Practice IB Mathematics Applications & Interpretation (AI) Topic SL 5.8—trapezoid Rule with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.8—trapezoid Rule and mirrors Paper 1, 2, 3 style where relevant.
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A farmer is planning a new orchard. The shape of one section is defined by the region bounded by the curve , the -axis, and the vertical line , where and are measured in metres.
Divide the interval into 4 equal sub-intervals and state the -values of the endpoints.
Calculate the value of at each endpoint.
Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the orchard section, giving your answer in .
Calculate the exact area of the orchard section by integrating from 0 to 4, giving your answer in .
Compare the approximation with the exact value and explain the difference.
An architect is designing a glass panel. The shape of the panel is defined by the region bounded by the curve , the -axis, and the vertical line , where and are measured in metres.
Divide the interval into 4 equal sub-intervals and state the -values of the endpoints.
Calculate the value of at each endpoint.
Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the panel, giving your answer in .
Calculate the exact area of the panel by integrating from 0 to 4, giving your answer in .
Compare the approximation with the exact value and explain the difference.
The rate at which water flows into a tank, litres per minute, is modelled by the function for , where is the time in minutes after pumping begins. The area under the graph of over this interval represents the total volume of water entering the tank.
Divide the interval into equal sub-intervals and write the values of at each endpoint.
Use the trapezoidal rule with sub-intervals to approximate the area under the curve between and .
Calculate the exact value of the area by integrating over the same interval, and compare your result with the trapezoidal approximation, giving values to significant figures.
A city is planning to build a new park. The shape of the park is defined by the region bounded by the curve , the -axis, and the vertical line , where and are measured in kilometers.
Divide the interval into 4 equal sub-intervals and state the -values of the endpoints.
Calculate the value of at each endpoint.
Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the park, giving your answer in .
Calculate the exact area of the park by integrating from 0 to 2, giving your answer in .
Compare the approximation with the exact value and explain the difference.
The height of a plant above the soil, cm, is modelled by the function for , where is the number of weeks since planting. The area under the graph of over this interval represents the accumulated height (in cm·weeks) over the weeks.
Divide the interval into equal sub-intervals and write the values of at each endpoint.
Use the trapezoidal rule with sub-intervals to approximate the area under the curve between and .
Calculate the exact value of the area by integrating over the same interval, and compare your result with the trapezoidal approximation, giving values to significant figures.