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: 
Total marks: 5
When 
.
Equation of tangent is given by 
Total marks: 5
(a)
Let 
—(1)
—(2)
—(3)
—(4)
Using GC, 
(b)
Using GC,
When 
When 
Thus, we have that range of values of 
is given by 
.
Total marks: 6
(a) 
since 
for 
is perpendicular to 
.
since 
(b) Let 
be the required angle.
Since 
, then 
Since 
, then 
We have that 
and 
.
Total marks: 10
(a)
(b)
(c)
![= \bigg[ \frac{x \sin nx}{n} + \frac{\cos nx}{n^2} \bigg]_0^{\pi}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-80477c22fedd156a4e48c7364a5dbf36_l3.png "Rendered by QuickLaTeX.com")
When is an even integer, 
When is an odd integer, 
Thus, 
or 
(d)
![= \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}}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-bc57ed8d4abacb0aab5fd5f1ae4c91b7_l3.png "Rendered by QuickLaTeX.com")
Total marks: 7
(a) ![\sum_{r=2}^n \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-d8ec13734f6af3c4272ec7c7a3d5df9f_l3.png "Rendered by QuickLaTeX.com")
(b)![\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](http://theculture.sg/wp-content/ql-cache/quicklatex.com-4e7144eabf008a15cc874a8d61ca6f70_l3.png "Rendered by QuickLaTeX.com")
When 
and ![\sum_{r=2}^n \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg] \rightarrow - \ln2](http://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 to infinity 
.
(c) ![\sum_{r=10}^{20} \ln \bigg[ \frac{(r-1)(r+1)}{r^2} \bigg]](http://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]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-66ea1dd0a3bda8d61a5550aeac213634_l3.png "Rendered by QuickLaTeX.com")
, where 
and 
.
Total marks: 8
(a)
![= \big[ \frac{1}{2}(1 + \cos 2\theta) \big]^2](http://theculture.sg/wp-content/ql-cache/quicklatex.com-93b28e1c88d7336c5e15f4ec336b2fb4_l3.png "Rendered by QuickLaTeX.com")
(b)
First, 
.
When 
When 
.
![= \frac{81\pi}{8} \bigg[ \frac{1}{4} \sin 4 \theta + 2 \sin 2 \theta + 3 \theta \bigg]_{\frac{\pi}{6}}^{\frac{\pi}{2}}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-4737bd4c74be64d13af8084e9be804d5_l3.png "Rendered by QuickLaTeX.com")
Total marks: 10
(a)
Using GC,
(b) 
(c) Since the 
, 
does not exist.
(d) For the inverse function to exist, we need f to be a one-one function. Thus 
.
(e) Observe that if , then 
, and 
Let 
Domain of 
Total marks: 10
(a)(i)
(a)(ii)
When 
.
(b) If we observe the first equation, 
suggests to us that 
is a real number.
—(1)
—(2)
From (2), we let 
, then 
.
By comparing the imaginary part, 
.
By comparing the real part, 
.
From (1), we have 
or 
When 
When 
Total marks: 13
(a)
At B, 
Solving, 
and 
. Thus, 
and 
(b)(i)
Shortest distance 
(b)(ii) Hence, we let required angle be .
(c)
normal vector, 
Total marks: 13
(a) 
, where 
is a positive constant.
(b) When 
(c)
, where 
is an arbitrary constant.
, where 
When 
(d)
Let 
, we find that 
For 
Thus, the no of additional days 
.
(e)(i)
As 
. 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.
(e)(ii)
Total marks: 13
Note: Money and time should be left in decimals. Money should be given in two decimal places, unless otherwise stated.
(a)
Amount saved ![= a + (a + 50) + [a+2(50)] + \ldots [a+35(50)] = \frac{36}{2}[2a + (36-1)(50)] > 50000](http://theculture.sg/wp-content/ql-cache/quicklatex.com-290693c82ac0d1aa54ccc043e83267fe_l3.png "Rendered by QuickLaTeX.com")
Using GC,
Thus, smallest value of 
.
(b)
Let 
be the amount owed at the end of months.
 - x](http://theculture.sg/wp-content/ql-cache/quicklatex.com-5a1c5dcc4b7d1f68c7aea884c1a77990_l3.png "Rendered by QuickLaTeX.com")
 - x](http://theculture.sg/wp-content/ql-cache/quicklatex.com-ac5655a200b6772fb132f34464ecaba0_l3.png "Rendered by QuickLaTeX.com")
(c)(i) Let 
,
Using GC, 
Thus, he needs 
to repay the loan fully.
(c)(ii) Total interest paid 
.
(d)(i) 
Using GC,
Thus, Wei will repay the loan at the rate of 
per month for 
months and the final repayment of 
(d)(ii) Total interest paid in (di) 
Total savings 
[…] 2023 A-level H2 Mathematics (9758) Paper 1 […]
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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 🙂