Trapeziums Sectors and Composite Figures
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Trapeziums Sectors and Composite Figures — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionArea of Circular Sectors and SegmentsConcept Practice
2 marks~3 minCriterion B
A circle has centre OO and radius rr. Sector OABOAB has central angle θ°\theta°.
a
Explain why sector OABOAB represents the fraction θ360\dfrac{\theta}{360} of the full circle. [1]
b
Justify why the area of sector OABOAB is given by A=θ360×πr2A = \dfrac{\theta}{360} \times \pi r^2. [1]
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Solutions

2QuestionEstimating and Approximating Irregular AreasAssessment Practice
5 marks~8 minCriterion D
A river cross-section is surveyed at seven points across its 16 m width. The distances xx (m) from the left bank and corresponding depths yy (m) are:

xx (m): 0, 2.5, 5.0, 8.0, 11.5, 14.0, 16.0

yy (m): 0.0, 1.8, 2.4, 3.1, 2.9, 1.5, 0.0
a
Calculate the cross-sectional area of the river using the trapezoidal rule. Show all working. [3]
b
The average water velocity at this cross-section is 1.2 m/s. Calculate the volume flow rate QQ (m3^3/s). [1]
c
A flood warning is issued when QQ exceeds 42 m3^3/s. Advise the river authority whether a flood warning should be issued, and justify your advice by identifying one limitation of the trapezoidal rule that affects the reliability of this conclusion. [1]
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Solutions

3QuestionArea of Circular Sectors and SegmentsConcept Practice
2 marks~3 minCriterion C
A landscape architect designs a decorative stone paving feature. One section is a circular sector with radius 8 cm and area 32π32\pi cm2^2.
a
Calculate the central angle θ\theta of the sector in degrees. [1]
b
The architect states that this sector is a semicircle, so it can be paired with an identical piece to form a complete circle with no wasted material. Justify whether the architect's statement is correct. [1]
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Solutions

4QuestionEstimating and Approximating Irregular AreasConcept Practice
2 marks~3 minCriterion A
The outline of a lake is modelled using vertical strips of equal width h=20h = 20 m. The strip heights (in metres) are:

y0=0,y1=12,y2=18,y3=22,y4=16,y5=8,y6=0y_0 = 0,\quad y_1 = 12,\quad y_2 = 18,\quad y_3 = 22,\quad y_4 = 16,\quad y_5 = 8,\quad y_6 = 0

State the trapezoidal rule formula for estimating the area of the lake, using correct mathematical notation with hh, y0y_0, y6y_6, and y1y_1 through y5y_5 clearly identified, and hence calculate the estimated area. [2]
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Solutions

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