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

Hi A-Level/H2 Math Students

2013 J1 – Teaching integration by parts

The success of doing integration by parts often depends on the choice of u and v. Notice that we need to choose one term to differentiate and one term to integrate.

There are 3 types

Type 1: If only one of the two parts of the integrand is integrable, then integrate the one that is integrable.

Example
(a) ∫ x^3 ln xdx (b) ∫ x tan-1 xdx

Type 2: If both parts of the integrand are integrable separately, then choose the one that will ultimately give zero if differentiated a sufficient number of times as the function u for differentiation.

Example
(a) ∫ x cos x dx (b) ∫ x^2 e^3x dx

Type 3: If both parts of the integrand are integrable separately and neither gives zero on repeated differentiation, then it does not matter which function we choose to differentiate.

Example
Find ∫ e^x cos x dx .

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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 3: Dynamics

1. A toy rocket of is fired vertically into the air. Its mass decreases at a constant rate as the fuel burns and is ejected out as exhaust gas. The rocket rises to a height such that, during the flight, the gravitational field strength of the Earth may be considered to have the constant value of 9.81 N kg−1. Use appropriate physics law(s) to explain how the toy
rocket works. [2]

2. In qualitative terms, what can be stated about the subsequent motion as a result of knowing that
(i) the collision is elastic [1]
(ii) the collision is head-on [1]

3. An astronaut in a spacecraft orbiting the Earth may be described as weightless. Explain why this is so. [2]

4. A stone is dropped from a point a few metres above the Earth’s surface. Considering the system of the stone and the Earth, discuss briefly how the principle of conservation of momentum applies before the impact of the stone with the Earth. [2]

5. When a man falls from a height and undergoes free fall, his momentum increases.
Explain if principle of conservation of momentum is violated. [2]

6 Two strong magnets are held stationary with the north pole of one pushed against the north pole of the other. On letting go, the magnets spring apart. It is apparent that the kinetic energy of the magnets has increased. Explain how the law of conservation of momentum and law of conservation of energy apply in this case. [2]

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

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

Key Points – Static Electricity

1. Protons and electrons have electric charge. A proton positively charged while and electron is negatively charged.

2. SI unit of electric charge is the coulomb (C)

3. The electric force is the attraction between unlike charges or the repulsion between like charges.

4. In electrical conductors, there are electric charges (usually electrons) that can move freely within the object.

5. Electrical Insulators are materials in which the electric charges cannot move freely.

6. Electric charges is due to the transfer of electrons from one object to another.
– solid insulators can be charged by rubbing.
– solid conductors can be charged by induction.

7. Discharging is the process of neutralising a charged object by removing excess charges.

8. An electric field is a region in which an electric charge experience an electric force. The direction of the electric field line represents the direction of the force experiences by a small positive test charge within the electric field

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

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

Speed of Reaction – Important definitions

1. the speed of reaction is the amount of reactant used up or the amount of product obtained per unit time.

2. Activation energy is the minimum energy that the reacting particles must possess for a reaction to occur.

3. An effective collision is a collision that successful in producing a chemical reaction.

4. A catalyst is a substance that increases the speed of a chemical reaction.

5. An enzyme is a substance that catalyses biochemical reactions.

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

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

Speed of Reaction – Important definitions

1. the speed of reaction is the amount of reactant used up or the amount of product obtained per unit time.

2. Activation energy is the minimum energy that the reacting particles must possess for a reaction to occur.

3. An effective collision is a collision that successful in producing a chemical reaction.

4. A catalyst is a substance that increases the speed of a chemical reaction.

5. An enzyme is a substance that catalyses biochemical reactions.

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

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

Key Points – Static Electricity

1. Protons and electrons have electric charge. A proton positively charged while and electron is negatively charged.

2. SI unit of electric charge is the coulomb (C)

3. The electric force is the attraction between unlike charges or the repulsion between like charges.

4. In electrical conductors, there are electric charges (usually electrons) that can move freely within the object.

5. Electrical Insulators are materials in which the electric charges cannot move freely.

6. Electric charges is due to the transfer of electrons from one object to another.
– solid insulators can be charged by rubbing.
– solid conductors can be charged by induction.

7. Discharging is the process of neutralising a charged object by removing excess charges.

8. An electric field is a region in which an electric charge experience an electric force. The direction of the electric field line represents the direction of the force experiences by a small positive test charge within the electric field

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

2014 S3 – Teaching simultaneous linear equations

2014 S4 – Teaching Partial Fraction
– Definitions
– Partial Fractions of Proper fractions
– The cover-up method
– Partial fractions of improper fractions

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

2014 S3 – Teaching Number System & Factors and Multiples

2014 S4 – Teaching Congruence and Similarity

Congruence
– SSS
– AAS
– SAS
– RHS

Similarity
– Equal corresponding angles
– Proportional corresponding sides
– 2 pairs of proportional sides with equal included angle
– Ratio of areas and volumes

For Exam based questions with full worked solution. Please contact Mr Ong @9863 9633

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

Cell structure and function

Compare contrast question
– Take note when compare contrast question is asked, you have to consider BOTH similarities and differences
– List out the common features that you intend to compare. Do not merely list down all the content that you know.
– Comparison should point-to-point.

Question: Name 3 organelles which are surrounded by double membranes. Compare & contrast between the double membranes of these 3 organelles. [7]
KEWL

1. What are the keywords in Qns?  Compare contrast; DOUBLE MEMBRANE!!
(Hence do not waste time writing about the functions of each organelle)
2. What are the keywords in Ans?  list out features (see below in brown)
3. When writing in prose, ensure that the comparison is point to point. Do not list out all the features of one organelle in a paragraph and another organelle in another paragraph. Do not expect the marker to do comparison for you. You have to demonstrate ability to point out the comparison for the marker.

Double membrane
Nucleus
Mitochondria
Chloroplast
 Membrane made of basic phospholipids bilayers with proteins interspersed within them
 Intermembranal space in between the two membranes
 Compartmentalisation: Double membrane separates the interior of the organelle from its surroundings.

Pores?
Nucleus – Perforated with pores
Mitochondria – No pores on membrane
Chloroplast – No pores on membrane

Inner membrane?
Nucleus
 Inner membrane is continuous with the outer membrane
 inner membrane not folded & is smooth
Mitochondria
 Inner membrane is not continuous with outer membrane
 Inner membrane folded into cristae  increase surface area for enzymatic action to take place
Chloroplast
 Inner membrane is not continuous with outer membrane
 Inner membrane is generally smooth but gives rise to form fluid-filled sacs called thylakoids which stack up to form grana

Outer membrane?
Nucleus
 outer membrane is smooth but is continuous with RER
Mitochondria
 Outer membrane is smooth and is not continuous with any other organelle
Chloroplast
 Outer membrane is smooth and is not continuous with any other organelle

Presence of membrane proteins?
Nucleus
 relatively less proteins embedded in the inner membra
Mitochondria
 presence of stalked particles and transport proteins on the inner membrane
Chloroplast
 Relatively less proteins embedded in the inner membrane
 presence of stalked particles and transport proteins on the thylakoid membranes

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

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

Hi H2/H1 Economics Tuition Students

An Introduction to Macroeconomics

Essential Question: How does AD/AS analysis help explain and illustrate macroeconomic phenomenon in an economy?

Key Question 1: What is aggregate demand (AD) and aggregate supply (AS) and what are their key determinants?

Part 1: Making Sense of AD-AS

1. Explain what is aggregate demand and why AD curve is downward sloping?

AD = C+I+G+X-M.
As price falls, ability and willingness to consume rises so C rises.
I will also rise as it is cheaper for firms to make purchases.
G is independent of GPL.
As for X, as the country’s goods becomes more competitive, exports rises. At the same time local goods become cheaper relative to foreign goods and this causes M to fall.
Thus AD is inversely proportional to prices and hence slopes downwards.

2. Explain what is aggregate supply and why AS curve is upward sloping?

Aggregate supply is the total output that firms in the economy are willing and able to supply at different price levels in a given time period.
AS can be differentiated into short run AS and long run AS. SRAS is the output which will be supplied at different price levels in a period of time when prices of factors of production remain unchanged. LRAS is the output which firms would produce after price level and factor prices have fully adjusted.
AS curve is upward sloping because output of all firms varies directly with price levels

3. What are the components of aggregate demand?

The components are consumption expenditure, investment expenditure, government expenditure and net exports

4. What are the determinants of consumption expenditure, investment expenditure and government expenditure?

Determinants of consumption expenditure
 Accessibility of credit
 Level of interest rates
 Government policy
 Price expectations
 Savings
Determinants of investment expenditure
 Interest rates
 Business expectations
 Government policy
Key Question 1: What is aggregate demand (AD) and aggregate supply (AS) and what are their key determinants?
 Technological change
 Infrastructure
Determinants of Government expenditure
 Budget policies

5. What are the factors that shift aggregate supply?

Factors that shift AS curve can be broadly divided into 2 main groups:
1) Factors that affect productive capacity
 Discovery of new resources
 Advances in technology
 Immigration
2) Factors that affect the costs of production
 Increases in prices of factor inputs like raw materials
 Increases in wages

For complete model essay contact Angie Hp 96790479 or Mr Ong 98639633

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A Level GP/General Paper Tuition Singapore

Is pragmatism an impediment to real progress in Singapore?

Singaporeans are often seen and stereotyped as a pragmatic group of individuals who are constantly hard at work, extending their office hours or striving in the rat-race of working life in order to get the next big promotion. These habits are by no means harmful or perfectly noble intentions that we as individuals should aspire to, but the complaint often voiced by Singaporeans themselves is that our pragmatism has become a stumbling block to our own success. Often, this is due to the over-emphasis on materialistic rewards as the sole yardstick for success. The resulting consequence is that Singaporeans fear innovation and taking the path less trodden simply because it is not as secure to do so or because the fear of failure is too great. I believe that pragmatism has become an impediment to real progress in Singapore as the nation needs mavericks and new innovations in order to remain at the forefront of progress in the future.

Opponents of the given statement would argue that it is precisely the pragmatic nature of Singapore – in terms of governance, education and societal aspects – that propelled Singapore from a Third World to a First World nation. After separation from Malaysia, Singapore was forced to quickly rebrand herself as an attractive manufacturing hub for Trans-national Corporations (TNCs)in order to ensure her economic survival. The large-scale urban redevelopment and planning that ensued in order to create proper manufacturing zones in Jurong and Paya Lebar resulted in the displacement of many village communities, which caused unhappiness to the people. However,these policies were necessary in order to ensure the long-term economic viability of the nation.Being pragmatic about this affair may not have been easy for the government, but on hindsight, it acted to ensure progress for this nation.

In another aspect, Singapore is pragmatic in its investment in new tourism ventures. This has allowed most of its ventures to be carried out with optimal success precisely because the government was realistic and ‘safe’ in adopting tried-and-tested tourism ventures. Some examples
include, the building of the Singapore Flyer which was modelled after the famous London Eye, the building of the Integrated Resorts on Sentosa and at Marina Bay, which are modelled after the Las Vegas Casino and Entertainment Strip, as well as the hosting of the Formula One Races, which was an improvement of the Formula One races held in neighbouring Malaysia’s Sepang Circuit. Singapore has a penchant for modelling other countries’ successful tourism ventures and injecting improved infrastructure and management with the intention of superceding these models-cumrivals. While detractors may argue that this lack of innovation and ‘Singapore’ method of practical investment is uncreative, who can argue with the landslide success that all these attractions have
had in attracting tourists to Singapore as well as diversifying the entertainment scene in this country?

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

Atoms, Molecules and Stoichiometry Part 1

1 Define the following terms:

(a) Isotopes are atoms of the same element with the same number of
protons but different number of neutrons.

(b) Relative isotopic mass is the number of times the isotope is heavier than 1/12 the mass of an atom of carbon-12.

(c) Relative atomic mass of an element is the average mass of its atoms in the isotopic mixture, compared to 1/12 the mass of an atom of carbon-
12.Symbol: Ar

(d) Relative molecular mass of a molecule is the average mass of its
molecule compared to 1/12 the mass of an atom of carbon-12.
Symbol: Mr

(e) Avogadro’s Law states that equal volumes of all gases under the same
conditions of temperature and pressure contain the same number of
molecules/atoms (valid for ideal gases or gases under ideal-like
conditions).

(f) Molecular formula gives the actual number of the number of atoms of
each element present in the compound.

2 Concept : Limiting Reagent and Dilution

The process of obtaining iodine from oil field brines involves the following three step process. In the first reaction, 250 g of sodium iodide (NaI) is reacted with 340 g of silver nitrate (AgNO3).

NaI + AgNO3 —> AgI + NaNO3
2AgI + Fe —> FeI2 + 2Ag
2FeI2 + 3Cl2 —> 2FeCl3 + 2I2

(a) Determine the limiting reagent in the first reaction.
No of mol NaI available = +25023 127 = 1.6667
No of mol AgNO3 available = ++340108 14 48 = 2.00
NaI ≡ AgNO3 ⇒ NaI is the limiting reagent

(b) Calculate the mass of iodine crystals that can be obtained from the whole process.
NaI ≡ AgI ≡ ½ FeI2 ≡ ½ I2
No mol of I2 obtained = ½ ( 1.6667 ) = 0.83335
Mass of I2 obtained = 0.83335 x 2(127) = 212 g

(c) The iodine crystals obtained was then dissolved in 50.0 m3 of organic solvent, trichloromethane. Calculate the concentration of iodine solution in g dm-3.

Concentration of I2 = 50000212 = 0.00423 g dm-3

(d) In a further experiment, a certain volume of organic solvent, trichloromethane was added to lower the concentration of the iodine solution calculated in (c) to 1.40 X 10-5 mol dm-3. Calculate the volume of trichloromethane added to achieve this effect.

CoVo = CdVd ⇒ (0.00423254)(50000) = (1.40 x 10-5) (Vd)
Vd = 59480 dm3
∴ Volume of trichloromethane = 59480 – 50000 ≈ 9.48 x 103 dm3

(e) State the assumption made in determining your answers in parts (c) and (d).

Iodine is soluble in organic solvent / trichloromethane

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

2013 A Level H2 Math topics not tested in Paper 1.

(1) Functions
(2) Maclaurin Series + Binomial Expansion
(3) Maxima/Minima + Rate of Change (but seldom tested)
(4) Transformations/Further Curves Sketching
(5) Recurrence Sequences
(6) Vectors (questions on lines, though they usually involve planes with column vectors given)
(7) Integration – by parts and volume of revolution

All the best for P2
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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 2: Kinematics

1. Define displacement, speed, velocity and acceleration. [4]

2. Derive the 3 kinematics equations which represent uniformly accelerated motion in a straight line. [3]

3. State the conditions that must be satisfed for the kinematics equations to be valid. [2]

4. State the feature of a velocity-time graph that enables acceleration to be determined. [1]

5. Explain why, for all real vertical throws, the time taken to reach maximum height must be shorter than the time taken to return to the starting point. [2]

6. Explain why the acceleration has the value g only at this particular time. [2]

7. Explain why a body falling through air reaches a terminal velocity. [2]

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

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

Power Revision

O Level Chemistry – 2 hrs Each Lesson

1. Atomic Structure/Ionic, Covalent and Metallic Bonding – 2 lessons
2. Formulae & Equation Writing – 1 lesson
3. Mole & Chemical Calculations – 2 lessons
4. Acids and Bases – 1 lesson
5. Salts – 1 lesson
6. Chemical Analysis – 1 lesson
7. Metals – 2 lessons
8. Periodic Table – 2 lessons

Power Revision

O Level Physics – 2 hrs Each Lesson

1. Kinematics – 2 lessons
2. Dynamics – 2 lessons
3. Forces – 1 lesson
4. Turning Effect of Forces – 1 lesson
5. Work Done, Energy & Power – 1 lesson
6. Thermal Physics – 2 lessons
7. Light – 2 lessons
8. Current Electricity/DC Circuits/Practical Electricity – 3 lessons

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

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