FORM 5
Objectives of Teaching Advanced
Mathematics
The main objectives of teaching Advanced Mathematics in
secondary schools are to help and enable students:
(a) To acquire appropriate and desirable mathematical skills and
techniques,
(b) To develop foundation and mathematical knowledge, techniques
and skills and capabilities for studying mathematics and other related subjects
in higher education.
(c) To apply mathematical concepts, arguments and skills in
problem solving;
(d) To solve mathematical problems;
(e) To acquire mathematical knowledge and skills necessary for
concurrent studies in other subjects;
(f) To think and work with accuracy and conciseness.
Content Selection and Organization
The content included in this syllabus is a continuation of the
content covered at ordinary level. The topics, sub-topics objectives,
teaching/ learning strategies and teaching aids in the syllabus have been
carefully selected and organized to match the student's level of understanding
in mathematics. Some of the topics included in the syllabus have been
approached and arranged spirally with simpler concepts in the first year.
Teachers are advised to follow the suggested sequence of topics in the
syllabus.
Methods of Teaching and Learning
Mathematics
The teacher is advised to use various methods of teaching
according to the nature of the topic with an aim of achieving the laid down
objectives. The methods of teaching that are commonly used are discussions,
group work, lecture, enquiry and discovery.
Students should be encouraged to participate actively in
discussions, questioning and answering questions, making case studies and
visiting areas relevant to mathematics lessons. The pupils can also achieve
more from lessons which allow them to make observations and analysis of
mathematically oriented problems.
Assessment of Student Progress and
Performance
When assessing pupil's performance, the teacher is advised to use
continuous assessment. It is expected that every mathematics teacher will periodically
assess students in order to identify their strengths and weaknesses. In this
way it will be possible to help the weak and encourage the strong ones.
The students should be given homework and tests regularly.
These assignments help to indicate and check attainment levels of the students.
Also the students’ exercise books should always be marked and necessary
corrections made before the teacher and students can proceed to other topics or
sub-topics. At the end of Form VI, the students will be expected to do the
national examination in advanced mathematics. The continous assessment, class
tests as well as the final terminal examinations will help to determine the
effectiveness of content, materials, teacher's methods as well as the extent to
which the objectives of teaching mathematics have been achieved.
InstructionaI Time
The number of periods per week allocated for teaching
mathematics is as specified by the Ministry of Education and Culture. According
to the length of content of this syllabus, 10 periods per week are recommended.
The teacher is advised to make maximum use of the allocated time. Lost
instructional time should be compensated through the teacher's own arrangement
with the head of mathematics department or head of school.
TOPICS
2.1. Basic operations of
sets
2.2. Simplification of set
expressions
2.3. Number of members of
a set
3.1. Statement
3.2. Logical connectives
3.3. Laws of algebra of
propositions
3.4. Validity of arguments
3.5. Electrical Networks
4.1. Rectangular Cartesian
Coordinates
4.2. Ratio theorem
4.3. Circles
4.4. Transformations
5.1. Graph of functions
5.2. Inverse of a function
5.3. Inverse
function
6.1. Indices and
logarithms
6.2. Arithmetic
progression
6.3. Geometric Progression
6.4. Other types of series
6.5. Proof by
mathematical Induction
7.1. Trigonometrical
ratios
7.2. Pythagoras theorem
in trigonometry
7.3. Compound angle
formulae
7.4. Double angle formulae
7.5. Form of a cosØ + bsinØ = c
7.6. Factor formulae
7.7. Sine, and Cosine
rules
7.8. Radians and small
angles
7.9. Trigonometrical
Function
7.10.Inverse trigonometrical functions
8.1. Root of a Polynomial
function
8.2. Remainder and Factor
Theorem
8.3. Inequalities
8.4. Matrices
8.5. Binomial
theorem
8.6. Partial fractions
10.1. The Derivative
10.2. Differentiation of a
function
10.3. Applications of
differentiation
10.4. Taylor’s theorem and
maclaurin’s theorem
11.INTEGRATION
11.1. Inverse of
Differentiation
11.2. Integration of a
function
11.3. Application of
integration
12. COORDINATE GEOMETRY II
12.1. Conic section
12.2. The parabola
12.3. The ellipse
12.4. The hyperbola
12.5. Polar coordinates
13. VECTORS
13.1. Vector representation
13.2. Dot product
13.3. Cross (vector)
product
13.4. Equation of a
straight line
13.5. Equation of a
plane
13.6. Scalar triple product
14. HYPERBOLIC FUNCTION
14.1. Hyperbolic cosine and
sine functions
14.2. Derivative of
Hyperbolic function
14.3. Integration of
hyperbolic functions
15. STATISTICS
15.1. Scope and limitations
15.2. Frequency
distribution tables
15.3. Measures of central
tendency
15.4. Measures of
dispersion
16. PROBABILITY
16.1. Fundamental principle
of counting
16.2. Permutations
16.3. Combinations
16.4. Sample spaces
16.5. Probability
axioms and theorems
16.6. Conditional
probability
17. STATISTICS II
17.1. Probability
density functions
18. COMPLEX NUMBERS
18.1. Complex numbers and
their operations 18.2. Polar form of a
Complex number
18.3. De moivre’s theorem
18.4. Euler’s formula
19. DIFFERENTIAL EQUATIONS
19.1. Differential Equations
19.2. Solutions to Ordinary
differential equations 19.3. First order
differential equations
19.4. Second order
homogeneous differential equations
20. VECTORIAL MECHANISM
20.1. Vector
differentiation
20.2. Relative motion
20.3. Motion in a straight
line.
20.4. Projectile motion on
non-inclined plane 20.5. Newton’s laws of
motion
20.6. Power Energy and
momentum
21. NUMERICAL METHODS
21.1. Errors
21.2. Linear interpolations
21.3. Roots by iterative
methods
21.4. Numerical Integration