Hong Kong Diploma of Secondary Education Examination
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
Transformation and Tessellation
©香港考試及評核局
保 留 版 權 2009
Hong Kong Examinations and Assessment Authority
All Rights Reserved 2009
1
Draft as of September 2009
Instructions
1.
This task consists of FOUR parts, Part A, Part B, Part C and Part D. Students are required to attempt
ALL parts.
2.
All working must be clearly shown.
Teacher Guidelines
1.
This task requires students to:
a.
apply transformations including reflection, dilation, rotation and translation to tessellate;
b.
apply the problem-solving skills: understand the problem, formulate a strategy and solve the
problem; and
c.
solve the extended part of the problem.
2.
It is anticipated that in general, students will be able to complete the task in 2 hours. However, teachers
can exercise their professional judgment in adjusting the time allowed to cater for the ability level of their
students.
3.
Teachers should remind students to bring equipment including a pair of compasses, ruler with cm scale,
protractor, set square, glue and a pair of scissors to complete the task.
4.
If necessary, teachers may give a brief description of the task.
5.
Teachers may feel free to modify the question and the marking guidelines to cater for the ability level of
their students, some examples of which may include:
a.
considering another animal diagram in Part C;
b.
encouraging students to use computer software to draw the diagrams.
6.
Feedback should be provided to students after marking the task, e.g. discussing different approaches in
handling each part of the task.
Transformation and Tessellation (E)
2
Draft as of September 2009
Part A
(a)
Draw a rhombus ABCD of side 4 cm and ∠A = 60° .
(b)
Rotate rhombus ABCD anticlockwise about point A through 90° to form a diagram R . Draw the
diagram R .
(c)
Use diagram R to draw the tessellation.
Part B
(a)
Use the instructions below to construct a diagram S :
1.
2.
3.
4.
5.
(b)
Draw a rectangle ABCD with AB = 6 cm and BC = 4 cm .
Mark points E and F on AB such that AE = 1 cm and AF = 4 cm .
Construct two semi-circles which lie inside rectangle ABCD , one centred at E with a radius of
1 cm and the other centred at F with a radius of 2 cm .
Translate these two semi-circles 4 cm towards CD .
Rub off line segments AB and CD and hence form diagram S .
Use diagram S to draw the tessellation.
Part C
The figure below shows a diagram of a parrot:
(a)
Use the instructions below to construct the parrot diagram on the sheet provided (see annex), leaving all
your construction lines in your diagram:
1.
Mark the point F on AB such that AF = 2 cm .
2.
Draw the semi-circle AEF which lies inside the square ABCD with AF as a diameter.
3.
Draw the right-angled triangle BFG which lies inside the square ABCD such that ∠BGF = 90°
and FG = AF .
4.
Rotate the region formed by the semi-circle AEF and ΔBFG anticlockwise about point A
through 90° .
5.
Mark point M such that M is the mid-point of AD .
6.
Construct a minor arc of the circle centred at M , passing through B and C and lying outside
square ABCD .
7.
Reflect this minor arc BC with respect to the line segment BC to form another arc BHC .
8.
Rotate arc BHC clockwise about point C through 90° .
9.
Add a black circular eye.
(b)
Use the diagram of the parrot drawn in (a) to draw the tessellation.
Transformation and Tessellation (E)
3
Draft as of September 2009
Part D
Design an animal diagram other than a parrot such that the diagram can tessellate on a plane. The diagram
should include at least a circular arc and a line segment. When you construct the diagram, use at least two
different transformations such as reflection, dilation, rotation and translation.
(a)
Write down the instructions similar to (a) of Part C for constructing your designed diagram.
(b)
Draw your designed diagram.
(c)
Use your designed diagram to draw the tessellation.
END OF ASSESSMENT TASK
Transformation and Tessellation (E)
4
Draft as of September 2009
Annex
A
D
B
C
Transformation and Tessellation (E)
5