Date | November 2019 | Marks available | 2 | Reference code | 19N.2.SL.TZ0.S_4 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | S_4 | Adapted from | N/A |
Question
The following diagram shows a right-angled triangle, ABC, with AC=10cm, AB=6cm and BC=8cm.
The points D and F lie on [AC].
[BD] is perpendicular to [AC].
BEF is the arc of a circle, centred at A.
The region R is bounded by [BD], [DF] and arc BEF.
Find BˆAC.
Find the area of R.
Markscheme
correct working (A1)
eg sinα=810, cosθ=610, cosBˆAC=62+102−822×6×10
0.927295
BˆAC=0.927 (=53.1∘) (A1) N2
[2 marks]
Note: There may be slight differences in the final answer, depending on the approach the candidate uses in part (b). Accept a final answer that is consistent with their working.
correct area of sector ABF (seen anywhere) (A1)
eg 12×62×0.927, 53.1301∘360∘×π×62, 16.6913
correct expression (or value) for either [AD] or [BD] (seen anywhere) (A1)
eg AD=6cos(BˆAC)(=3.6)
BD=6sin(53.1∘)(=4.8)
correct area of triangle ABD (seen anywhere) (A1)
eg 12×6cosBˆAD×6sinBˆAD, 9sin(2BˆAC), 8.64 (exact)
appropriate approach (seen anywhere) (M1)
eg Atriangle ABD−Asector, their sector − their triangle ABD
8.05131
area of shaded region =8.05 (cm2) A1 N2
[5 marks]