AL Pure Math
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Why Pure Math exists ?
Content of the syllabus
Public Examination
Consideration for its pre-requisite (before F. 6)
Consideration for its study (during F. 6-7)
Consideration for future planning (after F. 7)
Remark
By Lee Shing Foon
Why Pure Math exists ?
• It is intended as an extended curriculum of
F. 4-5 Additional Maths .
• Let students understand and apply more
mathematical concepts and theorems .
• Let students study and use more calculation
technique .
• Let students have more logical reasoning
and good presentation of their works .
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Content of the syllabus
There are three major study areas :
• Algebra
- consisting of Algebra I , and Algebra II .
• Calculus
- consisting of Function and Limit ,
Differentiation , and Integration .
• Coordinate Geometry
- consisting of polar coordinate geometry ,
2-dimensional coordinate geometry ,
and 3-dimensional coordinate geometry .
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Algebra I
Consisting of the following small topics :
(basically learnt in F.4-5 Add. Maths)
• Mathematical induction
• Binomial Theorem
• Inequality
• Polynomial and its theories
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• Complex Numbers
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Algebra II
Consisting of the following related large
topics : (mainly learnt in F.6-7)
• Matrix
• Determinant
• System of Linear Equations
• Vectors
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Function and Limit
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Function
Limit of a sequence
Limit of a function
Continuity of a function
Differentiability of a function
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Differentiation
• Derivative - definition and calculation
• Application of differentiation :
- Sketching graph
- using L’Hospital Rule to find limit
- Mean Value Theorem
- for function
- for proving inequality
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Integration
• Indefinite Integration
-definition and technique , i.e. substitution
and integration by parts .
• Definite Integration
-reduction formula , improper integration .
• Application of Definite Integration
-finding area , arc length , volume and surface
area of solid of revolution
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-finding limit
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Polar Coordinate Geometry
• its definition e.g. r = a ( 1 + cos x )
• its graph sketching
• finding its area and arc length
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2-D Coordinate Geometry
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Straight line
Pair of straight lines
Circle
Parabola
Ellipse
Hyperbola
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3-D Coordinate Geometry
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Equation of a Straight line
Equation of a Plane
Calculating their distance
Proving they are parallel or skew or
intersecting .
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Content
Public Examination
• There will be two examination papers .
All requires detailed calculating steps and no
multiple choice will be given .
• Paper I
- 3 hours with 100 marks total
- mainly about Algebra
• Paper II
- 3 hours with 100 marks total
- mainly about Calculus and Coordinte
Geometry
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Consideration for its pre-requisite
(before F. 6)
• In the syllabus , there is no pre-requisite for
studying AL Pure Math .
• But , because the major part of AL Pure Math
syllabus is developed from the F.4-5 Add. Math
syllabus , it is advised that students can get a
minimum of D grade in Add. Math in HKCEE ,
a minimum of C grade is much preferred .
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Consideration for its study
(during F. 6-7)
• Students need more (at least as double as)
understanding than studying F.4-5 Add. Maths .
• Students need more (at least as double as)
hardworking than studying F.4-5 Add. Maths .
• Some mathematical technique is very difficult to
handle , both for students and teachers . So ,
don’t be afraid and keep on interesting in doing
Pure Math practices .
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Consideration for future planning
(after F. 7) - p.1
• You can choose not to study AL Pure Math if
you want to study the following in university :
e.g. Medicine , Business Administration ,
Journalism , Social Work , Hotel
management , Architecture , Psychology ,
Finance , Economics , Geography , Physics ,
Chemistry , Biology , Chinese Medicine ,
Accountancy , Translation , Pharmacy ,
Laws .
Consideration for future planning
(after F. 7) - p.2
• You need to study AL Pure Math if you want to
study the following in university :
(For some university subjects , the mathematical
requirement of AL Pure Math can be replaced by
studying Applied Maths or Maths & Statistics .)
e.g. Computer Studies , Environment Science
and Management , Computer Engineering ,
Electronic Engineering , Information
Technology .
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Remark :
• For university subject requirement about AL
Pure Math , please see the prospectus of
different university , or consult career
teachers to know the most updated
information .
• You may ask the following teachers to know
more advice about AL Pure Math :
- Your Math/Add.Math teacher in F.5
- Mr. Fung Wah Sing , Mr. Wong Chun Tat ,
Mr. Li Wang Kin and Mr. Lee Shing Foon . Home