ALGEBRA II
GRADE 10, 11
Name: ________________________________________
TEACHER: ___________________________
Instructions
BLUE OR BLACK INK ONLY
1. Make sure you read through the assessment.
2. Read the instructions for each question
carefully.
3. Be sure to answer all required questions.
4. CHECK your answers before handing in your
paper.
5. Calculators are not allowed.
DATE: ________
MYP CRITERIA:
/8
TOTAL:
B, C, D
%
Unit Topic: THINKING WITH MATHEMATICAL MODELS: QUADRATICS
Performance Task Description
You are a civil engineer and your company has been contracted by the Municipality to construct
a bridge that will link Al Lulu Island to Abu Dhabi Mainland. Before construction can commence
your department has been given the task to perform a feasibility study and estimate the cost of
the project. Follow the guiding questions by answering each one to the best of your abilities
while communicating mathematically your justifications where necessary.
1. The image above shows the proposed position of the bridge between coordinates (0, 0) and
(-120, 90). Use the red line l to calculate the length of the bridge in meters.
2. The graph below is the side view of the bridge. Label the graph with the length l which you
𝑙
calculates in question 1 and hence label the midpoint by calculating 2 .
3. Use the graph in question 2 to formulate the equation of the bridge and using the general
quadratic equation stated below
𝒉(𝒙) = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
whereby h(x) represents the height in meters with
respect to x and x represents the horizontal length in meters
4. After a series of tests using a model bridge you and your team of engineers realise that your
bridge requires a triangular beam as shown below to increase the rigidity of the bridge. If the
height of the horizontal beam is 20m above the ground such that it is riveted on the bridge at
(P, 20) and (Q, 20).
i. Calculate the length of P and Q from the origin (0, 0)
ii. What is the distance between P and Q
𝒉(𝒙)/𝒎
20
20
0
Q
P
𝒙/𝒎
5. 3 months after the first phase of performing feasibility studies you and your team of civil
engineers are satisfied with the design of the bridge and with the help of the finance
department have come up with the equation shown below that helps you calculate the cost of
constructing the bridge.
𝑪 = 𝟒𝟐, 𝟎𝟎𝟎𝒍𝟐 + 𝟓𝟑, 𝟓𝟎𝟎𝒍 + 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎
l represents the length of the bridge in meters
while C represents the cost is dirhams
i. Based on the length you got in question 1, calculate the cost of constructing the bridge.
ii. According to the equation above how much will it cost the Municipality for your consultancy
services rendered before the commencement of the construction?
iii. After the construction of the bridge the total cost of the project was 1 billion dirhams. Use
the equation above to calculate the actual length of the bridge.
iv. The equation below is used to get the percentage error between the calculated length and
the actual length.
𝐴𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ − 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ
× 100%
𝐴𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
Calculate the percentage error? Is this margin of error acceptable?
Achievement
Level
0
1-2
3-4
Descriptor
The student does not reach a standard
described by any of the descriptors below.
Criterion A: Knowledge and understanding
You are able to:
i. Use limited Mathematical Language
iii.Communicate through lines of reasoning that
are difficult to interpret.
Criterion C: Communication
You are able to:
i. use limited mathematical language (notation,
symbols and terminology) in both oral and
written explanations
ii. use limited forms of mathematical
representation to present information
iii. move somehow between different forms of
mathematical representation
v. somehow organize information using a
logical structure.
Criterion A: Knowledge and understanding
You are able to:
i.Use some appropriate Mathematical language.
iii.Communicate through lines of reasoning that
are able to be understood, although these are
not always clear
Criterion C: Communication
You are able to:
i. use some appropriate mathematical language
(notation, symbols and terminology) in both
oral and written explanations
ii. use some appropriate forms of mathematical
representation to present information
iii. Move between some different forms of
mathematical representation
v. organize some information using a logical
structure.
5-6
Criterion A: Knowledge and understanding
You are able to:
i.Usually use appropriate Mathematical
Language.
iii.present information correctly
Criterion C: Communication
You are able to:
i. Usually use appropriate mathematical
language (notation, symbols and terminology)
in both oral and written explanations
ii. Usually use appropriate forms of
mathematical representation to present
information
iii. Usually move between different forms of
mathematical representation
v. Usually organize information using a logical
structure.
Task Specific descriptor
You do not reach a standard described by any of the
descriptors below.
Your work is of low ability and minimal effort has been shown.
 scale not used
 failed to use the quadratic equation to relate it to the
distance between the island and the mainland
 information is not presented in an orderly and logical
manner
 poorly communicated using Mathematical language
Your work is of limited ability and some effort has been shown.
 found a reasonable position for the bridge and your
justification was both qualitative and quantitative
 scale not accurate but usable measurements
 quadratic equation that is related to the distance
between the island and the mainland
 maximum height of the bridge not accurate but showed
evidence of using the quadratic equation
 midpoint inaccurate but attempted using the quadratic
equation
 arranged your information in a reasonably organized
and logical manner
 vaguely communicated using Mathematical language
You have:
 found a reasonable position for the bridge and your
justification was both qualitative and quantitative
 a correct scale and your drawing or design on paper is
congruent with real measurements
 Established a quadratic equation that is related to the
distance between the island and the mainland
 determined the maximum height of the bridge correctly
using the quadratic equation and you have explained if
the height of the bridge is practical or not practical
explicitly
 determined the midpoint using the quadratic equation
 determined the discriminant of the formula of your
bridge
 arranged your information in a reasonably organized
and logical manner
 communicated using the appropriate Mathematical
language
7-8
Criterion A: Knowledge and understanding
You are able to:
i.Consistently use appropriate Mathematical
language.
iii.Move effectively between different forms of
mathematical representation
Criterion C: Communication
You are able to:
i. use appropriate mathematical language
(notation, symbols and terminology) in both
oral and written explanations
ii. use appropriate forms of mathematical
representation to present information
iii. move between different forms of
mathematical representation
v. organize information using a logical
structure.
You have:
 found the most economically and environmentally
sensible position for the bridge and your justification
was both qualitative and quantitative
 a correct scale and your drawing or design on paper is
congruent with real measurements
 Established the correct quadratic equation that is
related to the distance between the island and the
mainland
 Correctly determined the maximum height of the bridge
correctly using the quadratic equation and you have
explained if the height of the bridge is practical or not
practical explicitly
 Correctly determined the midpoint using the quadratic
equation
 Correctly determined the discriminant of the formula of
your bridge
 arranged your information in a well-organized and
logical manner
 communicated well using the appropriate Mathematical
language