Easy -1.2 This is a straightforward application of the sector perimeter formula (2r + rθ = perimeter) with simple algebraic manipulation. Given r=2 and perimeter=6, students substitute to get 4 + 2θ = 6, yielding θ=1. The multiple-choice format and single mark confirm this is a routine recall question requiring minimal problem-solving.
3 The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius 2
\includegraphics[max width=\textwidth, alt={}, center]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-03_374_455_1187_790}
The angle \(A O B\) is \(\theta\) radians and the perimeter of the sector is 6
Find the value of \(\theta\)
Circle your answer. [0pt]
[1 mark]
1
\(\sqrt { 3 }\)
2
3
Condone lack of symmetry or absence of curve to the left of \((0, -2)\)
Correctly labels all three intersections with coordinate axes: \((3, 4)\), \((1, 0)\), \((5, 0)\), \((0, -2)\)
A1
Accept coordinates of each point or \(x\) values on \(x\) axis and \(y\) value on \(y\) axis; ignore any other values
Total: 3 marks
Question 4b:
Answer
Marks
Guidance
Obtains at least one correct critical value using a correct method (can be read off graph or calculator)
M1
Condone use of equals or incorrect inequality sign
\(2 < x < 4\) written in correct form
A1
Accept \(x > 2\), \(x < 4\) or \((2, 4)\)
Subtotal: 2 marks
## Question 3:
$1$ | R1 | Circles the correct answer
---
## Question 4a:
Sketches an inverted V shape graph | M1 | Condone lack of symmetry
Sketches inverted V shape in correct quadrants | A1 | Condone lack of symmetry or absence of curve to the left of $(0, -2)$
Correctly labels all three intersections with coordinate axes: $(3, 4)$, $(1, 0)$, $(5, 0)$, $(0, -2)$ | A1 | Accept coordinates of each point or $x$ values on $x$ axis and $y$ value on $y$ axis; ignore any other values
**Total: 3 marks**
---
## Question 4b:
Obtains at least one correct critical value using a correct method (can be read off graph or calculator) | M1 | Condone use of equals or incorrect inequality sign
$2 < x < 4$ written in correct form | A1 | Accept $x > 2$, $x < 4$ or $(2, 4)$
**Subtotal: 2 marks**
3 The diagram shows a sector $O A B$ of a circle with centre $O$ and radius 2\\
\includegraphics[max width=\textwidth, alt={}, center]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-03_374_455_1187_790}
The angle $A O B$ is $\theta$ radians and the perimeter of the sector is 6\\
Find the value of $\theta$
Circle your answer.\\[0pt]
[1 mark]\\
1\\
$\sqrt { 3 }$\\
2\\
3
\hfill \mbox{\textit{AQA Paper 1 2020 Q3 [1]}}