Trapeziums Sectors and Composite Figures
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Trapeziums Sectors and Composite Figures — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionArea of Circular Sectors and SegmentsConcept Practice
2 marks~3 minCriterion A
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]
Question diagram

Solutions

2QuestionArea of Circular Sectors and SegmentsAssessment Practice
5 marks~8 minCriterion B
A circle has radius rr and centre OO. A sector of the circle has central angle θ°\theta°.
a
State the arc length of the sector and the area of the full circle. [1]
b
A sector is dissected into many thin triangular strips, each with vertex at OO, height approximately rr, and base along the arc. The strips are rearranged into a shape that approximates a rectangle. Show that the area of the sector is θ360πr2\dfrac{\theta}{360}\pi r^2. [2]
c
A designer claims that a sector with θ=120°\theta = 120° and r=8r = 8 cm has sufficient area to cover a surface of 165 cm2165\ \text{cm}^2. Assess whether this claim is correct, justifying your answer with a calculation. [2]
Question diagram

Solutions

3QuestionArc Length and Sector Area CalculationsAssessment Practice
6 marks~9 minCriterion D
A landscape architect is designing a circular fountain with a radius of 2.5 m. A sector with a central angle of 120° will be decorated with tiles. The client's budget allows for exactly 6.5 m² of tiling. The architect's radius measurements have a tolerance of ±0.1 m, and tile grout reduces the effective tiled area by 2%.
a
Calculate the area of the 120° sector using

A=θ360πr2A = \frac{\theta}{360} \pi r^2

where θ\theta is the central angle in degrees. [2]
b
Deduce whether the sector area exceeds the budget, stating the difference. [1]
c
Advise the architect whether the design is feasible within the budget, justifying your recommendation by considering the effect of the radius tolerance on the calculated area and the impact of grout on the effective tiled area. [3]
Question diagram

Solutions

4QuestionArc Length and Sector Area CalculationsAssessment Practice
6 marks~9 minCriterion C
A landscape architect is designing decorative stone edging for four circular garden beds. Each bed uses a sector of stone with an arc length of 10 cm per unit scale. The sectors have radii of 3 cm, 6 cm, 9 cm, and 12 cm respectively.

The perimeter of a sector is given by P=L+2rP = L + 2r, where LL is the arc length and rr is the radius.
a
Calculate the perimeter of each sector. Record your results as ordered pairs (r,P)(r, P) in order of increasing radius. [2]
b
Deduce the perimeter of a sector with radius 15 cm and the same arc length. Justify your reasoning using the pattern in your results. [2]
c
The architect claims that doubling the radius of a sector always produces a more efficient design because the perimeter does not double. Assess this claim using the formula P=L+2rP = L + 2r, and interpret what this means for the architect's choice of sector size. [2]

Solutions

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