All The Best For Your H1 / H2 Maths Papers This Week!

Tuition given in the topic of H1/H2 (A Level) Maths Tutor from the desk of The Higher Council at 11:56 pm (Singapore time)

Hello everyone, it’s me again.

How time flies and the ‘A’ Level H1 Maths / H2 Maths papers are now upon us.

Though I’m very busy with my classes with just days to go, I would like to take the time to say something ~~(after I’ve been ‘poked’ (Facebook-style) by my sister)~~ to those of you taking your H1/H2 Maths papers this week.

Get Your Basic Concepts/Techniques Right!

Before you enter your exam hall, you should be familiar and confident with the following pure maths basic concepts and techniques (without relying on any formula sheet):

Completing the square/factorisation of cubic functions
Basic trigonometric ratio values & *trigonometric identities (these are assumed knowledge/topics for self-study)
Concepts of sine rule, cosine rule, similar triangles, Pythagoras’ Theorem
*Inequalities (yes, I know some of you hate this)
*Partial fractions
*Geometry & locus concepts
*Formulae of area & volume of various basic geometrical shapes
*Doing substitutions correctly

Topical Groupings

For Paper 1, some topics are usually lumped together in questions in the following groupings:

Graphs/Transformation/Inequalities/Functions
Differentiation & their applications (N.B. make sure your get your differentiation right as subsequent part(s) i.e. rate of change, maxima/minima etc. depend on it)
Integration (*by substitution, by parts, area or volume)
*AP/GP/Summation/Mathematical Induction/Recurrence
*Vectors (vector equations of straight lines vs the (chim) planes)
*Complex numbers (roots & Argand diagrams)
*Differential Equations (Separation of Variables, Applications)

Final Round of Practice

I’m not an advocate of spotting questions but if you’re taking H2 Maths and are already sufficiently well-prepared, here are some stuff to practice for a final round:

*Parametric equations (tangent/normal or area of integration)/ Maclaurin’s expansion
*Solving system of linear equations (using the RREF function in your GC)
*Inequalities (incl. modulus functions)
*Vectors (vector equations of straight lines is easier to score compared to planes!)
*Complex numbers (practice TYS questions – don’t be stressed by your prelim questions)
*Curve sketching (basic curves, circles, parabolas, hyperbolas, oblique asymptotes etc.)
*Using your GC to perform sketching, locate roots, compute areas etc. (a quick run-through to boost your confidence of its keystrokes/usage)
*Recurrence (familiarise your GC‘s SEQUENTIAL MODE to input recurrence equations)

*H2 topics

At this point, I would like to say that no matter how tough your prelim papers were, please be confident that most ‘A’ Level questions are ‘do-able’ PROVIDED you are firm and confident in your concepts.

Even if you’ve always found certain topics to be tough, remember that there are still a lot of easy marks to collect everywhere in the paper – so don’t give up just because you can’t do part (a) i.e. even if you can’t prove (a), you can still quote the prove directly for part (b).

Therefore, even if you can’t do the plane portion of the vector question, you should still be able to do the straight line portion. And even if you can’t prove the differential equation, you should instinctively use the proof to complete the integration (via Separation of Variables) in the subsequent part 😉

Last but not least, like what my sister has been telling her O Level students, please follow the 5 Cs and read the questions Calmly, Carefully and Correctly before answering them, lookout for Clues contained within them, and do those which you are more Confident in solving first.

Good Luck!

頑張って!!!

The Higher Council

Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

Comments & Reactions

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12 Comments

Nash commented in tuition class
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OMG cher!!! How to do Qn4 >__< gaaah! I can send the paper over the weekend if u want =X
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Reply Nash
Mr Loi Friend Mr Loi on Facebook commented in tuition class
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Nash: Are you taking H1 or H2 Mathematics? If it's H2, are you referring to the (the function/curve sketching/integration question)?
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Reply Mr Loi
kohes commented in tuition class
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Part (i): $\text{f}(27)+\text{f}(45)=\text{f}(3)+\text{f}(1)=6+5=11$
Part (ii): Sketch the case when $0<{x}\leq4$ . Then just copy the graph to the left and right. You should get something zig-zag.
Part (iii): $36\frac{2}{3}$
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Reply kohes
kohes commented in tuition class
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6:41pm
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That is, if you are referring to the H2 Maths Paper.
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Reply kohes
Zenology commented in tuition class
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7:02pm
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Damn I didn't get 36 2/3. Is e answer def right?
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Reply Zenology
kohes commented in tuition class
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Here is my working:
$\int_{-4}^{-2}\text{f}(x)\text{d}x=\int_{0}^{2}\text{f}(x)\text{d}x=11\frac{1}{3}$
$\int_{-2}^{0}\text{f}(x)\text{d}x=10$
$\int_{2}^{3}\text{f}(x)\text{d}x=4$
By adding up all the areas, it will be $36\frac{2}{3}$ .
I think Mr Loi is writing solutions now 🙂
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Reply kohes
Nash commented in tuition class
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H2 paper... Aiyah totally messed up >_< oh wells... must work hard for P2,
If i drew curvy line instead of zig-zag (like the cosine curve kind) should be ok right?
BTW, how do u know that f(27)+f(45) gives u those 2 things?
Q1)i didnt know how to do...14marks gone =_=
but is it supposed to use ax^2+bx+c=10,6,5 and then solve using simultaneous eqns?
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Reply Nash
kohes commented in tuition class
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3:21pm
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I think you will still get some marks, it is not exactly zig-zag. The x = 0 to x = 2 part of the graph should be parabolic joining (0, 7) and (2, 3), concave downwards, while the x = 2 to x = 4 part should be a straight line joining (2, 3) and (4, 7).
For (i), the question stated $\text{f}(x)=\text{f}(x+4)$ . In my opinion, this equation is not completely understood by many.
See it as $\text{f}(1)=\text{f}(1+4)$ , which is equal to $\text{f}(5)$ . This process is repeated:
$\text{f}(5)=\text{f}(5+4)=\text{f}(9)=$ .
Note that $\text{f}(1)=\text{f}(5)=\text{f}(9)=\ldots=\text{f}(45)$ . Therefore, we have $\text{f}(1)=\text{f}(45)=7-(1)^2=6$
Similarly, $\text{f}(3)=\text{f}(3+4)=\ldots=\text{x}(27)=2(3)-1=5$ .
Well... a lot of people could not do this question, so you do not need to worry! All the best for your Paper 2 🙂
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Reply kohes
kohes commented in tuition class
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3:22pm
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Oops, type too fast... The line should read:
Similarly, $\text{f}(3)=\text{f}(3+4)=\ldots=\text{f}(27)=2(3)-1=5$ .
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Reply kohes
nana commented in tuition class
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3:42pm
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wow wow! totally impressed by the working. really alot of people dun know?? i totally died there.
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Reply nana
Nash commented in tuition class
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Ya ALOT of ppl from my sch dunno so im alittle reassured...
For qn 2 right the summation bit I just realised i forgot to multiply by 1/2 Since A=2 and the second part was 1/(r^3-r). does that mean my whole working is wrong? i wrote the series would converge to 1/2 instead of the correct ans of 1/4 because of this >_<...
Crap few more mistakes like this and i can kiss my A or B goodbye
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Reply Nash
Mr Loi Friend Mr Loi on Facebook commented in tuition class
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Ok guys I've finally managed to get the 2009 H2 Maths Paper 1 suggested solutions all done up - let's all head over there!
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Reply Mr Loi