H1 & H2 Mathematics Consolidation

• wee_ws

  10 Feb 12, 08:36

  Hi students,

    In the footsteps of eagle, I will look into mathematical content :)

    Questions and responses will be consolidated in this thread.

    Kindly highlight the difficulty you faced and answer accompanying the question. Do not simply expect us to spoonfeed you as learning is a very personal experience.

    Questions regarding IB maths and AP Calculus could also be posted here.

  Cheers,
  Wen Shih

• wee_ws

  10 Feb 12, 08:40

  Posted 30 Jan in reply to a query about Getting Ready for JC:

  Hi Xavolon,

    For H2 Maths, relevant knowledge from O-level E & A Maths are:

    1. Proportion and variation

    2. Perimeter, area and volume

    3. Linear & quadratic inequalities

    4. Sum and product of roots of a quadratic equation

    5. Binomial expansion

    6. Long division, factor and remainder theorems

    7. Surds and indices

    8. Logarithmic and exponential functions

    9. Solving of simultaneous equations (both linear, one linear and one non-linear)

    10. Matrices

    11. Graphs of circles, parabolas, logarithmic, exponential, trigonometric, y = 1/x, y = 1/x^2, y^2 = kx and y = |ax+b|

    12. Differentiation techniques and its applications

    13. Integration techniques and area of a region

    14. Coordinate geometry, simple geometrical results, similarity, congruency

    15. Trigonometric identities

    16. Sequences and patterns

    17. Vector geometry

    18. Set theory

    19. Probability

    20. Mean and standard deviation

    You may also obtain further details on pages 12 and 13 of the syllabus document at:

    http://www.seab.gov.sg/aLevel/2013Syllabus/9740_2013.pdf

    Please note that some content I have listed above are not stated in the syllabus. From my experience, such content are necessary to extend to A-level H2 Maths.

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  10 Feb 12, 08:43

  By LastRide7 on 25 Jan 2012:

  The complex number q is given by q = (e^iθ)/(1 - e^iθ) where 0<θ<2pi. Find the real part of q.

  Solution I posted on the same day:

  Hi,

    We try to make the denominator of q real, which is done by multiplying q top and bottom by e^(-iθ/2) giving

    e^(iθ/2) / [ e^(-iθ/2) - e^(iθ/2) ].

    Since e^(iθ/2) + e^(-iθ/2) = 2 cos (θ/2), the above expression simplifies to

    [ cos (θ/2) + isin (θ/2) ] / [ -2 cos (θ/2) ], so that

    real(q) = -1/2.

    I have written about this type of problem before, so you may find it useful to read it:

    http://sgforums.com/forums/2297/topics/356377?page=3#post_10226565

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  10 Feb 12, 08:49

  By knt on 23 Jan 2012:
  Solve the DE (sec x)(dy/dx) = e^(sin x) + y given that y = 1 when x = 0.
  
  Solution I posted on 23 Jan 2012:

  Hi,

    I believe it is assessed under H3 Maths where the integrating factor method is to be used to solve the question.

    We rewrite the DE as

    (dy/dx) - (cos x) y = (cos x) e^(sin x).

    Integrating factor is e to the power of integral of -cos x dx, leading to

    e^(-sin x).

    Multiplying both sides of the DE, we obtain

    e^(-sin x) (dy/dx) - (cos x) e^(-sin x) y = cos x

    => d/dx [ y e^(-sin x) ] = cos x.

    Integrating both sides wrt x, we obtain

    y e^(-sin x) = integral of cos x dx

                       = sin x + c.

    When x = 0 and y = 1, c = 1.

    Now y e^(-sin x) = sin x + 1 is the particular solution, from which we arrive at

    y = (sin x + 1) e^(sin x).

   

  Cheers,
  Wen Shih