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

Method for solving simultaneous equations

1. Substitution Method

2. Elimination Method

3. Graphing Method

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

Hi A-Level/H2 Math Students

Examination Skills

DO
1. Plan your timetable well so that you are able to allocate time to revise all the topics.

2. Revise all tutorials, lecture tests, short quizzes given by your tutors, Common Test, and Past Years GCE ‘A’ Level Questions

3. Optimise the use of Graphic Calculator whenever possible.

4. Practice time management.

DO NOT
1. Practice questions without understanding – must grasp correct concepts
learnt from every question.

2. Skip topic(s).

3. Be complacent.

Important notes on accuracy of answers

In general,
1. Only if the final answer is not exact, then leave your answer to 3 significant figures unless otherwise stated.

2. For angles, leave your answer to 1 decimal place(in degree) or
3 significant figures(in radian) unless otherwise stated.

3. In Statistics, intermediate values should be stated fully if it is exact. If not, an accuracy of 5 significant figures is recommended unless otherwise stated.

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

Atoms, Molecules and Stoichiometry – Notes

4. Empirical and Molecular Formulae

Molecular Formula:
The actual number of atoms of the different elements in the compound.

Empirical Formula:
The simplest whole number ratio for the atoms of different elements in the compound.

The empirical formula of a compound may be calculated from experimental data (from combustion analysis or elemental analysis). The molecular formula can be determined from the empirical formula provided the molar mass or the relative molecular mass of the compound is known.

Note:
In the calculation of empirical formula from experimental data, it is a common procedure to round off figures to the corresponding nearest whole numbers in order to get the simplest ratio. Great care should be exercised when the following figures are obtained and these figures are usually multiplied by a factor in order to get the correct simplest ratio.

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A Level GP/General Paper Tuition Singapore

Model Essay

Is killing ever acceptable?

The recent Boston bombing incident in 2013 saw both world leaders and earnest youths alike coming together to discuss the efforts that should be undertaken to calm the furore brought about by citizens around the world – namely the severity of the punishment that ought to be dished out to those responsible for the incident. The fire was then intensified when the government and Boston officials stated that the verdict for the bombers was still death, but in its wake it left behind many debates forming about whether killing can ever be acceptable and the criteria for it to hold true. Killing should be seen as acceptable if the majority of the world are advocates as the government’s job is to ensure that the needs of the many are fulfilled, not the needs of the minority. It should also be acceptable if it brings about more benefits than harm which can come in the form of closure stemming from revenge or deterring future incidents and also if it is done in order to ensure one’s survival such as self-defence or protecting the family. Yet, recent years have also seen a new form of killing, euthanasia, which is also controversial. All in all it is of my opinion that killing is indeed acceptable when it brings about more gain than harm, but not when it is done to satisfy twisted desires such as enjoying the intentional cessation of life.

Indeed, murders are not acceptable when they are done not in the pursuit of self-defence but rather as a means to eliminate someone’s life for selfish reasons. There are times when murderers justify themselves in a way that sounds logical, such as when one wants to cause a genocide of the human race because he or she is an advocate of the environment and they feel that Mother Earth would be better without humans selfishly consuming but rarely giving back natural resources. When they justify themselves in this manner, it is indeed a grey area and intricate to discuss about because of its multi-faceted nature. After all no one on earth can provide a rebuttal that humans benefit Gaia, as it is very clear that we have consumed much more than the relatively few trees we have planted back. However, this does not make it acceptable as allowing them to cause mass murders is tantamount to passing a mandate for people to kill anyone. Hence the killing by such a person is unacceptable because the majority of the world does not place the environment over their lives and since the needs of the many outweigh those of the few, it cannot be justified. Thus, in cases such as these and including other similar murders by the mentally insane are all not acceptable because benefits do not outweigh the cost of human lives.

However, killing is acceptable when it provides closure stemming from retribution, something essential in calming the storm in the hearts of the victim’s kin. There is an obvious benefit of alleviating the pain that the murder has inflicted on society because when one is murdered, that person is not the only one who feels the pain. The people who have shared their lives with the victim also feel scared and damaged indirectly by the murderer. In these cases, killing the murderer will provide relief for the victims and this can be seen as compensation for the losses the victim’s kin suffered. In the case of the Boston bombings, the furore and fiery hatred that have emerged would not have been calmed if the perpetrator who caused the bombings was spared from the claws of death – death row penalty – and governments would also come under fire as they may feel that the judicial system is flawed and useless. Others may argue that humans, as represented by the government, should not play god and determine who should live and who should perish. Hence the benefits do outweigh the cost of these murders and as such it is acceptable. Furthermore, the fact that the government considered sparing the bomber’s death but was futile points to the notion that the government decided that calming people’s anger was more important and hence went with the decision to end his life. This supports the fact that benefits outweigh the cost and that it is hence acceptable.

As difficult as it may be to justify murders, killing is acceptable as it acts as a strong deterrence to potential murders and hence it keeps the world safer in the long run. By showing the world that the intentional cessations of life will not be tolerated and that severe punishments will be meted out, of which its severity will be proportional to the atrocities of the crimes committed, it provides a disincentive for potential murderers to not commit these crimes. As they fear the punishments that await them, they will not be as willing to kill. For example in the case of Singapore, the death penalty exists and has been largely attributed as the reason for low crimes in Singapore. Precisely because Singapore has a zero-tolerance policy on kidnaps, murders and other major crimes, there are very few brave or rather naïve enough to try and commit these acts of atrocities. If Singapore did not dole out the death penalty for drug traffickers then Singapore would be largely filled with drug lords who are motivated by the massive wealth from such trafficking acts. This supports the notion that without fear, people will do just about anything as long as they desire it. Hence in this case it is justifiable to kill offenders to make an example out of them. While detractors of the death penalty – the critics, skeptics and luddites – may argue that if the point is to instill fear in the world, then it would be the same as an enslaved society with people at the top having absolute power. I disagree with this because the fact that we have jails and that only the harshest of crimes are met accordingly with death sentences all point to the notion that we still are cognizant of where to draw the line. Hence, these killings are acceptable.

Lastly, the newest kind of killing is due to the idea of euthanasia where patients can end their lives peacefully without pain or to speed up their inevitable deaths. Killing is acceptable in these cases as it allows them to cheat death by dying sooner rather than later and hence bypass all the pain of waiting for death. This is especially so when family members know that the victim is suffering just by living perhaps due to kidney failure, or that they are in a comatose state and are unable to truly live life. Their loved ones can pull the plug on the victim hence ending his or her suffering. This is then morally acceptable since it would be immoral to deny them euthanasia and instead force them to live in agony or to find more painful ways of committing suicide. Over the years euthanasia has experienced a rise in popularity, evident from its increased presence in media such as newspapers and social media. This supports the point that this form of killing is acceptable. It is only not acceptable in cases where the victim is still hanging on to his life but it is the family members who want to pull the plug on him as there is an extreme financial burden of keeping the victim on life support such has plugging him to a kidney dialysis machine. Hence, killings done by euthanasia are also acceptable so long as the victim wants to undergo it. Thus, killing is acceptable in this case.

In conclusion, while there is extreme hardship in justifying murders and accepting it, the need for killing is an undeniable reality. In obvious cases where killing is done for self-survival or to protect the people around him, the act of killing for revenge and closure killing is largely acceptable by both the government and the public. However, grey areas such as killing to ensure that natural resources in the future are still available are not seen as acceptable because the costs of human lives are too much. Hence the most important criteria in assessing whether or not killing is acceptable has much to do with the opinion of the majority. The minority may never accept killing, arguing that everyone should be given a second chance, but the harsh reality of the world is that if your kin was murdered, you would challenge the entire world in order to get revenge and closure for yourself. Hence it may not be acceptable but for some, they have to accept that it is a necessary act.

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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 12 Current of Electricity

1. A resistor of resistance R is connected across a battery of e.m.f. E and internal resistance r. The e.m.f. of the battery can be expressed as
E = I (R + r)
where I is the current through the circuit. Explain how this equation is consistent with the principle of conservation of energy.[2]

2. In Singapore, the national voltage is set at 230 V while the American system uses 110 V. If a 2 kW kettle designed for use in Singapore is used in USA, suggest and explain any concerns in doing so. [2]

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

TOPIC 1: CELLULAR FUNCTIONS – Part 10

LEARNING OUTCOME

j)Investigate and explain the effects of temperature, pH, enzyme concentration and substrate concentration on the rate of enzyme catalysed reactions, and explain these effects.

ESSAY ANSWER

Temperature
The rate of reaction increases with temperature until the optimum temperature is reached. Optimum temperature is the temperature at which the enzyme is functioning at its maximum rate. The effects of temperature on the rate of reaction is expressed as the temperature coefficient (Q10 value) and it is calculated as follows:

Q10 = rate of reaction at (10+x) deg C/ rate of reaction at x deg C

For most enzymes, the Q10 value is approximately 2. This means that the rate of reaction doubles for every increase of 10ºC. This is only applicable between an approximate temperature range of 15°C to 25°C.
Certain organisms have been able to adapt to high temperatures. Enzymes in
these heat-tolerant organisms have a higher optimum temperature than most
normal organisms, eg. thermophilic bacteria. Despite this, the rate of reaction takes on the same trend (i.e. decreases rapidly) as temperature increases beyond its optimum temperature.

pH
Optimum pH is pH is at which the rate of an enzyme-catalysed reaction is
at its maximum. Usually matches the usual pH environment which the enzyme
is found in. At this pH, the intramolecular bonds which maintain the
secondary and tertiary structures of the enzyme are intact. Conformation of active sites is most ideal for binding of substrate and the frequency of successful collisions between enzyme and substrate molecules is the highest. The number of enzyme-substrate complexes formed per unit time is at its highest and the rate of reaction is at its maximum.

At pH lower or higher than the optimum, the concentration of hydrogen
ions (H+) would have changed and this would alter the charges on the R
groups of the amino acid residues of the enzyme molecule. The ionic bonds
and hydrogen bonds that help maintain the conformation of the enzyme
molecule would be disrupted and the binding of the substrate would be
affected. Enzyme work within a narrow range of pH. If the pH is altered by a small extent from the optimum pH, the effects are normally reversible. If the pH is restored to the optimum pH, the maximum activity of the enzyme will be restored. However, if the pH is altered by a large extent, the conformation of the enzyme molecule would be severely affected and denaturation of the enzyme might be irreversible.

Enzyme concentration
An increase in the enzyme concentration leads to an increase in the rate of reaction. The rate of reaction is directly proportional to the enzyme
concentration. The more enzyme molecules present, the more active sites
available for the substrate to be catalysed, hence the higher the rate of
reaction. The following conditions must be present for the rate of reaction to increase linearly in proportion to the enzyme concentration:
– Substrate concentration must be kept at high level and must not be a
limiting factor.
– Concentration of the enzyme is much less than that of the substrate.
– Factors such as pH and temperature must be constant.

At low enzyme concentration, adding more enzymes increases the rate of
reaction. As enzyme concentration increases, the frequency of successful
collisions between the enzyme and substrate molecule increases. With more
enzyme presents, it is more likely that a substrate will bind to an empty active site on an enzyme. More enzyme-substrate complexes are formed. Rate of reaction increases linearly with increasing enzyme concentration.

At very high enzyme concentration, the substrate concentration is the
limiting factor. An increase in the enzyme concentration would not result in any further increase in the rate of reaction.

Lastly, for reactions with different enzyme concentrations, if the amount of substrate were the same for all reactions, the total amount of product will eventually be the same.

Substrate Concentration
At fixed enzyme concentration, reaction rate increases as substrate
concentration increases; i.e. the rate of reaction is directly proportional to the substrate concentration.

At low substrate concentration; as substrate concentration increases, the
frequency of successful collisions between the enzyme and substrate
molecules increases. More enzyme-substrate complexes are formed and rate
of reaction increases. Active sites of the enzyme molecules are not all
occupied at this point. Rate of reaction is limited by substrate
concentration.

At high substrate concentration; the rate of reaction will continue to increase with increases in substrate concentration, until a point where further increase in substrate concentration will no longer produce a significant change in the rate of reaction. This is because the active sites of all enzyme molecules are saturated with substrate molecules. Any extra substrate molecule has to wait until the enzyme-substrate complex has released the products before it can bind to the active site. Enzyme concentration is now the limiting factor.

The maximum rate for a particular enzyme reaction is denoted as Vmax. The
Michaelis constant (KM) is the concentration of substrate required to make
the reaction proceed at half the maximum rate. It is the same for a particular enzyme but varies from one enzyme to another. It is a measure of the affinity of the enzyme for its substrate. A low KM value indicates a high affinity of the enzyme for the substrate, and vice versa.

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

Topic 2.2 Macroeconomic Aims, Problems/Issues, Consequences and Policies

Syllabus

Macroeconomic Problems and their Causes
• Undesirable rates of economic growth
• High inflation rate
• High unemployment rate
• Persistent or large balance of payments deficit

Outcome
• Explain the meaning of undesirable rates of economic growth, high inflation rate, high unemployment rate and persistent or large balance of payments deficit.
• Analyse the causes and consequence of macroeconomic problems.

Macroeconomics Lecture 8 : Unemployment

8.1 Unemployment Definitions

Unemployment refers to a situation where a worker of working age will like to work but cannot find work.

The economy’s natural rate of unemployment refers to the amount of unemployment that the economy normally experiences.

Note : Natural does not imply that this rate of unemployment is desirable. Nor does it imply that it is constant over time or has no influence to economic policy.

8.2 Measuring Unemployment

The government statistics agency measures unemployment by surveying households and classify adults into anyone of the three categories :

• Employed;
• Unemployed;
• Not in the workforce

A person is considered employed if he or she spent some of the previous week working at a paid job. A person is unemployed if he or she is on temporary layoff or is looking for a job. A person who fits neither of the first 2 categories, such as a full-time student, homemaker, or retiree, is not in the labour force.

Labour Force = Number of employed + Number of unemployed

Unemployment Rate = (Number of Unemployed / Labour Force) X 100

Labour Force Participation Rate = (Labour Force / Adult Population) X 100

Unemployment Rate and Labour Force Participation Rate may be computed for specific groups of people, for example, amongst men, women, people above 55 etc.

! Stop and Think : Refer to handout to find out how Singapore defines unemployment

8.3 Shortcomings of the Unemployment Rate and More insights into Unemployment

It is not easy to distinguish between a person with a full-time job and a person who is not working at all; it is much harder to distinguish between a person who is unemployed and a person who is not in the labour force.

Movements into and out of the labour force are, in fact, very common. More than one-third of the unemployed are recent entrants into the labour force. These entrants include young workers looking for their first jobs, such as recent graduates. They also include older workers who had previously left the labour force but have now returned to look for work. Moreover, not all unemployment ends with the job seeker finding a job.

Because people move into and out of the labour force so often, statistics on unemployment are difficult to interpret. On the one hand, some of those who report themselves unemployed may not, in fact, be trying hard to find a job. They may be calling themselves unemployed because they want to qualify for a government aid or because they actually working and being paid “under the table”.

On the other hand, some of those who report being out of the labour force may, in fact, want to work. These individuals may have tried to find a job but have given up after an unsuccessful search. Such individuals, called discouraged workers, do not show up in unemployment statistics, even though they are truly workers without jobs.

In light of the above, alternative measures that take into account discouraged workers, workers who falsely declare their employment status etc are constructed to give economists a better idea of the extent of joblessness.

If unemployment is short-term, it may not be a big problem. But if unemployment is long term, then it is a serious problem. Economists have found that most spells of unemployment are short, and most unemployment observed at any given time is long-term.

In the short-run, there are always some workers without jobs, even when the overall economy is doing well. In other words, the unemployment rate is not likely to fall to zero. Instead, it fluctuates around the natural rate of unemployment.

In the long-run, unemployment can be due to frictional unemployment or structural unemployment.

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

Hi A-Level/H2 Math Students

Permutations and Combinations

Fundamental Principles of Counting

Addition Principle
If there are r choices for performing a particular task, and the number of ways to carry out the kth choice is ,nk for k = 1, 2, 3, …, r, then the total number of ways of performing the task is equal to the entire sum of the number of ways for all the r different choices i.e.

n1+n2+n3…………nk

Multiplication Principle
If one task can be performed in m ways, and following this, a second task can be performed in n ways (regardless of which way the first task was performed), then the number of ways of performing the 2 tasks in succession is m × n.

Permutations
A permutation is an ordered arrangement of objects.

Combinations
A combination is a selection of objects in which the order of selection does not matter.

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

Atoms, Molecules and Stoichiometry – Notes

3 THE MOLE & RELATED CONCEPTES

• The word ‘mole’ is derived from the Latin word meaning a collection, mass or pile.
Just as 1 dozen is a collective term for 12 items, 1 mole is a collective term for 6.02 x 10^23 of elementary entities or particles which may be electrons, ions, atoms or molecules.

• The Avogadro constant (L) is the constant of proportionality between the number of specified entities of a substance and amount of that substance, experimentally found to be 6.02 x 10^23 mol−1.

3.2 Molar Mass (g mol−1)

• Molar mass refers to the mass of one mole of a substance (element or compound).
(Units = g mol−1)
• The molar mass of a substance is numerically equal to the Ar or Mr of that substance except that it has units of g mol−1 while both Ar and Mr have no units.

E.g. Molar mass of NaCl = 23.0 + 35.5 = 58.5 g mol−1
while Relative formula mass of NaCl = 58.5

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A Level GP/General Paper Tuition Singapore

Model Essay

3. ‘The arts cannot change the world, but they make it more beautiful.’ Discuss this view with reference to one of the following: painting, sculpture or music.

Key words:
– ‘change the world’  affect real-world outcomes; alter people’s viewpoints with regards to various social, political, etc issues; influence the way people think; challenge set notions / the status quo

– ‘make it more beautiful’  serves a purely aesthetic purpose

Question requirements:
– discuss the purposes of art  challenge the notion that the sole purpose of art is to beautify the world

– discuss society’s perception of the arts, and how far it has the potential to successfully influence society itself

– specific examples of whichever art form is chosen

Pitfalls:
– students spend too much time discussing what ‘the arts’ encompass

– failure to see the link between changing the world and making it more beautiful

Possible stands / viewpoints:
– the arts can change the world, by influencing people’s views on current social & political issues affecting their society or raising awareness of these issues  art as a reflection of society, hence having the potential to change the world by highlighting what the artist sees as a problem e.g. Goya’s etchings (scenes of war)

– art uses aesthetic value to arouse emotions, hence changing mindsets  artist changes the world by manipulating the audience’s emotions to the point where they might take action to make a negatively perceived situation better e.g. the Vietnam wall

– however, art can simply be for art’s sake  art doesn’t try to change people’s views or attitudes, it can merely be a vehicle for entertainment or something whose main purpose is to beautify the world e.g. still life art

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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 11 Superposition

1. Briefly explain how an interference pattern may be obtained when waves from two sources meet. [2]

2. It is not possible to observe interference fringes between light beams which are planepolarised in perpendicular planes. Explain. [2]

3. A progressive sound wave of wavelength l is incident on an open pipe as shown below. The length of the pipe is l. A stationary wave is formed in the pipe. Explain the formation of the stationary wave in the pipe. [3]

4. Light of wavelength 650 nm is incident normally on a double slit arrangement. The interference fringes formed are viewed on a screen placed parallel to and at a distance of 1.60 m from the double slit.
Describe the changes (s) to the fringes if
a. both slits are made narrower whilst keeping the slit separation constant [1]
b. the light emerging from one of the two slits is reduced in intensity to half of its previous value [2]
c. both slits are covered with sheets of polaroid and that in front of one of the slits is slowly rotated. [1]

5 Two sources S1 and S2 produce waves of the same frequency on the surface of some water. State three conditions that must be satisfied from waves from the two sources to produce an OBSERVABLE interference pattern on the water surface. [3]

6 Show how the principle of superposition of waves can be used to explain the formation of two sources interference fringes. [3]

7. Sound waves and water waves can go round corners but light waves seem to travel only in straight lines. [2]

8. Explain why a pillar in a concert hall can block the view of the audience but it has little effect on their hearing

9. Explain what is meant by diffraction of waves.

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

TOPIC 1: CELLULAR FUNCTIONS – Part 9

LEARNING OUTCOME

(i)Follow the time course of an enzyme-catalysed reaction by measuring rates of formation of products (e.g. using catalase) or rate of disappearance of substrate (e.g. using amylase).

ESSAY ANSWER

The time course of an enzymatic reaction can be monitored by either
measuring formation of products of reaction or by measuring the
disappearance of substrate of reaction.

By measuring formation of products of reaction
(using catalase and hydrogen peroxide as an example)
Catalase is an enzyme that catalyses the decomposition of hydrogen peroxide (H2O2) into water and oxygen gas.

2 H2O2 —–>
2 H2O + O2

Depending on the experimental setup, rate of formation of oxygen can be
measured by:
– Counting oxygen (O2) bubbles formed
– Measuring volume of water displaced by oxygen
– Measuring the volume of O2 produced using a gas syringe

By measuring the disappearance of substrates of reaction
(using amylase and starch as an example)
Amylase catalyses the breakdown of starch into maltose.
starch ——–> maltose

Depending on the experimental setup, rate of disappearance of starch can be measured by:
– Iodine in potassium iodide test
– Benedict’s test

Iodine in potassium iodide test
As the reaction progresses, less starch will be present and more maltose will be present. The activity of amylase was observed by using iodine in potassium iodide solution. Iodine reacts with starch to form a blue-black colour. As amylase breaks down starch, less and less starch will be present and the colour of the solution will become lighter and lighter. When all the starch has been digested, the solution will remain light-brown in colour. The colour change was observed using spot-plates (e.g. white tiles).

Benedict’s test
As the reaction progresses, less starch will be present and more maltose will be present. The activity of amylase was observed by using the Benedict’s solution. Benedict’s solution contains copper sulfate. Reducing sugars reduce soluble blue copper sulfate containing Cu2+ to insoluble reddishbrown copper oxide containing Cu+, which is seen as a precipitate. As amylase breaks down starch, more and more maltose which is a reducing sugar will be present and the initial blue colouration of the mixture turns green (low concentration of reducing sugar), then yellowish (middle concentration of reducing sugar) and may finally form a brick red precipitate (high concentration of reducing sugar).

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

Topic 2.2 Macroeconomic Aims, Problems/Issues, Consequences and Policies

Syllabus

Macroeconomic Problems and their Causes
• Undesirable rates of economic growth
• High inflation rate
• High unemployment rate
• Persistent or large balance of payments deficit

Outcome
• Explain the meaning of undesirable rates of economic growth, high inflation rate, high unemployment rate and persistent or large balance of payments deficit.
• Analyse the causes and consequence of macroeconomic problems.

Macroeconomics Lecture 7 : Inflation Part 3

7.1 Redistributive Effects of Inflation

Recall the following :

Nominal Income : Number of dollars received as wages, rent, interest or profits.

Real Income : Measure of the amount of goods and services nominal income can buy; it is the purchasing power of nominal income, or income adjusted for inflation.

Real Income = Nominal Income / Price Index (in hundredths)

Anticipated Inflation : Inflation whose full extent was expected.

Unanticipated Inflation : Inflation whose full extent was unexpected.

When unanticipated inflation occurs, not everyone’s nominal income rises at the same pace as the price level. Therein lies the potential for redistribution of real income from some to others.

There are generally two groups of people who are affected by inflation, namely, (a) those hurt by inflation and (b) those unaffected or helped by inflation.

(A) Hurt by Inflation

Unanticipated inflation hurts fixed-income recipients, savers and creditors. Inflation redistributes real income away from them and toward others.

(i) Fixed Income Receivers

People whose incomes are fixed see their real incomes fall when inflation occurs.

Examples :
• Retirees who receive pensions or annuity payments that are not pegged to inflation.
• Landlords who receive lease payments of fixed dollar amounts during the contracted lease period.
• Workers whose incomes are dictated by fixed pay schedules.
• Minimum wage workers and families living on fixed welfare incomes.

(ii) Savers
Unanticipated inflation hurts savers. As prices rise, the real value, or purchasing power, of an accumulation of savings deteriorates. Paper assets such as savings accounts, insurance polices, and annuities that were once adequate to meet rainy-day contingencies or provide a comfortable retirement decline in real value during inflation.

(iii) Lenders / Creditors

Unanticipated inflation harms creditors because as prices go up, the value of the dollar goes down. So the borrower pays back less valuable dollars than those received from the lender.

(B) Unaffected or Helped by Inflation

(i) Flexible Income Receivers

People who have flexible incomes may escape inflation’s harm or even benefit from it. For example, some union workers get automatic cost-of-living adjustments in their pay when the CPI rises, although such increases rarely equal the full percentage rise in inflation.

Some flexible-income receivers and all borrowers are helped by unanticipated inflation. The strong product demand and labour shortages implied by rapid demand-pull inflation may cause some nominal incomes to spurt ahead of the price level, thereby enhancing real incomes.

Examples :
• Some property owners faced with an inflation-induced real estate boom may be able to boost flexible rents more rapidly than the rate of inflation.
• Some business owners may benefit from inflation. If product prices rise faster than resource prices, business revenues will increase more rapidly than costs. In those cases, the growth rate of profit incomes will outpace the rate of inflation.

(ii) Borrowers / Debtors

Unanticipated inflation benefits borrowers. Borrowers borrows “dear” dollars but, because of inflation, pays back the principal and interest with “cheap” dollars whose purchasing power has been eroded by inflation. Real income is redistributed away from the lenders towards the borrowers.

The redistribution effects of inflation are less severe or are eliminated altogether if people anticipate inflation and can adjust their nominal incomes to reflect the expected price level rises or anticipated inflation.

Nominal Interest Rate = Real Interest Rate + Inflation Premium

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

Algebra

Expansion of Algebraic Expressions

1. a(b+c) = ab + ac

2. a(b-c) = ab – ac

3. (a+b)^2 = a^2 + 2ab + b^2

4. (a-b)^2 = a^2 – 2ab + b^2

5. (a+b)(a-b) = a^2 – b^2

6. (a+b)(c+d) = ac + ad + bc + bd

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O-Level Additional Mathematics Tuition Singapore

Indices & Surds

4 Keys Areas

– Rules of indices and surds

– Solving exponential equations

– Simplifying surds

– Denominators containing surds ie rationalising denominator.

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