Reaction & Changes

Physical changes

When a substance undergoes physical changes, its physical composition changes but its chemical composition remain the same.

Eg: Ice, water and water vapour may exist in different physical states - solid, liquid and gas respectively - but they are still made up of the same chemical composition, H₂O.

Also, physical changes are reversible.

Eg: Water turns into ice when cooled. To get back the water, heat the ice.

Forces like temperature and pressure can effect physical changes.


Chemical changes

The chemical composition of a substance is changed when it undergoes chemical changes. As a result, a new substance is formed. The process is irreversible.

So, how can a chemical change in a substance be identified?

• Change in colour.
• Release or absorption of energy or heat.
• Release of odour.
• Production of gases or solids.

Note: In a chemical reaction, matter is neither destroyed nor created. The particles of an original substance are rearranged to form a new substance. The number of particles that exists before and after the reaction is the same.

Exothermic vs Endothemic

In chemical reactions, heat is either released (exothermic reaction) or absorbed (endothermic reaction). Any change of physical state from solid to liquid is an endothermic reaction as heat is absorbed to push the particles further apart to change its physical state.

However, any change of physical state from liquid to solid is an exothermic reaction as heat is released to push the particles closer together.

To determine whether a reaction is endothermic or exothermic, use a thermometer.

[Chemistry Form 4] Conductive

• Conductors are substances that can conduct electricity in a solid or molten state, and are not chemically changed.
  
  
• Electrolytes are substances that can conduct electricity either in a molten state or an aqueous solution, as well as undergo chemical changes at the same time.
  
  
• Non-electrolytes are substances that cannot conduct electricity either in a molten state or an aqueous solution.
  
  
• Electrolysis is the decomposition of a chemical compound into its constituent elements when an electric current passes through an electrolyte.
  
  
• An electrolytic cell ia a device that uses electrical energy to generate chemical reactions.
  
  
• Electrodes are conductors that transmit electricity through the electrolyte during electrolysis.
  
  
• Cathode is the electrode that is connected to the negative terminal of a battery.
  
  
• Anode is the electrode through which the electrons leave the electrolyte and move to the external circuit.
  
  
• Molten compounds or aqueous solutions can conduct electricity due to the presence of free moving ions.
  
  
• During electrolysis, cations move towards the cathode, where they will be discharged by accepting electrons, whereas anions move towards the anode, where they will be discharged by donating electrons.
  
  
• A voltaic or galvanic cell is a device that converts chemical energy into electrical energy.

Gilt & Gold Leaf Treasures

Covering objects with a thin layer of gold is an ancient technique.

If you can't afford a solid gold ring, you can opt for a gilded or gold-plated one, thanks to Italian chemist, Luigi Brugnatelli's invention of modern electroplating in 1805.

Even before his discovery, the act of coating ordinary metal objects with gold and silver had been in practice.

Some kings would have gilded crowns; aristocrats would order for picture frames, statues, tombs and ceilings to be coated with gold leaves.

Gilded statues and ceilings could be found in temples and public building as well.

Over those years, several gilding techniques were used. For example, when gilding an iron crown, smiths would hammer a thin layer of gold, lay it over the crown and then bake the two into one piece.

Other objects that could not be heated like wooden picture frames and ceilings were treated differently.

Artists would hammer gold into very fine sheets called gold leaves, and then cut and glued them in place on the objects.

Archaeologists have found gilded and gold leaf artworks dating back to 1,500BC in Greece, Egypt and China.

As these works from the Minoan, Egyptian and Shang dynasties are very sophisticated, many believe that the techniques used in their production are much older - exactly how old, though, remains a mystery.

Facts;

1. By weighing his king's crown in water, ancient Greek mathematician Archimedes could work out whether it was solid gold or gilded.
   
   
2. One of seven wonders of the ancient world was a 12m high gilded statue of the Greek god Zeus at a temple in Olympia.
   
   
3. Alessandro Volta was a professor of physics at the University of Pavia in Italy.
   
   
4. Gold plating is used in electronics to create corrosion-resistant connectors and circuit boards.

Gilded frame ready for burnishing
with agate stone tool

A Chinese Tang Dynasty gilt hexagonal
silver plate with a Fei Lian beast
pattern, 8th century CE.

[Mathematic Form 1] Commission

Commission is the amount of money paid to an agent for his or her effort in selling a product or service.

Commission = Percentage commission (commission rate) x Amount of sales

Eg:
1. A book salesman will receive a commission of 15% on the sale of books. If his sales of book reach RM2,500, find the commission the salesman will get.

Commission = Percentage commission (commission rate) x Amount of sales
Commission = 15% x RM2,500
Commission = (15/100) x RM2,500 = RM375

The salesman will get RM375 as commission.

2. Yazid gets a commission of RM15 for the sale of shoes at RM500. Calculate the percentage of commission given to him.

Percentage of commission = (Commission / Amount of sales) x 100%
Percentage of commission = (RM15 / RM500) x 100% = 3%

The percentage of commission given to Yazid is 3%.

3. Hisham will be given a commission of 5% for every notebook he sells. If he sells 3 notebooks which cost RM3,500 each, how much commission will he receive?

Percentage of commission = 5%
Amount of sales = RM3,500 x 3 = RM10,500

Commission = Percentage commission (commission rate) x Amount of sales
Commission = 5% x RM10,500
Commission = (5 / 100) x RM10,500 = 0.05 x RM10,500 = RM525

Hisham will get RM525 as commission.

4. Rahman was paid a commission of RM4,000 for selling a house. If the price of the house was RM250,000, what was the commission rate?

Commission = RM4,000
Amount of sales = RM250,000
Percentage commission (commission rate) = (Commission / Amount of sales) x 100%
Commission rate = (RM4,000 /RM 250,000) x 100%
Commission rate = 0.016 x 100% = 1.6%

The commission rate is 1.6%.

5. A salesman receives RM1,500 as commission for the sale of books. If the commission is 25%, find the amount of sales that the salesman has obtained.

Commission = RM1,500
Percentage commission = 25%

Percentage commission (commission rate) = (Commission / Amount of sales) x 100%
Amount of sales = (Commission / Percentage commission) x 100%
Amount of sales = (RM1,500 / 25%) x 100%
Amount of sales = RM6,000

The amount of sales that the salesman has obtained is RM6,000.

[Mathematic Form 1] Discount

A discount is a reduction in the original selling price.

Discount = Original selling price - New selling price

Percentage discount = (Discount / Original selling price) x 100%

Eg:
a) A shirt was sold at RM45 during sale. If the original price of the shirt was RM60, calculate the discount and the percentage discount.

Discount = Original selling price - New selling price
= RM60 - RM45
= RM15

Percentage discount = (Discount / Original selling price) x 100%
= (RM15 / RM60) x 100%
= 25%

Hence, the percentage discount is 25%

b) During a sale, a handbag is sold at a discount of 30%. What is the new selling price if the original price is RM80?

Percentage discount = (Discount / Original selling price) x 100%
30% = (Discount / RM80) x 100%
Discount = (Percentage discount / 100%) x Original selling price
Discount = (30% / 100%) x RM80 = 0.3 x RM80 = RM24

Discount = Original selling price - New selling price
New selling price = Original selling price - Discount = RM80 - RM24
New selling price = RM56

c) A dress with an original price of RM150 was sold at RM90 during a sale. What is the percentage discount offered?

Original selling price = RM150
New selling price = RM90
Discount = Original selling price - New selling price
Discount = RM150 - RM90 = RM60

Discount = (Percentage of discount / 100%) x Original selling price
Percentage discount = (Discount / Original selling price) x 100%
Percentage discount = (RM60 / RM150) x 100% = 0.4 x 100%
Percentage discount = 40%

Hence, the percentage discount offered = 40%

d) Nina saved RM105 when she bought a dining table at a discount of 15%. Calculate the original price of the table.

Discount = RM105
Percentage discount = 15%

Percentage discount = (Discount / Original selling price) x 100%
Original selling price = (Discount / Percentage discount) x 100%
Original selling price = (RM105 / 15%) x 100% = 7 x 100 = RM700

Hence, the original price of the table is RM700.

[Mathematic Form 1] Simple Interest & Dividend

Simple interest is an additional amount of money given

• by the bank when you save money
• to the bank when you borrow money

Simple Interest = Interest Rate x Principal x Time

Eg:
1. Ahmad deposited RM3,000 in a bank for 3 years at an interest rate of 3.5% per annum. How much interest will Ahmad receive at the end of the period?

Simple Interest = Interest Rate x Principal x Time
= 3.5% x RM3,000 x 3
= (3.5/100) x RM3,000 x 3
= RM315

Hence, Ahmad will receive RM315 as interest at the end of the period.

2. Mak Limah borrowed RM50,000 from a bank. She has paid RM3,000 as simple interest for 3 years. Calculate the interest rate per annum paid by Mak Limah.

Interest Rate = [ Simple Interest / (Principal x Time) ] x 100%
= [ RM3,000 / (RM50,000 x 3) ] x 100%
= 2%

Hence, the interest rate paid by Mak Limah is at 2% per annum.

Dividend

Dividend: profit that is paid to a company's shareholders for their investment in the company.

Dividend = Rate of Dividend x Investment

Eg:
1. Danial bought RM28,000 worth of shares in a company and was given a dividend of 13%. Calculate the amount of dividend received by Danial.

Dividend = Rate of Dividend x Investment
= 13% x RM28,000
= (13/100) x RM28,000
= RM3,640

Danial will receive RM3,640 as dividend.

2. Anita bought 8,000 units of share at RM0.50 per unit. At the end of the year, she was paid a dividend of RM220. What is the rate of dividend given to her?

Investment = 8,000 x RM0.50 = RM4,000
Rate of Dividend = (RM220/RM4,000) x 100% = 5.5%

The rate of dividend given to Anita is 5.5%.

[Mathematic Form 4] Cartesian Coordinates

Cartesian coordinates are rectilinear two-dimensional or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular coordinates. The three axes of three-dimensional Cartesian coordinates, conventionally denoted the x-, y-, and z-axes (a notation due to Descartes) are chosen to be linear and mutually perpendicular. In three dimensions, the coordinates x, y, and z may lie anywhere in the interval

In René Descartes' original treatise (1637), which introduced the use of coordinates for describing plane curves, the axes were omitted, and only positive values of the x- and the y-coordinates were considered, since they were defined as distances between points. For an ellipse this meant that, instead of the full picture which we would plot nowadays (left figure), Descartes drew only the upper half (right figure).

The inversion of three-dimensional Cartesian coordinates is called 6-sphere coordinates.

The scale factors of Cartesian coordinates are all unity, h_i=1. The line element is given by



and the volume element by



The gradient has a particularly simple form,



as does the Laplacian




The vector Laplacian, , is

The divergence is




and the curl, , is






The gradient of the divergence, , is

[Biology Form 4] Enzyme Extraordinaire

Many reactions take place within the cells of living organisms. If these reactions were to happen at a normal pace, they would take forever!

So, cells depend on specific protein molecules to speed up or catalyse the rate of the biochemical reactions in them. These catalysts are called enzymes.

Since enzymes are proteins in nature, they are easily affected by factors such as temperature and pH. Hence, conditions within the cell must be optimal for enzymes to function effectively.

The best way to master the topic on enzymes is to use the comprehensive S.M.A.R.T. guide.

S.M.A.R.T. guide to learning biology

Structure function relationship - knowing the function of every structure.

1. Structure: What chemical compound is an enzyme made up of?
Proteins.

2. Function: What is the role played by enzymes in living organisms?
Enzymes speed up the rate of chemical reactions in living organisms.

Mastery of facts - by asking the right questions and learning from the answer.
A simple way to accomplish this is by using the alphabetical ABCDEFG sub-guide. ABCDEFG means "Always (A) Begin (B) with CDEFG".

C is for characteristics

3. State the characteristics of enzymes:

a) Enzymes are made up of proteins.

b) They are catalysts that speed up the rate of a reaction.

c) They are not destroyed / altered by the reactions they catalyse.

d) Enzymes have specific active sites where they bind with substrates.

e) Enzymes show substrate specificity - they can only bind with specific substrates.

f) Enzymes are needed only in small amounts.

g) Enzyme-catalysed reactions are reversible - they catalyse reactions in either direction.

h) The activity of enzymes can be slowed down by inhibitors.

i) Enzymes work more effectively with the help of co-factors.

j) Enzymes are affected by factors such as temperature, pH, substrate concentration and enzyme concentration.

Continue @ Enzymes Extraordinaire II >>>

[Chemistry Form 5] IUPAC Rules

1. Identify the longest continuous carbon chain, also called the parent chain (which includes the functional group, if there is any). Then name it.
   
   
2. Identify and name groups (or substituents) attached to the parent chain.
   
   
3. Number the chain consecutively, starting at the end that is nearest to a substituent group.
   
   
4. Designate the location of each substituent group by an appropriate number and name.
   
   
5. Use prefixes like di, tri and tetra to indicate the number of times the substituent groups occur.
   
   
6. In alkene, the root/parent chain must be numbered from the end that is nearest to a double bond carbon atom. If the double bond is in the centre of the chain, the nearest substituent rule is used to determine the end where numbering starts.

** IUPAC - International Union of Pure and Applied Chemistry

Did you know?

Pears are ethylene producers. So, instead of storing them next to ethylene-sensitive vegetables like carrots, place the next to other ethylene producers in the coldest part of the refrigerator. Ethylene or ethene, whose formula is C₂H₄, is the simplest alkene.

[Chemistry Form 4] Elements

Initially, Antoine Lavoisier classified "elements" into four groups based on their chemical properties. He included oxygen, nitrogen, hydrogen, heat and light under gases. His classification was unsuccessful because his table consisted of non-elements and compounds.

Then, J.W. Dobereiner introduced the law of triads. He divided the elements into groups of three with similar chemical properties. For example, one group comprises lithium, sodium and potassium, and the other chlorine, bromine and iodine. His attempt was unsuccessful because the classification was limited to a few elements only.

Further progress was made when John Newlands arranged the elements according to increasing relative atomic volume. He proposed the law of octaves, which stated that elements with similar properties recurred after every eight elements. However, his pattern only worked for the first few elements.

Lothar Meyer plotted the graph of atomic volume against the atomic mass of each element and found that elements that have similar chemical properties occupied equivalent position in the graph. For example Li, Na, K, Rb (alkali metals) occupied the tips of the curve plotted.

Dmitri Mendeleev arranged the elements according to increasing relative atomic mass in horizontal groups called periods. Elements with similar chemical properties were arranged in vertical columns called groups.

When the pattern began to go wrong, he would leave a gas in his table. He claimed that the gaps were for elements that had not yet been discovered. He even changed the order round when similar elements didn't line up.

In the early stages, other chemists doubted his ideas but when the element germanium, which was discovered in 1886, matched his prediction, Mendeleev's periodic table was accepted.

Years later, Henry Moseley contribute further to the development of the modern periodic table. He arranged the elements according to increasing proton number and had elements with the same number of valence electrons listed under the same group.

[Science Form 2] Food Chain & Energy

In a food chain, energy is passed from one link to the other. When a herbivore eats, only a fraction of the energy that it gets from its food becomes new body mass; the rest of the energy is lost as waste or used to carry out its life processes, such as movements, digestion and reproduction.

When a herbivore is eaten by a carnivore, it passes only a small amount of its total energy to the carnivore. Of the energy transferred from the herbivore to the carnivore, some energy will be "wasted" or "used up" by the carnivore. The carnivore then has to eat many other herbivores to get enough energy to grow.

Because of the large amount of energy that is lost in each link, the amount of energy that is transferred through the links get less.

The further along the food chain you go, the less food there is, and hence, less energy remains available. In other words, a large mass of living things at the base is required to support a smaller number of consumers at the top of the link. Hence, many herbivores are needed to support a few carnivore.

[Science Form 1] The Importance Of Water

One of the most importance resources that the earth gives us is water. All living things, including humans, animals and plants, need water in order to survive.

While water is important to all living beings, it plays a different role for plants and for humans and animals. Let us differentiate the functions of water in human beings, animals and plants.

All the statements below tell us about the importance of water.

Importance of water to plants:

1. Water helps to support aquatic plants.
2. The process of transpiration involves water.
3. Water is needed for the germination of seeds.
4. Water helps to transport synthesised food to all parts of plant.
5. Water dissolves and transports mineral salts from the roots to the leaves.

Importance of water to human beings and animals:

1. Water dissolves and transports digested food to all parts of the living thing.
2. Water dilutes blood and enables it to transport oxygen efficiently.
3. A person will die of dehydration if he loses 20% of water from his body.
4. Water is important in excretion. It helps rid the body of unwanted substances.
5. Water controls body temperature.
6. Water keeps the lung moist for exchange of gases through respiration.
7. Water supports and maintains the body shape of invertebrates.
8. Water is needed in many household and daily activities.

Did you know?

• 70% of the earth's surface is covered in water.
• Our body is made up of 60% to 95% of water.

[Biology Form 5] Aquatic Adaptation

Aquatic plants - also called hydrophytic plants or hydrophytes - are plants that have adapted to living in aquatic environments.

One of the main problems facing submerged aquatic plants is their inability to obtain oxygen. Unlike terrestrial plants, these plants cannot obtain the vital gas through their stomata because they are submerged in water.

Therefore, the stems, roots, and leaves of submerged aquatic plants posses aerenchyma cells, which supply oxygen to the rest of the plants.

Aerenchyma is a parenchyma tissue with large intercellular air spaces. It stores and transports oxygen to living tissues.

Air spaces within the tissues help to keep the aquatic plant buoyant so that its leaves can reach the top of the pond, thus maximising the amount of sunlight it receives.

Submerged aquatic plants utilise living in water to their fullest advantage. Since these plants are in no danger of drying out, the leaves have few or no cuticles on the surface of their leaves.

In addition, the stems of these plants are limp and delicate with little strengthening tissue because they utilise the water for support.

The leaves tend to be thin, flexible and narrow. These finely dissected leaves offer little resistance to running water and can be dragged through the water without tearing.

*******
Characteristics of hydrophytes:

1. A thin cuticle. Cuticles primarily prevent water loss, thus most hydrophytes have no need for cuticles.
2. Stomata that are open most of time because water is abundant and therefore there is no need for it to be retained in the plant. This means that guard cells on the stomata are generally inactive.
3. An increased number of stomata, that can be on either side of leaves.
4. A less rigid structure: water pressure supports them.
5. Flat leaves on surface plants for floatation.
6. Air sacs for floatation.
7. Smaller roots: water can diffuse directly into leaves.
8. Feathery roots: no need to support the plant.
9. Specialized roots able to take in oxygen.

For example, some species of buttercup (genus Ranunculus) float slightly submerged in water; only the flowers extend above the water. Their leaves and roots are long and thin and almost hair-like; this helps spread the mass of the plant over a wide area, making it more buoyant. Long roots and thin leaves also provide a greater surface area for uptake of mineral solutes and oxygen.

Wide flat leaves in water lilies (family Nymphaeaceae) help distribute weight over a large area, thus helping them float near surface.

Many fish keepers keep aquatic plants in their tanks to control phytoplankton and moss by removing metabolites.

Many species of aquatic plant are invasive species in different parts of the world. Aquatic plants make particularly good weeds because they reproduce vegetatively from fragments.

*******

[Mathematic Form 4] True Or False?

A statement is a sentence that is either true or false, but not both. For example:

a) A hexagon has six sides. (A true statement)

b) 8 + 5 > 14 (A false statement: 8 + 5 = 13; 13 < 14)

c) What is the square root of 25? (A question; not a statement)

d) Stand up. (An instruction; not a statement)

e) Wow! (An exclamation; not a statement)


True or false statements can also be constructed from numbers and mathematical symbols.

Eg:

True statements:
a) 9 + 21 > 16
b) 16 - 10 < 7
c) 16 = 9 + 7

False statements:
a) 21 + 9 < 16 + 7
b) 7 + 9 = 21 - 16
c) 7 > 16 + 21

[Biology Form 4] Diffusion

Various substances pass through the plasma membrane of a cell. The simplest mode of transport for these substances is by diffusion.

Diffusion is defined as the movement of substances from an area of high concentration to an area of low concentration. When substances move in this manner, we say that they are moving along the concentration gradient.

This movement process is simple and passive, which means that the substances move easily from the region of high concentration to the one whose concentration is lower without requiring any energy.

When water moves from an area of high concentration to an area of low concentration across a semi-permeable membrane, its movement called osmosis.

Therefore, when a cell absorbs water by diffusion through its semi-permeable cell membrane, we say that water has entered the cell through osmosis.

Eg: Roots absorb water through osmosis because the soil solution around the roots has a higher water concentration than the root cells.

Certain substances need help in the diffusion process. These substances move into a cell by diffusion through the membrane but they are brought in by special carrier proteins. Such a diffusion process is known as facilitated diffusion.

An active diffusion takes place when a substance moves from an area of low concentration to an area of high concentration, with the use of energy. This movement goes against the concentration gradient.

An active diffusion process usually involves transporting important ions into and out of a cell, whose plasma membrane may have special protein pumps to engage in it.

Schematic representation of mixing of
two substances by diffusion

Self diffusion, exemplified with an isotopic tracer of
radioactive isotope ²²Na

Example of chemical (classical, Fick's, or Fickian) diffusion of
sodium chloride in water

Illustration of low (top) and
high (bottom) entropy.

[Mathematic Form 4] Lines of Argument

An argument involves a given set of statements called premises. From the statements, a conclusion can be made.

The following are three simple forms of arguments that can be used to make a conclusion.

Argument (Form I)
Premise 1 : All A are B
Premise 2 : C is A
Conclusion: C is B
Eg:
Premise 1 : All heptagons have 7 sides.
Premise 2 : Object Y is a heptagon.
Conclusion: Object Y has 7 sides

Argument (Form II)
Premise 1 : If p, the q.
Premise 2 : p is true.
Conclusion: q is true
Eg:
Premise 1 : If k = 5, then 3k - 1 = 14
Premise 2 : k = 5
Conclusion: 3k - 1 = 14

Argument (Form III)
Premise 1 : If p, then q.
Premise 2 : Not q is true.
Conclusion: Not p is true.
Eg:
Premise 1 : If an integer, x, is a factor of 6, it is also a factor of 12.
Premise 2 : x is not a factor of 12
Conclusion: x is not a factor of 6

More Arguments...

1. Premise 1 : If x is an even number, it is divisible by 2.
Premise 2 : x is an even number.
Conclusion: x is divisible by 2.

2. Premise 1 : If p > q, then p > r.
Premise 2 : p > q.
Conclusion: p > r.

3. Premise 1 : All hexagons have six sides.
Premise 2 : J is a hexagon.
Conclusion: J has six sides.

4. Premise 1 : If cos x = 0.5, then x = 60^o or 120^o
Premise 2 : cos x = 0.5
Conclusion: x = 60^o or 120^o

5. Premise 1 : All prime numbers have only two factors.
Premise 2 : 9 is not a prime number.
Conclusion: 9 has more than two factors.

[Physics Form 4] Impulsive Influence

Why does a stationary car have inertia but no momentum?

An object is said to have inertia when it resists any changes to the status of its motion. Inertia is proportional to mass. Since a stationary car is a matter with mass, naturally, it has inertia.

Momentum is the product of mass and velocity. A stationary car has no velocity. Hence, it has no momentum.

In order to set a stationary car in motion, a force is needed to overcome its inertia. Or you may also say that a force is needed to overcome the limitating frictional force exerted on the car.

Unlike a stationary car, a car in motion possesses both inertia and momentum. The momentum of a car is greater when it travels at a higher velocity.

Eg: A car has a greater momentum when it travels at 20m/s instead of 10m/s.

A moving car undergoes a change of momentum when it is stopped. Since the rate of momentum change is proportional to the impulsive force, a larger force is needed to stop the car traveling at a higher velocity.

Eg: A larger impulsive force is needed to stop the car moving at 20m/s instead of 10m/s.

Father of Mathematics

Archimedes was the world's greatest mathematician but for centuries few people realised his talents. Archemedes was born around 287BC in Syracuse on the island of Sicily.

Althogh Sicily is now a part of Italy, it was at that time a part of Greece. The Greeks and their neighbours, the Romans of Italy, were fighting for dominance.

As Archimedes was a friend of King Hieron II, the ruler of Syracuse, he took part in the wars against the Romans.

The young Archimedes showed exceptional skills as a mathematician and engineer. Not only did he prove that the surface area of any sphere is four times that of its greatest circle, he also worked out the steps to calculate the volume of a sphere.

When King Hieron was presented with a crown, Archimedes was able to determine the gold content in it by weighing it in water. His other contributions included the Archimedes' claw, a weapon that could sink ships, and the Archimedes' screw, a machine that could pump up water without using electricity.

Archimedes was such a genius that when the Romans invaded Syracuse, their general gave orders that the mathematician should not be harmed.

However, Archimedes killed by a Roman soldier in one of the battles. He was buried in a tomb decorated with his favourite mathematical proofs.

Althogh Archimedes' formulae were popular, much of his work was forgotten until his books were translated. Arabic versions in the 8th century inspired scientists in the Middle East whereas Latin translations in the 16th century inspired European scientists.

Johannes Kepler, Galileo Galilei, Rene Descartes and Pierre de Fermat were among the influential scientists inspired by Archimedes.

Hence, it is no wonder that Archimedes is now called the father of mathematics.

A sphere has 2/3 the volume and surface area of its circumscribing cylinder.
A sphere and cylinder were placed on the tomb of Archimedes at his request.

Archimedes may have used his principle of buoyancy to determine whether
the golden crown was less dense than solid gold.


The Archimedes screw can raise water efficiently.

Archimedes may have used mirrors acting collectively as a
parabolic reflector to burn ships attacking Syracuse.

Archimedes used the method of exhaustion
to approximate the value of π.

As proven by Archimedes, the area of the parabolic segment in the upper figure
is equal to 4/3 that of the inscribed triangle in the lower figure.

Archimedes is said to have remarked about the lever:
Give me a place to stand on, and I will move the Earth.

[Biology Form 4] Plasma Membrane

How do substances enter and leave a cell? They have to permeate the plasma membrane - a layer that separates the cell from its surrounding. To "permeate" means to "pass through".

The plasma membrane (also called the cell membrane or plasmalemma) is the biological membrane separating the interior of a cell from the outside environment.

It is a semipermeable lipid bilayer found in all cells. It contains a wide variety of biological molecules, primarily proteins and lipids, which are involved in a vast array of cellular processes such as cell adhesion, ion channel conductance and cell signaling.

The plasma membrane also serves as the attachment point for both the intracellular cytoskeleton and, if present, the extracellular cell wall.

The plasma membrane is about 7nm-8nm thick. Proteins and a double layer of phospholipid molecules are the main molecules that make up plasma membrane.

A phospholipid is an amphipathic molecule. It has a hydrophobic tail that is not attracted to water and a hydrophilic head that has an affinity for water.

The heads of the phospholipid molecules face an aquatic environment on the outside of the cell, while internally, the tails face the water-rich cytoplasm.

Since the plasma membrane is made up of lipids, only molecules that dissolve in fats/lipids and are non-polar in nature can pass through the phospholipid bi-layer freely. These molecules include steroid hormones eg: estrogen and testosterone and gases (like oxygen and carbon dioxide).

Other substances are allowed in selectively by the cell membrane. This means that the membrane "chooses" the molecules that can pass through it. To do this, the membrane has several types of proteins acting as passageways for the entry of specific molecules. Without these proteins, certain molecules cannot enter a cell at all.

For example, hydrophilic water-soluble polar molecules such as glucose and amino acids can only be taken into a cell if a special carrier protein for them is present in the membrane. These molecules avoid contact with the lipid bi-layer by passing through such transport proteins that span the membrane. Thus, glucose must bind to a carrier protein first before it can be transported across the membrane.

Some carrier proteins are called ion pumps because they hydrolyse ATP and engage in the active transport of ions such as potassium and sodium into and out of the cell.

Other special proteins also include pore proteins, which allow water and certain ions to enter the cell through them.

In short, the plasma membrane acts as an important barrier between the cell and its environment. It is very selective, allowing only certain molecules to pass through. This nature of the membrane is called "semi-permeable".

Illustration of an Eukaryotic cell membrane

Diagram of the arrangement of amphipathic lipid molecules
to form a lipid bilayer. The yellow polar head groups
separate the grey hydrophobic tails
from the aqueous cytosolic and
extracellular environments.

Disappearing Life - As Forests Disappear, Biodiversity Does Too

When people first started farming some 10,000 years ago, about two thirds of the world's land were covered within forests.

By 2005, less than one third of the earth's land is forested. As the forests dissapper, so do many of the animals and plants that lived there.

Studies predict deforestation will cause 42% of South-East Asia's land species to dissappear by 2100.

Our oceans are also in trouble. Over-fishing is killing the ecosystems. Since 1950, about 30% of shark, tuna, and cod have recorded a decline in their population. Other seafood species have also declined by more than 90%.

Scientists warn that unless fishing methods change, there will be no seafood left by 2048. Sustainable farming, fishing, and forestry methods can help. Human population control is also vital.

World population hit 6.5 billion on Jan 25, 2006 and is predicted to reach 9 billion in 2050. Scientists say that if world population growth doesn't slow down, 80% of the world's forest will be gone by 2030.

Facts:

• South America is the continent with the most forests. About half of its land is covered with forest.
• Deforestation was once declared a national emergency in the Phillipines, Thailand and India.
• About 25% of mammals, 12% of birds, 33% of all amphibians and 70% of the world's known plants are listed as threatened.

[Science Form 2] Food Chain

A food chain demonstrates the feeding relationship between living organisms in an ecosystem.

It consist of a sequence of organisms starting with a producer (i.e. plants), followed by a primary consumer, the secondary consumer and ending with the tertiary consumer.

A simple food chain could start with the grass (producer), which is consumed by rabbits (primary consumer), who get consumed by foxes (secondary consumer).

Grass -> Rabbit -> Foxes

Sometimes, you may find that a food chain can appear more complex than the one above.

Take a look at the below illustration.

GRASS -> Grasshopper -> Rat -> Snake -> Hawk -> Mushroom -nutrient-> GRASS

After the hawk dies, fungi (like mushrooms and other decomposers break down the carcass and turn the remains of the hawk into nutrients, which are released into the soil.

The nutrients (with other factors like sunshine and water) will cause the grass to grow.

It's an interesting circle of life!

[Biology Form 5] Clotting Helps!

Our blood is exposed to the air when there is a wound. We do not want harmful microorganisms to infect the wound, nor do we wish to lose blood at the site of injury.

The good news is this: our blood contains platelets, which help blood to clot. A clot closes the wound and disallows blood loss.


Question & Answer

1. Which cells and proteins/enzymes are involved in the mechanism of blood clotting? What are their function?
Platelet (cell) - initiates the clotting of blood.
Thrombokinase (enzymes) - catalyses the conversion of prothrombin to thrombin.
Thrombin (enzymes) - catalyses the conversion of fibrinogen to fibrin.
Prothrombin (plasma protein) - produces thrombin when activated.
Fibrinogen (plasma protein) - produces fibrin when activated.
Fibrin (thread-like structures) - traps red blood cell to produce a clot.

2. State the characteristics of blood platelets.
No regular shape, mere cell fragments, no nucleus, no haemoglobin.

3. Where are the plasma proteins involved in clotting of blood
a) synthesised?
Liver.
b) found?
Blood plasma.

4. What happens if:
i) clotting does not happen?
Loss of blood and blood pressure, and infection at the site of the wound due to exposure to microorganisms.
ii) a wounded person suffers from haemophilia?
Blood will not clot when there is a wound, resulting in loss of blood and possible death.

5. Name the factors that may affect the clotting of blood.
Presence of platelets; presence of plasma proteins (prothrombin and fibrinogen); presence of Vit K, calcium and other clotting factors.

6. How does the mechanism of blood clotting work?
i) Cut/wound/exposure of blood to the air.
ii) Platelets release the enzymes thrombokinase.
iii)Thrombokinase converts prothrombin to thrombin.
iv) Thrombin catalyses the conversion of fibrinogen to fibrin.
v) Fibrin traps red blood cells and a clot is then formed.

[Chemistry Form 4] Periodic Table Of Elements

The periodic table of elements presents an organised display of all known elements. It has horizontal rows, called periods, and vertical columns, called groups, which arrange the elements in such a way that those with similar properties fall under the same group.

Element in the same group have the same number of valence electrons.
Eg: Elements in the first group have one valence electron while those in the second group have two valence electrons.

In addition, elements arranged along the same period share a common feature, i.e. the same number of electron shells.
Eg: Elements in the first period have one shell to contain their electrons while those in the second period have two shells to contain theirs.

Another arrangement evident in the periodic table is that metals are on the left and non-metals are on the right.

The need to organise elements into groups based on their properties arose when more and more elements were made known. Thus, scientists began to develop the periodic table of elements.

Below are scientists with their respective contribution to the development of the periodic table;

1. Lothar Meyer (1830-1895)
This German chemist recognised periodic behaviour based on his graphs of the atomic volume of elements against their atomic weight.

2. Dmitri Mendelev (1834-1907)
This Russian chemist made a table of elements and left a gap for elements that had not yet been discovered.

3. Antoine Lavoisier (1743-1794)
This French chemist classified elements into four groups - gases, non-metals, metals and earths.

4. John Newlands (1837-1898)
This English chemist's law of octaves stated that when elements were placed in the increasing order of atomic weight, the properties of elements fell into a pattern at regular intervals.

5. Henry J. G. Moseley (1887-1915)
This British chemist rearranged the elements in order of increasing atomic number.

6. Johann Dobereiner (1780-1849)
This German chemist proposed the law of triads, which stated that elements came in groups of three.

Soap - Cleaning Concoction

Soap. We use it in our daily life since birth but just much do us actually know about it.

What is soap?
Soap is a mixture of salts of fatty acids.
Eg: Natural soaps are sodium or potassium salts or fatty acids, which are originally sourced by boiling lard or other animal fat together with lye or potash (potassium hydroxide). (Note that fat is an acid, lye or potash is a base, and soap is a salt).

Like all salts, soap contain a positive ion, usually Na⁺ or K⁺, and a negative ion.

How is soap produced?
Soap is produced through a chemical reaction between an acid and a base. This process is known as saponification. A myriad of products, ranging from bar soap and toothpaste to shaving cream is made through method. The only difference is the type of fat and the type of base that the product is made from.

The following are the descriptions of five different types of soap.

1. Deodorant soaps
   Soaps that have been added with antibacterial agents to reduce odour-causing bacteria.
   
   
2. Cream soaps
   Soaps that contain cold cream materials, moisturisers and emollients; particularly good for dry and delicate skin.
   
   
3. Medicated soaps
   Soaps that contain antibacterial ingredients to treat acne and other skin disorders; require thorough rinsing and are not recommended for sensitive skin.
   
   
4. Oatmeal soaps
   A rough-textured soap that has been added with oatmeals as a mild abrasive and lather; good for oily, dry, and normal skin.
   
   
5. Floating soaps
   Soaps that have air bubles in them to lower their density, thus causing them to float.

[Science Form 2] Types of Eye Defects

The eye can detect colours because of the cone cells in the retina at the back of the eye. These cells, if functioning properly, can detect the three primary colour:- red, blue and green, and combinations of them.

For someone who has colour-blindness, these cells do not work properly, resulting in their inability to see certain things in their actual colour.

A person who has hypermetropia/hyperopia/long-sightdness has blurred vision when looking at objects close to them, but clearer vision when looking at objects in the distance.

This is because images of the objects they are looking at are formed behind the retina. By placing a convex lense in front of the eye with this defect, this condition can be corrected.

On the other hand, a person who has clear vision when looking at objects close to them, but blurred vision when looking at objects in the distance has a vision defect called myopia.

This happens because light from the objects form their respective images before it reaches the retina. By placing a concave lense in front of the eye with this defect, the images move back to the retina. Thus, a clear vision can be obtained.

Another condition in which one has blurred vision when looking at objects both near and far is called presbyopia. It is a perfectly natural condition that will eventually affect us all, and can be corrected by wearing bifocal glasses.

Positioning a cylindrical lense in front of an eye that has astigmatism will refract light in one direction more than in the other.

Thus, a person who has distorted vision as a result of this condition will then be able to see clearly.

Schematic diagram of the human eye