# Oxford PAT 2009, Questions 10, 11 and 12

## 4 thoughts on “Oxford PAT 2009, Questions 10, 11 and 12”

1. Shan says:

how do you know that the 2nd angle is also 30 degrees?

1. By the 2nd angle, you mean (in question 10) the acute angle at the top of the smaller triangle?

To prove that this is also 30 degrees, you should be able to show that the hypotenuse of the smaller triangle is parallel to the side of the equilateral triangle. Then the two labelled angles are ‘corresponding angles’.

To prove that the hypotenuse is parallel to the side of the equilateral, notice that each end of the hypotenuse is the same perpendicular distance from the side of the equilateral, and it should be easy from there. But you don’t need to formally prove that fact in order to answer the question.

2. rickardo says:

i dont understand how b=3 at the end.
Im so frustrated i keep not getting things i dont know if its an off day feeling really demotivated now

1. Hi Rickardo — don’t get too dispirited. Firstly we all go though frustrations like this and it always gets better after a decent night’s sleep. Secondly the fact that you are looking at these questions now means that by November you will be much better prepared than most people taking the test.

You are referring to question 11, right? Let me go through it step by step. An arithmetic progression is one in which the difference between successive terms is the same for every pair of terms in the sequence. Because we have four terms, we have three differences between successive terms, so we have two equations. Actually we only needed one equation, which makes the question a bit confusing to look at, but in any case we can see that both equations simplify to the same one: a = 3a/b. Multiplying both sides by b, we get ba = 3a. We are told in the question that a is not equal to zero, so we can divide both sides by a (this wouldn’t be valid if a were equal to zero), and this leaves us with b = 3.

I hope this helps. Keep persevering and things will fall into place.