This task will assess the following:-
 Areas of Similar Figures
You are allowed to use a CALCULATOR during the assessment
 Circumference of a Circle
 Area of a Circle
and a simple, non-electronic translating DICTIONARY
 Arc Length of a circle
 Area of a Sector
 Use of calculator for calculations involving 𝛑
 Volume of Prisms and Cylinders
 Surface areas of Prisms and Cylinders
Criterion B: Investigating Patterns

selects and applies mathematical problem-solving techniques to recognize patterns,

describes patterns as relationships or general rules,

draws conclusions consistent with finding and,

provides justifications or proofs.
Years 7 and 8
Achievement
Level descriptor
Level
0
1–2
3–4
5–6
7–8
The student does not reach a standard described by any of the descriptors given below.
The student is able to use a simple problem-solving technique so that patterns can emerge
The student is able to select and apply an appropriate problem-solving technique, and can describe
the emerging pattern
The student can select and apply appropriate problem-solving techniques, and can suggest a
mathematical rule to describe an emerging pattern
The student can select and apply appropriate problem-solving techniques, and can offer, with
sensible reasons, a correct mathematical rule to describe an emerging pattern
The largest field
Johnny has a 20 m long fence. He wants to enclose a rectangular field so that the field
has the largest area. Johnny started to form different rectangular areas with his fence
and calculated the area of each.
Length of fence
in m
Width of field
in m
Length of field
in m
Area of field
20
20
20
20
20
1
2
3
4
5
9
8
7
6
5
9
16
in m
2
1.
Copy and complete the table above.
2.
From the table, what will be the dimensions of the rectangular field with the
maximum area?
3.
What do you notice about the dimensions you found?
4.
Mr. William has a fence of 24 m length. Create a table like the one above and find
the dimensions of the rectangular field with the maximum area.
Length of fence
in m
Width of field
in m
Length of field
in m
Area of field
24
24
24
24
24
24
1
2
3
4
5
6
11
10
11
in m
2
5.
Now, without creating a table, find the maximum area of a rectangular field that can
be enclosed by the following fences: length 100 m, 200 m and 400 m.
6.
If the length of the fence is x, what will be the dimensions of the rectangular field
with the maximum area?
7.
Based on your investigations above, complete the sentence below. A rectangle of
fixed perimeter will have maximum area when
because
IB Taskbank Mathematics
2