HONG KONG DIPLOMA OF SECONDARY EDUCATION
EXAMINATION
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
Cheese Cake
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.
Cheese Cake Marking Guidelines (E)
2
Marking Guidelines
Solution
Performance
Part A
1.
2.
For the base of the cheese cake A, it is a triangle with sides 3, 4 and 5 units.
Since 32  42  25 and 52  25 , we have 32  42  52 .
Therefore, the triangle is a right-angled triangle. (Converse of Pythagoras Theorem)
Then, the base of the cheese cake A is a right-angled triangle.
1
The volume of cheese cake A   3  4  5  30 cubic units
2
Evidence:
1. The answer
2. The proof
Weak:
The answer is incorrect and
the proof is not done
Fair:
The answer is correct but
the proof is not done
Good:
The answer is correct but
the proof is not completed
Very good: Correct answer and valid
proof are given
Part B
1.
2.
1
The volume of the cheese cake B   3  4 10  60 cubic units
2
The total surface area of the cheese cake B
1
  3  4  5 10  2   3  4
2
 132 square units
Evidence:
1. The answers
2. The drawings
Weak:
Attempt the questions, but
only the volume or total
surface area of one type of
cheese cake is correct
Fair:
Attempt the questions, but
only the volumes and total
surface areas of two types
of cheese cakes are correct
Good:
The volumes and total
surface areas of 4 types of
cheese cakes are correct.
Any 3 figures in Question 2
are drawn correctly
The five other new cheese cakes are as follows:
4
3
5
5
5
4
Very good: All answers and figures
drawn are correct
cheese cake D
3
4
54
4
5
3
cheese cake E
Cheese Cake Marking Guidelines (E)
3
Marking Guidelines
Solution
Performance
4
54
4
3
5
3
cheese cake F
5
5
3
4
3
3
5
cheese cake G
5
5
3
4
3
4
5
3.
4.
cheese cake H
1
All the volumes of cheese cakes in Question 2   3  4  5  2  60 cubic units
2
The result is the same as Question 1 and all the volumes are equal to 60 cubic units.
The total surface area of cheese cake C
1
  3  4  4   3  5  5  2  104 square units
2
The total surface area of cheese cake D
1
  3  4  4   4  5  5  2  114 square units
2
The total surface area of cheese cake E
1
  3  4  4   3  4   5  2  94 square units
2
Cheese Cake Marking Guidelines (E)
4
Marking Guidelines
Solution
The total surface area of cheese cake F
1
  3  4  4   3  4   5  2  94 square units
2
Performance
The total surface area of cheese cake G
1
  (3  3)  4  2   5  5  3  3  5  104 square units
2
The total surface area of cheese cake H
1
  (4  4)  3  2   5  5  4  4   5  114 square units
2
All six total surface areas are different from the one obtained in Question 1.
Part C
1.
2.
Evidence:
1. The answers
2. The explanation
All the volumes of these seven new types of cheese cakes
1
5
  3x    4 x      2  60 x cubic units
2
 x
Weak:
Attempt the questions, but
only the answer for
Question 1 is correct
Fair:
The answer for Question 1
and part of the answers for
Question 2 are correct
Good:
The answers for Questions 1
and 2 are correct
The seven new cheese cakes are shown as follows:
4x
5x
5x
4
4x
3x
3x
3x
5x
5
x
5x
5
x
4x
Very good: All the answers are correct
and the explanation for
Question 3 is valid
cheese cake L
cheese cake K
3x
4x
4
5x
4x
5
x
4x
3x
4x
4
5x
3x
5
x
3x
cheese cake M
cheese cake N
Cheese Cake Marking Guidelines (E)
5
Marking Guidelines
Solution
5x
3
Performance
5x
4x
3x
3x
5
x
cheese cake O
5x
3
4x
5x
3x
4x
5
x
cheese cake P
4x
3x
5x
4x
5
x
cheese cake Q
3x
5x
5
x
The total surface area of new cheese cake K  24 x 2  80 square units
The total surface area of new cheese cake L  24 x 2  90 square units
The total surface area of new cheese cake M  24 x2  70 square units
The total surface area of new cheese cake N  24 x2  70 square units
Cheese Cake Marking Guidelines (E)
6
Marking Guidelines
Solution
Performance
The total surface area of new cheese cake O  24 x 2  80 square units
The total surface area of new cheese cake P  24 x 2  90 square units
The total surface area of new cheese cake Q  12 x 2  120 square units
3.
10
. If the cheese cake with the largest
2
total surface area has a quadrilateral base, then
x can be any value greater than or equal to
12 x 2  120  24 x 2  90
30  12 x 2
5
 x2
2
x
5
5
or x 
2
2
Therefore, x 
5
10
(=
).
2
2
Cheese Cake Marking Guidelines (E)
7