ADDITIONAL MATHEMATICS : TYPES OF RELATION

Types of Relation	Diagram
1	One to One Relation In this relation, each object in the domain has only one image in the codomain.
2	One to Many Relation In this relation, one or more than one of the objects in the domain has more than one image in the codomain.
3	Many to One Relation In this relation, there are more than one objects in the domain that have the same image in the codomain.
4	Many to Many Relation In this relation, one or more than one of the objects in the domain has more than one image in the codomain, and there are more than one object in the domain that have the same image in the codomain.

ADDITIONAL MATHEMATICS : Domain, Codomain, Image, Object and Range

In the relation between one set and another, the first set is known as the domain and the second set is known as the codomain.

Elements in the domain is called objects, whereas elements in the codomain mapped to the objects is called the image. Elements in the codomain not mapped to the objects are not the image.

All images in codomain can be written as a set known as range.

The Movement of Substances across the Plasma Membrane

Plasma Membrane

Passive Transport

Diffusion

Diffusion is the net movement of particles from an area of high concentration to an area of a lower concentration. The steeper the concentration gradient, the more rapid the rate of diffusion.

Two examples of diffusion are:

• Oxygen (required for respiration) passes through cell membranes and gas exchange surfaces (e.g. alveoli in lungs) by diffusion
• Carbon dioxide enters leaves and leaf cells by diffusion

If you spray a can of air freshener in a room in one corner and have another person sit somewhere else in the room, how come he/she can smell it after a few seconds? The air freshener diffuses throughout the room- from an area of high concentration (the area where you sprayed the air freshener) to and area of low concentration (where the other person is).

Osmosis

Osmosis is the movement of water from an area of high water concentration (more dilute) to an area of a low water concentration (stronger) through a partially permeable membrane.

A partially permeable membrane allows water molecules to pass through (as they are smaller) but not solute molecules (they are too big). It acts like a sieve. Visking tubing is a partially permeable membrane. It is used in dialysis machines.

Turgor

Plant cells need to be turgid (i.e rigid) to support plant tissues. Plant cells become turgid when the concentration inside the cell is higher than outside. Therefore water moves into the cell by osmosis, and the vacuole swells and pushes against the cell wall.

If the concentration inside the cell is lower than outside, water moves out of the cell, the vacuole shrinks and the cell loses its shape and becomes flaccid. We call a cell which is flaccid (due to water loss from osmosis) plasmolysed. A plant that contains plasmolysed cells is said to wilt and the leaves droop, collapsing and hanging down from the stem.

Turgor is used to control the opening and closing of stomata, the pores on the underside of leaves. The stomata are surrounded by guard cells that can become turgid or flaccid. Stomata allow carbon dioxide into the leaf and water to escape through evaporation. They can control the rate of water loss from the plant. They also control transpiration where water loss from the leaves due to evaporation causes the flow of water and fresh minerals up the plant.

If an animal cell becomes turgid it can be in danger of bursting because it does not have a cell wall to protect it.

Active Transport

Diffusion and osmosis can only work if the concentration gradient is right. Sometimes an organism needs to transport something against a concentration gradient. The only way this can be done is through active transport, using energy produced by respiration. In Active transport, the particles move across a cell membrane from a lower to a higher concentration.

Examples of active transport

In plants: Plants need mineral salts (e.g. nitrates) for making proteins and growth. Nitrates are at a higher concentration inside the root cells than they are when dissolved in the water around the soil particles. If the plant relied on diffusion alone, the vital nitrate salts would drain out of the cells into the soil. So energy is deployed by the cells to actively transport nitrates across the cell membrane into the root cells, against the concentration gradient.

In humansActive transport takes place during digestion of food in the small intestine. After food has been absorbed by the villi for some time, the concentration of food molecules inside the villi increases, making it impossible for more food to diffuse into the villi. So simple sugars, amino acids, minerals and vitamins are actively absorbed into the villi, from an area of lower to an area of higher concentration