each section will appear in ascending order
of their mark allocations and candidates are advised to attempt them
sequentially. Candidates should be aware that credit for later parts of a
question may generally be available even when earlier parts have not been
completed successfully.
The examination will consist of two, equally weighted,
three-hour papers. Candidates will take Paper 1 and one of Papers 2, 3, 4.
Paper 1 and 2
80% of the marks available in the examination will be
allocated to questions on Pure Mathematics;
20% of the marks available in the examination will be
allocated to questions on Applications.
Paper 1 and 3 or paper 1 and 4
50% of the marks available in the examination will be
allocated to questions on Pure Mathematics;
50% of the marks available in the examination will be
allocated to questions on Applications.
PAPER
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TOPICS
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WEIGHT
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MARKS
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DURATION
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Paper 1
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Pure Mathematics
1-17
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100%
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120
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3 hours
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Paper 2
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Pure Mathematics
1 -21
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60% (72)
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120
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3 hours
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Mechanics 1-4
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20% (24)
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||||
Statistics 1-5
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20% (24)
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||||
Paper 3
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Statistics 1-5
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20% (24)
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120
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3 hours
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Mechanics 1 -12
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80% (96)
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||||
Paper 4
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Statistics 1 - 11
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80% (96)
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120
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3 hours
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Mechanics 1 -4
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20% (24)
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Paper 1
Pure Mathematics
- a paper containing about 17 questions set on topics 1 -17
of the Pure Mathematics list (120 marks),
and one of the following three papers:
Paper 2
Pure Mathematics, Mechanics and Statistics
- a paper containing-about 8 questions set on topics 1 - 21
of the Pure Mathematics list (72 marks)
-about 4 questions (which will also be common to Paper 3 &
4) set on topics 1 - 4 of the Mechanics list (24 marks)
and about 4 questions (which will also be common to Paper 3 &
4) set on topics 1 - 5 of the Statistics list (24 marks)
Paper 3
Mechanics and Statistics
- a paper containing about 12 questions set on topics 1 - 12
of the Mechanics list (96 marks)
and about 4 questions set on topics 1 - 5 of the Statistics
list (24 marks)
Paper 4
Statistics and Mechanics - a paper containing about 12
questions set on topics 1 - 11 of the Statistics list (96 marks)
and about 4 questions set on topics 1 - 4 of the Mechanics list
(24 marks)
SPECIFICATION GRID
PM = Pure Mathematics
M = Mechanics
S = Statistics
Component
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Paper 1
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Paper 2
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Paper 3
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Paper 4
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Skills
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||||
Skill 1
Knowledge Comprehension
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PM=50%
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PM = 18%
M = 6%
S = 6%
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M =24%
S = 6%
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S =24%
M = 6%
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50%
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30%
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30%
|
30%
|
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Skill 2
Application Analysis
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PM = 40%
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PM = 33%
M = 11%
S = 11%
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M = 44%
S = 11%
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S = 44%
M = 11%
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40%
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55%
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55%
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55%
|
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Skill 3
Synthesis Evaluation
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PM = 10%
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PM = 9%
M= 3%
S = 3%
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M = 12%
S = 3%
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S = 12%
M = 3%
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10%
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15%
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15%
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15%
|
|
TOTAL
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100%
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100%
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100%
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100%
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Summary of Content for each paper (Detailed lists appear further below.)
Paper 1 Pure Mathematics 3 hours (120 marks)
1
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Indices and proportionality
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2
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Polynomials
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3
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Identities, equations and inequalities
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4
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The modulus function
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5
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Graphs and coordinate geometry in two dimensions
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6
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Vectors (I)
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7
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Functions
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8
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Sequences and series
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9
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Series expansions
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10
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Plane trigonometry
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11
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Trigonometrical functions
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12
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Logarithmic and exponential functions
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13
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Differentiation
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14
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Integration
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15
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First order differential equations
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16
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Numerical methods
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17
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Complex Numbers (I)
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18
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Complex numbers (II)
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19
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Vectors (II)
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20
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Mathematical Induction
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21
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Matrices
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Paper 2 Pure Mathematics, Mechanics and Statistics
3 hours (120 marks)
Pure Mathematics 72 marks
1 - 21 As Paper 1 above
Mechanics 24 marks
1 Forces
and equilibrium
2 Kinematics
of motion in a straight line
3 Newton's
laws of motion
4 Motion
of a projectile
Statistics 24 marks
1 Representation
of data
2 Probability
3 Discrete
random variables
4 Continuous
distributions
5 The
Normal distribution
Paper 3 Mechanics and Statistics 3hours (120 marks)
Mechanics 96 marks
1 Forces
and equilibrium
2 Kinematics
of motion in a straight line
3 Newton's
laws of motion
4 Motion
of a projectile
5 Momentum
6 Equilibrium
of a rigid body under coplanar forces
7 Centre
of mass
8 Hooke's
law
9 Energy,
work and power
10 Uniform
motion in a horizontal circle
11 Linear
motion under a variable force
12 Simple
harmonic motion
Statistics 24 marks
Topics 1 - 5 as paper 2
Paper 4 Statistics and Mechanics 3 hours (120 marks)
Statistics 96 marks
1 Representation
of data
2 Probability
3 Discrete
random variables
4 Continuous
distributions
5 The Normal
distribution
6 Linear
combinations of random variables
7 Samples
8 Statistical
inference
9 c2 tests
10 Bivariate
data (Regression and correlation)
11 The
Poisson distribution
Mechanics 24 marks
Topics 1 - 4 as Paper 2
CURRICULUM OBJECTIVES
The following pages contain detailed lists of curriculum
objectives for each of the three broad areas:
Pure
Mathematics; Mechanics; Statistics.
It should be noted that individual questions may involve
ideas from more than one section of the following list and that topics may be
tested. in the context of solving problems and in the application of
Mathematics. In particular, candidates will be expected to develop
understanding of the process of mathematical modelling through the study of one
or more application areas.
The following skills will be needed:
Abstraction from a real world situation to a mathematical
description. The selection and use of a simple mathematical model to describe a
real world situation.
Approximation, simplification and solution.
Interpretation and communication of mathematical results and
their implications in real world.
Progressive refinement of mathematical models.
Pure Mathematics List
Mechanics List
(Coming soon)
Statistics List
(Coming soon)
(Coming soon)
Statistics List
(Coming soon)