2018 HSC q (1 Viewer)

[hs17]

Can someone pls explain how to do the last part (iv)--> Ans is 9 root3

 

[5uckerberg]

Can someone pls explain how to do the last part (iv)--> Ans is 9 root3 View attachment 32794

Okay to find the area
First, find the angle OA makes with the x-axis.
Next, find the angle OP makes with the x-axis, please note that both of them require the use of inverse tan
Here use Pythag, to find the length which respectively will give us and I am sorry but if you do not do 3U this question relies on the calculator.
As the next part is just like if you have 3U knowledge you are going to have an unfair advantage over the 2U counterparts because the area is which is found by using trig expansion. I find this question is not Mathematics Advanced friendly.

Oh wow, did they discard the distance formula in the new syllabus? If they did mathematics Advanced candidates now have to use a calculator

 

[hs17]

thank you sm!

 

[specificagent1]

is this part of the new syllabus?

 

[CM_Tutor]

There is a formula called the perpendicular distance formula that allows you to find the distance from P to K, the point on the line OA (extended) where PK and OA are perpendicular. This distance is the height h of the triangle allowing you to use Area is where b is the base of the triangle, and thus is length OA.

However, under the syllabus that came in in 2020, the perpendicular distance formula is no longer taught, which makes finding the area of the triangle much messier. I don't think a question like this would be asked under the new syllabus without giving you some easier way to get at the area.

 

[CM_Tutor]

Note: To MX1 students, a question like this can be done with vector methods