RI JC GP Prelims paper 1 2017

RI JC GP Prelims paper 1 2017

JC General Paper
  1. ‘The protection of animals is an indulgence.’ Do you agree?
  2. ‘In an increasingly uncertain world, there is little point in predicting the future.’ Discuss
  3. Would the world be a better place without religion?
  4. ‘We should abolish state funding for the Arts.’ How far do you agree that this should be the case for your society?
  5. ‘Business should have no place in politics.’ Do you agree?
  6. ‘Scientific knowledge cannot be trusted because it is unreliable.’ Is this a fair statement?
  7. ‘Celebrities today do little that is worth of celebration.’ Discuss.
  8. Are machines making humans obsolete?
  9. Consider the importance of non-conformity in your society.
  10. ‘Achieving greater income equality for all is a desirable but unrealistic goal.’ Do you agree?
  11. How effective is technology in making us healthier?
  12. ‘History is just set of lies.’ Discuss.
Making Use of this September Holidays

Making Use of this September Holidays

JC Mathematics, Mathematics

This is a little reminder and advice to students that are cheong-ing for their Prelims or A’levels…

For students who have not taken any H2 Math Paper 1 or 2, I strongly advise you start waking at up 730am and try some papers at 8am. I gave my own students similar advices and even hand them 4 sets of 3 hours practice papers. Students need to grind themselves to be able to handle the paper at 8am. It is really different. Not to mention, this September Holidays is probably your last chance to be able to give yourself timed practices.

For students who took H2 Math Paper 1, you might be stunned with the application questions that came out. For NJC, its Economics. For YJC, its LASER. For CJC, a wild dolphin appeared. And more. These application questions are possible, due to the inclusion of the problems in real world context in your syllabus. You can see the syllabus for yourself. I’ve attached the picture below. So for Paper 2, expect these application questions to be from statistics mainly, as suggested in your scheme of work below.

Scheme of Examination Source: SEAB

For students that have took H2 Math paper 1 & 2, and this is probably ACJC. The paper was slightly stressful, given the mark distributions, but most of the things tested are still technically “within syllabus”. For one, the directional cosine question, is a good reminder to students that they should not leave any pages un-highlighted. AC students should be able to properly identify their weaknesses and strengths this time round. If its time management, then start honing that skill this holidays – by having timed practice. A quick reminder that the TYS papers are not 3 hours, since some of the questions are out of H2 Mathematics 9758 syllabus. Students can consider the ratio of 1 mark to 1.5 min to gauge how much time they have for each paper.

R-Formulae seems to be popular about the prelims exams this time round, making waves in various schools. Perhaps it was because it appeared in the specimen paper, and if you’re keen on how it can be integrated or need a refresher. I did it recently here.

Lastly, for the students that are very concerned on application questions. Check the picture below. It contains some examples that SEAB has given. Students should also be clear about the difference between a contextual question and an application question.

Integration & Applications Source: SEAB

With that, all the best to your revision! 🙂

Anderson JC GP Prelims paper 1 2017

JC General Paper
  1. Should small countries be allowed to take the lead in global affairs?
  2. To what extent can the Arts effect positive social change today?
  3. ‘Experiences are more valuable than material possessions.’ Do you agree?
  4. ‘People in the workplace should embrace, rather than fear, technological advancements.’ Discuss.
  5. ‘The news today deals with what is popular, rather than what is important.’ How far do you agree with this statement?
  6. Evaluate the claim that a more connected world has resulted in greater divisions.
  7. ‘Public figures today are overly concerned about what people think of them.’ What is your view?
  8. Consider the view that there is no value in slowing down in today’s competitive world.
  9. Discuss the appeal and value of creativity in your society.
  10. Considering the increasing threat of terrorism, are governments justified in limiting people’s rights?
  11. To what extent is animal testing acceptable in scientific research?
  12. ‘Economic development is favoured at the expense of the welfare of people.’ How true is this of your society?
Trigonometry Formulae & Applications (Part 2)

Trigonometry Formulae & Applications (Part 2)

JC Mathematics, Secondary Math

I meant to share more on factor Formulae today. However, a few students are not so sure how to get the R-formulae correctly during their preliminary exams recently. So I thought that I’ll share how they can derive the R-Formulae from the MF26.

The following is the R-Formulae which students should have memorised. It is under assumed knowledge, just saying…

a \text{cos} \theta \pm b \text{sin} \theta = R \text{cos} (\theta \mp \alpha)

a \text{sin} \theta \pm b \text{cos} \theta = R \text{sin} (\theta \pm \alpha)

where R = \sqrt{a^2 + b^2} and \text{tan} \alpha = \frac{b}{a} for a > 0, b > 0 and \alpha is acute.

So here, I’ll write the addition formulae that’s found in MF26.

\text{sin}(A \pm B) \equiv \text{sin}A \text{cos} B \pm \text{cos} A \text{sin} B

\text{cos}(A \pm B) \equiv \text{cos}A \text{cos} B \mp \text{sin} A \text{sin} B

I’ll use an example I discussed previously.

f(x) = 3 \text{cos}t - 2 \text{sin}t

Write f(x) as a single trigonometric function exactly.

Lets consider the formulae from MF26.

\text{cos}(A \pm B) \equiv \text{cos}A \text{cos} B \mp \text{sin} A \text{sin} B

R\text{cos}(A \pm B) \equiv R \text{cos}A \text{cos} B \mp R \text{sin} A \text{sin} B

We can let

3 = R \text{cos} B ---(1)

2 = R \text{sin} B ---(2)

\Rightarrow \sqrt{ 3^2 + 2^2 } = \sqrt{ R^2 \text{cos}^2 B + R^2 \text{sin}^2 B}

\Rightarrow \sqrt{13} = R

\Rightarrow \frac{R \text{sin} B}{R \text{cos} B} = \frac{2}{3}

\Rightarrow \text{tan} B = \frac{2}{3}

Putting things together, we have that

 f(x) = \sqrt{13} \text{cos} ( t + \text{tan}^{\text{-1}} (\frac{2}{3}))

Temasek JC GP Prelim Paper 1 2017

Temasek JC GP Prelim Paper 1 2017

JC General Paper

Temasek Junior College 8807 H1 General Paper Paper 1 2017

  1. Can government surveillance eradicate the threat of terrorism?
  2. Examine the claim that globalization creates equal opportunities for all.
  3. ‘The government is not doing enough to support local sportsmen in your society.’ What is your view?
  4. To what extent is a universal language desirable?
  5. Should people in your society be fearful of the future?
  6. ‘Graciousness is lost as society progresses.’ Is this an accurate reflection of your society?
  7. How far do you agree that technology gives us greater control in life?
  8. Consider the view that what is posted online is all talk and no action.
  9. ‘Failure should never be acceptable.’ Discuss.
  10. Do you agree that only parents should be allowed to discipline their children?
  11. Is volunteerism always good?
  12. ‘The world today values appearance over substance.’ Is this a fair comment?
Tampines GP Prelim Paper 1 2017

Tampines GP Prelim Paper 1 2017

JC General Paper

Tampines Junior College 8807 H1 General Paper Paper 1 2017

  1. How realistic is it for your society to embrace diversity?
  2. Protecting the environment should be given greater priority than eradicating poverty. How far do you agree?
  3. ‘Appearance can be deceiving.’ To what extent is this true of the media today?
  4. Discuss the view that smart devices have not made us smarter.
  5. Education is the key to solving all social problems. Discuss.
  6. Should firms have the responsibility to improve the quality of life of the communities they operate in?
  7. Assess the view that literature is of little use to society.
  8. Wealth is no guarantee of a better life. How far do you agree?
  9. History is of little significance to a modern society. Discuss.
  10. ‘Failure is always an option.’ Discuss.
  11. A free and unrestricted media is essential for society to progress. How far do you agree?
  12. How far is the arts a reflection of your society’s level of development?
Trigonometry Formulae & Applications (Part 1)

Trigonometry Formulae & Applications (Part 1)

JC Mathematics, Secondary Math

Upon request by some students, I’ll discuss a few trigonometry formulae here and also some of their uses in A’levels. I’ve previously discussed the use of factor formulae here under integration.

I’ll start with the R-Formulae. It should require no introduction as it is from secondary Add Math. This formulae is not given in MF26, although students can derive it out using existing formulae in MF26.

a \text{cos} \theta \pm b \text{sin} \theta = R \text{cos} (\theta \mp \alpha)

a \text{sin} \theta \pm b \text{cos} \theta = R \text{sin} (\theta \pm \alpha)

where R = \sqrt{a^2 + b^2} and \text{tan} \alpha = \frac{b}{a} for a > 0, b > 0 and \alpha is acute.

Here is a quick example,

f(x) = 3 \text{cos}t - 2 \text{sin}t

Write f(x) as a single trigonometric function exactly.

Here, we observe, we have to use the R-Formulae where

R = \sqrt{3^2 + 2^2} = \sqrt{13}

\alpha = \text{tan}^{\text{-1}} (\frac{2}{3})

We have that

 f(x) = \sqrt{13} \text{cos} ( t + \text{tan}^{\text{-1}} (\frac{2}{3})).

I’ll end with a question from HCI Midyear 2017 that uses R-Formulae in one part of the question.

A curve D has parametric equations

x = e^{t} \text{sin}t, y = e^{t} \text{cos}t, \text{~for~} 0 \le t \le \frac{\pi}{2}

(i) Prove that \frac{dy}{dx}  = \text{tan} (\frac{\pi}{4} - t).

I’ll discuss about Factor Formulae soon.  And then the difference and application between this two formulae.

Random Questions from 2017 Prelims #2

Random Questions from 2017 Prelims #2

JC Mathematics, Mathematics, Secondary Math

Today I’ll share a question that came out of CJC Prelim 2017 Paper 1 for H2 Mathematics 9758. I think some of my student would have seen this question before and we discussed it in class before. Very technical question. This is question 11, I’ll share only the first part which is on the application of ratio theorem or mid point theorem. The second part is on application: Ray Tracing which I’ll discuss in class.

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. For the triangle show below, O, A and B are vertices, where O is the origin. \vec{OA} = a and \vec{OB} = b. The midpoints of OB, OA and AB are M, N and T respectively.

It is given that X is the point of intersection between the medians of triangle OAB from vertices A and B.

(i) Show that \vec{OX} = \frac{1}{3} (a +b)

(ii) Prove that X also lies on OT, the median of triangle OAB from vertex O.

ACJC Prelims paper 1 2017

ACJC Prelims paper 1 2017

JC General Paper
  1. ACJC 2017 H1 General Paper 8807 Prelim Paper 1
  2. To what extent does education prepare the young for a world that is constantly changing?
  3. ‘Science imparts knowledge but not wisdom.’ Do you agree?
  4. Have we placed too much emphasis on work today?
  5. Is being original always beneficial?
  6. ‘It is better to be feared than to be popular.’ Discuss the view with reference to leadership.
  7. Can diseases ever be eliminated?
  8. ‘The media creates more problems than benefits for politicians.’ Discuss.
  9. How far, in your society, are children a good investment?
  10. Consider the view that the poor are more likely to commit crimes than the rich.
  11. Evaluate the claim that environmental conservation is a desirable, but unrealistic, goal.
  12. ‘Music breaks all barriers.’ Can music be so powerful?
  13. ‘Economic development is key to a country’s stability.’ To what extent is this true in your society?

To those taking your prelims for GP really soon… here is an example of a prelim paper this year… Could you do these questions? What help would u need?

Random Questions from 2017 Prelims #1

Random Questions from 2017 Prelims #1

JC Mathematics

Last year, I shared a handful of random interesting questions from the 2016 Prelims. Students feedback that they were quite helpful and gave them good exposure. I thought I share some that I’ve seen this year. I know, its a bit early for Prelims. But ACJC just had their paper 1. 🙂

This is from ACJC 2017 Prelims Paper 1 Question 7. And it is on complex numbers.

(a) Given that 2z + 1 = |w| and 2w-z = 4+8i, solve for w and z.

(b) Find the exact values of x and y, where x, y \in \mathbb{R} such that 2e^{-(\frac{3+x+iy}{i})} = 1 -i

I’ll put the solutions up if I’m free.

But for students stuck, consider checking this link here for (a) and this link here for (b). These links hopefully enlightens students.

Just FYI, you cannot \text{ln} complex numbers as they are not real…