O Level Math - Don't Go Around In Circles Solving A Circles Question

Don’t get thrown off by seemingly complicated diagrams.

You start by first observing for ALL the shapes and structures that relate to the properties of a circle - they are there for a reason: to guide you. 

It is very likely that the question setter's suggested solution to the question makes use of ALL the hints available (of course there may be more elegant solutions that exist). Hence, note down ALL the hints, then start to manipulate the equations and you'll arrive at your answer. 

Observation	Relevant Properties
Radius & Tangent	Radius perpendicular to tangent
Butterfly	Angles in same segment
Angle at centre	Angle at centre = Twice angle at circumference
Diameter	Angles in semicircle
Chords from contact with tangent	Angle in alternate segment
Chords	Bisector of Chord & Perpendicular of Chord; Equal Chords & Chords equidistant from centre
Cyclic quadrilaterals	Opposite Angles of cyclic quad; External angle of cyclic quad
Tangents	Tangent perpendicular to radius; Tangents from external point: Equal Tangents & Angle between tangents equal; Angles between radii equal; Angles in alternate segment (Alternate Segment Theorem)

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H2 Econs - An Economical Explanation Of Fiscal Policy (FP). Plus: Multiplier (K) Effect!

• Expansionary Fiscal Policy (FP) works by reducing taxes (T) and increasing government expenditure (G). 
• Lower household tax results in higher disposable income (Y), hence consumption (C) increases. 
• Lower corporate tax increases post-tax profits, hence investment (I) increases. 
• The injection of autonomous G leads to a large increase in aggregate demand (AD) and a more than proportionate increase in real National Income (Y) via the multiplier effect. (How does it start?)

A quick and easy way to rmb the full elaboration of the multiplier effect is to ask yourself these 5 questions, including the one above.

• The K effect is based on the idea that one expenditure creates income, which induces greater expenditure;  (What is it?)

• With an initial increase in C,G, & I, AD and hence real NY increases. Higher household Y leads to induced C, resulting in further increases in AD and real NY.    (How does it continue?)

• The process repeats until the initial G injected is withdrawn in the form of Taxes (T), Savings (S) and Import Expenditure (M). (How does it end?)

• Thus, an initial autonomous injection of income leads to a large increase in AD and a more than proportionate increase in real NY. With higher AD, firms face unplanned disinvestment/ fall in stocks, hence they hire more factors of production (FOPs) including labour, thus employment increases and moves towards full employment (Yf). (What is the overall effect on NY and unemployment?)

So putting it together, you have a model elaboration for FP Policies:

Expansionary Fiscal Policy (FP) works by reducing taxes (T) and increasing government expenditure (G). Lower household tax results in higher disposable income (Y), hence consumption (C) increases while lower corporate tax increases post-tax profits, hence investment (I) increases. Furthermore, the injection of autonomous G leads to a large increase in aggregate demand (AD) and a more than proportionate increase in real National Income (Y) via the multiplier (K) effect.

The K effect is based on the idea that one expenditure creates income, which induces greater expenditure. With an initial increase in C,G, & I, AD and hence real NY increases. Higher household Y leads to induced C, resulting in further increases in AD and real NY. The process repeats until the initial G injected is withdrawn in the form of Taxes (T), Savings (S) and Import Expenditure (M).

Thus, an initial autonomous injection of income leads to a large increase in AD and a more than proportionate increase in real NY. With higher AD, firms face unplanned disinvestment/ fall in stocks, hence they hire more factors of production (FOPs) including labour, thus employment increases and moves towards full employment (Yf).

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H2/3 Chemistry - Learn These Common Out-Of-Syllabus A Level Org Chem Reactions And Answer Such Questions With Greater Confidence

Hi guys, as you know, your JC chem departments loves to set you plenty of questions which come from undergrad books! Below is a list of common out-of-syllabus concepts for org chem we think you'll see over-and-over again in school tests and worksheets, so they'll be useful for you to know!

Although not compulsory, having a little understanding of these concepts helps you answer the "Suggest" type of questions with more confidence. Eg. "suggest the mechanism for the epoxide formation", "suggest a role of Mg in the Grignard reaction"

1. Thermodynamic vs Kinetic Control and how it may affect addition and elimination for example
2. Oxymercuration-demercuration
3. Hydroboration-oxidation
4. Preparation and Reduction of Alkynes
5. Ozonolysis of Alkenes and Alkynes
6. Acidity of Terminal Alkynes
7. Allylic bromination
8. Grignard reagents
9. Uses of Crown Ethers
10. Formation of epoxides (skip to the intramolecular SN2 reaction part)
11. Diels-Alder reaction
12. The Benzyne intermediate
13. Imine and Enamine formations from Carbonyls
14. Protecting groups
15. Claisen condensation
16. Michael reaction
17. Hofmann elimination
18. HVZ reaction

This list probably isn't exhaustive, but we'll continue to update it :)


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O Level Bio - A Breathtaking Summary of Mammalian Respiratory System

• Factors influencing rate of gaseous exchange (diffusion): surface area, concentration gradient, length of diffusion path

• Air Pathway: Nose --> Pharynx --> Larynx --> Trachea --> Bronchi --> Bronchioles
• Nose
• Hair and mucus trap dust, microoraganisms and foreign particles
• Air warmed and moistened
• Sensory cells detect odour molecules
• Trachea
• C-shaped cartilage rings support trachea and keep it open
• Gland cells on epithelium secrete mucus
• Cilia on epithelium sweep mucus particles up pharynx
• Bronchi
• Right: 3 tubes; Left: 2 tubes
• Gland cells
• Divides into bronchioles (smaller tubes)

•  Alveoli (air sacs) are adapted for efficient gaseous exchange:
•  Thin: Shorter diffusion path, higher rate of diffusion
• Moist: Oxygen dissolves in thin film of moisture to enhance binding to plasma Hb of RBCs
• Extensive blood capillaries: Increased surface area for diffusion
• Membrane permeable to oxygen and carbon dioxide

• Ribs, Diaphragm and Intercoastal Muscles work together to enable breathing:
• During inspiration
• Diaphragm contracts, flattens downwards
• Intercoastal muscles: external muscles contract, internal muscles relax
• Ribs and sternum move up and out
• Volume of thoracic cavity increases, hence pressure decreases. Internal pressure becomes lower relative to atmospheric pressure, hence air diffuses in down the concentration gradient 

 

• The respiratory and circulatory systems are regulated together by plasma carbon dioxide levels
• During physical exertion, heart rate and CO2 level increases
• Higher CO2 stimulates faster rate of inspiration and expiration, taking in O2 and removing CO2 is removed
• Higher heart rates allows oxygenated blood to be transported to muscles more efficiently

You probably are wondering if there will be a follow up with a hack notes on Fishes' Respiratory System. Well we don't have plans to upload any yet, but you sure can get notes and worksheets on the Respiratory System of Fishes if you sign up as a student here :)

H2 Econs - A Sample Lesson Plan

RIJC 2013 Y6 Prelims Paper 2

Q1) Globalisation and technological advancement have caused rising income inequality in many countries. Minimum wage policy is implemented in many countries to improve the welfare of low skilled workers and narrow the income gap.

a) Account for the increasing income gap between skilled and unskilled labour in Singapore. (10m) 

This is how we approach an essay question:

Write with speed!!!

Before starting any essay, take a look at the mark allocation, determine your time limit, then determine the scope (choose the most credit-worthy rigorous frameworks).

So 10marks = 15mins = Intro + Conclusion + 2-3 content paragraphs + 1 diagram = 1.5 pages.

Here for the content paragraphs, we will explain the changes in DDSS conditions in both markets of skilled and unskilled labour brought about by globalisation. (A question on wages, just like a question on differential prices, makes use of a DDSS & elasticities framework.) We should also make use of  at least 1 elasticity concept for rigour.

For a DDSS question, it is imperative that you have both DD and SS factors for scope. If you use an elasticity concept, you are almost guaranteed of an L3 mark range.

Remember to use concise language, abbreviations etc.so you write faster! Intro:

• Widening wage (W) gap leads to increasing income (Y) gap. – If you don’t make the distinction between wages and income, the examiner might think you have confused the two

• W gap widens as W of skilled workers are increasing, while W of unskilled workers are falling. – often students leave out these very ‘obvious’ explanations. You must rmb to explain step-by-step!

• Wage rates are determined by demand (DD) and supply (SS) factors in the labour market. – This tells the examiner you’ll be using a DDSS framework

• Globalisation has influenced labour market in SG, as accounted for by Theory of Comparative Advantage (CA). – and CA framework

We shall first explain why rising DD against an inelastic SS has led to sharp increases in the W rates of skilled labour.

We plan this paragraph as follows: CA theory --> Singapore has CA in KI industries, with egs. --> KI industries are sunrise industries --> employ more skilled workers -->  DD for skilled workers increases --> W rises, holding SS constant (diagram) --> W also increases as firms willing to pay premium to hire and retain talents.

• Theory of CA suggests that countries benefit from trade if they specialize in the production of goods they have CA in

• Singapore has abundance of capital and skilled labour, hence specializes in knowledge intensive industries eg. pharmaceutical, bio-medical, financial services – rmb to highlight some examples, otherwise your marker can give you an L1 for “failing to make reference to context” 
• Such knowledge-intensive industries require skilled labour to operate high-tech machinery due to technological advancement, and provide value-added services
• As these sunrise industries expand, they employ more skilled labour hence DD for skilled labour rises from DD₀ to DD₁. Holding SS constant, a shortage of labour of Q₁Q₂ arises at prevailing wage rate W₀. Hence firms offer higher W while workers ask higher W, exerting upward pressure on W. Thus W₀ rises to W₁. - Always rmb to state changes in DD/SS --> recognise surplus/shortage --> explain the price correction mechanism involving sellers and buyers --> exerting upward/downward pressure on price   
• Furthermore, W for skilled labour also rises as firms may be willing to pay a premium to hire and retain talented workers
• The supply of skilled labour is inelastic (PES<1), due to longer training and education, hence W increases more than proportionately when DD increases, further sharpening the wage disparity.   

Next, we explain that DD for unskilled labour is falling while SS is rising due to globalisation, causing W rates to fall.

• As firms acquire high-tech capital as a result of technological advancement, DD for unskilled labour falls from DD3 to DD4.

• Freer labour movement as a result of globalisation has allowed influx of unskilled foreign labour into SG from LDCs with labour abundance eg. China, India, Phillipines, Indonesia.

• SS of low-skilled labour increases from SS3 to SS4, resulting in surplus at prevailing W3 of Q3Q4. Employers offer lower wages and workers ask lower wages, hence exerting downward pressure on W, causing it to fall to W4.

Now we end off with a simple conclusion. The conclusion is the last thing your marker reads, and especially if your essay is a long one, you will want to remind your examiner briefly the frameworks you have used, so that they can award you appropriately.

The frameworks we used here are: globalisation, theory of CA, DD and SS, and elasticities, so we can write a conclusion as such:

• In conclusion, the increasing income gap is due to increase in DD for skilled labour and increase in SS of unskilled labour brought about by globalisation, in line with Singapore's CA in knowledge-intensive industries. The price inelasticity of supply of skilled labour further widens the wage and hence income gap.

Putting them together...

Widening wage (W) gap leads to increasing income (Y) gap. W gap widens as W of skilled workers are increasing, while W of unskilled workers are falling. Wage rates are also determined by demand (DD) and supply (SS) factors in the labour market. Globalisation has influenced labour market in SG, as accounted for by Theory of Comparative Advantage (CA).

The Theory of CA suggests that countries benefit from trade if they specialize in the production of goods they have CA in. Singapore has abundance of capital and skilled labour, hence specializes in knowledge intensive industries eg. pharmaceutical, bio-medical, financial services. As these sunrise industries expand, they employ more skilled labour hence DD for skilled labour rises from DD₀ to DD₁. Holding SS constant, a shortage of labour of Q₁Q₂ arises at prevailing wage rate W₀. Hence firms offer higher W while workers ask higher W, exerting upward pressure on W. Thus W₀ rises to W₁. Furthermore, W for skilled labour also rises as firms may be willing to pay a premium to hire and retain talented workers. The supply of skilled labour is inelastic (PES<1), due to longer training and education, hence W increases more than proportionately when DD increases, further sharpening the wage disparity. 

<Diagram as described above>

As firms acquire high-tech capital as a result of technological advancement, DD for unskilled labour falls from DD3 to DD4. Freer labour movement as a result of globalisation has allowed influx of unskilled foreign labour into SG from LDCs with labour abundance eg. China, India, Phillipines, Indonesia. SS of low-skilled labour increases from SS3 to SS4, resulting in surplus at prevailing W3 of Q3Q4. Employers offer lower wages and workers ask lower wages, hence exerting downward pressure on W, causing it to fall to W4.

<Diagram as described above>

In conclusion, the increasing income gap is due to increase in DD for skilled labour and increase in SS of unskilled labour brought about by globalisation, in line with Singapore's CA in knowledge-intensive industries. The price inelasticity of supply of skilled labour further widens the wage and hence income gap.

Concise, with scope and depth, and totally doable within 15min right?


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