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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Hi A-Level/H2 Math Students

J1 – 30 min Modular Differentiation and Applications

J2 – 30 min Modular Revision Vectors

From A Level Math Tutors

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A-Level Physics Tuition Singapore/H2 Physics Tuition/JC Physics Tutor

Hi A-level/H2/JC Physics Tuition students

Superposition – Definitions

1. Principle of Superposition
When two or more waves meet at a point, the resultant displacement at that point is equal to the vector sum of the displacements due to the individual waves at that point.

2. Interference
An effect that occurs when two or more waves superpose to produce a new wave pattern.

3. Coherence
A term used to indicate that the phase difference between two waves remains constant and does not vary with time.

4. Stationary (or standing) waves
A wave in which vibrational energy is stored, rather than transmitted.

5. Nodes
Positions along a standing wave where the amplitude of vibration is zero.

6. Antinode
Positions along a standing wave where the amplitude of vibration is a maximum.

7. Diffraction
The spreading of waves at an edge or a slit so that the waves do not travel in straight lines.

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A-Level Biology Tuition Singapore/H2 Biology Tuition/JC Biology Tutor

Key notes on Lipids and carbohydrate

1. Lipids
a. Kinks and melting temperature
The presence of double bonds results in the introduction of kinks in the fatty acid tails of triglycerides.

These kinks result from the differing bond geometry between a C-C bond and a C=C bond (again, you will eventually learn this in Chemistry). The presence of kinks in the fatty acid tails prevents the close packing of triglycerides.

When the triglycerides are less closely packed, hydrophobic interactions are formed to a smaller extent. Hence, less thermal energy is required to break enough of these interactions to liquefy the triglycerides.
The above points also hold true for the fatty acid tails found in phospholipids.

2. Carbohydrates
a. Aldo and keto sugars

All sugars possess a carbonyl group (C=O); the position of the C=O group along the carbon skeleton of the sugar determines whether the sugar
is an aldose sugar or a keto sugar.

Aldose sugars have a terminal carbonyl group (i.e.the C=O involves the first C in the chain).

Ketose sugars have their C=O group at other positions along the chain.

b. Ring structures
Cyclization of sugars (i.e. conversion from the straight-chain form to the ring form) occurs when a bond is formed between the carbon with the carbonyl group and another carbon in the chain.

Refer to
http://www.stolaf.edu/people/giannini/flashanimat/carbohydrates/glucose.swf for animation on how this occurs.

The α-form of the ring structure is defined as the –OH attached to the anomeric carbon being on the opposite side of the ring as the sixth carbon. For most sugars, this is reflected by the –OH projecting downwards, below the plane of the ring.

The β-form of the ring structure is defined as the -OH attached to the anomeric carbon being on the same side of the ring as the sixth carbon. For most sugars, this is reflected by the –OH projecting upwards, above the plane of the ring.

c. Anomeric carbon
Anomeric carbon is defined as the carbon in the ring structure that has both an ether oxygen and an alcohol group attached to it; more simply put, the anomeric carbon is the only carbon atom in the ring that forms bonds to two oxygen atoms.

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Key Points – Turning Effect of Moment

1. The moment of a force about a point is the product of the force F and the perpendicular distance d from the pivot to the line of action of the force

Moment = F x d

2. The SI unit ofr moment of a force is Newton meter – Nm

3. moment of a force is a vector. The direction of the moment is either clockwise or anticlockwise about the pivot.

4. There are two conditions for an object in equilibrium.

a) Net force is zero ie F(net) = 0
b) Net moment due to the external force is zero

5. The principle of moments states that when an object is in equilibrium, the sum of the clockwise moments is equals the sum of the anticlockwise moments.

6. The centre of gravity of an object is the point through which its entire weight appears to act.

7. CG of regular-shape objects can be determined by geometrical symmetry.

8. CG of irregular-shape objects can be determined by the plumbline experiments.

9. The stability of an object increases when the base area increases or the CG is lowered.

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O-Level Singapore/O-Level/Physics and Chemistry Tuition/Physics Tutor

Chemical Bonding – Important Definitions

1. An ion is a charged particle formed from an atom by loss or gain of electrons

2. A cation is a positively charged ion formed when an atom loses valence electrons(s)

3. An anion is a negatively charged ion formed when an atom gains valence electrons(s)

4. A simple ion is an ion formed from single atoms eg Na+, A polyatomic ion is an ion containing more than one kind of atom eg NH4+ or SO42-

5. An ionic bond is the strong electrostatic fore of attraction between positive and negative ions in an ionic compound.

6. A covalent bond is the bond formed by sharing of electrons between two non-metal atoms.

7. A molecule is a small group of atoms held together by covalent bonds.

8. A metallic bond is the force of attraction between positive metal ions and the ‘sea of delocalised electrons’

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O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

Chemical Bonding – Important Definitions

1. An ion is a charged particle formed from an atom by loss or gain of electrons

2. A cation is a positively charged ion formed when an atom loses valence electrons(s)

3. An anion is a negatively charged ion formed when an atom gains valence electrons(s)

4. A simple ion is an ion formed from single atoms eg Na+, A polyatomic ion is an ion containing more than one kind of atom eg NH4+ or SO42-

5. An ionic bond is the strong electrostatic fore of attraction between positive and negative ions in an ionic compound.

6. A covalent bond is the bond formed by sharing of electrons between two non-metal atoms.

7. A molecule is a small group of atoms held together by covalent bonds.

8. A metallic bond is the force of attraction between positive metal ions and the ‘sea of delocalised electrons’

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O-Level Additional Mathematics Tuition Singapore

S3 – Teaching Proof in Plane Geometry

S4 – Practice Exam questions focusing on Trigonometry 1

If you need help please in this topic contact Mr Ong @9863 9633

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O Level E Maths Tuition Singapore/Tuition O Level E Maths/Tutor

S3 – Teaching Trigonometry 1

S4 – Revising Probability and practice P2 prelim question

From O-Level Elementary Mathematics Singapore Tutor

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A Level GP/General Paper Tuition Singapore

Nanotechnology

Nanotechnology is the science of the tiny – the precision engineering of substances at molecular and atomic level. The scale is amazingly small. A nanometer is a billionth of a meter: the width of a human hair is 80,000 nanometers and this industry is manufacturing complex nanomaterials 30 nm wide or less.

Advantages/Benefits

Nanotech is all around you, already: in clothing, electronics, manufacturing and increasingly in health and cosmetics. If you buy a clear sunscreen that promises it blocks ultraviolet light, it is using nano-particles of metals like zinc or titanium – it’s clear because the particles are too small to affect ordinary light. L’Oreal (backed by the food company Nestlé) is marketing anti-ageing cosmetics that exploit the tininess of the particles, ‘nanosomes’, and their ability to penetrate deep into skin cells.

As yet there are officially no foods on sale in Europe that contain nanomaterials, though they exist in the States.

Nano-packaging with ‘self-cleaning’ abilities will be the first application you’ll see – but the science behind that isn’t very different from that in the ‘anti-bacterial’ food containers on sale now. It is with nano-engineered food ingredients that things get mind-boggling. Precisely-engineered nano-scale filters allow you to remove all bacteria from milk or water without boiling. Or take the red out of red wine. Water into oil doesn’t go? Nano-encapsulation technology can already allow you to dissolve as much oil in water, and the other way round, as you wish.

It does this by encasing the water or oil molecules individually in capsules that the liquid will accept. This has enormous implications for altering the fats and salt content of our foods. For cooks, it will turn sauce-making on its head, allowing the emulsification of any two liquids – just for starters, that’s a vinaigrette you won’t have to stir together before pouring. The nano-capsules, 2,000 times narrower than a hair, allow the suspension of almost any substance in clear liquids, without altering their look, or giving any taste.

Future trends

Fancy a programmable drink? Beverage companies such as Kraft are working on prototypes of soft drinks containing nano-capsules that will carry a range of flavours, colours, preservatives or nutrients. You buy the drink and then choose which elements to activate. Your milk carton will tell you when its contents are sour, thanks to particles that sense the gases of decomposition and change colour, and nano-molecules in the ink on the label that tell you how old it is and duly change colour. Kraft and Unilever have products on test.

Atomic-level encapsulation techniques will get more sophisticated. Food processors will offer engineered food catering to your specific tastes, and all sort of options to shoppers. If your chicken is going to sit in the fridge for a while, just activate the nano-encapsulated preservatives held dormant in its flesh. Fancy a fillet with a tarragon-and-butter taste? Trigger a different nano-capsule. Nano-encapsulation could let chefs choose, exactly, how strong a taste or smell should be and when it should be delivered, and design a food’s mouth-feel. The capsule’s casing is to be made of substances ranging from starches, proteins and fats, and can be tailored to break down and release its contents to order. A chef might decide that some flavours in his dish would only be released to the eater a certain number of seconds or minutes after chewing, or when they sip a glass of wine.
Another nano-system to excite cooks uses stable molecules to tie down volatile ones: manufactured starch such as cyclodextrin is being used to bond to those frustratingly evanescent flavours in food – like the fast-fading taste of dill, for example.
Different prospectives
Potential risks of nanotechnology can broadly be grouped into three areas:
• the risk to health and environment from nanoparticles and nanomaterials;
• the risk posed by molecular manufacturing (or advanced nanotechnology);
• societal risks.
There are several potential entry routes for nanoparticles into the body. They can be inhaled, swallowed, absorbed through skin or be deliberately injected during medical procedures (or released from implants). Once within the body they are highly mobile and in some instances can even cross the blood-brain barrier.
How these nanoparticles behave inside the organism is one of the big issues that needs to be resolved. The behavior of nanoparticles is a function of their size, shape and surface reactivity with the surrounding tissue. They could cause overload on phagocytes, cells that ingest and destroy foreign matter, thereby triggering stress reactions that lead to inflammation and weaken the body’s defense against other pathogens. Apart from what happens if non-degradable or slowly degradable nanoparticles accumulate in organs, another concern is their potential interaction with biological processes inside the body: because of their large surface, nanoparticles on exposure to tissue and fluids will immediately adsorb onto their surface some of the macromolecules they encounter. This may, for instance, affect the regulatory mechanisms of enzymes and other proteins.

Situation in Singapore
• Acceptance – NUS Nanoscience and nanotechnology initiative where it is said to be ranked fifth for research papers on this.
• There are industries that deal with nanotechnology being set up here. Eg BASF

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A-Level Economics Tuition Singapore/H2/H1 Economics Tuition

Hi J1 H2 Economics Tuition Students

J1 H2 Economics for Academic Year 2013

Microeconomics Topic 2.2 Government Intervention in the Market

H2 Syllabus :

• Government Failure

H2 Learning Outcome :

• Discuss how governments may create inefficiencies when they intervene in markets due to factors such as political objectives, administrative costs and lack of information.

1. What is Government Failure?

Government Failure refers to situations where inefficiency and inequity may have worsened following government intervention in markets designed to correct market failure.

2. Sources of Government Failure

(a) The pursuit of self-interest amongst politicians and civil servants rather than operating on behalf of citizens leads to a misallocation of resources. For example, politicians and bureaucrats may gain prestige from starting a new spending program even if the cost of the program exceeds its social benefit.

(b) Electoral pressures leading to inappropriate government spending and tax decisions. For example, decisions to continue with agriculture subsidies in countries which public finances can ill afford due to a big proportion of the electorate being farmers.

(c) Short-Termism which is a tendency to look for short term solutions to economic problems rather than making considered analysis of long term considerations. This could be more serious in democratic societies. The risk is that myopic decision-making will only provide short term relief to particular problems but does little to address structural problems. For example, instituting minimum wage legislation to allow workers to earn a decent level of living will often ignore the need to increase the productivity of such workers so that the market will reward them with higher real wages.

(d) Imperfect Information – Governments, like any economic agents, rarely possess complete information on which to base a decision. It is not surprising, then that governments may make the wrong policy response to a problem because they lack knowledge in costs, benefits, long term effects, behavioural changes etc. Governments needs information to answer these 3 questions, namely (i) What to intervene in? (ii) How to intervene? And (iii) By how much to intervene?

(e) Market Distortion – The free market mechanism is the best way of finding out (a) what consumer preferences are and (b) aggregating these preferences based on the number who are willing and able to pay for particular goods and services. Government intervention to correct one market failure may lead to the creation of far more serious market failure.

(f) Costs of administration and enforcement – Government intervention can prove costly to administer and enforce. The administrative costs of administering and enforcing a particular policy to correct market failure may outweigh the social benefits from the correction.

(g) Regulatory Capture – This happens when the industries under the control of a regulatory body can strongly influence the way they are being regulated to their own advantage. Examples of regulatory capture can be found in finance, telecommunication, utilities and environmental protection.

(h) Time Lags – It takes time for the government to identify the market failure, decide if intervention is required, formulate policies to address the identified market failure, and implement those policies. The political system also determines the time lags.

For complete notes and exam based question with model answers please contact Angie Hp 96790479 or Mr Ong 98639633

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A-Level Chemistry Tuition Singapore/H2 Chemistry Tuition/JC Chemistry Tutor

Reaction Kinetics – Concepts

1. Types of rate:
• Initial rate is change in concentration of reactants or product at time t = 0.
• Instantaneous rate is rate of reaction at any given time/instant.
• Average rate is total concentration of reactant used or total concentration of product formed over total time.

2. The minimum energy which colliding molecules must possess for successful collision/reaction is called the activation energy, Ea.

3. Rate law or rate equation is the mathematical relationship between the rate of a reaction and the concentration of the reactants in a reaction. E.g. A + B —> Products
The rate law is
Rate = k[A]^m[B]^n
where k is the rate constant
m is the order of reaction with respect to reactant A
n is the order of reaction with respect to reactant B
(m + n) is the overall order of the reaction
4. The order of reaction with respect to a particular reactant is the power to which the concentration of that reactant is raised in an experimentally determined rate equation / rate law.

5. The rate constant, k, is the proportionality constant in the experimentally determined rate law.

6. The half-life (t1/2 ) of a reaction is the time taken for the concentration of a reactant to fall to half its initial value. It is constant only for a first order reaction as it is independent of reactant concentrations.

7. A catalyst is a substance that increases the rate of a reaction by providing an alternative reaction pathway that has lower activation energy.

8. Biological catalysts such as enzymes are very selective in the reactions that they catalyze, and some are absolutely specific, operating for only one substance in only one reaction. For reactions that normally produce a pair of optical isomers (racemic mixture) when carried out in the lab, enzymes are able to selectively produce one optical isomer in the body.

For exam based questions with solutions please contact @9863 9633

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A-Level Mathematics Tuition Singapore/JC Maths/H2 Math Tuition and Tutor

Hi A-Level/H2 Math Students

J1 – Teaching Differentiation

J2 – 30 min Modular Revision Recurrence Relationship, Graphical Techniques and Binomial Expansions

From A Level Math Tutors

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A-Level Physics Tuition Singapore/H2 Physics Tuition/JC Physics Tutor

Hi A-level/H2/JC Physics Tuition students

Definitions –Wave

1. Progressive Wave
A wave in which energy is carried from one point to another by means of vibrations or oscillations within the wave.

2. Transverse wave
A wave in which the displacements of the particles in the wave are at right angles to the direction of transfer of the energy of the wave.

3. Longitudinal wave
A wave in which the displacements of the particles in the wave are along the direction of transfer of energy of the wave.

4. Wavelength
The shortest distance between two points on a progressive wave which are vibrating in phase, or the distance travelled by the wave energy during one complete oscillation of the source.

5. Speed of a wave
The distance travelled per unit time by the energy of the wave.

6. Period of a wave
The time for one oscillation of the source of the waves or of a particle in the wave.

7. Frequency of wave
The number of oscillations completed per unit time.

8. Displacement of a particle along a wave
The distance in a stated direction of a particle in the wave from its mean or equilibrium position.

9. Unpolarised Wave
An unpolarised transverse wave is one in which the particles‟ direction of vibration is changing all the time in a random manner.

10. Plane Polarized wave
When the plane of vibration of a transverse wave is fixed in one particular plane and is normal to the direction of energy transfer, the wave is said to be plane polarised.

11. Wavefront
A wave front is an imaginary surface or line joining points which are at the same phase.

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O-Level Singapore/O-Level/Pure Physics Tuition/Physics Tutor

Key Points – Mass, Weight and Density

1. Inertia depends only on the mass of the object. Even if temperature or density of the object changes, as long as the mass remains constant, its inertia remains constant.

2. When ice melts, its density increases. Mass remains constant since the number of molecules remains the same.

Density = Mass/Volume

Therefore volume decreases

For more key points and exam based questions with full worked solution, please contact Mr Ong @9863 9633

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O Level Chemistry Tuition Singapore/Chemistry O Level Tuition/Tutor

Atomic Structure – Key Points

1. Not all element have isotopes. Elements like Beryllium, Fluorine and Phosphorus do not have isotopes.

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