Standard +0.3 This is a straightforward application of arc length formula to find the angle, then using standard area formulas (sector minus triangle). It requires multiple steps but uses only routine techniques with no conceptual challenges beyond basic radian geometry.
\includegraphics{figure_5}
The diagram shows a triangle \(OAB\) in which angle \(OAB = 90°\) and \(OA = 5\) cm. The arc \(AC\) is part of a circle with centre \(O\). The arc has length 6 cm and it meets \(OB\) at \(C\). Find the area of the shaded region. [5]
Use Pythagoras and double angle formula in the expansion
M1
Obtain the given result correctly
A1
Total:
4
Answer
Marks
Guidance
5(ii)
Use the identity and carry out a method for finding a root
M1
Obtain answer 20.9°
A1
Obtain a second answer, e.g. 69.1°
A1FT
Obtain the remaining answers, e.g. 110.9° and 159.1°, and no others in the given
Answer
Marks
Guidance
interval
A1FT
Total:
4
Question
Answer
Marks
Question 5:
--- 5(i) ---
5(i) | Attempt cubic expansion and equate to 1 | M1
Obtain a correct equation | A1
Use Pythagoras and double angle formula in the expansion | M1
Obtain the given result correctly | A1
Total: | 4
--- 5(ii) ---
5(ii) | Use the identity and carry out a method for finding a root | M1
Obtain answer 20.9° | A1
Obtain a second answer, e.g. 69.1° | A1FT
Obtain the remaining answers, e.g. 110.9° and 159.1°, and no others in the given
interval | A1FT
Total: | 4
Question | Answer | Marks
\includegraphics{figure_5}
The diagram shows a triangle $OAB$ in which angle $OAB = 90°$ and $OA = 5$ cm. The arc $AC$ is part of a circle with centre $O$. The arc has length 6 cm and it meets $OB$ at $C$. Find the area of the shaded region. [5]
\hfill \mbox{\textit{CAIE P3 2018 Q5 [5]}}