Trapeziums Sectors and Composite Figures

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

1QuestionArea of Circular Sectors and SegmentsConcept Practice

2 marks~3 minCriterion B

A circle has centre

O

and radius

r

. Sector

OAB

has central angle

\theta°

Explain why sector

OAB

represents the fraction

\dfrac{\theta}{360}

of the full circle. [1]

Justify why the area of sector

OAB

is given by

A = \dfrac{\theta}{360} \times \pi r^2

. [1]

Solutions

2QuestionArc Length and Sector Area CalculationsAssessment Practice

6 marks~9 minCriterion D

A satellite orbits Earth in a circular path with a radius of 6900 km. A sensor records data points at 12° intervals along its path. The arc length between consecutive data points is predicted using

s = r\theta

, where

\theta

is in radians.

Show that 12° is equal to

\dfrac{\pi}{15}

radians. [1]

Calculate the predicted arc length between consecutive data points. Round your answer to the nearest kilometre. [2]

The actual measured arc lengths for three consecutive intervals are:

Interval 1	actual: 1442 km
Interval 2	actual: 1448 km
Interval 3	actual: 1440 km

For each interval, calculate the percentage error between the actual and predicted arc lengths, using:

\text{Percentage error} = \frac{|\text{actual} - \text{predicted}|}{\text{predicted}} \times 100\%

Round each answer to one decimal place. [2]

A mission engineer states: "The circular orbit model is reliable enough for navigation purposes." Using your results from parts (b) and (c), advise the engineer whether the circular orbit model should be accepted for navigation use. [1]

Solutions

3QuestionCombining Shapes Semi-Circles Rectangles TrapeziumsConcept Practice

2 marks~3 minCriterion A

A landscape architect designs a garden bed in the shape of a rectangle with a semicircle attached to one of its shorter ends. The rectangle measures 8 cm by 4 cm. The semicircle's diameter equals the width of the rectangle.

A total of 40 cm² of specialist planting fabric is available to cover the garden bed.

Calculate the total area of the combined shape, using

\pi = 3.14

. Justify whether the available fabric is sufficient to cover the garden bed. [2]

Solutions

4QuestionArea 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

32\pi

^2

Calculate the central angle

\theta

of the sector in degrees. [1]

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]

Solutions

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