Rigel Kent

The number 13 is sometimes considered inauspicious in certain cultures and so it is not uncommon for superstitious triskaidekaphobic persons to avoid the use of 13 in their daily life and ask: How many different lucky \(n\)-digit numeric passcodes can be formed such that they do not contain 13 . The special case of \(n = 4\) is actually a problem in the 2019 SPM additional mathematics paper (Paper 1, Question 22). For the uninitiated, this special case of \(n = 4\) can be quite intimidating . Four-digit numeric passcode on a iOS device To get our engine started, let's consider the first trival case when \(n = 1\). Apparently there is no single-digit passcode which contains the pattern 13 or \(\mathbb{S}_{\rm unlucky}^{(1)} = \varnothing\). Thus we do not have any unlucky passcodes when \(n = 1\): $$n(\mathbb{S}^{(1)}_{\rm unlucky}) = 0, \quad n(\mathbb{S}^{(1)}_{\rm lucky}) = 10^1 - n(\mathbb{S}_{\rm unlucky}^{(1)}) = 10$$ where \(n(\mathbb{S}^{...

Normally students are given closed-ended problems with nicely labeled diagram in math exams. This type of problems usually has only one standard answer. Ocassionally, however, some not-so-well-conceived open-ended problems found their way into our exam papers. This year, some SPM candidates fucked up their add math paper because they couldn't even get their engines started for a number of problems in the question booklet. And when the exam was over, traumatised students burnt their math book to show their discontent. Traumatised students burnt their math book after the exam In Question 5 for example, students were horrified by a strange-looking diagram. The diagram has absolutely no labels and students are expected to prepare the answers with only two ingredients: (a) that the three dark-coloured leaf-shaped objects are congruent and (b) that the perimeter of object is 20\(\pi\). The given leaf-shaped object is a peculiar type of folium formed by glueing two...

\(\pi\) is a fundamental constant in mathematics. It is also an important constant in science for it appears naturally in so many applications: in the period of a simple pendulum in mechanics , Maxwell-Boltzmann distribution for gas molecules in thermodynamics, Coulomb's law for electrostatic force in electromagnetic theory, Heisenberg's uncertainty principle in quantum mechanics, Einstein's field equation in general relativity theory. Since \(\pi\) is such an important constant, it should be properly introduced to students, both historically and mathematically. In Malaysian secondary schools, this constant is first taught to a typical 14-year-old when he/she is learning the geometric properties of the circle. In a recent book titled "Essential Mathematics Form 2", published by Longman, the authors wrote, in page 163, the value of \(\pi\) is an estimated value, which is \(\frac{22}{7}\) or 3.142 This remark is technically incorrect. I guess the authors p...

In most of the secondary school level mathematics reference books found in local bookstores, the mathematical object "circle" is introduced as follows: A circle is a set of points that are equidistant from a fixed point. There is something wrong with this description. It is rather vague because a set of points could mean the following set of 8 points {P1, P2, P3, P4, P5, P6, P7, P8}: Although these points are equidistant from a fixed point, this particular set does not form or look like a circle. This problematic description of "circle" is not entirely the fault of the reference book authors, because it actually originates from page 45 of the Curriculum Specifications for Form 2 Mathematics, compiled in 2002, by the Curriculum Development Centre, Ministry of Education Malaysia. I must say that it is rather difficult to describe "circle" or any other mathematical objects with words. A better version (but still imprecise) would be: A circle is a c...