Things to note for 9758 H2 Mathematics

It has been awhile since the A’levels. We talked and met up with several of our students. Some students are working and some are preparing their Personal Statements for overseas University Applications.

A few of them also remarked that they wish they put more efforts into studying A’levels.  An advice to this year JC2 – Do not wait till it is too late.

Students should also have a clear understanding of their syllabus, especially their scheme of exam. I still have JC2s this year who get stunned by the applications questions I threw at them (P.S. Aside from spending time with family, I wrote many sets of applied questions.). You may read more about your syllabus here. Or see the following images.

Integration & Applications Source: SEAB
Scheme of Examination Source: SEAB

How much practice or emphasis your school put on this, is up to them. But it is clear that application takes up 25% of your marks. The entire syllabus can be found here.

PLEASE DON’T WALK INTO THE EXAM HALL BLUR BLUR…

Release of A’levels Results 2016

For students who took A’levels in 2016, please note that information for the release of A’levels Results 2016 can be found in the following!

Release of A’levels 2016

Grade Profile (i.e. Number of As you need to get into courses for)

SMU

NTU

NUS

P.S. Results does not define you. When one door closes, another opens.

Checklist for Vectors

Many schools have been doing vectors recently. Thought I’ll share a little summary/ checklist I have done for my students.

Basic Concepts

  • Operations on Vectors
    • Addition & Subtraction
    • Scalar multiplication
    • Dot Product (Scalar)
      1. a • a = |a|2
      2. If a ⊥ b, then a • b = 0
      3. a • b = b • a
    • Cross Product (Vector)
      1. a × a = 0
      2. a × b = − b × a
  • Unit Vectors
  • Parallel Vectors ( a = k)
  • Collinear Vectors ( Parallel with a common point )
  • Ratio Theorem ( Found in MF26)
    • Midpoint Theorem
  • Directional Cosines
  • Angles between two Vectors
  • Length of Projection
  • Perpendicular Distance

Lines

  • Equations
    • Vector Form ( : r = a + λb, λ∈ ℜ )
    • Parametric Form
    • Cartesian Form
  • Line & Line
    • Parallel ( Directions are parallel to each other. )
    • Same ( Same Equations )
    • Intersecting ( There is a unique solution for λ and μ. )
    • Skewed ( Not parallel AND not Intersecting. )
  • Angle between two lines ( Angle between their directions )
  • Point & Line
    • Foot of Perpendicular
    • Perpendicular (Shortest) distance
    • Point on Line

Planes

  • Equations
    • Parametric Form ( π r = a + λb + μc, λ, μ ∈ ℜ )
    • Scalar Product Form ( r • n = a • n  = d )
    • Cartesian Form
  • Point & Plane
    • Foot of Perpendicular
    • Perpendicular (Shortest) distance
    • Distance from O to Plane
    • Point on Plane
    • Reflection of Point
  • Line & Plane
    • Relationships
      1. Parallel
        • Line intersects Plane entirely ( Infinite Solutions )
        • Do not intersect ( No Solution )
      2. Not Parallel
        • Intersects at a point ( One Solution )
    • Intersection Point
    • Angle between Line & Plane
    • Reflection of Line
  • Plane & Plane
    • Relationships
      1. Parallel
        • Same ( Infinite Solutions )
        • Do not intersect ( No Solution )
      2. Not Parallel
        • Intersects at a line ( Infinite Solutions )
    • Intersection Line ( Use of GC )
    • Angle between two Planes ( Angle between their normals )

A little history of e

Some students remarked on why I actually recognise e, that is, e=2.718281828.... Well, e is a rather unique constants. Firstly, for all JC students, we see it our daily algebra & complex numbers. Students exposed to university statistics will see e appearing in the formula for normal distribution, that is, f(x | \mu , \sigma^2) = \frac{1}{\sqrt{2 \sigma^2 \pi}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}}.

Secondly, the story of how it came about is pretty cool as you will observed in the video below.

The Story of e

Hopefully it provides you with another perspective towards this constants! And now you should be more cautious when signing up savings plans that give interest per annum or per month.

P.S. I once confused a banker when I asked her about this. 🙂

How to maintain your self discipline to study?

Dear all, this is a general post on how to keep your study momentum up during this december holidays. As you already know, this december holidays is not only a time for you to rejuvenate yourself from the hectic JC life, it is also an important revision time for you! It is a time when you consolidate all that you have learnt in this year, so that you would have a good foundation to start JC2. (For those who didn’t do well in the promos, you should be doing catch up. For those who did well, you could possibly revise your learning and embark on a head-start program.)

So what are the 3 tips for you to have self-discipline?

One of the reason why students do not have self-discipline is because they do not believe in themselves and their abilities to attain academic success. They attach negative talk to themselves such as they are stupid, lazy and not cut out for straight As. Hence, their inner beliefs shape their actions and their revision process. One way to change it would be to change your identity. Start thinking to yourself that you deserve Straight As everyday and you will soon internalize it and manifest these behaviours. 

Secondly, you should attach pain to the notion of you not achieving your goals. Each time when you think about how you would not achieve your goals, it will automatically propel you to take action! It could possibly be a lack of self esteem, respect from your parents and society. Regret for not achieving your aims etc.

Finally, you could think about how to reward yourself whenever you achieve your goals and to get a trusted person to be accountable for you. One way to do this is to tell your friends or parents what you desire to achieve for the A levels, and to get them to monitor your revision schedule. I know this sounds unappealing to you, but this could perhaps be the best way to make sure you stay discipline to your goals!!

Have a good break everyone! Of course have a fruitful revision time too!

Commentary for 2016 A level paper

1. ‘Any adaptation of a novel for a film, television or the theatre is never as effective as the original.’ Discuss. (Media)

2. Assess the view that traditional buildings have no future in your society. (Arts and SG Society)

3. ‘Longer life expectancy creates more problems than benefits.’ Discuss. (S&T)

4. Considering the money involved, should developing countries be allowed to host major sporting events? (Sports)

5. ‘Human need, rather than profit, should always be the main concern of scientific research.’ Discuss.  (S&T)

6. ‘Countries experiencing conflict should be left to sort out their own problems.’ How far do you agree? (International politics) 

7. How far has modern technology made it unnecessary for individuals to possess mathematical skills? (S&T + Maths)

8. ‘People who do the most worthwhile jobs rarely receive the best financial rewards.’ To what extent is this true of your society? (General)

9. Evaluate the claim that equality of opportunity for females is a desirable, but unrealistic, goal. (Gender)

10. Assess the view that most natural disasters are the result of human activity. (Environment)

11. Is competition always desirable? (General)

12. ‘Everyone has an opinion, but not everyone’s opinion is of equal value.’ What is your view? (General)

Based on the above questions, it appears that this year’s paper is relatively easy to prepare for and address. Common topics that come out yearly include science and technology and arts and culture. This year’s paper has a high percentage of science and technology question (Q3, Q5 and Q7), 2 being comparison in nature and 1 being a general question. Topics of focus are narrow and specific. Hence, for students preparing for questions on science and technology, they should be well versed in the different sectors and to be prepared for a specific question type. General and opinionated questions form the other bulk of this year’s paper (Q8, Q11 and Q12). It would be harder to predict and prepare for these questions, but they tend to appeal to students who either have a flair for smoking or did not prepare for the other content-based topics.

Moving forward, students should know what type of questions they are strong in, whether they should do a specific question type or a more open-ended/general question. Second, students should also know the question requirements in order to tackle the essay effectively. Absolute terms, matrix questions and even criteria questions have been evident for this year’s paper.

Are you prepared enough at this stage if you are taking A levels in 2017?

Some questions that students ask recently.

I’ve been asked many times recently about what university course to take, and also what university to go too, etc. Some students ask me how does Financial Mathematics work? So I’ve come across an article here. This article illustrates how to be a quant, which is just one of the jobs available to someone who studies financial mathematics.

I should clarify that studying Finance is a far cry from studying Financial Mathematics. They are very different. For the pragmatic students, the latter earns more. Is it easy? I shared some undergraduate reviews that I’ve done previously, here. It is on some simple ideas of Financial Mathematics, its basics.

So I’ll share a bit more in near future on studying Operations Research, Bayesian Methods, Data Mining and Analytics. Hopefully it will give students a better idea of studying Mathematics in university. And please remember, that H2 Mathematics is a far cry from University Mathematics. Students are better off doing Engineering if you fancy H2 Mathematics. And I’m sorry that I can’t share too much on Pure Math, as the above mentioned are my forte.

Thanks! And now let’s all go for holidays!