Probability Question #4

Probability Question #4

JC Mathematics

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears k times (k = 1, 2, 3), he wins $ k. If his number fails to appear, he loses $1. Calculate the gambler’s expected winnings

Vectors Question #4

Vectors Question #4

JC Mathematics

Another interesting vectors question.

The fixed point A has position vector a relative to a fixed point O. A variable point P has position vector r relative to O. Find the locus of P if r \bullet (ra) = 0.

Vectors Question #3

Vectors Question #3

JC Mathematics

This is a question a student sent me a few days back, and I shared with my class.

Find the Cartesian equation of the locus of all points (plane) that is equidistant of the xy plane and xz plane.

The following should aid students to visualise.

xy-, xz-, yz-planes

Sidenote: I think Vectors is a very important topic for 9758 as its applications are wide. Students should do their best to understand the topic. I will share a few more applied questions next week when I have time.

A little reminder to students doing Calculus now

A little reminder to students doing Calculus now

JC Mathematics

When \frac{dy}{dx} = 0 , it implies we have a stationary point.

To determine the nature of the stationary point, we can do either the first derivative test or the second derivative.

The first derivative test:

First Derivative Test

Students should write the actual values of \alpha^-, \alpha, \alpha^+ and \frac{dy}{dx} in the table.

We use this under these two situations:
1. \frac{d^2y}{dx^2} is difficult to solve for, that is, \frac{dy}{dx} is tough to be differentiated
2. \frac{d^2y}{dx^2} = 0

The second derivative test:

Second Derivative Test

Other things students should take note is concavity and drawing of the derivative graph.

APGP Question #3

APGP Question #3

JC Mathematics, Mathematics

This is a question from a recent ACJC JC2 test.

A philanthropist started a donation matching programme to encourage more people to donate regularly to a particular charity.

(a) For a person who donates $a in the first month, and for each subsequent month donates $ b^2 more than the previous month, the philanthropist will donate $a in the first month and for each subsequent month, b times the amount he donated the previous month.

(i) John is a regular donor of the charity. Find the values of a and b such that the philanthropist donates $20 in the third month, and ten times more than John in the seventh month.

(ii) Find the total amount of money donated by John and the philanthropist in one year, leaving your answer to the nearest dollar.

(b) In a revised donation matching programme, if a donor makes a monthly donation of $c, the philanthropist will donate according to the following plan:

First month : No donation (0\% donation rate)
Second month : 10 \% of the total amount donated by the donor in the first two months
Third month : 20 \% of the total amount donated by the donor in the first three months
Fourth month : 30 \% of the total amount donated by the donor in the first four months

and so on.

(i) Show that the total amount of money the philanthropist will donate at the end of the 4^{th} month is $2c.

(ii) By expressing the total amount of money, the philanthropist will donate at the end of the n^{th} month as a summation, and using the result \sum_{r=1}^n r^2 = \frac{n}{6}(n+1)(2n+1), show that the total amount of money the philanthropist will donate at the end of the n^{th} month is $ \frac{(n-1)n(n+1)}{30} c .

Vectors Question #2

Vectors Question #2

JC Mathematics

If c = |a| b + |b| a, where a , b and c are all non-zero vectors, show that c bisects the angle between a and b.

Post-Results 2016

Post-Results 2016

Chemistry, JC Chemistry, JC General Paper, JC Mathematics, JC Physics, Mathematics, Studying Tips, University Mathematics

Let’s face it. Some of us will not get the dream results we want. Don’t give up and let fear conquer you.

For students unsure of the available courses, they can check out the following post. It contains the grade profile for local universities.

Our Team will be here if you need help/ advice. Feel free to text us.

P.S. Today, I saw an image shared by Mr Wee, which said that “You’re the architect of your own life”. So let’s not let the grades define us.

Things to note for 9758 H2 Mathematics

Things to note for 9758 H2 Mathematics

JC Mathematics, Studying Tips

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…