C3 June 2014 Q9

Notes

B1 Accept \(R=\sqrt{20}\) or \(2\sqrt{5}\) or awrt 4.47
Do not accept \(R=\pm\sqrt{20}\)
This could be scored in parts (b) or (c) as long as you are certain it is \(R\)

M1 for sight of \(\tan\alpha=\pm\dfrac{4}{2},\ \tan\alpha=\pm\dfrac{2}{4}\). Condone \(\sin\alpha=4,\cos\alpha=2\Rightarrow\tan\alpha=\dfrac{4}{2}\)
If \(R\) is found first only accept \(\sin\alpha=\pm\dfrac{4}{R},\ \cos\alpha=\pm\dfrac{2}{R}\)

A1 \(\alpha=\) awrt 1.107. The degrees equivalent \(63.4^\circ\) is A0.
If a candidate does all the question in degrees they will lose just this mark.

Notes

(b)(i)

B1ft Either 104 or if \(R\) was incorrect allow for the numerical value of their \(\text{'}4+5R^2\text{'}\).
Allow a tolerance of 1 dp on decimal \(R\)'s.

(b)(ii)

M1 Using \(3\theta\pm\text{their '}1.107\text{'}=\dfrac{\pi}{2}\Rightarrow\theta=..\)
Accept \(3\theta\pm\text{their '}1.107\text{'}=(2n+1)\dfrac{\pi}{2}\Rightarrow\theta=..\) where \(n\) is an integer
Allow slips on the lhs with an extra bracket such as \(3\left(\theta\pm\text{their '}1.107\text{'}\right)=\dfrac{\pi}{2}\Rightarrow\theta=..\)
The degree equivalent is acceptable \(3\theta-\text{their '}63.4^\circ\text{'}=90^\circ\Rightarrow\theta=\)
Do not allow mixed units in this question

A1 awrt 0.89 radians or \(51.1^\circ\). Do not allow multiple solutions for this mark.

Notes

(c)(i)

B1 4

(c)(ii)

M1 Using \(3\theta\pm\text{their '}1.107\text{'}=2\pi\Rightarrow\theta=\ldots\)
Accept \(3\theta\pm\text{their '}1.107\text{'}=n\pi\Rightarrow\theta=..\) where \(n\) is an integer, including 0
Allow slips on the lhs with an extra bracket such as \(3\left(\theta\pm\text{their '}1.107\text{'}\right)=2\pi\Rightarrow\theta=..\)
The degree equivalent is acceptable \(3\theta-\text{their '}63.4^\circ\text{'}=360^\circ\Rightarrow\theta=\) but
Do not allow mixed units in this question

A1 \(\theta=\) awrt 2.46 radians or \(141.1^\circ\) Do not allow multiple solutions for this mark.