Standard +0.3 This question requires completing the square to find the circle's center and radius, then applying the standard segment area formula (½r²(θ - sin θ)). While it involves multiple steps, each is routine: algebraic manipulation, recognizing the segment area formula, and calculator work. The formula is commonly taught and the question is straightforward application rather than problem-solving.
A circle has equation \(x^2 + y^2 - 6x - 8y = 264\)
\(AB\) is a chord of the circle.
The angle at the centre of the circle, subtended by \(AB\), is \(0.9\) radians, as shown in the diagram below.
\includegraphics{figure_5}
Find the area of the minor segment shaded on the diagram.
Give your answer to three significant figures.
[5 marks]
Question 5:
5 | Uses appropriate method to find
radius eg complete the square by
using or on LHS or RHS
PI by co2rrect 2radius 17 or 289
3 4 | 3.1a | M1 | ( x−3 )2 −9+( y−4 )2 −16=264
( x−3 )2 +( y−4 )2 =289
1
×172×0.9=130.05
2
1
×172sin0.9=113.19
2
Area of segment = 16.9
Deduces correct radius or radius
squared or fully correct
completed square form seen | 2.2a | A1
Uses appropriate method to find
area of sector using radius 17 or
their stated value of radius or
value of radius clearly shown on
diagram | 1.1a | M1
Uses appropriate method to find
area of triangle using radius 17
or their stated radius | 1.1a | M1
Obtains area correct to at least 3
significant figures
AWRT 16.9 | 1.1b | A1
Total | 5
Q | Marking instructions | AO | Mark | Typical solution
A circle has equation $x^2 + y^2 - 6x - 8y = 264$
$AB$ is a chord of the circle.
The angle at the centre of the circle, subtended by $AB$, is $0.9$ radians, as shown in the diagram below.
\includegraphics{figure_5}
Find the area of the minor segment shaded on the diagram.
Give your answer to three significant figures.
[5 marks]
\hfill \mbox{\textit{AQA Paper 3 2019 Q5 [5]}}