Get LOTS of extra practice and support during my Zoom lessons this weekend. PAT is Saturday, ESAT is Sunday. zphysicslessons.net/physics-tutoring Good luck!!
12:05. Whenever I come across questions that involve something like tan(arccost) or cos(arcsinx), I like to use triangles! So in this case, I will use a parameter t and let t = arcsinx. From that, we can determine that x = sin t. Drawing a right-angle triangle with acute angle t, we can have the opposite side be x and the hypotenuse be 1, because sin t = x/1 = x. But we want cos t, where t=arcsinx, so we want to find the adjacent side, which we can do by pythagoras. Finally, we can obtain cos t or cos(arcsinx) as sqrt(1-x²).
@@Gabriel-zd8iy This is a constant so differentiates to zero. 16 is probably the easiest to find though, 4C1 x x/2 x 2^3 = 2^5 x / 2 = 16x, which differentiates to 16. I just wanted to point it out.
Excellent question - the best way I believe is spotting tricks..e.g. not expanding, using the difference of squares formula, finding turning points and number of roots via sketching… etc. Approximation for mental maths in my experience can also save a lot of time. I hope this helps! Good luck!
Problem 1 Answer A also has x^3/4 so your method is not valid for a student taking the SAT exam as they would be confused Heres a better way to approach this. If we use chain rule we’d bring the power forward and multiply and take one off the power So thats 4(2+x/2)^3 Now we dont need to expand the entire thing We all probably know when expanding cubic term we cube the first term of the expression, here its 2 So if we expand it, 4 would get multiply we would get 4 * 2^3 which is 32. Now when using the chain rule we also differentiate the inner expression, so that’s be 1/2 if you do it So 32/2 =16 and thats your first term for your derivative and theres only one answer with 16 as first, so D
So probably easier to consider the next term as well and see that it will equal 16. Chain Rule was my first instinct as well but typically working with the terms is a little quicker. If you are just as quick with the chain rule though I'd say go for it!
Hello Sir first of all thank you for this video it really helps (am still watching it :) ). I have question to you. As it is known, pat consists of multiple-choice questions only this year so we wont likely have the very unique type of questions that were worth a lot of marks (formula derivation, graph sketching etc.). So how will the difficulty of the pat change according to you because I really am not sure. Thank you again
Interesting question, unfortunately, I can’t really make a guess as it is very likely to be inaccurate. What I can say though is that if you have covered the syllabus, done lots of past paper practice and all the practice tests available - you will have a great chance of doing well. Good luck!
Hello there! Great video- thank you. I am preparing for the BMSAT - not the ESAT or PAT but just wanted to see if any of the methods used could save me a bit of time! Just wanted to ask you if you had any tips for speeding up on more GCSE level maths questions - particularly geometry problems! The maths itself isn't hard, it is just trying to find the quickest path! Thank you again!
excellent question! I think it is a great idea to make a list of all the geometry theorems in the spec and then to find a problem for each. You would get used to spotting them a little quicker. I hope this helps. Good luck next week!
excellent question , because the curve is symmetric, you can say that half the range will produce half the integral. It's a pure time saving technique and you should get the same answer with a lot more algebra and arithmetic without the trick.
ops should be 2 and 3 are non-zero! thanks for the spot! I was flilming this late after work, I had a feeling I might have made a slip somewhere! Just to note, the maths is correct but the chosen answer should correspond to my working out.
@@Juno-q7d I’d recommend doing all the available past papers. I find the senior physics challenge a different style of questions but olympiad problems are generally a good practice for it.
