Portfolio Tasks 2011 2012
• Using a spreadsheet, or geometric software, simulate the positions of the two runners for a variety of values of the speeds u and v , the time t and the distance d . • Using the data generated above, discuss the condition(s) necessary for Buddy to catch up with Angie. Again, include estimates for: o the time at which Buddy catches up with Angie. o the distance travelled by each runner when Buddy catches up. • Discuss the assumptions in the above model. What limitations does it have when applied to other situations?
For final assessment in 2011 and 2012
–8–
MATHL/PF/M11/N11/M12/N12
MODELLING A FUNCTIONAL BUILDING
HL TYPE II
To the student: The work that you produce to address the questions in this task should be a report that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question and answer” format. As an architect you have been contracted to design a building with a roof structure similar to the one shown below.
In this task you are to model such a building and produce a report to the contractor with all necessary specifications.
(This task continues on the following page)
For final assessment in 2011 and 2012
–9–
MATHL/PF/M11/N11/M12/N12
You are to design an office block inside a structure with the following specifications: The building has a rectangular base 150 m long and 72 m wide. The maximum height of the structure should not exceed 75 % of its width for stability or be less than half the width for aesthetic purposes. The minimum height of a room in a public building is 2.5 m. • Create a model for the curved roof structure when the height is 36 m. • Find the dimensions of the cuboid with maximum volume which would fit inside this roof structure. • Use technology to investigate how changes to the height of the structure affect the dimensions of the largest possible cuboid. • For each height, calculate the ratio of the volume of the wasted space to the volume of the office block. •
For final assessment in 2011 and 2012
–8–
MATHL/PF/M11/N11/M12/N12
MODELLING A FUNCTIONAL BUILDING
HL TYPE II
To the student: The work that you produce to address the questions in this task should be a report that can stand on its own. It is best to avoid copying the questions in the task to adopt a “question and answer” format. As an architect you have been contracted to design a building with a roof structure similar to the one shown below.
In this task you are to model such a building and produce a report to the contractor with all necessary specifications.
(This task continues on the following page)
For final assessment in 2011 and 2012
–9–
MATHL/PF/M11/N11/M12/N12
You are to design an office block inside a structure with the following specifications: The building has a rectangular base 150 m long and 72 m wide. The maximum height of the structure should not exceed 75 % of its width for stability or be less than half the width for aesthetic purposes. The minimum height of a room in a public building is 2.5 m. • Create a model for the curved roof structure when the height is 36 m. • Find the dimensions of the cuboid with maximum volume which would fit inside this roof structure. • Use technology to investigate how changes to the height of the structure affect the dimensions of the largest possible cuboid. • For each height, calculate the ratio of the volume of the wasted space to the volume of the office block. •