Kasti Quest - Math 4 GS & LS

mesa177

This thread was posted after jadf24 expressed interest in challanging math and physics questions. I will post a couple of questions over the weekends; these questions revolve around the math topics taught at the GS and LS levels. These questions are derived from quizes, exams and term tests of Hariri High School II, and the author of the questions is Mr. Hussam Kasti (if you're reading this,!! هاي استاذ كستي ). As such, the thread is named in his honor.

Each question posted will reveal the difficulty level of the question (medium, hard or excruciating: easy questions can be found in the Shamel book and are pointless to post here), the time expected to solve (the time slot is driven by where the question was posted i.e. quiz, exam, etc... and how much time Mr. Kasti alloted for us to solve at the meantime), and of course the topics you need to know in order to solve it. As such, I expect those who intend to solve it to respect my wishes of knowing any required formulas beforehand (i.e. no peeking into your books and copybooks to remember formulas), and to solve the question within the time limit specified (time yourselfs to have a better evaluation).

Please note that this is not me asking you solve my homework: I graduated 5 years ago, and I've already solved these questions. I will post the solution after one week of posting the question.

PS: Any special requests will be taken into consideration. I'm looking for a good question in conics for next week.

So, here goes the first question of the series:

Question 1:

Question 2:

In the eternal words of Mr. Kasti: "Concentrate & Relate".

GeorgeN

I don't know about other people, but in my school the closest LS students got to trigonometry was in complex numbers. Our teacher specifically said that LS students are never asked to solve trigonometric functions including any sort of derivation / integration; but now I just feel stupid because all of that sounds like chinese to me, and I just passed bacc last year, d'oh.

mesa177

GeorgeN wroteI don't know about other people, but in my school the closest LS students got to trigonometry was in complex numbers. Our teacher specifically said that LS students are never asked to solve trigonometric functions including any sort of derivation / integration; but now I just feel stupid because all of that sounds like chinese to me, and I just passed bacc last year, d'oh.

But the subject of antiderivatives; sequences, and trigonometry were given in grade 11 - scientific section. The only new topics covered by GS & LS students is integration and natural logarithm (oh snap, add "natural logarithm" to the list of "required knowledge").

mesa177

Ra8 solved this problem, and after solving the problem myself (the question was in MrClass's quiz not mine and I don't have the solutions so I'm solving them too), we quite agree that g(x) = 1/cosx not 2/cosx. I actually solved it in three different ways, all leading to 1/cosx. Has anyone tried to solve this problem and got the same answer?

mesa177

Appologies to all those who have been waiting like Ra8 for another problem to be posted, but work overwhelms us sometimes. I'll try to post the solution and a new problem asap.

mesa177

Ok, so here's the solution for question 2:

mesa177

In honor of the second term exams which have to be lurking soon enough (this week or next week), I've assembeld a group of question for you to solve. It is fundamental to stick to the time limit: otherwise solving the question is pointless. Time management is just as important as solving the question and getting the right answer.

So here it goes:

Note: I won't post the answers until I get at least 1 solution. I'll give you two weeks, and then we'll see what happens.

Remeber: Concentrate and relate...