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O-Level Additional Mathematics Tuition Singapore

Simultaneous equations in 2 unknowns

Solving Simultaneous equations in 2 unknowns x, y can be done in three ways
• Substitution
• Elimination
• Matrix method (only if both equations are linear)

A. Use of substitution method
Solve for x, y:
x^2- 2xy -y^2= 0
x – 2y = 4

Answers: y = -1, x = 2 and y =- 3 , x = 4

B. Use of elimination method
Solve for x, y:
2x – 3y = 7
-4x + 19y = -1

Answer: x = 5, y = 1

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

Scales and Maps

1. If the linear scale of a map is 1 : x, it means that 1 cm on the map represents x cm on the actual piece of land.

2. The scale of a map can also be represented as a representative fraction (R.F.).

For example, the scale of 1 : 100 can also be expressed as 1/100

Similarly, if the R.F. is 1/50 , the scale will be 1: 50.

Note ; When we use R.F. , the numerator must always be 1.

3. From the scale of a map, we can also find the actual area of a site from its area on the map.

For example, if the scale of a map is 1cm to 5km,
then 1 cm2 on the map will represent (5km)^2 = 25km^2.

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

Hi A-Level/H2 Math Students

Binomial Distribution

1. A Binomial situation arises when
• there is a fixed number, n, of repeated & independent trials
• each trial has only two mutually exclusive outcomes, namely ‘success’ or ‘failure’
• the probability of success, p, is the same for each trial

2. The binomial random variable X is the number of successes in the n trials carried out.
It is denoted by X ~ B(n, p).

3. If X ~ B(n, p), then
• P(X = x) = nCx p^x (1-p)^n-x , where x = 0, 1, 2, … , n
• use binompdf (n, p, x) to compute P(X = x)
• use binomcdf (n, p, x) to compute P(X ≤ x)

Please contact Mr Ong @9863 9633 if you need help in Binomial Distribution.

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

Lesson Plan for 12th
April 2014 JC1

Applications of Elasticity

I) Recap/Extension

a) Price Elasticity of Demand

b) Elasticity Concepts of Supply
i. Price elasticity of supply (PES)
1. Definition
2. Formula
3. Significance of values and signs
4. Movement along supply curve
5. Factors of PES (Definition, Graphs)
a. Extent of spare production capacity

 Definition of spare production capacity:
 Availability of large spare production capacity enables a firm to
increase output when there is an increase in price and demand,
without a significant increase in costs and thus supply will be price
elastic. An increase in price will lead to a more than proportionate
increase in quantity supplied, ceteris paribus.
 Graphs
 Example: Fisherman with many spare boats.

b. Level of inventories or stocks

c. Ease and cost of factor substitution

 The greater the ease and lower the cost of factor substitution, the
more price elastic the supply will be.
 When the price increases, producers want to increase their
quantity supplied in order to increase their profits. Assuming that
the production of the good is a labor-intensive one, an increase in
the demand for labor to meet the rise in production would lead to
a higher wage rate, which in turn increases production costs. The
increase in production cost could reduce the extent of the
increase in production.
 However, if the firm could substitute labor with capital, there
could a significant increase in quantity supplied of the good in
response to an increase in price, ceteris paribus.

d. Time period
i. Market Period
 One where producers cannot respond to a change in
demand and price. All factors of production are fixed in
supply and whatever the price, the producer is willing and
able to offer the same amount of the good.
 The value of PES is thus zero and supply is perfectly price
inelastic. An increase in price does not lead to any
increase in output or quantity supplied, ceteris paribus.
 Diagram.
 Example: Fresh vegetable, fishes in the market during
market period
ii. Short run
 One where producers can respond slightly to a change in
demand and price. There is at least one fixed factors of
production, but production can increase by increasing the
use of the variable factor.
 The value of PES is thus more than zero but less than 1.
Supply is relatively price inelastic because of constraints
by the fixed factor. An increase in price leads to a less
than proportionate increase in quantity supplied, ceteris
paribus.
 Diagram.
 Example: Fisherman hires more labor to work on his boat
(fixed capital)
iii. Long run
 One where producers can make all the desired resource
adjustments. All factors of production are variable.
 The value of PES is more than 1, and price elastic. An
increase in price will lead to a more than proportionate
increase in quantity supplied because all factors of
production are variable.

e. Nature of good
 Agricultural goods and long gestation period.

II) Application of PED to firm

a) Pricing Decisions

 Helps the producers decide on whether to change the price for his goods
 Case 1: Price Elastic Demand
 Case 2: Price Inelastic Demand

b) Output Decisions

 Helps the producers decide on whether to mass produce his goods.
 Case 1: Price Elastic Demand
 Case 2: Price Inelastic Demand

c) Other strategies

 Helps producers decide on knowing whether there are many substitutes to his goods and thus decide on appropriate strategies to increase revenue.
 Case 1: Price Elastic Demand = branding, product differentiation and improving product quality
 Case 2: Price Inelastic Demand

III) Application of PED to government

a) To raise tax revenue
b) To discourage consumption of socially undesirable goods

IV) Application of YED to firm and government (Only for H2)

 For firm = what to produce, how much to produce during economic boom and bust.
 For government = planning what to produce and how much to produce on social goods.

V) Application of XED to firm and government (Only for H2)

 For firm = Helps firms estimate the nature and closeness of the relationship between its goods and that of others. Knowledge of the concept helps firms in making the right business plans such as advertising or expansion of the firm after considering expected changes in prices of rival goods. This knowledge also helps the producers in deciding how to respond to rivals actions with appropriate product and marketing strategies

 For government = Balance of payments and imports.

Please contact Angie Hp 96790479 or Mr Ong 98639633 if you need help in Economics and complete Notes

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

Hi A-level/H2/JC Physics Tuition students

Mastering Qualitative Questions

Chapter 19 Lasers and Semiconductors Part 1

1. Explain how laser action is achieved.

2. Explain why the energy of electrons in solids is represented by energy bands, whereas those in isolated gas atoms are represented by discrete energy levels.

3. Compare the conditions under which the optical emission line spectra and the characteristic x-ray spectra are produced.

4. Using the ideas of population inversion and stimulated emission, explain how a laser could deliver an intense and directed light beam.

5 The existence of the line spectra as demonstrated in (a) is an example for spontaneous emission. Einstein in 1917 published his groundbreaking paper on the basic principles of stimulated emission. Explain clearly how does stimulated emission occur.

For the above questions models answer, please contact Mr Ong @9863 9633

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

TOPIC 1: CELLULAR FUNCTIONS – Part 17

LEARNING OUTCOME

(q)Explain the need for reduction division (meiosis) prior to fertilisation in sexual reproduction.

KEY WORDS

Conservation of diploid number

ESSAY ANSWER

Meiosis halves the number of chromosomes going into gametes, so that the
diploid number in the zygote can be conserved when the gametes fused
together during fertilisation.

During fertilisation, the number of chromosomes doubles in the zygote. In order to conserve the diploid number in the organism, there has to be an equivalent reduction in the chromosome number in the gametes that fused together.

This reduction is made possible by meiosis, which is also known as reduction division.

For exam based questions and solutions, please contact Hp @9863 9633

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A Level GP/General Paper Tuition Singapore

General Paper: Paper 1 Part 3
Revision Guide (Skills)

Writing the Essay

1. Introduction

a) General Statements
Deal with the assumptions to highlight the significance of the issue.
Choose one to two ways of showing this:
 Provide a clarification of key terms relevant to the issue/generic concept
 Provide quotes and a following ‘wrap-up’ to link it back to the issue
 Provide examples that illustrate the significance of the issue
 Provide points of view (POVs) and discuss explicitly the significance of the issue

b) Thesis Statement
• Provide an acknowledgement (the view you don’t quite agree with as much)
• Provide your ultimate stand (the view you agree with more)
• Provide some clarification: Why do you not agree as much with the one view? Why do you agree more with another view? What are the conditions you are going to consider?

c) Brief Overview of Arguments
Provide a summary of your TSs.
[Ask: “How am I going to prove my ultimate stand?”]
*If you have a clear thesis statement and you’ve already discussed the significance of the issue quite extensively, this is not needed.

2. Body Paragraphs

a) Topic Sentences
i) Does this provide a reason for your stand?
ii) Have I engaged all the key terms of the question?
iii) Do I have clear transitional phrases to distinguish between my supporting, counter and rebuttal
paragraphs?

b) Reasoning
i) Have I explained ‘Why/How/When/For Whom’ something happens?
ii) Can I keep asking why/how/when/for whom?

c) Examples
i) Does the example illustrate the reasoning?
ii) Is the example a concrete one?
(“For example, there are many poor people in China” – is not a concrete example!)
iii) Have I used the key words of the TS to provide coherence?

d) Link back to the TS
i) What have I shown in this paragraph and with the example especially?

3. Conclusion Paragraph

a) Have I summarized the arguments presented earlier?

b) Can I provide an insight or afterthought?
[This provides the (rarely observed in the present moment) conditions that would allow the acknowledgment to be true]

c) Have I reiterated my ultimate stand?

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

Atomic Structure – Notes

1. THE SUB-ATOMIC PARTICLES OF MATTER

(a) The 3 fundamental sub-atomic particles in matters are protons, neutrons and electrons.

(b) Protons and neutrons are collectively known as nucleons.

(c) An atom is electrically neutral and contains equal numbers of electrons and protons.

DO YOU KNOW?

• The nucleons reside in the small nucleus of the atom whereas the electrons revolve around it in the “vast” empty space.

• The size of an atom is easily more than 10 000 times that of the nucleus.

• The nucleus accounts for most of the mass of an atom since the mass of the electron is negligible as compared to the mass of the protons and neutrons.

Try it out! 1

Which of the following statements is incorrect?

A The nucleus is positively charged.
B An atom is electrically neutral.
C The region where electron moves is mostly empty space.
D An electron is 1840 times heavier than a proton.

Ans : D

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

Kinetic Particle Theory

Important Definitions

1. The melting point is the temperature at which a solid changes into a liquid.

2. The boiling point is the temperature at which a liquid turns rapidly into a gas.

3. The freezing point is the temperature at which a liquid becomes a solid.

4. Condensation is the process by which a gas or vapour changes into a liquid or a solid.

5. Sublimation is the process by which a solid changes directly into a gas without going through the liquid state.

6. Evaporation is the process by which a liquid changes into a vapour at any temperature below its boiling point.

7. Diffusion is the mixing process in gases or solutions due to the random motion of particles.

If you need help in the above topics, please contact Angie @96790479 or Mr Ong @98639633

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

Macromolecules

1. A macromolecule is any long-chain molecule that contains hundreds or thousands of atoms, joined together by covalent bonds.

2. A macromolecule is formed by linking together many small repeating units known as monomers.

3. The process of joining together a large number of small molecules (monomers) to form a macromolecule is called polymerisation. The macromolecule formed is called a polymer.

4. Macromolecules are common in living things.
For example, the organic compounds, proteins and starch, found in animals and plants are examples of natural macromolecules.

5. Synthetic macromolecules, such as plastics, are now manufactured on a large scale.

6. Different macromolecules have different units and different linkages.

If you need help in the Organic Chemistry, please contact Angie @96790479 or Mr Ong 98639633

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

Kinematics

Acceleration of Free Fall

1. Free fall is defined as the motion of an object under the influence of gravity only. In other words, the only force acting on the object must be its own weight.

Examples:
A coin dropped in a vacuum column
A hammer thrown upwards by an astronaut on the surface of the Moon

2. Any object that moves in air experiences a force called air resistance that tends to slow its motion down. Therefore, objects that experience air resistance are not moving in free fall. However, the effect of air resistance is often assumed as negligible to simplify calculations.

Examples:
A ball thrown upwards in air (with air resistance ignored)
A rock dropped from a tower (with air resistance ignored)

Exam Tip
Always assume air resistance is negligible while solving questions on falling objects, unless explicitly stated otherwise. The effect of air resistance is a common reason why the calculated value differs from actual value obtained in experiments.

3. The acceleration of an object falling freely, without air resistance, is known as acceleration of free fall, g. It is determined to be approximately 10 m s-2. This value varies slightly at different places on the Earth’s surface because the Earth’s gravitational pull varies.

4. In common experiments, the effect of air resistance is usually not negligible. It can be seen
in the following ways:
(a) It always opposes the motion of objects.
(b) It increases with the speed of the object.
(c) It increases with the cross-sectional area of the object.
(d) It increases with the density of air.

5. Air resistance increases as speed increases. Eventually, the acceleration of the object becomes zero, and it reaches its maximum speed (or magnitude of velocity). This maximum constant velocity is called terminal velocity. The direction of terminal velocity is understood to be downwards for a falling object.

6. The value of terminal velocity of a falling object depends on the cross-sectional area and weight of the object. An opened parachute greatly increases air resistance. This reduces the terminal velocity of a parachutist who has jumped out of a plane so that he can land on the ground at a safe speed.

If you need help in the above topics, please contact Angie @96790479 or Mr Ong @98639633

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O-Level Additional Mathematics Tuition Singapore

Remainder Theorem
When a function f (x) — usually a polynomial function, y = a0 + a +
a2x2 + a3x3 +……….
where a = constant is divided by a linear factor (x — k) the remainder upon Long Division is the value f (k).

Factor Theorem
This is a special case of the Remainder Theorem. When a function f (x) is divided by a liner factor (x — k) and the remainder = 0, then (x — k) is a factor off (x).

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

Approximation and Estimation

1. The following figures in a number are significant:
i. All non-zero figures
ii. All zeros between significant figures
iii. All zeros at the end of a decimal

2. The following figures in a number are not significant:
i. All zeros at the start of a decimal less than 1.
ii. All zeros at the end of a whole number may or may not be significant, depending on how the estimation is made

Time
1. 1 minute (min) = 60 seconds (s).
2. 1 hour (h) = 60 minutes (min)

Standard Form
1. A number in the standard form can be written as A x 10″, where A<10, and n is an integer

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

Hi A-Level/H2 Math Students

Probability Part 1

BASIC PROBABILITY CONCEPTS

a) An experiment is a situation involving chance or probability that leads to results called outcomes.

Tossing a fair die once.

b) An outcome (sample point) of an experiment is the result of a single trial of the experiment.

{1} or {2} or . . . or {6}

c) The sample space, S, (or probability space) of an experiment is the set of all possible outcomes.

S = {1, 2, 3, 4, 5, 6}

d) An event, E, is one or more outcomes of an experiment and it is a subset of the sample space S. E = {set of even numbers}
= {2, 4, 6}

e) Probability is the measure of how likely an event is.

P(E) = 3/6 = 1/2

Experiment A: Tossing a fair coin and noting the outcome.
Sample Space, = {H, T}
P({H}) = P({T}) = 1/2 .

Experiment B: Tossing a fair die and noting the outcome.
Sample Space, = {1, 2, 3, 4, 5, 6}, and
P({1}) = P({2}) = P({3}) = P({4}) = P({5}) = P({6}) = 1/6

Experiments A and B each have a Uniform Space where each outcome is equally likely. A uniform space is a finite sample space with all outcomes equally likely, i.e. the probability of each outcome is 1/n where n is the number of outcomes.

Experiment C: Selecting a coloured ball, at random, from a box containing 3 white balls, 2 black balls and 4 blue balls.

Sample Space, = {white, black, blue}
P({white}) = 3/9 = 1/3
P({black}) = 2/9
P({blue}) = 4/9

As we can see, the outcomes in Experiment C are NOT equally likely to occur. We are more likely to choose a blue ball than any other colour. We are least likely to choose a black ball.

Please contact Mr Ong @9863 9633 if you need help in Probability

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

Lesson Plan for 29th and 30th March 2014

International Trade Notes Part I
I) Explain the principle of comparative advantage

a) The theory of comparative advantage is based on the following assumptions:
 There are no trade restrictions/trade barriers
 There are no transport costs
 There are no exchange rates
 Constant opportunity cost of production
 Perfect mobility of resources within a country

b) Suppose there are two countries – Utopia and Happyland. These countries produce two products – hardware and software. According to the theory of comparative advantage each country should specialize in production of a good where it has a lower opportunity cost.

c) Pre trade situation and opportunity costs
The graph below shows production possibilities for Utopia and Happyland.

Figure 1 Production and consumption possibilities before trade
Assume that before trade each country uses a half of its resources to produce hardware and another half to produce software.

To produce 1 more Hardware Utopia has to give up 5 units of Software, e.g. 1 hardware = 5 Software

To produce software more Utopia has to give up 1/5 Hardware, e.g.
1 Software = 1/5 Hardware

Happyland:
To produce 1 more Hardware Happyland has to give up 15 units of Software, e.g.
1 hardware = 15 Software
To produce software more Happyland has to give up 1/15 Hardware, e.g.
1 Software = 1/15 Hardware
In conclusion, Utopia has a comparative advantage (lower opportunity cost) in production of Hardware and should specialize in production of Hardware.

Happyland has a comparative advantage (lower opportunity cost) in production of Software and should specialize in production of Software.

d) Specialization
The table below shows specialization based on comparative advantage.

e) Trade
As each country produces only one good, they will have to trade to be able to consume some of the other good. The terms of trade must settle somewhere between the two opportunity cost ratios to ensure that both countries benefit. As we saw earlier:
In Utopia 1 Hardware = 5 Software and in Happyland 1 Hardware = 15 Software, so the terms of trade (the world price) is 1 Hardware = 10 Software If the countries agreed to trade 75 units of Hardware for 750 units of Software, then Utopia and Happyland will have the following amounts of Hardware and Software available for consumption:

Figure 2 Production and consumption

Both countries are better off from specialisation and trade, because they can reach higher levels of consumption of both goods than was possible before specialisation. After trade they are both able to consume beyond their production possibility curves.

f) Limitations of comparative advantage theory
 Trade Barriers. For example, tariff.
 Transport costs and exchange rates may change the relative prices of goods and may distort
comparative advantages. For example, production of bricks in Singapore.
 Non constant opportunity cost of production
 Imperfect mobility of factors of production
 Imperfect competition may lead to prices being different to opportunity cost ratios.

II) Sources of Comparative Advantage

 Differences in factor endowments
 Economies of Scale

III) Explain the benefits (both mutual and individual) of free trade

 Consumption gains
 Lower prices
 Larger variety of goods and services
 Economies of scale. Without international trade, a country would not specialize
in producing the goods in which it has a comparative advantage in due to small
domestic market.
 Economic growth
 Employment
 Balance of payments surplus
 Increased efficiency
 Technological transfers and potential growth.

IV) Protectionism

a) Definition
b) Protectionist Measures
i. Tariffs
ii. Import quota
iii. Subsidies
iv. Procurement Policies
v. Voluntary Export Restraints
vi. Exchange Controls
vii. Health and safety regulations
viii. Embargoes

V) Explain the reasons for protectionism

 Declining industry argument/Reduce structural unemployment
 Correct balance of payment deficit
 Infant Industry argument
 Anti-dumping
 Protecting jobs during a recession/Reduce cyclical unemployment
 Environmental cost – Free trade tends to encourage relocation of polluting
firms from developed to less developed countries
 Diversification
 Strategic industry argument

VI) Explain reasons against protectionism

 Allocative Inefficiency in long run
 Downward multiplier effects/Beggar Thy Neighbor
 Retaliation
 Allocative inefficiency in short run
 Increased cost of production for downstream producers
 Lack of substitutes

Please contact Angie Hp 96790479 or Mr Ong 98639633 if you need help in Economics and complete Notes

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