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 METHODS20.1. 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
21.1. Errors
21.2. Linear interpolations
21.3. Roots by iterative methods
21.4. Numerical Integration
