Possible Questions for H2 Mathematics (2010)

October 26, 2010Wei Jie 1 Comment »

The H2 Mathematics paper seems to be more challenging each year, especially with the possibility of unexpected questions, which leave students claiming that a particular question type was not taught. In this article, we explore the possible question which may appear in this year’s paper. Hopefully, this can help you score some additional marks here and there.

Functions may well be relatively easy for most students this year, as schools have prepared them to expect unorthodox questions.

For the transformation of graphs, sketching the curve of y = f'(x) has not surfaced over the past three years. A possible question would be to sketch such a curve, given the original curve. Pay careful attention to the stationary points and asymptotes, indicating the transformed points and asymptotes in your answer where necessary. Albeit unlikely, students may be asked to sketch the curve of y = f(x), given the curve of y = f'(x) and another transformed curve.

This year, a question involving the method of differences may possibly be tested. Recall that this is achieved when there is a common function, i.e. f(1) – f(2) + f(2) – f(3) + … – f(n – 1) + f(n – 1) – f(n) = f(1) – f(n). Schools would have placed much emphasis on this topic. While problems involving decomposition by partial fractions abound, always remember that the function may be exponential, logarithmic or even trigonometric – think along the addition formulae.

Questions involving vectors can be quite unpredictable at time, but have the scalar and vector products at your fingertips. These equations can be rearranged to give surprising results which can solve the question more effectively. Perhaps, this year’s question may involve a three-dimensional diagram, such as an odd-shaped container. Of course, do not forget about the ratio theorem, which is found in List MF15, and of course, the midpoint theorem, which can be subsequently derived from the ratio theorem. When finding the angles between lines, vectors and planes, it is advisable to check whether the angle is acute or obtuse. And chances are, vectors will appear in both papers.

For other Pure Mathematics topics such as complex numbers and differential equations, read the full article at the Mathematics Handy Guide website.

http://handyguide.mathsguidebook.com/viewer?2010-h2-mathematics-possible-questions

Questions involving vectors can be quite unpredictable at time, but have the scalar and vector products at your fingertips. These equations can be rearranged to give surprising results which can solve the question more effectively. Perhaps, this year’s question may involve a three-dimensional diagram, such as an odd-shaped container. Of course, do not forget about the ratio theorem, which is found in List MF15, and of course, the midpoint theorem, which can be subsequently derived from the ratio theorem. When finding the angles between lines, vectors and planes, it is advisable to check whether the angle is acute or obtuse. And chances are, vectors will appear in both papers.

One response to this entry

  • Wen Shih Says:

    Other possibilities:
    – Rates of change
    – Formulation of a differential equation
    – Conjecture
    – Approximating an area by rectangles above or below the curve
    – Questions with arbitrary values

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