HONG KONG DIPLOMA OF SECONDARY EDUCATION
EXAMINATION
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
Financial Planning
Marking Guidelines
教育局 課程發展處 數學教育組
Mathematics Education Section, Curriculum Development Institute
The Education Bureau of the HKSAR
Assessment Scale
The assessment scale for tasks on Problem-solving is shown in the following table.
Level of
performance
Very good
Good
Fair
Weak
Marks
Mathematical Knowledge and Problem-solving Skills
13 – 16
The student demonstrates a complete understanding of
the underlying mathematical knowledge and
problem-solving skills which are relevant to the task,
and is consistently competent and accurate in applying
them in handling the task. Typically, the student is able
to formulate a correct strategy, carry out the strategy
and demonstrate a complete understanding of the
significance and possible limitations of the results
obtained.
9 – 12
The student demonstrates a substantial understanding
of the underlying mathematical knowledge and
problem-solving skills which are relevant to the task,
and is generally competent and accurate in applying
them in handling the task. Typically, the student is able
to formulate a correct strategy and attempts to carry out
the strategy for completing the task.
5–8
The student demonstrates a basic understanding of the
underlying
mathematical
knowledge
and
problem-solving skills which are relevant to the task,
and is occasionally competent and accurate in applying
them in handling the task. Typically, the student has a
basic understanding of the task and is able to formulate
a correct strategy for solving the task.
1–4
The student demonstrates a limited understanding of
the underlying mathematical knowledge and
problem-solving skills which are relevant to the task,
and is rarely competent and accurate in applying them
in handling the task. Typically, the student has a bare
understanding of the task and can only attempt to
complete the simplest part of the task.
Marks
Mathematical Communication Skills
4
The student communicates ideas in a
clear, well organised and logically true
manner
through
coherent
written/verbal
accounts,
using
appropriate and correct mathematical
presentation to express, interpret and
critically review the results obtained.
3
The student is able to communicate
ideas properly through written/verbal
accounts, using appropriate forms of
mathematical presentation such as
mathematical formulae or geometric
facts.
2
The student is able to communicate
basic ideas with limited success in
using appropriate mathematical terms
and terminology.
1
The student attempts to communicate
ideas using some basic forms of
mathematical presentation such as
symbols, notations, diagrams, tables,
graphs etc., but has little success in
doing so.
‧
The full mark of a SBA task on Problem-solving submitted should be scaled to 20 marks, of which 16 marks are awarded for the
mathematical knowledge and problem-solving skills while 4 marks are awarded for the mathematical communication skills.
‧
Teachers should base on the above assessment scale to design SBA tasks and the marking guidelines for assessing students with
different abilities.
Financial Planning_Marking Guidelines
2
Marking Guidelines
Solution
Part A
1.
(a)
At the end of 1st month, the amount = A(1  r )
(b)
At the end of 2nd month, the amount = A(1  r ) 2  A(1  r )
(c)
At the end of 3rd month, the amount = A(1  r ) 3  A(1  r ) 2  A(1  r )
Performance
Evidence:
The solution
Weak:
Incorrect method and wrong
solution
Fair:
Correct method but wrong
solution
Good:
Correct method with some
parts of the solution being
correct
Very Good: Correct method and solution
At the end of nth month, the amount
2.
 A(1  r )  A(1  r )
n

 A (1  r )  (1  r )
n
n 1
n 1
 A(1  r )
 (1  r )
n2
n2
 ...  A(1  r )  A(1  r )
2
 ...  (1  r ) 2  (1  r )

 (1  r ) n  1 
 A

 (1  r )  1 
(1  r ) n  1
A
r
Evidence:
The proof
Weak:
Attempt to do the proof but
the method is wrong or
irrelevant
Fair:
Attempt to do the proof by
using a relevant method
Good:
Use appropriate method to
do the proof but the proof is
not complete
Very Good: The proof is complete and
clearly presented
Evidence:
The solution
Part B
3.
Let $ x be the monthly saving.
36
 0.05 
1 

12 
200000  x 
0.05
12
x  5,160.85
Weak:
Use irrelevant formula to
calculate the saving amount
Fair:
Use relevant formula, but
substitute the monthly
interest rate wrongly
Good:
Use relevant formula and
make correct substitution,
but calculate the monthly
saving amount wrongly
1
 It is necessary to save $5,160.85 each month to cover the marriage cost.
Very Good: Use relevant formula, make
correct substitution and
calculate the monthly saving
amount correctly
Financial Planning_Marking Guidelines
3
Marking Guidelines
Solution
Performance
First scenario: The inflation rate is 4% per annum.
Evidence:
1. The assumption on the annual
inflation
2. The conclusion (based on the
assumption)
3. The supporting calculation
Let the amount of monthly saving required be $ x .
Weak:
Conclusion given is not
supported by any
assumption or calculation
Fair:
Conclusion matches with
the assumption given
Good:
Conclusion matches with
the assumption given. Some
supporting calculation is
provided
Part C
4.
The acceptance of the offer is highly dependent on the annual inflation rate.
Two relevant scenarios are given below for illustration.
216
 8% 
 8% 
320000(1  0.04)18  x 1 
  x 1 

12 
12 


  8% 216 
 1 
  1
12 

320000(1  0.04)18  x  

8%



12
x  1,350.30
215
 8% 
 ...  x 1 

12 

 The offer from the bank manager is unacceptable.
Second scenario: The inflation rate is 5% per annum.
By similar method, the amount of monthly saving required is $ 1,604.12.
 The offer from the bank manager is acceptable.
Financial Planning_Marking Guidelines
4
Very Good: Conclusion matches with
the assumption given.
Appropriate and thorough
supporting calculation are
provided