HONG KONG DIPLOMA OF SECONDARY EDUCATION
EXAMINATION
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
Swimming Pool
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 for assessing students with different abilities and to
develop the marking guidelines.
Swimming Pool Marking Guidelines (E)
2
Marking Guidelines
Solution
Performance
Part A
1.
Volume of the swimming pool = 50  25 1.3  1625 m3
2.
The total surface area of the swimming pool
Evidence:
The solutions
  50  25   1.3  2  50  25
 1445 m 2
Weak:
Incorrect working and answers
Fair:
Correct working, but all
answers are incorrect
Good:
Correct working with only 1
correct answer
Very good: Correct working and answers
for both parts
Part B
1.
50 m
A
D
5m
T
N
1m
E
6m
H
2.
Weak:
Incorrect
answers
Fair:
Some working and answers
are correct
Construct a right-angled triangle MTN where MT // HA and TN // AD .
Then, MT = 6  1 = 5 m and TN = 50  5  5 = 40 m.
MN 2  MT 2  NT 2 (Pythagoras’ Theorem)
Good:
The working and answers
are correct, but part of the
explanation is not clear
MN  52  402  5 65 m
Very good: The working and answers
are correct. Valid and clear
explanation is also given
5m
M
The bottom surface area of the original swimming pool
 50  25
 1250 m2
3.
Evidence:
1. The solutions
2. The explanation
More tiles are required to cover the bottom of the renovated swimming pool.
The bottom surface area of the renovated swimming pool
  5  5 65  5  25
 125  2  65  m2  1250 m2
As the bottom surface area of the renovated swimming pool is larger than that of the
original pool, more tiles are required to cover the bottom of the renovated swimming
pool.
Swimming Pool Marking Guidelines (E)
3
working
and
Marking Guidelines
Solution
Performance
Part C
1.
Evidence:
1. The solutions
2. The explanation
3. The suggested path
The equation of the path is
y  5 x 2  6 x  1
6 

 5  x 2  x   1
5 

2

3
9
 5   x      1
5  25 

Weak:
Incorrect
answers
Fair:
The working and answers
are correct
Good:
The working and answers
are correct. Valid
explanation is also given
2
3  14

 5  x   
5
5

Hence, the maximum height that Tony can attain is
2.
14
m.
5
0  5 x 2  6 x  1
0  5x2  6 x  1
2
6   6   4  5   1
2 5
x
3  14
5
3  14
5
3  14
(rejected for x > 0)
5
3  14
Hence, AQ =
m.
5
x
3.
or x 
From Question 2, AQ = 3  14 m < 1.5 m. Therefore, Tony’s path is not safe.
5
There are many possible safe diving paths.
The equation of one of the safe paths is y  5x 2  8 x  1 .
Verification:
When y = 0,
0  5 x 2  8 x  1
0  5x 2  8 x  1
x
8  ( 8) 2  4(5)( 1)
2(5)
4  21
5
4  21 or
4  21 (rejected for x > 0)
x
x
5
5
x
Swimming Pool Marking Guidelines (E)
and
Very good: Correct
working
and
answers,
and
valid
explanation are given.
Feasible diving path is also
provided
For the equation of the path is y  5 x2  6 x  1 ,
put y = 0, then
x
working
4
Marking Guidelines
Solution
Performance
The distance between A and the point that Tony reaches the surface of water is
4  21 m, which is within the range of 1.5 m to 4.5 m from A.
5
Therefore, the suggested diving path is safe.
Swimming Pool Marking Guidelines (E)
5