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: 
Question 7: 
Question 8: 
Question 9: 
Question 10: 
Question 11: 
.
—(1)
—(2)
—(3)
—(4)
is given by 
.
since 
for 
is perpendicular to 
.
since 
be the required angle.
, then 
, then 
and 
.
![= \bigg[ \frac{x \sin nx}{n} + \frac{\cos nx}{n^2} \bigg]_0^{\pi}](https://theculture.sg/wp-content/ql-cache/quicklatex.com-80477c22fedd156a4e48c7364a5dbf36_l3.png "Rendered by QuickLaTeX.com")
or 
![= \bigg[ \frac{x \sin 2x}{2} + \frac{\cos 2x}{2^2} \bigg]_0^{\frac{\pi}{4}} - \bigg[ \frac{x \sin 2x}{2} + \frac{\cos 2x}{2^2}\bigg]_{\frac{\pi}{4}}^{\frac{\pi}{2}}](https://theculture.sg/wp-content/ql-cache/quicklatex.com-bc57ed8d4abacb0aab5fd5f1ae4c91b7_l3.png "Rendered by QuickLaTeX.com")
![\sum_{r=2}^n \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg]](https://theculture.sg/wp-content/ql-cache/quicklatex.com-d8ec13734f6af3c4272ec7c7a3d5df9f_l3.png "Rendered by QuickLaTeX.com")
![\sum_{r=2}^n \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg] = \ln \frac{n+1}{n} - \ln 2 = \ln (1 + \frac{1}{n}) - \ln 2](https://theculture.sg/wp-content/ql-cache/quicklatex.com-4e7144eabf008a15cc874a8d61ca6f70_l3.png "Rendered by QuickLaTeX.com")
and ![\sum_{r=2}^n \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg] \rightarrow - \ln2](https://theculture.sg/wp-content/ql-cache/quicklatex.com-83ca24e529971ca10cc6ef066d237527_l3.png "Rendered by QuickLaTeX.com")
, which is a constant (finite). Thus the series is convergent.
.![\sum_{r=10}^{20} \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg]](https://theculture.sg/wp-content/ql-cache/quicklatex.com-01f2865bde7b41d0962d89b2ac440e4b_l3.png "Rendered by QuickLaTeX.com")
![= \sum_{r=2}^{20} \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg] - \sum_{r=2}^9 \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg]](https://theculture.sg/wp-content/ql-cache/quicklatex.com-66ea1dd0a3bda8d61a5550aeac213634_l3.png "Rendered by QuickLaTeX.com")
, where 
and 
.
![= \big[ \frac{1}{2}(1 + \cos 2\theta) \big]^2](https://theculture.sg/wp-content/ql-cache/quicklatex.com-93b28e1c88d7336c5e15f4ec336b2fb4_l3.png "Rendered by QuickLaTeX.com")
.
.
![= \frac{81\pi}{8} \bigg[ \frac{1}{4} \sin 4 \theta + 2 \sin 2 \theta + 3 \theta \bigg]_{\frac{\pi}{6}}^{\frac{\pi}{2}}](https://theculture.sg/wp-content/ql-cache/quicklatex.com-4737bd4c74be64d13af8084e9be804d5_l3.png "Rendered by QuickLaTeX.com")
, 
does not exist.
.
, and 
.
suggests to us that 
is a real number.
—(1)
—(2)
, then 
.
.
.
or 
and 
. Thus, 
and 
, where 
is a positive constant.
, where 
is an arbitrary constant.
, where 
, we find that 
.
. We observe that Andrew’s mass will decrease and approach 88kg in the long run. Thus, it is not possible for him to achieve 80kg.
![= a + (a + 50) + [a+2(50)] + \ldots [a+35(50)] = \frac{36}{2}[2a + (36-1)(50)] > 50000](https://theculture.sg/wp-content/ql-cache/quicklatex.com-290693c82ac0d1aa54ccc043e83267fe_l3.png "Rendered by QuickLaTeX.com")
.
be the amount owed at the end of 
 - x](https://theculture.sg/wp-content/ql-cache/quicklatex.com-5a1c5dcc4b7d1f68c7aea884c1a77990_l3.png "Rendered by QuickLaTeX.com")
 - x](https://theculture.sg/wp-content/ql-cache/quicklatex.com-ac5655a200b6772fb132f34464ecaba0_l3.png "Rendered by QuickLaTeX.com")
,
.
per month for 
months and the final repayment of 
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do you have the h1 answers😭😭
Hi, I did do the stats for my h2 math students to try. Haven’t got time to do the pure math section though.
2023 A-level H1 Mathematics (8865) Paper 2 Suggested Solutions
Will they deduct a mark if I never explicitly state out what is the value for a and b for qn5c?
Will they deduct a mark if I never explicitly state out what is the value for a and b for qn5c? what score would you think can get an A for this paper?
I think the answer for Question 11(d)(i) is wrong because he pays at the end of the month but interest is added at the beginning of the month. So there is one more round of interest added before the final payment.
I have written out a solution for the papers (since I’m a tutor for H2 Math) — but I may also have misread the question 😅
Indeed. Thanks for pointing out 🙂
11di Need to consider interest in the final month before repayment?
Indeed. Thanks for pointing out 🙂