H2 Mathematics has one of the highest distinction rates of all subjects (around 50% each year). This means that around half of all Singaporean A level candidates score an A for H2 Maths!
H2 A Level Distinction Rates Compilation (National Average)
(For year 2010)
H2 Mathematics Distinction Rate: 51.9%
H2 Biology Distinction Rate: 43.7%
H2 Economics Distinction Rate: 33.8%
H1 Mathematics Distinction Rate: 33.1%
H1 Economics Distinction Rate: 33.8%
Literature Distinction Rate: 30.1%
History Distinction Rate: 23.7%
Geography Distinction Rate: 28.3%
Source: http://ajc.edu.sg/pdf/aj_broadcast/newsroom/news_archives/linkaj_may_2011.pdf
H2 Maths Notes and Resources
Check out the highly summarized and condensed H2 Maths Notes here! (Comes with Free H2 Math Exam Papers.)
Is H2 Maths the easiest H2 subject to get A?
Answer: Yes, provided the student does study conscientiously and not lag behind too much. Based on the statistics above, one can easily see that based on probability alone, H2 Maths is the easiest H2 subject to get A. Since more than 50% of students get A for H2 Maths, in a sense it is easier to get A for H2 Maths than flipping a heads on a coin!
However… (Please Read)
H2 Maths is also the easiest to fail! Without sufficient practice and effort to understand the subject material, sub-30 (below 30/100) marks are extremely common for H2 Maths. Last minute cramming will simply not work, and if a student lags too far behind in terms of syllabus, it will take extra effort to just even catch up.
In Depth Analysis of H2 Maths Distinction Rate
The 50% National Distinction Rate for H2 Maths can be quite misleading to think that every student has 50% chance of getting A for H2 Maths. The truth is that H2 Maths Distinction Rate varies a lot from school to school.
For example, AJC’s H2 Maths Distinction Rate is 62.7%, which is very much higher than the 50% average National Distinction Rate.
Raffles Institution (RI/RJC) Distinction Rate hovers around 70% to 80%!
Victoria JC (VJC)’s H2 Maths Distinction Rate is around 66.6%.
Hwa Chong (HCI) H2 Maths Distinction Rate is around 80% (8 out of 10 students scored an A for H2 Maths in HCI for three consecutive years).
Upon some thinking, one will quickly realize that if so many schools have Distinction Rate significantly above 50%, there has to be many schools with Distinction Rate significantly below 50%, in order for the National Distinction Rate to be around 50%!
The only people who know the exact Distinction Rate for the above mentioned JCs would be the internal staff and students, since the school website will probably not publish the statistics for obvious reasons.
The Best Time to Study H2 Maths is Now!
For students who are in schools with super high H2 Maths Distinction Rate, congratulations, your chances of getting A for H2 Maths are very good. However, do not be complacent till the very last day, as the race is not over yet.
For students who are in schools with very low H2 Maths Distinction Rate, the odds are unfortunately stacked against the student. However, do not lose heart, as anything is possible if one puts one’s heart and mind into it.
Good luck!
H2 Maths Notes and Resources
Check out the highly summarized and condensed H2 Maths Notes here! (Comes with Free H2 Math Exam Papers.)
be a measure defined on a 
-algebra X.
) is an increasing sequence in X, then
) is a decreasing sequence in X and if 
, then
. A decreasing sequence means the opposite, i.e. 
.
for some n, then both sides of the equation are 
, and inequality holds. Henceforth, we can just consider the case 
for all n.
and 
for n>1. Then 
is a disjoint sequence of sets in X such that
, 
(since (
) is a disjoint sequence of sets)
, we have that 
for n>1, so the finite series on the right side telescopes to become
, so that 
is an increasing sequence of sets in X.![\begin{aligned} \mu (\bigcup_{n=1}^\infty E_n) &=\lim \mu (E_n)\\ &=\lim [\mu (F_1)-\mu (F_n)]\\ &=\mu (F_1) -\lim \mu (F_n) \end{aligned}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Baligned%7D++++%5Cmu+%28%5Cbigcup_%7Bn%3D1%7D%5E%5Cinfty+E_n%29+%26%3D%5Clim+%5Cmu+%28E_n%29%5C%5C++++%26%3D%5Clim+%5B%5Cmu+%28F_1%29-%5Cmu+%28F_n%29%5D%5C%5C++++%26%3D%5Cmu+%28F_1%29+-%5Clim+%5Cmu+%28F_n%29++++%5Cend%7Baligned%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
, it follows that
.
, let 
denote the constant path 
mpping all of I to the point x. If f is a path in X from 
to 
, then ![[f]*[e_{x_1}]=[f]](https://s0.wp.com/latex.php?latex=%5Bf%5D%2A%5Be_%7Bx_1%7D%5D%3D%5Bf%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
and ![[e_{x_0}]*[f]=[f]](https://s0.wp.com/latex.php?latex=%5Be_%7Bx_0%7D%5D%2A%5Bf%5D%3D%5Bf%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
.
be the path defined by 
. ![[f]*[\bar{f}]=[e_{x_0}]](https://s0.wp.com/latex.php?latex=%5Bf%5D%2A%5B%5Cbar%7Bf%7D%5D%3D%5Be_%7Bx_0%7D%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
and ![[\bar{f}]*[f]=[e_{x_1}]](https://s0.wp.com/latex.php?latex=%5B%5Cbar%7Bf%7D%5D%2A%5Bf%5D%3D%5Be_%7Bx_1%7D%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
.
is a continuous map, and if F is a path homotopy in X between the paths f and f’, then 
is a path homotopy in Y between the paths 
and 
.
is a continuous map and if f and g are paths in X with f(1)=g(0), then
, where h=f*g as defined previously.
.
denote the constant path in I at 0, and we let 
denote the identity map, which is a path in I from 0 to 1. Then 
is also a path in I from 0 to 1.
(Straight-line homotopy) Then 
is a path homotopy in X between the paths 
and 
(Lemma 1). Furthermore by Lemma 2, 
which is equivalent to 
.
denotes the constant path at 1, then 
is path homotopic in I to the path i, shows that 
. Then 
is a path in I beginning and ending at 0. The constant path 
is also beginning and ending at 0. Again, because I is convex, there is a path homotopy H in I between 
is path homotopy between 
and 
. Very similarly, we can use the fact that 
is path homotopic in I to 
. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions.
and measures should be additive over disjoint sets in X.
for all 
) of sets in X, then
.
, we say it is finite. More generally, if there exists a sequence 
and such that 
for all n, then we say that 
be definied on X by 
, for all 
. We can see that 
be defined by 
, 
if 
. 
defined on B which coincides with length on open intervals. I.e. if E is the nonempty interval (a,b), then 
. This measure is usually called Lebesgue measure (or sometimes Borel measure). It is not a finite measure since 
. But it is 
, we define the product f*g of f and g to be he path h given by the equations![h(s)=\begin{cases}f(2s) &\text{for }s\in [0,\frac{1}{2}], \\ g(2s-1)& \text{for }s\in[\frac{1}{2}, 1]\end{cases}](https://s0.wp.com/latex.php?latex=h%28s%29%3D%5Cbegin%7Bcases%7Df%282s%29+%26%5Ctext%7Bfor+%7Ds%5Cin+%5B0%2C%5Cfrac%7B1%7D%7B2%7D%5D%2C+%5C%5C+g%282s-1%29%26+%5Ctext%7Bfor+%7Ds%5Cin%5B%5Cfrac%7B1%7D%7B2%7D%2C+1%5D%5Cend%7Bcases%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
![[f]*[g]=[f*g]](https://s0.wp.com/latex.php?latex=%5Bf%5D%2A%5Bg%5D%3D%5Bf%2Ag%5D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
![H(s,t)=\begin{cases}F(2s,t) &\text{for }s\in[0,\frac{1}{2}],\\ G(2s-1,t)&\text{for }s\in[\frac{1}{2},1]\end{cases}](https://s0.wp.com/latex.php?latex=H%28s%2Ct%29%3D%5Cbegin%7Bcases%7DF%282s%2Ct%29+%26%5Ctext%7Bfor+%7Ds%5Cin%5B0%2C%5Cfrac%7B1%7D%7B2%7D%5D%2C%5C%5C+G%282s-1%2Ct%29%26%5Ctext%7Bfor+%7Ds%5Cin%5B%5Cfrac%7B1%7D%7B2%7D%2C1%5D%5Cend%7Bcases%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
.
belongs to X for every set E belonging to Y.
the set 
belongs to X.
for every Borel set E.
.
if f and f’ are path homotopic.
and 
are equivalence relations.
. The map F(x,t) is the required homotopy.
. Let F be a homotopy between f and f’. We can then verify that G(x,t) = F(x, 1-t) is a homotopy between f’ and f.
, we show that 
. Let F be a homotopy between f and f’, and let F’ be a homotopy between f’ and f”. This time, we need to define a slightly more complicated homotopy G: X x I -> Y by the equation![G(x,t) = \begin{cases} F(x,2t) &\text{for }t\in [0,\frac{1}{2}],\\ F'(x, 2t-1) &\text{for } t\in [\frac{1}{2}, 1].\end{cases}](https://s0.wp.com/latex.php?latex=G%28x%2Ct%29+%3D+%5Cbegin%7Bcases%7D+F%28x%2C2t%29+%26%5Ctext%7Bfor+%7Dt%5Cin+%5B0%2C%5Cfrac%7B1%7D%7B2%7D%5D%2C%5C%5C+F%27%28x%2C+2t-1%29+%26%5Ctext%7Bfor+%7D+t%5Cin+%5B%5Cfrac%7B1%7D%7B2%7D%2C+1%5D.%5Cend%7Bcases%7D&bg=ffffff&fg=1a1a1a&s=0&c=20201002)
) in M(X,X) such that:
for 
.
for each 
, let 
be the set
.
, let 
.
are disjoint.
on 
is true.
, i.e. 
, thus 
for each 
are also in M(X,X).
, let 
be the “truncation of f” defined by 
be defined similarly. We will work out the proof that 
to 
.
is measurable.
, and using an earlier corollary that says that if a sequence 
is in M(X,X) converges to f on X, then f is also in M(X,X), we have that 
belongs to M(X,X).
, and hence fg also belongs to M(X,X).
implies 
.
consists of a half-line which is either of the form 
or the form 
. (We will show later that both cases can occur.) Thus, the set will belong to the Borel algebra B which is the 
, then when 
, the set will be 
.
, 
belong to X and the real-valued function 
defined by 
is measurable.
and 
, then we have that 
which is in X since it is the complement of the union of A and 
.
, then 
, which is a union of two sets in X and hence also in X.
and 
when 
, and 
when 
, due to a similar reason as above. Therefore f is measurable!
belongs to X.
belongs to X,
belongs to X,
belongs to X,
belongs to X,
and 
are complements of each other, hence statement (a) is equivalent to statement (b). This is due to one of the properties of 
belongs to X for each n.
, it follows that 
. Thus, (a) implies (c).
, and hence if (c) is true, each 
is in X, and the union of them is also in X (definition for 
, or even “<” and nothing would change!
by Stephen Covey (Highly recommended to read), there are four types of activities:
.
. It is a very good practice for children gearing up for Math Olympiad since they love to test logic questions in Math Olympiad.
.
.
, suitable for students who really need some encouragement and motivation to overcome fear of math! Albert Einstein once said, “You never fail until you stop trying.” Hence, even if you have not done well in math for the past years, there is still hope, don’t give up!
and transform the 100 tuple 
into the 100 tuple 
if 
is an even number. We say that a permutation 
of 
is good if starting from 
one can obtain it after finite number of steps. Find the total number of distinct good permutations of 
. In fact, any book by 
.
is an interesting book by Professor Diaconis, featuring Magic Tricks that have a mathematical background! This book is a great idea for a gift for students, teachers, or friends!
would be ideal in beginning the journey in Math Olympiad. Note that Math Olympiad is nothing like normal school math, and even a fresh university graduate in a math-related major say Engineering/Accounting would have great problems solving a Primary 6 Math Olympiad question, if he doesn’t have the necessary Math Olympiad background!
is an interesting book by Professor Diaconis, featuring Magic Tricks that have a mathematical background! This book is a great idea for a gift for students, teachers, or friends!
.
, what are the possible dimensions of the subspace 
?
.
, the 
can take the values of 0, 1, or 2.
. Like all “For Dummies” book, it is not overly abstract, rather it presents Linear Algebra in a fun way that is accessible to anyone with just a high school math background. Linear Algebra is highly useful, and it is 
.
, also by Ian Stewart, and I have to say his style is very accessible to the average reader. Not overly technical or abstract, he actually explains Galois Theory in as concrete a way as possible, which is not easy, since Galois Theory is one of the most abstract topics in mathematics.
.
Mathtuition88 