2023 STEP 3 Math
For people who took STEP 3 Math today, what are your thoughts on the paper, and what did you make of its difficulty compared to those of previous years? Which questions did y'all solve, and what are your predicted grade boundaries?
I'll start the ball rolling-
1. I did Questions 1,4,5,6,7,8
2. Predicted Grade Boundaries: 82 S, 67 1
I'll start the ball rolling-
1. I did Questions 1,4,5,6,7,8
2. Predicted Grade Boundaries: 82 S, 67 1
Scroll to see replies
I attempted questions 1, 2, 4, 5, 6, 7, 8 but i think i may have actually completed 1,2, 6 and 7. the first one and the 7th one were nice in my opinion and the second one was ok ish (a bit messy). The 6th one led you through it well but some of my reasoning was questionable lol. I wish i was able to do q8 but in the moment i was too unsure about moving past the second part :/.
Polar one-full
Poisson stats one-full except 1 part
Prime number- full except the second part of the last part
First Mechanics one-2/3 Complete
Question 1 coordinate- first part(not complete)
Second mechanics one-first part(barely started)
The difficulty of the questions themselves was normal. However, I found it quite long compared to previous years as questions had multiple parts. Q8 was over a page! I’m surprised you guys attempted it. It was so long!
I would predict the boundaries for 1 to between 59-61. S should be 75-80.
I was hoping for a 1 but now I’m unsure.
Poisson stats one-full except 1 part
Prime number- full except the second part of the last part
First Mechanics one-2/3 Complete
Question 1 coordinate- first part(not complete)
Second mechanics one-first part(barely started)
The difficulty of the questions themselves was normal. However, I found it quite long compared to previous years as questions had multiple parts. Q8 was over a page! I’m surprised you guys attempted it. It was so long!
I would predict the boundaries for 1 to between 59-61. S should be 75-80.
I was hoping for a 1 but now I’m unsure.
(edited 10 months ago)
Original post by CriticalBoson
Q8 was over a page! I’m surprised you guys attempted it. It was so long!
luckily i didnt get too stuck into it before i left it to do another question. all questions nowadays are so long its hard to choose whether its worth starting one incase you dont finish it.
(edited 10 months ago)
I got nearly a full on the DE (Q8)
All of Integration except (iv)
Half of the cos polynomial question
Most of the prime numbers q except the actual solutions
About half of the poisson question
And then again half of the hyperbolic one (kind of messed that one up)
Hoping for about 60 for a 1 but will likely be higher
All of Integration except (iv)
Half of the cos polynomial question
Most of the prime numbers q except the actual solutions
About half of the poisson question
And then again half of the hyperbolic one (kind of messed that one up)
Hoping for about 60 for a 1 but will likely be higher
Original post by _jameswatson_
luckily i didnt get too stuck into it before i left it to do another question. all questions nowadays are so long its hard to choose whether its worth starting one incase you dont finish it.
I agree.
I feel like STEP is somewhat of a luck game. I think they shouldn’t have the choice of 12 questions because it introduces luck to your mark. It's difficult to gauge question difficulty(especially later parts) after reading a question. If you (luckily) choose a question in which later parts are straightforward, you score higher. It’s better to just have 6 questions. The argument of having 12 questions because people have certain stronger topics is flawed. The theory involved is very easy for most test takers and what’s difficult is the problem solving. Since all the questions aren’t of equal difficulty, it’s a luck game.
Original post by CriticalBoson
I agree.
I feel like STEP is somewhat of a luck game. I think they shouldn’t have the choice of 12 questions because it introduces luck to your mark. It's difficult to gauge question difficulty(especially later parts) after reading a question. If you (luckily) choose a question in which later parts are straightforward, you score higher. It’s better to just have 6 questions. The argument of having 12 questions because people have certain stronger topics is flawed. The theory involved is very easy for most test takers and what’s difficult is the problem solving. Since all the questions aren’t of equal difficulty, it’s a luck game.
I feel like STEP is somewhat of a luck game. I think they shouldn’t have the choice of 12 questions because it introduces luck to your mark. It's difficult to gauge question difficulty(especially later parts) after reading a question. If you (luckily) choose a question in which later parts are straightforward, you score higher. It’s better to just have 6 questions. The argument of having 12 questions because people have certain stronger topics is flawed. The theory involved is very easy for most test takers and what’s difficult is the problem solving. Since all the questions aren’t of equal difficulty, it’s a luck game.
But can't you argue that they are actually testing how judiciously you choose your questions? It's kind of like testing your mathematical intuition to tell whether a question is easy or hard? Also, I'm pretty sure in the Tripos exams there is a choice of questions too, and the format of STEP is meant to mimic the Tripos.
Original post by _jameswatson_
luckily i didnt get too stuck into it before i left it to do another question. all questions nowadays are so long its hard to choose whether its worth starting one incase you dont finish it.
Yeah, but longer questions do have more guidance as compared to shorter ones. It's kind of like a slow building up to the final part of the question, I guess.
Does anyone remember the rough solution sketch to the last part of the polar problem Q2? My proof that the limit was 1 was quite iffy, and I straight up skipped finding the last limit because I ran out of time.
Justifying the final solution in q8 seemed very tedious (also glossed over it due to a lack of time haha) - seemed to require showing that (i) h(pi/2 - x) (or any multiple of it) was a valid solution to the y''-py'+qy equation; then (ii) showing that it was continuously differentiable at bounds; (iii) justifying (in brief) the periodicity condition, and repeating all this again for the other bound in (b) to show that h(x) was a valid solution (or any multiple of it). This just seemed like way too much working to write for a final part - hope it isn't worth 8 marks or something... Anyone has any insight on this?
Otherwise I think I cleared the entirety of Q5(NT), 7(Integral), 11(E(D), E(Z) problem), and only managed to do Q6(i) and (ii)(a) becuase I ran out of time. Hopefully it's S-able...
Justifying the final solution in q8 seemed very tedious (also glossed over it due to a lack of time haha) - seemed to require showing that (i) h(pi/2 - x) (or any multiple of it) was a valid solution to the y''-py'+qy equation; then (ii) showing that it was continuously differentiable at bounds; (iii) justifying (in brief) the periodicity condition, and repeating all this again for the other bound in (b) to show that h(x) was a valid solution (or any multiple of it). This just seemed like way too much working to write for a final part - hope it isn't worth 8 marks or something... Anyone has any insight on this?
Otherwise I think I cleared the entirety of Q5(NT), 7(Integral), 11(E(D), E(Z) problem), and only managed to do Q6(i) and (ii)(a) becuase I ran out of time. Hopefully it's S-able...
Original post by Anonymous
Does anyone remember the rough solution sketch to the last part of the polar problem Q2? My proof that the limit was 1 was quite iffy, and I straight up skipped finding the last limit because I ran out of time.
I said that since the numerator and denominator were quadratics in k, you could disregard the lower order terms. Then I used the fact that tan(alpha)=1/k in order to deal with the alphas in the expression which got it down to 1 in the end.
did the same with the second limit and after checking I got the correct limit.
idk how rigorous the method I did is tho xd
Original post by Anonymous
I got nearly a full on the DE (Q8)
All of Integration except (iv)
Half of the cos polynomial question
Most of the prime numbers q except the actual solutions
About half of the poisson question
And then again half of the hyperbolic one (kind of messed that one up)
Hoping for about 60 for a 1 but will likely be higher
All of Integration except (iv)
Half of the cos polynomial question
Most of the prime numbers q except the actual solutions
About half of the poisson question
And then again half of the hyperbolic one (kind of messed that one up)
Hoping for about 60 for a 1 but will likely be higher
the integration for IV was very arbitrary, you had to consider (e^(ax/2) k(X) - e^-(ax/2))^2
Original post by _jameswatson_
I said that since the numerator and denominator were quadratics in k, you could disregard the lower order terms. Then I used the fact that tan(alpha)=1/k in order to deal with the alphas in the expression which got it down to 1 in the end.
did the same with the second limit and after checking I got the correct limit.
idk how rigorous the method I did is tho xd
did the same with the second limit and after checking I got the correct limit.
idk how rigorous the method I did is tho xd
Sounds rigorous enough for step at least, I think it was simpler for the second part of the limit to consider limit of R/T as limit of R/S × S/T because S/T was easy to calculate (1/3) is what I got and then R/S we know limits to 1. I checked numerically afterwards and I think this is right (not 100% sure though)
Original post by Anonymous
Sounds rigorous enough for step at least, I think it was simpler for the second part of the limit to consider limit of R/T as limit of R/S × S/T because S/T was easy to calculate (1/3) is what I got and then R/S we know limits to 1. I checked numerically afterwards and I think this is right (not 100% sure though)
hm i get with k=1000: R/T = 0.36058918292. Your way does sound nicer than my way though so its probably better plus ive probably put the wrong thing into the calculator
(edited 10 months ago)
Original post by _jameswatson_
hm i get with k=1000: R/T = 0.36058918292. Your way does sound nicer than my way though so its probably better plus ive probably put the wrong thing into the calculator
the limit should tend to 2pi/(3pi+8) if i remember correctly
Original post by CriticalBoson
I agree.
I feel like STEP is somewhat of a luck game. I think they shouldn’t have the choice of 12 questions because it introduces luck to your mark. It's difficult to gauge question difficulty(especially later parts) after reading a question. If you (luckily) choose a question in which later parts are straightforward, you score higher. It’s better to just have 6 questions. The argument of having 12 questions because people have certain stronger topics is flawed. The theory involved is very easy for most test takers and what’s difficult is the problem solving. Since all the questions aren’t of equal difficulty, it’s a luck game.
I feel like STEP is somewhat of a luck game. I think they shouldn’t have the choice of 12 questions because it introduces luck to your mark. It's difficult to gauge question difficulty(especially later parts) after reading a question. If you (luckily) choose a question in which later parts are straightforward, you score higher. It’s better to just have 6 questions. The argument of having 12 questions because people have certain stronger topics is flawed. The theory involved is very easy for most test takers and what’s difficult is the problem solving. Since all the questions aren’t of equal difficulty, it’s a luck game.
I disagree, I think the point is that you aren't supposed to have seen any of the content, and all the questions are of reasonably similar difficulty, I will give you that this year there were some harder and some easier ones on the pure (I unfortunately didn't get time to look at any stats), but in general other than notable exceptions if there's a hard result they give you suitable guidance. A recent notable exception would be 2020s q8 which was a proof of the countability of the rationals (proving a function is bijective from the naturals to the rationals) as I feel this question is not very approachable from the standpoint of A-level maths, as well as another question I did (I can't remember the year) regarding kempner series, the harmonic series without a bunch of terms, although this one was certainly more doable. In the other direction there certainly are some questions throughout the years that are a bit lacking but they tend to be few and far between. Step is supposed to be hard after all.
Original post by Anonymous
the limit should tend to 2pi/(3pi+8) if i remember correctly
odds are I made a mistake somewhere 😭😭 I hate algebra
Original post by Anonymous
For people who took STEP 3 Math today, what are your thoughts on the paper, and what did you make of its difficulty compared to those of previous years? Which questions did y'all solve, and what are your predicted grade boundaries?
I'll start the ball rolling-
1. I did Questions 1,4,5,6,7,8
2. Predicted Grade Boundaries: 82 S, 67 1
I'll start the ball rolling-
1. I did Questions 1,4,5,6,7,8
2. Predicted Grade Boundaries: 82 S, 67 1
I did those exact same questions as you.
How do you think the marks were broken down for all of the qs I can't rlly tell?
Original post by Anonymous
Does anyone remember the rough solution sketch to the last part of the polar problem Q2? My proof that the limit was 1 was quite iffy, and I straight up skipped finding the last limit because I ran out of time.
Justifying the final solution in q8 seemed very tedious (also glossed over it due to a lack of time haha) - seemed to require showing that (i) h(pi/2 - x) (or any multiple of it) was a valid solution to the y''-py'+qy equation; then (ii) showing that it was continuously differentiable at bounds; (iii) justifying (in brief) the periodicity condition, and repeating all this again for the other bound in (b) to show that h(x) was a valid solution (or any multiple of it). This just seemed like way too much working to write for a final part - hope it isn't worth 8 marks or something... Anyone has any insight on this?
Otherwise I think I cleared the entirety of Q5(NT), 7(Integral), 11(E(D), E(Z) problem), and only managed to do Q6(i) and (ii)(a) becuase I ran out of time. Hopefully it's S-able...
Justifying the final solution in q8 seemed very tedious (also glossed over it due to a lack of time haha) - seemed to require showing that (i) h(pi/2 - x) (or any multiple of it) was a valid solution to the y''-py'+qy equation; then (ii) showing that it was continuously differentiable at bounds; (iii) justifying (in brief) the periodicity condition, and repeating all this again for the other bound in (b) to show that h(x) was a valid solution (or any multiple of it). This just seemed like way too much working to write for a final part - hope it isn't worth 8 marks or something... Anyone has any insight on this?
Otherwise I think I cleared the entirety of Q5(NT), 7(Integral), 11(E(D), E(Z) problem), and only managed to do Q6(i) and (ii)(a) becuase I ran out of time. Hopefully it's S-able...
For Q8 I thought for the last bit i.e. (b) since h'(x)>=0 for -3/4pi to pi/4, and h'(x) is e^-x(cosx-sinx) or smthn like that, its periodic 2pi so adding 2pi to the interval gives 5/4pi to 9/4pi hence h'(x)>=0 in this interval also thus h(x) is a solution?
Original post by Anonymous
I did those exact same questions as you.
How do you think the marks were broken down for all of the qs I can't rlly tell?
How do you think the marks were broken down for all of the qs I can't rlly tell?
This is what i thought, let me know if you disagree with any of the mark allocations and if i missed any parts.
Q1
(i) Show that the line between P and Q is tangent to the circle (7/8 marks)
(ii) Show that as P varies there are two values of Q that satisfy this equation (2/3 marks)
Find q1q2 and q1 + q2 in terms of P (1/2 marks)
(iii) Show that for all p =/+-1 there are two values of q such that a triangle is formed which is tangent to the circle (7/8 marks)
Q5
(i) Show that if this equation is true then this is true (2 marks)
Hence find p and q that satisfy this (3 or 4 marks)
(ii) Show that is this equation is true then this equation is true (1 or 2 marks)
Explain why p+q=n-1 (2 or 3 marks)
Hence find p and q (2 or 3 marks)
(iii) Show that these two inequalities hold (1 or 2 marks)
Hence show that there are no p q prime such that equals power of 3 (4 or 5 marks)
Q8
(i) Verify that this is a solution to the differential equation shown (2 marks)
Show that y=0 and dy/dx=1 at x =0 (1 mark)
(ii) Write the solution g1(x) and find g2(x) for this differential equation (4 or 5 marks)
(iii) What is the transformation of the two solutions (2 marks)
(iv) Prove that if this satisfies this DE then this satisfied this DE for a range which you should state (3 or 4 marks)
(v) Show that h’(pi/4)=0 (1 mark)
Hence find solution (a) (2 or 3 marks)
Solution (b) (2 or 3 marks)
Q7
(i) Show that integral sub thingy (2 marks)
(ii) Show that integral of g(x)-x all squared is 0 (2 or 3 marks) and hence explain why g(x) is 0 in this interval (1 or 2 marks)
(iii) Find h- (4 or 5 marks)
(iv) Explain why a is 2 (3 marks) hence find k (4 or 5 marks)
Q6
(i) Show that cosh^2x > x^2+1 (2 or 3 marks)
Hence sketch the function (4 marks)
(ii)
(a)Explain why there are at least 2 solutions (2 marks)
(b) Show that this function is increasing (2 marks)
c) Show that this other function is increasing (2 marks)
d) Hence show that there are exactly 2 solutions (2 or 3 marks)
iii) Sketch it (3 or 4 marks)
Q4
(i) Cos(2n+1) de moivre (4 or 5 marks)
(ii) Choosing suitable t find the coefficient of x^2n+1 ( show that its 2^2n) (3 or 4 marks)
(iii) Show that the coefficient of x^2n-1 is (2n-1)2^2n-2 (4-6 marks)
(iv) Write down the coefficient of x^2n (1 mark) and find the coefficient of x^2n-2 (4-6 marks)
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