Oxford PAT 2011, Questions 9 and 10

7 thoughts on “Oxford PAT 2011, Questions 9 and 10”

1. George says:

Hey you see for question 9, I don’t get the reason that when x tend to infinity, y tends to infinity then you state that biggest x will result with a minimum value which I don’t think it is true.

E.g. Say the range of x is between 0 and 100.
The minimum value of x will be 0, the maximum value of x will be 100. So the maximum or minimum value we calculated by differentiation is the only the local maximum or minimum value not the maximum value or minimum value at a bigger picture.

Are I right to understand in this way?
Thanks

1. George says:

When we deal questions like this in general, we still need to check the maximum value of x which is 1.9 in this case and minimum value of x which is 0.8 in this case right? So we need to plot in the value x=1.9 into the y. THEN we compare it with the y value when x =1

(We can also check this by symmetry of the graph)

1. Yes you are right — strictly speaking you should check the value of the polynomial at x=1.9 to ensure it isn’t actually bigger than the value at x=1, and its value at x=0.8 to ensure it isn’t smaller than the value at x=5/3.

But when you are under time pressure, with no calculator, I wouldn’t recommend doing this step: I think there is a kind of unspoken understanding in the question that when you have found the maxima and minima here they will actually be the real maxima and minima in the range defined by the constraints on x and I wouldn’t plan on spending time doing the arithmetic in order to check the result unless I had time left over at the end.

2. Ewan says:

Hi, been flicking through quite a few questions now, and have found that once I see how you’ve started each one I can work through and get the right answers. The only issue is figuring out where to start with each problem! I guess that’s what the examiners are going for, to get you really thinking, but do you have any tips on ways to approach questions and first sight?

Thanks

1. Good question. There’s obviously no right answer, but here are some ideas.

1. Get to know the syllabus and the key formulas really well by practicing, using questions from textbooks or wherever you can find them. The more you practice, the more you will now and the more confident you will get.
2. Don’t just look at these answers without having a really good try at the questions — every question that you get right on your own is worth ten where you just look up the answer, and even in cases where you fail to get the right answer, the time you spend thinking about the question is still valuable.

3. When trying a PAT question, read every word and look for technical terms (e.g. in the first question: maximum/minimum, difference) or familiar patterns that hint at some other equation (e.g. in the second question: x^2 + 2xy + y^2 = (x + y)^2). Underline them if it helps.

4. On a bit of rough paper, try to rephrase the question into a more mathematical form, using the keywords to help you (e.g. in the first question: “the differential of y1 – y2 is zero”). For a physics or geometry question, draw a diagram if you can.

5. Try to refine your rephrased question to generate an actual bit of maths you can work on.

6. Give yourself a chance to get inspired. Question 10 is a good example: it’s really very easy when you see the trick, but you need to see the trick. To succeed here you need the confidence and knowledge that comes from steps (1) and (2).

As a basic principle: keep practicing and questioning your understanding. That way you’ll build up your knowledge and confidence. If you persevere you will be surprised how quickly you can improve.

1. Ewan says:

Hi, thanks for the advice, and for the website too, enormously helpful.