AIBU to ask for help with a Maths question?

[Fernx0x0]

DD is trying to practice for her admissions test for Economics at University. She is completely stumped by some of the practice questions. Does anyone have any ideas how to arrive at the correct answer for the attached questions?

ErrolTheDragon

MrsSkylerWhite
Confused. Are they taking applications for 2022 already?

Yes, of course. The early applications (med, vet, oxbridge) had to be in a couple of weeks ago. The Cambridge pre-assessments are tomorrow/Thursday, not sure about Oxford. (Don't know whether other economics courses do a test.)“

Blimey! Glad ours weren’t doing maths or economics!

For the stats problem:
You need to think about what a mode is - the most common number. For the mode to change it must mean that numbers removed are the mode. You can formulate the following:
mn - 2d / (n-2) = m+2
And rearrange for answer E

For the circles, i drew the image, but you can create triangles in the middle segment. angle is 60deg (equil. triangle) therefore slice of pie (120) is one third of circle (or pi/3 area). There are two of these and obviously overlap on the actual 1x1x1 triangle so deduct this to make 2/3 *pi -1

The first question can’t be answered unless I see the end of the missing line
2nd question answer is D
3rd question answer is A - need to differentiate and then complete the square twice - you get the answers by looking carefully at why the square root of (5p^2 - p) had to be positive (in order to root out and get a real root not an imaginary root)
My notes are too messy to post - I’ll write them up tomorrow if you need them.

On the 2nd question you find the address of the 2 1cm sided equilateral triangles are (square root of 3)/4. The areas of the “minor segment” (60 degree sector - equilateral triangle area) is (pi/6) - [(root 3)/4].

Isn’t mathematics a wonderful subject? These questions are tricky because they need careful reasoning rather than advanced techniques.

For Q34, differentiate and set to 0 to get the equation for the turning points. Thus: 3x2 + 6sqrt5px + 3p = 0, or x2 +2sqrt5px + p =0

Given there are 2 distinct roots, the discriminant (b2 - 4ac in the usual notation) must be (strictly) positive. Hence 20p2 - 4p >0.

So 5p^2 - p >0, or p(5p-1) > 0.
Hence either:
p > 0 and 5p-1 > 0 or p < 0 and 5p-1 < 0 ( ie the terms are both positive or both negative to get a positive product)
In the first case, if 5p-1 > 0 then p > 0.2 (and is therefore positive)
In the second case, if p < 0 then 5p-1 < 0 automatically.

So the answer (I think) is that p < 0 or p > 0.2 - answer A. The inequalities are strict, so answers B, D, F and H would automatically be wrong.

@threestars

The economics exam for Cambridge tomorrow morning??

Yes it is! She is in the test now!

Thank you all so much for all of the help you posted with the way of tackling the questions on the practice paper. I printed them all out and she read them on the way to school this morning. It gave her something to focus on rather than worrying about the test, which was helpful.

We will see how it goes! Fingers crossed.

I hope it went ok for her. DS went in confident and came out disillusioned, all hope lost 😬
Economics and Maths paper 1 OK;paper 2 a write-off I think. Hope your DD is feeling better than that!

@Campfirewood

Just came here to swoon at the people who know how to answer this! Seriously impressive, fair play!

Haha - same! I really wish I’d been more interested in maths as a kid, it always amazes me the people on here answering these, I’m in total awe.

Op, hope your dd got on well, fair play to her for even attending this kind of test.

Reading these questions just reminds me of how much I hate maths! 🤯

Read the first sentence - realised there was no point in reading any further 😂

Good luck with that though!

Thank you all for your good wishes. The essay part of the test went well and the first set of Maths questions apparently went OK. The advanced Maths questions not so much. We will just have to cross our fingers and hope for the best!
@threestars Sorry to hear your DS was disillusioned. ECAA is such a hard test that he may have done better than he thinks as most applicants find it hard xxx

@Lalliella

The first question is missing some words from the 3rd line.

No 33. the intersecting circles is option d, 2pi/3 - (root3)/2. It's a good exapmle of the need to draw a diagram. As both circles are 1 and PQ is 1, the circles go through each other's centre. Find the area of each sector and add them. Each rhombus is 1/3 of the whole circle, so each is pi x 120/360, pi/3, total is 2pi/3. This counts the rhombus twice so subtract the overlap, the rhombus. The area of the rhombus is an area and Pythagoras or trig question.