Oxford PAT 2016

Guys, learn the a2 content on space. It comes up regularly on the PAT for estimating distances between planets etc.

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.
Add these areas to get the area of the quadrilateral.
Since, OC + OD = CD
You get the formula 1/2 X AB X CD.

Hope this helps.

For those wondering, the figure is below:

maybe it's a bit late idk but how do you know they are perpendicular?

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

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?

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

How would you approach this type of problems?

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 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:
https://www.youtube.com/watch?v=InDHwh1CvOg
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.

.

What kind of questions did they ask you in the interview?

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

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.

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 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.

What are some resources to practice maths section for the PAT other than past papers?