Coefficient of variation (CV) = (standard deviation/mean) x 100. Here SD = 2 sqrt2 which is approximately 2.83, and mean = 6. CV = (2.83/6) x 100, which is approximately 47.1 percent. A higher CV indicates greater relative variability.

CV = (SD/mean) x 100

When two dice are thrown, the total number of outcomes = 6 x 6 = 36. The outcomes giving a sum of 8 are (2,6), (3,5), (4,4), (5,3) and (6,2), which is 5 favourable outcomes. Probability = 5/36.

P(E) = favourable outcomes / total outcomes

Let A = the card is a king and B = the card is a heart. P(A) = 4/52, P(B) = 13/52, and P(A and B) = 1/52 (the king of hearts). By the addition theorem P(A or B) = P(A) + P(B) - P(A and B) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13.

P(A or B) = P(A) + P(B) - P(A and B)

The taxonomic categories in descending order are: Kingdom, Phylum (Division in plants), Class, Order, Family, Genus and Species. Species is the lowest category and represents a group of individual organisms with fundamental similarities that can interbreed. As we move up the hierarchy, the number of common characteristics decreases while the number of organisms in the group increases.

R. H. Whittaker (1969) proposed five kingdoms: Monera, Protista, Fungi, Plantae and Animalia. The main criteria used were: cell structure (prokaryotic or eukaryotic), body organisation (unicellular or multicellular), mode of nutrition (autotrophic or heterotrophic), reproduction and phylogenetic relationships.

Fungi are eukaryotic, mostly multicellular (except yeast), heterotrophic organisms with a cell wall made of chitin. Their body is made of thread-like hyphae forming a mycelium. Nutrition is saprophytic (on dead organic matter), parasitic or symbiotic; they store food as glycogen. The four classes are Phycomycetes (e.g. Rhizopus, Mucor), Ascomycetes (e.g. Penicillium, yeast), Basidiomycetes (e.g. mushroom, Puccinia) and Deuteromycetes (imperfect fungi, e.g. Alternaria).

Algae are chlorophyll-bearing, simple, thalloid, autotrophic and largely aquatic organisms. They reproduce vegetatively, asexually (by spores) and sexually. The three classes are: Chlorophyceae (green algae, with chlorophyll a and b, e.g. Spirogyra, Chlamydomonas); Phaeophyceae (brown algae, with chlorophyll a, c and fucoxanthin, e.g. Laminaria, Fucus); and Rhodophyceae (red algae, with chlorophyll a, d and phycoerythrin, e.g. Polysiphonia, Gracilaria).

Gymnosperms are plants that bear naked seeds, that is, the seeds are not enclosed inside a fruit because the ovules are not enclosed in an ovary. Characteristics: (1) they are woody perennials (trees or shrubs); (2) the ovules are exposed and develop into naked seeds; (3) they are heterosporous, producing haploid microspores and megaspores, and the pollen grains are usually dispersed by wind. Examples: Cycas, Pinus and Ginkgo.

Animals are classified on the basis of certain fundamental features: (1) levels of organisation (cellular, tissue, organ or organ-system); (2) symmetry (asymmetrical, radial or bilateral); (3) germ layers (diploblastic or triploblastic); (4) presence and nature of a body cavity or coelom (acoelomate, pseudocoelomate or coelomate); (5) segmentation of the body; and (6) presence of a notochord.

Arthropoda is the largest phylum of the animal kingdom. Characteristics: (1) they are triploblastic, bilaterally symmetrical, segmented and coelomate; (2) they have a chitinous exoskeleton and jointed appendages (the name means jointed legs); (3) the body is divided into head, thorax and abdomen, with an open circulatory system and respiration by gills, book gills, book lungs or tracheae. Examples: cockroach, prawn, butterfly, honeybee and spider.

The three fundamental (defining) characteristics of chordates are: (1) presence of a notochord, a flexible rod-like structure on the dorsal side that supports the body; (2) a dorsal, hollow, tubular nerve cord; and (3) paired pharyngeal gill slits at some stage of life. In addition they are triploblastic, coelomate, bilaterally symmetrical and have a post-anal tail. Examples: fishes, amphibians, reptiles, birds and mammals.

Placentation is the arrangement of ovules within the ovary of a flower. Types: (1) Marginal - the placenta forms a ridge along the ventral suture and ovules are borne on it, as in pea. (2) Axile - the placenta is axial and ovules are attached to it in a multilocular ovary, as in China rose, tomato and lemon. (3) Parietal - ovules develop on the inner wall of the ovary, as in mustard. (4) Free central - ovules borne on a central axis with no septa, as in Dianthus. (5) Basal - a single ovule is attached at the base, as in sunflower.

An inflorescence is the arrangement of flowers on the floral axis. In a racemose inflorescence, the main axis continues to grow (it has unlimited growth) and the flowers are borne laterally in an acropetal order (older flowers at the base, younger towards the tip), e.g. radish. In a cymose inflorescence, the main axis ends in a flower and so has limited growth, and the flowers are borne in a basipetal order (older flowers at the top or centre), e.g. Jasmine.

Simple permanent tissues are made of one type of cell. (1) Parenchyma - thin-walled living cells with intercellular spaces; they perform storage, photosynthesis and secretion. (2) Collenchyma - living cells with corners thickened by cellulose and pectin; they provide mechanical support and flexibility to young stems and leaves. (3) Sclerenchyma - dead cells with thick, lignified walls (fibres and sclereids); they provide mechanical strength and rigidity.

Xylem conducts water and dissolved minerals from the roots upward to other parts of the plant and gives mechanical support. Its components are tracheids, vessels, xylem fibres and xylem parenchyma. Phloem transports food (mainly sucrose) prepared in the leaves to the rest of the plant (translocation). Its components are sieve tube elements, companion cells, phloem fibres and phloem parenchyma. Both are complex (conducting) tissues.

Epithelial tissue is a covering or protective tissue that lines the free surfaces of the body and its organs; it rests on a basement membrane and has little intercellular material. Simple epithelium is a single layer of cells and its types are: (1) squamous epithelium - flat cells, found in the walls of alveoli and blood vessels, involved in diffusion; (2) cuboidal epithelium - cube-shaped cells, found in kidney tubules and glandular ducts, for secretion and absorption; and (3) columnar epithelium - tall cells, found in the lining of the stomach and intestine, for secretion and absorption.

Connective tissue links, supports and binds together other tissues and organs of the body; its cells are loosely spaced in an abundant matrix. Main types: (1) loose connective tissue, e.g. areolar tissue and adipose (fat-storing) tissue; (2) dense connective tissue, e.g. tendons (connect muscle to bone) and ligaments (connect bone to bone); and (3) specialised connective tissue, e.g. cartilage, bone and blood (a fluid connective tissue that transports materials).

(1) Prokaryotic cells lack a true membrane-bound nucleus (the genetic material lies free in the cytoplasm as a nucleoid), whereas eukaryotic cells have a well-defined nucleus enclosed by a nuclear membrane. (2) Prokaryotes lack membrane-bound organelles such as mitochondria, endoplasmic reticulum and Golgi bodies, while eukaryotes possess them. (3) The ribosomes are 70S in prokaryotes and 80S in the cytoplasm of eukaryotes. Examples: bacteria are prokaryotic; plant and animal cells are eukaryotic.

A mitochondrion is a double-membrane organelle. The outer membrane is smooth, while the inner membrane is folded inward to form finger-like cristae that increase the surface area; the inner space is filled with a matrix. It contains its own DNA and 70S ribosomes. Function: it is the site of aerobic respiration, where the Krebs cycle (in the matrix) and the electron transport chain (on the inner membrane) produce ATP, the energy currency of the cell. Because it produces most of the cell's ATP, it is called the powerhouse of the cell.

A chloroplast is a double-membrane organelle found in green plant cells. Its inner space, the stroma, contains stacks of disc-shaped membranes called thylakoids; a stack of thylakoids is a granum (plural grana), and grana are connected by stroma lamellae. The thylakoid membranes contain the green pigment chlorophyll. It has its own DNA and 70S ribosomes. Function: it is the site of photosynthesis - the light reactions occur on the thylakoid membranes and the dark reactions (Calvin cycle) occur in the stroma.