CAIE A-Level Mathematics AS 1.4.2 Arc Length and Sector Area Questions

State $2 r+r \theta=65$ and $\frac{1}{2} r^{2} \theta=225$
Form a 3-term quadratic or cubic in r or $\theta$ or $r \theta$ from correct arc and sector
formula

*M1

Condone sign errors.

Solve their 3 term quadratic or cubic to obtain values of r or $\theta$
Expect $2 r^{2}-65 r+450=(2 r-45)(r-10)$ or
$18 \theta^{2}-97 \theta+72=(9 \theta-8)(2 \theta-9)$.

r=10 and $\theta=4.5$ ignore r=22.5 and $\theta=\frac{8}{9}$, do not ignore r=0
B1 SC if no quadratic or cubic solution.
If r=0 included A0 or B0 SC.

Use correct formula for area of triangle with clear use of angle being $2 \pi-$ their $\theta$
Expect 1.783 or $102.2^{\circ}$, their $\theta$ must be reflex.

48.9
AWRT, WWW or a second answer.
Or greater accuracy;
condone absence of units.