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# Oxford PAT 2016

1. Guys, learn the a2 content on space. It comes up regularly on the PAT for estimating distances between planets etc.
2. (Original post by hellomynameisr)
Guys, learn the a2 content on space. It comes up regularly on the PAT for estimating distances between planets etc.
I've barely started PAT work yet, been mainly focusing on M2 and M3 work over summer. Are there any other obvious a2 physics topics I should be prioritising before attempting some papers?
3. (Original post by tangotangopapa2)
I don't have that book. Just looked at the online version of the book. That problem looks interesting.

The quadrilateral ACBD has, AC=AD and BC=BD where AB and CD are diagonals. It is easy to figure out that AB and CD are perpendicular.
Area of triangle ADB = 1/2 X AB X OD (Where O is the point where diagonals meet, not shown in the book. Draw it yourself) and area of triangle ACB is 1/2 X AB X OC.
Since, OC + OD = CD
You get the formula 1/2 X AB X CD.

Hope this helps.

For those wondering, the figure is below:

Attachment 576244
maybe it's a bit late idk but how do you know they are perpendicular?
4. (Original post by Inert1a)
maybe it's a bit late idk but how do you know they are perpendicular?
5. Now that the PAT syllabus is changed, is it still very important to do MCQs and long questions from the past papers?
6. (Original post by lawlieto)
I have a few questions about electromagnetism.

Is there always a magnetic field around a current carrying wire? Even if the current is "steady"? I mean, dI/dt is a constant, not a function of t?
Why are electric fields due to magnetic fields concentric circles? (edit: I have seen the example of putting a copper ring in a uniform magnetic field, and when the flux linkage was increased that induced an emf and hence a current in the ring, and when there's a current, there's an electric field driving the charges, and that electric field would be concentric circles, but the electric field due to changing magnetic field exists without the copper ring as well, or without charges, which I can't understand atm)

Thanks
May I link you to the following post?

http://www.thestudentroom.co.uk/show...8#post67267538
7. (Original post by 98matt)
I've barely started PAT work yet, been mainly focusing on M2 and M3 work over summer. Are there any other obvious a2 physics topics I should be prioritising before attempting some papers?
The syllabus is quite deceiving in the fact that it says that most of the content being assessed will be AS. But, when you look at past papers, there is a lot of A2 content. Look through a couple past papers (the physics section especially) and see if there are any questions you can't answer due to insufficient knowledge.

(Original post by tangotangopapa2)
Now that the PAT syllabus is changed, is it still very important to do MCQs and long questions from the past papers?
Practice is practice. I'd still do them
8. (Original post by hellomynameisr)
Practice is practice. I'd still do them
How would you approach this type of problems?

9. (Original post by tangotangopapa2)
How would you approach this type of problems?

I would look at it and cry for a good hour

After that one hour, I would start to depict the question bit by bit.

Firstly, f(x) > 0 for all values of x. Now we know that squaring any number would result in a positive outcome, yes? And for all values of x, this would be positive. Therefore, we know that it will have a quadratic like shape and will be in the top 2 quadrants

Second, a continuous function is one that has no holes or gaps in it. In simpler terms, you could draw it without lifting your pen from the paper. Whereas a function like y= 1/x would have to be sketched by lifting your pen off the paper.This is quite hard to explain for me so see this video:
It is not taught at A level (I think) so better do some research.

Third, df/dx = 0 only when x = 4. What do we know when the first derivative is equal to 0? It is a point where the gradient is 0. Therefore, when x = 4, the gradient will be 0 and so a local minimum will be at this point.

Lastly, when the second derivative is equal to 0, we know that these are point of inflection. These are when x = 2 and x = 6. So they basically turn about those point (something like that).

Lo and behold, we have all the information we need to sketch the function.

Hope this helps
10. (Original post by tangotangopapa2)
How would you approach this type of problems?

(Original post by hellomynameisr)
I would look at it and cry for a good hour

After that one hour, I would start to depict the question bit by bit.

Firstly, f(x) > 0 for all values of x. Now we know that squaring any number would result in a positive outcome, yes? And for all values of x, this would be positive. Therefore, we know that it will have a quadratic like shape and will be in quadrant one only.

Second, a continuous function is one that has no holes or gaps in it. In simpler terms, you could draw it without lifting your pen from the paper. Whereas a function like y= 1/x would have to be sketched by lifting your pen off the paper.This is quite hard to explain for me so see this video:
It is not taught at A level (I think) so better do some research.

Third, df/dx = 0 only when x = 4. What do we know when the first derivative is equal to 0? It is a point where the gradient is 0. Therefore, when x = 4, the gradient will be 0.

Lastly, when the second derivative is equal to 0, we know that these are point of inflection. These are when x = 2 and x = 6. So they basically turn about those point (something like that).

Lo and behold, we have all the information we need to sketch the function.

Hope this helps
f(x) > 0 for all x means it would be in two quadrants (the top half), not one! It just has to all be above the x axis. Also be careful for (d) that you don't draw stationary points (as df/dx isn't 0 here), while (c) gives you a stationary point (either maximum or minimum at x=4.

A bit of graph sketching which can be helpful for the PAT/interviews is in FP1 (for AQA at least), but it's all stuff you can figure out from what you have been taught already I think.
11. (Original post by Lau14)
f(x) > 0 for all x means it would be in two quadrants (the top half), not one! It just has to all be above the x axis. Also be careful for (d) that you don't draw stationary points (as df/dx isn't 0 here), while (c) gives you a stationary point (either maximum or minimum at x=4.

A bit of graph sketching which can be helpful for the PAT/interviews is in FP1 (for AQA at least), but it's all stuff you can figure out from what you have been taught already I think.
Oh yes! I see my mistakes. Thank you
12. (Original post by Lau14)
.
What kind of questions did they ask you in the interview?
13. (Original post by hellomynameisr)
What kind of questions did they ask you in the interview?
I had two interviews at my main college which were a mix of shorter maths and physics questions (a series of 10 quick questions e.g. what is cos(pi/6), some graph sketching, integration, differentiation, terminal velocity, energy conservation, stuff like that), and one interview at a second college where they did a longer question on electrostatics, starting easy and building it up to a more complicated situation (and again, more graph sketching).
14. (Original post by hellomynameisr)
I was able to get part A right but don't understand B and C

From the solutions, why does he do what he does in part B? I understand that p=v^2/r but how does he get the values to input them in from

And part C, how does he split up the circuit like that
I remember being like ' why are there two points labelled differently ( different letters) but at the same potential on the exam xD
15. What are some resources to practice maths section for the PAT other than past papers?The questions asked in PAT have quite a different nature compared to other and usually questions are of following properties/categories:

1) Often simple questions involving mental arithmetic is asked e.g. 2023^2 - 2022^2, (3.12)^5 correct to one decimal place.

2) Coordinate geometry of line includes, finding slope of line passing through two points or finding equation of the line passing through one point and having slope this (you need to find slope, e.g. perpendicular to another line). Coordinate geometry of circle is often asked but some of the questions that might put us off is like this: Find equation of line/lines tangent to the circle/curve and passing through this point (usually outside point).

3) Simple questions testing properties of logarithms.

4) Trigonometric equations; finding solution in a given interval. (Usually Pythagorean Identity has to be used and then quadratic equation has to be solved. Obviously, some extraneous results should be omitted). Some knowledge of inverse trigonometric function. e.g evaluate cos(tan^-1(sin(cot^-1x)))

5) Arithmetic and geometric sequence and series, including finding sum of infinite geometric series.

6) Factoring polynomials (degree 3 or 4) and finding all roots.

7) Simple application of binomial expansion formula (Knowledge of Pascal's triangle is enough).

8) Calculus: Rate of change e.g. If Rate of change of volume of water in cylinder is this, then what is the rate of change of height. Finding maxima/minima. Some harder questions like: Maximise area of rectangle of given perimeter. Simple knowledge of concavity, increasing/decreasing functions etc. is asked.

9) Calculus: Finding area by integration. Finding definite integrals. Usually you either have to split expression into partial fractions or use algebraic substitution.

10) Solving rational inequalities. Simple cautions to ensure no sign flip if you multiply equation by certain terms is often required.

edit: I forgot this. 11) Probability theory: Simple probability questions. Sometimes one may have to use conditional probability formula but never binomial/Possion/Nomal distribution formula. One type of tricky question is: 3 special dice (each can give score of 1-8) are rolled. The score is calculated as Ad1 + Bd2 + Cd3 + D where A,B,C and D are constants and d1-3 are individual score of the die. Find the constants so that : - The score ranges from 1-512 and each score has equal probability.

12) Roots of quadratic equation and their properties is assumed.

13) Simple algebraic manipulation eg. If a= x^2 + y ^2 and b = 2xy express x and y in terms of a and b.

14) Geometry. 95% of the time the question involves circle inscribed by polynomials ( most often equilateral triangle or square). You usually have to find the ratio of areas of two separate regions in the figure.

15) The hardest of all. Curve sketching. Questions range from trivial to extremely challenging. You might have to use properties of transformation of graph. Sketch graphs of completely different/complicated functions. Sketch graphs of y = f(x) +/- g(x), y = f(x)g(x) or f(x)/g(x) where you know the graph of y = f(x) and y=g(x) separately. Sometimes you might have to sketch inequalities like. -2 < y/x < 4 or 0< y/x^2 < 6pi.

MAT questions/ Senior Maths Challenge questions/ BMO questions don't have above mentioned properties. They deal with hard number theory, combinatorics, different type of algebra problems and provide very little help in brushing up above type of problems. So, what might help me to practice these type of problems? Thanks in advance.
16. (Original post by tangotangopapa2)
What are some resources to practice maths section for the PAT other than past papers?The questions asked in PAT have quite a different nature compared to other and usually questions are of following properties/categories:

1) Often simple questions involving mental arithmetic is asked e.g. 2023^2 - 2022^2, (3.12)^5 correct to one decimal place.

2) Coordinate geometry of line includes, finding slope of line passing through two points or finding equation of the line passing through one point and having slope this (you need to find slope, e.g. perpendicular to another line). Coordinate geometry of circle is often asked but some of the questions that might put us off is like this: Find equation of line/lines tangent to the circle/curve and passing through this point (usually outside point).

3) Simple questions testing properties of logarithms.

4) Trigonometric equations; finding solution in a given interval. (Usually Pythagorean Identity has to be used and then quadratic equation has to be solved. Obviously, some extraneous results should be omitted). Some knowledge of inverse trigonometric function. e.g evaluate cos(tan^-1(sin(cot^-1x)))

5) Arithmetic and geometric sequence and series, including finding sum of infinite geometric series.

6) Factoring polynomials (degree 3 or 4) and finding all roots.

7) Simple application of binomial expansion formula (Knowledge of Pascal's triangle is enough).

8) Calculus: Rate of change e.g. If Rate of change of volume of water in cylinder is this, then what is the rate of change of height. Finding maxima/minima. Some harder questions like: Maximise area of rectangle of given perimeter. Simple knowledge of concavity, increasing/decreasing functions etc. is asked.

9) Calculus: Finding area by integration. Finding definite integrals. Usually you either have to split expression into partial fractions or use algebraic substitution.

10) Solving rational inequalities. Simple cautions to ensure no sign flip if you multiply equation by certain terms is often required.

12) Roots of quadratic equation and their properties is assumed.

13) Simple algebraic manipulation eg. If a= x^2 + y ^2 and b = 2xy express x and y in terms of a and b.

14) Geometry. 95% of the time the question involves circle inscribed by polynomials ( most often equilateral triangle or square). You usually have to find the ratio of areas of two separate regions in the figure.

15) The hardest of all. Curve sketching. Questions range from trivial to extremely challenging. You might have to use properties of transformation of graph. Sketch graphs of completely different/complicated functions. Sketch graphs of y = f(x) +/- g(x), y = f(x)g(x) or f(x)/g(x) where you know the graph of y = f(x) and y=g(x) separately. Sometimes you might have to sketch inequalities like. -2 < y/x < 4 or 0< y/x^2 < 6pi.

MAT questions/ Senior Maths Challenge questions/ BMO questions don't have above mentioned properties. They deal with hard number theory, combinatorics, different type of algebra problems and provide very little help in brushing up above type of problems. So, what might help me to practice these type of problems? Thanks in advance.
So far i would say if you study from the papers toroughly, timing your attempts at the section and dont waste time quickly leave questions you dont get, and then mark the ones that gave you trouble and really understand why, i think most people doing the pat are good but approach questions taht wrong way, i have changed the way i approach maths questions now because of the practice for the pat.

You probably know the book but do some puzzles from professor povey's book

Also, if you have a math teacher, or someone really exprienced i would leave teh paper with them and ask them to go through it and try to set you some similar questions for practice, and if you can try writing some yourself (although this maybe quite tedious to do)
I havent gone over the mat papers yet are they difficult?

Perhaps PhysM23 could lend us some advice as he has gone through the exam and maybe go over some of things i've said here.
I'm sure if we look right we can find plenty of similar questions, even if the questions arent similar im sure it wouldnt be bad to do them
17. Hi guys,
Im thinking of applying to Oxford for engineering. I got 4As at AS this year, in Maths, Further Maths, Physics and Chem.
Ive not started any prep for the PAT.
What Maths modules should i cover?
A checklist of somesort with mlst of the things i need to do to be prepared would be great.
Thanks very much
18. (Original post by Lau14)
I had two interviews at my main college which were a mix of shorter maths and physics questions (a series of 10 quick questions e.g. what is cos(pi/6), some graph sketching, integration, differentiation, terminal velocity, energy conservation, stuff like that), and one interview at a second college where they did a longer question on electrostatics, starting easy and building it up to a more complicated situation (and again, more graph sketching).
what college was that. ? ( those questions are nothing like what I got asked)
19. (Original post by tangotangopapa2)
What are some resources to practice maths section for the PAT other than past papers?The questions asked in PAT have quite a different nature compared to other and usually questions are of following properties/categories:

1) Often simple questions involving mental arithmetic is asked e.g. 2023^2 - 2022^2, (3.12)^5 correct to one decimal place.

2) Coordinate geometry of line includes, finding slope of line passing through two points or finding equation of the line passing through one point and having slope this (you need to find slope, e.g. perpendicular to another line). Coordinate geometry of circle is often asked but some of the questions that might put us off is like this: Find equation of line/lines tangent to the circle/curve and passing through this point (usually outside point).

3) Simple questions testing properties of logarithms.

4) Trigonometric equations; finding solution in a given interval. (Usually Pythagorean Identity has to be used and then quadratic equation has to be solved. Obviously, some extraneous results should be omitted). Some knowledge of inverse trigonometric function. e.g evaluate cos(tan^-1(sin(cot^-1x)))

5) Arithmetic and geometric sequence and series, including finding sum of infinite geometric series.

6) Factoring polynomials (degree 3 or 4) and finding all roots.

7) Simple application of binomial expansion formula (Knowledge of Pascal's triangle is enough).

8) Calculus: Rate of change e.g. If Rate of change of volume of water in cylinder is this, then what is the rate of change of height. Finding maxima/minima. Some harder questions like: Maximise area of rectangle of given perimeter. Simple knowledge of concavity, increasing/decreasing functions etc. is asked.

9) Calculus: Finding area by integration. Finding definite integrals. Usually you either have to split expression into partial fractions or use algebraic substitution.

10) Solving rational inequalities. Simple cautions to ensure no sign flip if you multiply equation by certain terms is often required.

edit: I forgot this. 11) Probability theory: Simple probability questions. Sometimes one may have to use conditional probability formula but never binomial/Possion/Nomal distribution formula. One type of tricky question is: 3 special dice (each can give score of 1-8) are rolled. The score is calculated as Ad1 + Bd2 + Cd3 + D where A,B,C and D are constants and d1-3 are individual score of the die. Find the constants so that : - The score ranges from 1-512 and each score has equal probability.

12) Roots of quadratic equation and their properties is assumed.

13) Simple algebraic manipulation eg. If a= x^2 + y ^2 and b = 2xy express x and y in terms of a and b.

14) Geometry. 95% of the time the question involves circle inscribed by polynomials ( most often equilateral triangle or square). You usually have to find the ratio of areas of two separate regions in the figure.

15) The hardest of all. Curve sketching. Questions range from trivial to extremely challenging. You might have to use properties of transformation of graph. Sketch graphs of completely different/complicated functions. Sketch graphs of y = f(x) +/- g(x), y = f(x)g(x) or f(x)/g(x) where you know the graph of y = f(x) and y=g(x) separately. Sometimes you might have to sketch inequalities like. -2 < y/x < 4 or 0< y/x^2 < 6pi.

MAT questions/ Senior Maths Challenge questions/ BMO questions don't have above mentioned properties. They deal with hard number theory, combinatorics, different type of algebra problems and provide very little help in brushing up above type of problems. So, what might help me to practice these type of problems? Thanks in advance.
1) you use difference of two squares, these "tricks" come automatically after having spent your life with maths.
(2023-2022)*(2023+2022) looks easier, right?

2) C1/C2. These questions are awfully common in the core modules, given that you had an A* in maths, this should be fine? If not, you could do some C1/C2 Solomon papers, they are supposed to be more challenging than past papers.

3) C2, same argument as above

4) C2/C3 same argument as above above
.
.
.
11) Average S1/S2 question
15) Curve sketching is my hobby You just have to practice them really. C3 curve sketching is not going to be enough here, the one in edexcel FP2 should be more help, and of course, you should do your own practice from PAT past papers.

I think these shouldn't mean any problem to you with an A* in maths and A in further maths. If you don't feel secure enough, practice using Solomon papers or more advanced A level questions (there should be threads on it but I've been sitting on a bus for 18 hours and I'm even too tired to go to the toilet but I can help you find them later)
Maths is all about practice and a bit of knowledge.
20. (Original post by tangotangopapa2)
What are some resources to practice maths section for the PAT other than past papers?
Hey, for PAT last year, I mainly used the STEP papers (1&2) and the MAT for algebra, trigs, graphs etc. Step questions usually have a neat trick hidden away and it might be useful to learn how to spot these.

Also 'Advanced problems in Mathematics' and 'Core problems in Mathematics' by Siklos are well worth a read.

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