All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions
Numerical Answers (workings/explanations are after the numerical answers.)
Question 1: 
Question 2: 
Question 3: 
Question 4: 
Question 5: 
Question 6: Smallest 
, Translate the graph of 
units in the negative 
direction
Question 7: 
Question 8: 
Question 9: 
is maximum; 
Question 10: ![\frac{dN}{dt} = kN, k = \frac{1}{2}\ln3, t = 4.19; N = \frac{2}{\ln 3} [(50 \ln 3 - d) e^{0.5 \ln 3 t} + d]; d > 50 \ln3; t = 5.35](http://theculture.sg/wp-content/ql-cache/quicklatex.com-ee1138aed6ad37c92bd378e42ca54a13_l3.png "Rendered by QuickLaTeX.com")
Question 11: 
![\bigg[ \frac{a}{4}x^4 + \frac{b}{3}x^3 + \frac{c}{2}x^2 + dx \bigg]_0^1 = 6](http://theculture.sg/wp-content/ql-cache/quicklatex.com-d427376fa3d909595321352d744d9423_l3.png "Rendered by QuickLaTeX.com")
.
and 
.
.
![(1+z)^4 + (1 + z^*)^4 = 2 + 4(z + z^*) + 6[z^2 + (z^2)^*] + 4[z^3 + (z^3)^*] + [z^4 + (z^4)^*]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-27c10a3f8d1a1dc580632bae9c9ec76e_l3.png "Rendered by QuickLaTeX.com")
![(1+z)^4 + (1 + z^*)^4 = 2 + 4[2Re(z)] + 6[2Re(z^2)] + 4[2Re(z^3)] + 2Re(z^4)](http://theculture.sg/wp-content/ql-cache/quicklatex.com-0a0d7cccef49831889f0af84d62ed588_l3.png "Rendered by QuickLaTeX.com")
![(1+z)^4 + (1 + z^*)^4 = 2 + 4[2\cos \frac{\pi}{4}] + 12\cos \frac{\pi}{2} + 8\cos \frac{3\pi}{4} + 4\cos \pi](http://theculture.sg/wp-content/ql-cache/quicklatex.com-e8d096c734756febeea51bab2bff34b3_l3.png "Rendered by QuickLaTeX.com")
. 
.
and 
, thus the minimum is when 
and thus 
and thus we should translate the graph of 
is perpendicular to direction of 
, the lines are both perpendicular.
and 
.
and 
represents any position vector lying on 
and 
values for will give the intersection that this common perpendicular cuts 
is a maximum.
![= \frac{\pi}{2} \bigg[ \frac{1}{2} e^{2x} + \frac{1}{4} e^{2x} \cos 2x + \frac{1}{4} e^{2x} \sin 2x \bigg]_0^{\pi /2}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-ff7400f5c46c18ba31d5e6189009e19e_l3.png "Rendered by QuickLaTeX.com")
where 
since 
using GC.
where 
.![\therefore \quad N = \frac{2}{\ln 3}[(50 \ln 3 - d)e^{kt} + d]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-cd3d9e356ae2da3aa99c39d2310910bb_l3.png "Rendered by QuickLaTeX.com")
.![N = \frac{2}{\ln 3}[(50 \ln 3 - 58)e^{kt} + 58] = 0](http://theculture.sg/wp-content/ql-cache/quicklatex.com-ca75459948093df305a7ca6e4dcde707_l3.png "Rendered by QuickLaTeX.com")
![PS = a[2\pi - \beta - \sin (2\pi - \beta)] - a(\beta - \sin \beta)](http://theculture.sg/wp-content/ql-cache/quicklatex.com-7d7d8f273f156a8b1f90695e8d3600c5_l3.png "Rendered by QuickLaTeX.com")
![= a^2 \bigg[ \frac{3}{2} \theta - 2\sin \theta + \frac{1}{4} \sin 2 \theta \bigg]_{\beta}^{2\pi - \beta}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-6e28171547d62f8588f63392da6ceb0d_l3.png "Rendered by QuickLaTeX.com")
![= a^2 \bigg[ \frac{3}{2} (2\pi - \beta)- 2\sin (2\pi - \beta) + \frac{1}{4} \sin 2(2\pi - \beta) - ( \frac{3}{2} \beta - 2\sin \beta + \frac{1}{4} \sin 2 \beta) \bigg]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-4f44a420a252896c77ff552aeaa37844_l3.png "Rendered by QuickLaTeX.com")
![= a^2 \bigg[ 3\pi -\frac{3}{2} \beta + 2\sin \beta - \frac{1}{4} \sin \beta - \frac{3}{2} \beta + 2\sin \beta - \frac{1}{4} \sin 2 \beta) \bigg]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-6135b51f1d53adea7d6a751437be99af_l3.png "Rendered by QuickLaTeX.com")
![= a^2 [ 3\pi - 3 \beta + 4 \sin \beta - \frac{1}{2} \sin 2 \beta ]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-5bcedade1852bab951550e958f7a5bfd_l3.png "Rendered by QuickLaTeX.com")
.
.
, where 
, 
.Things that have yet to come out, but do not fully rely on these as examinations are surprising always.
Vectors algebra, planes, APGP, DE with substitution, Complex Conjugates and Functions (Piece wise with conics). All the best.
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question 6 should be -2a in positive x-axis
yes, indeed. typed wrongly.
can u do h1 math pls!!
sure! if I do get the time 🙂 All the best for the remaining papers!
yes pls do H1 math there are no suggested answers anywhere 🙁
Hello, I will finish up the pure math section soon.
http://theculture.sg/2021/11/2021-a-level-h1-mathematics-8865-paper-1-suggested-solutions/
Hello, I will finish up the pure math section soon.
http://theculture.sg/2021/11/2021-a-level-h1-mathematics-8865-paper-1-suggested-solutions/
Q4: Should
be 
instead?
yes, you are right. I believe it is below in the solutions. I probably missed it out in the final numeric section. Will add in. Thank you for pointing it out.
do u hv the qns ppr
so sorry, I don’t as I believe there is copyright laws involved. 🙁 But I believe reddit has it circulating.
Is it possible to state the marks allocation for each part
Hi, I believe you can go reddit and find the question paper circulating and it should help. I can’t share it as there are copyright laws involved.
11.b what if i did the integration correctly but put the limits wrongly? how manyy marks would i lose?
I would say a maximum of 3 marks since it is a 6 marks question.
Is there ecf for stats
there is no ecf in mathematics, simply method and answer mark.
If I didn’t simplify my expression in q2, how much marks I lose?