When Mr. Teng retired on 1 January 2018, he put a sum of $10,000 into a senior citizen fund that has a constant rate of return of 5% at the end of every month. Starting in February 2018, he withdraws $500 at the start of each month for groceries. Denote the amount of money that Mr. Teng has at the time years by .

(i) The differential equation relating and can be written in the form of . State the values of and .

(ii) Solve the differential equation and find the amount of money that Mr. Teng has after 15 months.

(iii) In which month will Mr. Teng no longer be able to withdraw the full $400?

Hopefully you find your holidays meaningful. Take the time to unwind and relax. Also, if you have completed the Set A and Set B. The solutions can be found here.

If you do have any questions, please WhatsApp me. 🙂

Hopefully, you guys have started on the Set B. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂

If you do have any questions, please WhatsApp me. 🙂

Hopefully, you guys have started on the Set A. You will find the following solutions useful. Click on the question. Please do attempt them during this December Holidays. 🙂

If you do have any questions, please WhatsApp me. 🙂

Here is the suggested solutions for H2 Mathematics (9758). They are all typed in LaTeX, so if it does not render, please leave a comment and let me know. Thank you.

The suggested solutions for H2 Mathematics (9740) is here.

Students of mine should obtain the modified A’levels Paper, and the solutions to the additional questions can be found here.

This is a new syllabus and this is the first time it will be tested. Personally, I don’t think it will be easy and students should not underestimate this upcoming A’levels. And I’m referring to the A’levels, on the whole. We saw how the Science Paper 4 were… unexpected.

The new H2 Mathematics (9758) syllabus has several topics removed, and these were mostly topics that were “drill-able”, aside from complex numbers. The new syllabus added in mainly, new integration forms, focus on parametric Equations with Cartesian equations, and of course, Discrete R.V. But let us leave the statistics out.

Students should familiarise themselves with the trigonometry Formulae in MF26. There are several topics that can be linked up with trigonometry, makes me wonder why it isn’t a chapter by itself. Complex numbers has a trigonometry form too, so make sure students know how to manipulate it, given the trigonometry Formulae.

Next, students should understand the use of Maclaurin’s. What does it mean for to be small, and the implications when they say is small compared to … And also finding the general term of a Maclaurin’s Expansion.

It won’t hurt to review how to find the Area using Shoe-lace method. And not forgetting our Sine Rule and Cosine Rule.

Do know how to prove a one-one function… Non-graphically. (i.e. not using the Horizontal Line Test)

Do know that the oblique asymptote of becomes when we do the transformation too.

Lastly, students must READ really carefully and discern every information. Having marked many scripts, many students do not read carefully and lose marks here and there. And they do add up… Be alert and read, take note of the forms that they want. Here are 10 little things to take note when you read the question.

Cartesian/ Polar/ Exponential for complex

Scalar/ Parametric/ Cartesian for vectors

Set/ range/ interval of values

Algebraically => show all the workings without a GC.. usually discriminant, completing the square or maybe some differentiation will be involved.

Without using a calculator => show your workings and check with a GC (secretly)

Decimal places, etc…

Rounding off when you’re dealing with an inequality

Units used in the questions, (ten thousands, etc)

Rate of change; leaking means the rate is negative…

All answers should be in 3 SF UNLESS OTHERWISE STATED. Degrees to 1 DP. RADIANS to 3 SF.

*For students: We half our values here as we scale by factor .

x- intercept
y- intercept
(ii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction.

x- intercept
y- intercept inconclusive

(iii)

*For students: We plus one to our values here as we translate by 1 unit in the positive x direction. Then, we half our values here as we scale by factor .

(i)
The average number of customers joining a supermarket checkout queue is a constant.
A customer joining a supermarket checkout is independent of another customer joining a supermarket checkout.

(ii)
Let denote the number of customers joining a supermarket checkout queue in a 5-minute period.

(iii)

(iv)
Let denote the number of customers leaving a supermarket checkout queue in a 3-minute period.

(ii)
Let X denote the mass of biscuit bars, in grams
Let denote the population mean mass of biscuit bars, in grams.

Test
against at 1% level of significance

Under approximately, by Central Limit Theorem.

Test Statistic,

Using GC,

Since , we do not reject at 1% level of significance and conclude with insufficient evidence that the mean mass differs from 32g.

(iv)
The sample size, is sufficiently large for the manager to approximate the the population distribution of the masses of the biscuit bars to a normal distribution by Central Limit Theorem.

(iii)
is within given data range, and we are performing interpolation, which is a good practice.
The r value is close to 1 which suggest a strong positive linear correlation between the average yields of corn and the amount of fertiliser applied.

(i)
The probability that the lights are faulty is constant.
The event that the light is faulty is independent of another light being faulty.
The light can only be either faulty or non faulty.

(ii)
Let denote the number of faulty lights in a box of 12.

(iii)
Required probability

(iv)
Let denote the number of faulty lights in a carton of 240.

Since and ,

approximately.

by continuity correction

(v)
Events in (iii) is a subset of events in (iv).

(vi)

(vii)
Required Probability

(viii)
From (vii), the quick test seem to be 94% accurate. However, from (vi), we understand that out of the number of lights identified faulty, 42.1% of them will be a mistake. As such, the quick test is not worthwhile, since light identified as faulty are mistakingly discarded. Moreover it will cost money to administer a test.

Students of mine who have been diligently doing the modified TYS I sent them, and have difficulties with the questions that were added in to make the paper a full 3 hour paper, will find the following solutions helpful. Please try to do them in a single 3 hour seating, these are modified to cater to the 9758 syllabus…

The rest of the solutions (that are questions from the original TYS) can be found here.