CBSE · Class 10 · All chapters

Biology — Complete Formula Sheet

Board Formulas

54 formulas · 6 chapters

Ch 5 · Cell — The Basic Unit of Life

1.Cell Theory (Schleiden and Schwann)★
$All living organisms = one or more cells; Cell = basic unit; New cell = pre-existing cell$
Refined by Rudolf Virchow. Three tenets — memorise all three.
2.Prokaryote vs Eukaryote★
$Prokaryote (no nucleus) vs. Eukaryote (true nucleus)$
Prokaryotes: bacteria, cyanobacteria. Eukaryotes: everything else — plants, animals, fungi, protists.
3.Diffusion
$Movement \propto concentration gradient (high \to low)$
Passive movement of molecules across a membrane, from high to low concentration.
4.Osmosis★
$Solvent movement across semi-permeable membrane: dilute \to concentrated$
Special case of diffusion — only the SOLVENT (water) moves. Bathing raisins in water shows osmosis.
5.Function of Mitochondrion
$Glucose + O_{2} ⟶ A T P (energy currency)$
Power-house of the cell — site of aerobic respiration; has its own DNA and ribosomes.
6.Function of Chloroplast
$C O_{2} + H_{2} O sunlight glucose + O_{2}$
Only in plant cells — traps sunlight for photosynthesis. Contains chlorophyll.
7.Function of Ribosome
$mRNA ⟶ Protein$
Site of protein synthesis. Present in all cells (prokaryote + eukaryote). Attached to rough ER.

Ch 5 · Life Processes

1.Photosynthesis (Overall)★
$6 C O_{2} + 6 H_{2} O sunlight, chlorophyll C_{6} H_{12} O_{6} + 6 O_{2}$
Autotrophic nutrition in green plants. Site: chloroplast (mesophyll cells). Occurs during the day.
2.Aerobic Respiration★
$C_{6} H_{12} O_{6} + 6 O_{2} ⟶ 6 C O_{2} + 6 H_{2} O + 38 ATP$
In presence of oxygen; site: mitochondria. Releases ~ 38 ATP per glucose.
3.Anaerobic Respiration (Muscle)
$C_{6} H_{12} O_{6} ⟶ 2 C_{3} H_{6} O_{3} + 2 ATP$
In absence of oxygen; site: cytoplasm. Product = lactic acid (in muscle cramps).
4.Anaerobic Respiration (Yeast)★
$C_{6} H_{12} O_{6} ⟶ 2 C_{2} H_{5} O H + 2 C O_{2} + 2 ATP$
Fermentation by yeast: glucose → ethanol + CO₂. Basis of bread rising and brewing.
5.Cardiac Output
$Cardiac Output = Stroke Volume \times Heart Rate$
Volume of blood pumped per minute. Adult at rest: ~ 5 L/min.
6.Rate of Transpiration
$Rate \propto leaf area, temperature, \frac{1}{humidity}$
Loss of water vapour, mostly through stomata. Creates the transpiration pull for xylem transport.
7.Urine Formation Three Stages
$Filtration \to Reabsorption \to Secretion$
Occur in the nephron: glomerulus (filter), PCT/loop/DCT (reabsorb), collecting duct (concentrate). Adult produces ~ 1.5 L urine/day.

Ch 6 · Control and Coordination

1.Reflex Arc Pathway★
$Stimulus \to Receptor \to Sensory neuron \to Spinal cord \to Motor neuron \to Effector \to Response$
Fast, involuntary response coordinated by the spinal cord (not the brain). Example: hand withdrawal from a hot object.
2.Neuron Structure Pathway
$Dendrite \to Cell body \to Axon \to Axon terminal \to Synapse$
Signal enters via dendrites, travels ELECTRICALLY along the axon, and crosses the synapse CHEMICALLY via neurotransmitters.
3.Divisions of the Human Nervous System
$Nervous System = CNS (Brain + Spinal Cord) + PNS (Nerves)$
PNS = somatic (voluntary skeletal muscle) + autonomic (involuntary; splits into sympathetic 'fight-or-flight' and parasympathetic 'rest-and-digest').
4.Three Parts of the Brain★
$Brain = Forebrain + Midbrain + Hindbrain$
Forebrain: thinking, memory, sensory. Midbrain: visual/auditory reflexes. Hindbrain: cerebellum (balance), medulla (heartbeat, breathing), pons (bridge).
5.Adrenaline (Stress Hormone)★
$Adrenaline (epinephrine): C_{9} H_{13} N O_{3}$
Secreted by the ADRENAL MEDULLA. Increases heart rate, BP and blood glucose — the fight-or-flight response.
6.Insulin (Blood-Sugar Regulator)
$Insulin: peptide, 51 amino acids, \sim 5.8 kDa$
Secreted by β-cells of the islets of Langerhans in the PANCREAS. LOWERS blood sugar by promoting cellular glucose uptake. Deficiency → diabetes mellitus.
7.Thyroxine (Metabolism Hormone)
$Thyroxine (T_{4}): C_{15} H_{11} I_{4} N O_{4}$
Secreted by thyroid gland; contains IODINE. Regulates metabolic rate. Iodine deficiency → goitre.
8.Auxin Redistribution (Phototropism)
$Light \Rightarrow auxin migrates to shaded side \Rightarrow cells elongate \Rightarrow shoot bends towards light$
Positive phototropism in shoots. Auxin is produced at the shoot tip.
9.Feedback Control of Hormones
$↑ Hormone \to target effect \to↓ gland activity (negative feedback)$
High thyroxine → pituitary secretes LESS TSH → thyroid slows down. Keeps hormone levels constant.

Ch 7 · How do Organisms Reproduce?

1.Reproduction Types★
$Reproduction = Asexual (1 parent, clones) + Sexual (2 parents, variation)$
Asexual is fast but genetically identical; sexual creates variation, useful for evolution.
2.Fission
$Parent cell ⟶ 2 (binary) or many (multiple)$
Binary: Amoeba, Paramecium. Multiple: Plasmodium. Simple asexual mode in unicellular organisms.
3.Budding
$Parent ⟶ parent + bud \to new individual$
Yeast, Hydra. Bud grows on the parent and detaches when mature.
4.Vegetative Propagation★
$Root/Stem/Leaf ⟶ new plant$
Potato (stem tuber), Bryophyllum (leaf buds), rose (stem cutting), ginger (rhizome). Widely used in agriculture.
5.Sexual Reproduction Steps
$Gametogenesis \to Fertilisation \to Zygote \to Embryo \to Development$
Fusion of male and female gametes (n + n → 2n). Zygote is the starting point of a new individual.
6.Pollination and Fertilisation in Flower
$Pollen \to stigma \to pollen tube through style \to ovary \to fusion with egg$
Pollen tube delivers 2 male gametes to the ovule (double fertilisation in angiosperms) — one fuses with the egg, the other with polar nuclei.
7.Menstrual Cycle Length
$Cycle \approx 28 days; ovulation on day \approx 14$
Menstruation (day 1-5), follicular (5-14), ovulation (~14), luteal (14-28). Regulated by FSH, LH, oestrogen, progesterone.
8.Human Chromosome Count in Gametes★
$Gamete: n = 23; Zygote: 2 n = 46$
Meiosis halves the chromosome number in gametes; fertilisation restores the diploid count.

Ch 8 · Heredity

1.Monohybrid Cross F₂ Phenotypic Ratio★
$T t \times T t \Rightarrow F_{2} = 3 Tall : 1 Dwarf$
$T$ : Dominant allele (tallness) · $t$ : Recessive allele (dwarfness)
F₁ heterozygotes (Tt × Tt) yield 75% dominant phenotype and 25% recessive phenotype in F₂.
2.Monohybrid Genotypic Ratio
$1 T T : 2 T t : 1 tt$
1 homozygous dominant : 2 heterozygous : 1 homozygous recessive.
3.Dihybrid Cross F₂ Phenotypic Ratio★
$R r Y y \times R r Y y \Rightarrow F_{2} = 9 : 3 : 3 : 1$
9 (both dominant) : 3 (first dominant, second recessive) : 3 (first recessive, second dominant) : 1 (both recessive).
4.Human Sex Determination★
$Father: X Y \times Mother: X X \Rightarrow 50% X X (girl) + 50% X Y (boy)$
Sex of the child is decided by the FATHER (Y chromosome from father → boy; X from father → girl).
5.Human Chromosome Number
$Somatic: 2 n = 46 (44 autosomes + 2 sex chromosomes)$
Gametes are haploid: n = 23 (22 autosomes + 1 sex chromosome). Fertilisation restores 2n = 46.
6.DNA — Base Pairing Rule
$A = T (2 H-bonds), G \equiv C (3 H-bonds)$
Adenine always pairs with Thymine; Guanine always with Cytosine. Ensures accurate replication.
7.DNA Nucleotide
$Nucleotide = Deoxyribose (C_{5} H_{10} O_{4}) + Phosphate (P O_{4}^{3 -}) + Base (A, T, G, C)$
DNA = double helix of nucleotides. Genes are stretches of DNA that code for proteins.
8.Test Cross
$Unknown (T_) \times tt \Rightarrow all tall \Rightarrow T T, else 1 : 1 \Rightarrow T t$
Cross an unknown dominant with a homozygous recessive. Offspring ratio reveals whether the unknown is TT (all tall) or Tt (1 tall : 1 dwarf).
9.Probability Rule (Independent Traits)
$P (A \cap B) = P (A) \times P (B)$
Probability of two independent traits appearing together = product of individual probabilities. Basis of the 9:3:3:1 ratio.

Ch 13 · Our Environment

1.Components of an Ecosystem
$Ecosystem = biotic components + abiotic components$
Biotic: plants, animals, microorganisms. Abiotic: temperature, rainfall, wind, soil, minerals. Forests, ponds and lakes are natural ecosystems; gardens and crop-fields are human-made (artificial) ecosystems.
2.Biotic Components by Nutrition
$Producers (autotrophs); Consumers (herbivores, carnivores, omnivores, parasites); Decomposers$
All green plants and certain bacteria (such as blue-green algae) make food by photosynthesis. Decomposers (bacteria and fungi) break down dead remains and wastes into simple substances that return to the soil.
3.A Food Chain
$Grass \to Grasshopper \to Frog \to Snake \to Eagle$
A series of organisms each feeding on the one before it. Arrows point in the direction of energy flow (from food to feeder). Many interconnected food chains form a food web.
4.Trophic Levels
$T_{1} : producers \to T_{2} : herbivores \to T_{3} : small carnivores \to T_{4} : large carnivores$
Each step of a food chain is a trophic level. Herbivores are primary consumers, small carnivores are secondary consumers and large carnivores are tertiary consumers.
5.Energy Captured by Green Plants
$Food energy \approx 1% of sunlight falling on leaves$
In a terrestrial ecosystem, green plants convert only about 1% of the sunlight that falls on their leaves into food energy.
6.Ten Per Cent Law★
$E_{n + 1} = \frac{10}{100} \times E_{n}$
$E_{n}$ : Energy available at trophic level n (J or kJ) · $E_{n + 1}$ : Energy available at the next trophic level (J or kJ)
On average only 10% of the food eaten is turned into the consumer's own body and passed on. The rest is lost as heat, used in digestion and work, or spent on growth and reproduction.
7.Energy at the nth Trophic Level
$E_{n} = E_{1} \times (\frac{1}{10})^{n - 1}$
$E_{1}$ : Energy available at the producer level (J or kJ) · $n$ : Trophic level number (producers are n = 1)
Apply the 10 per cent law once for every step. To go back down the chain, multiply by 10 for each step.
8.Length of Food Chains
$Usual food chain = 3 or 4 trophic levels$
The energy loss at each step is so large that very little usable energy remains after four trophic levels.
9.Number of Organisms at Each Level
$Producers > herbivores > carnivores (number of individuals, generally)$
There are generally more individuals at the lower trophic levels; the greatest number is of the producers.
10.Unidirectional Flow of Energy★
$Sun \to autotrophs \to herbivores \to carnivores$
Energy captured by autotrophs does not go back to the solar input, and energy passed to herbivores does not come back to autotrophs. Energy is not available to previous levels.
11.Biological Magnification★
$Concentration of non-biodegradable chemicals: T_{1} < T_{2} < T_{3} < \dots$
Pesticides and other chemicals wash into soil and water, are absorbed by plants and enter the food chain. Since they are not degradable, they accumulate at each trophic level. Humans at the top get the maximum concentration.
12.Formation of Ozone★
$O_{2} UV O + O; O + O_{2} \to O_{3}$
High-energy UV radiation splits some O₂ molecules into free oxygen atoms, which combine with O₂ to form ozone. The ozone layer shields the Earth from the Sun's UV radiation; at ground level ozone is a deadly poison.
13.Ozone Depletion and CFCs
$CFCs \Rightarrow ozone loss (from the 1980s); UNEP 1987: freeze CFC production at 1986 levels$
Chlorofluorocarbons are synthetic chemicals used as refrigerants and in fire extinguishers. It is now mandatory for manufacturers to make CFC-free refrigerators worldwide.
14.Biodegradable and Non-biodegradable
$Biodegradable: broken down by biological processes; Non-biodegradable: not broken down, persist$
Bacteria and other saprophytes break down biodegradable matter (vegetable peels, paper). Non-biodegradable substances such as plastics may stay in the environment for a long time or harm members of the ecosystem.