Maharashtra State Board · Class 10 · All chapters

Biology — Complete Formula Sheet

Board Formulas

30 formulas · 5 chapters

Ch 1 · Heredity and Evolution

1.Monohybrid Ratio (F₂ Generation)★
$3 : 1 (phenotype); 1 : 2 : 1 (genotype)$
Cross of two heterozygotes (Tt × Tt). 3 tall : 1 short by phenotype; 1 TT : 2 Tt : 1 tt by genotype.
2.Dihybrid Ratio (F₂)
$9 : 3 : 3 : 1$
Two independent traits. 9 both dominant : 3 one dom : 3 other dom : 1 both recessive.
3.Sex Determination in Humans★
$Father XY, Mother XX \to Offspring XX or XY$
Father's sperm determines sex — X from father → girl, Y from father → boy.
4.DNA Base Pairing
$A \equiv T, G \equiv C$
Adenine pairs with Thymine (2 H-bonds), Guanine pairs with Cytosine (3 H-bonds).
5.Gene, Chromosome, DNA★
$Gene \subset DNA \subset Chromosome$
Chromosome contains DNA, which is made up of genes (functional units).
6.Natural Selection (Darwin's Formula)
$Variation + Struggle for existence + Survival of fittest \to Evolution$
Favourable variations survive and reproduce; unfavourable die out.

1.Photosynthesis Equation★
$6 C O_{2} + 6 H_{2} O sunlight, chlorophyll C_{6} H_{12} O_{6} + 6 O_{2}$
Occurs in chloroplasts of green leaves. Endothermic — absorbs sunlight.
2.Aerobic Respiration★
$C_{6} H_{12} O_{6} + 6 O_{2} \to 6 C O_{2} + 6 H_{2} O + Energy (38 ATP)$
In mitochondria. Requires oxygen. Complete oxidation of glucose.
3.Anaerobic Respiration in Muscles
$C_{6} H_{12} O_{6} \to 2 Lactic acid + Energy (2 ATP)$
During heavy exercise, oxygen supply lags. Lactic acid causes cramps.
4.Fermentation in Yeast
$C_{6} H_{12} O_{6} \to 2 C_{2} H_{5} O H + 2 C O_{2} + Energy$
Yeast produces ethanol and CO₂ under anaerobic conditions. Used in brewing and bread-making.
5.Rate of Photosynthesis
$Rate \propto light intensity \times [C O_{2}] \times chlorophyll$
Limited by whichever factor is least available (limiting factor).
6.Glomerular Filtration Rate★
$GF R \approx 125 mL/min$
Rate at which blood is filtered in the nephrons. About 180 L/day, but only ~1.5 L becomes urine.

1.Reflex Arc Sequence★
$Stimulus \to Receptor \to Sensory neuron \to Spinal cord \to Motor neuron \to Effector \to Response$
Fast, automatic response. Bypasses the brain.
2.Nerve Impulse Speed
$v \approx 100 m/s (myelinated)$
Myelinated axons transmit faster due to saltatory conduction. Unmyelinated: ~1 m/s.
3.Neurotransmitter Release at Synapse
$Impulse \to C a^{2 +} influx \to Vesicles fuse \to Neurotransmitter release$
Chemical signal at gap between two neurons.
4.Auxin Effect on Plants★
$Auxin \to Cell elongation \to Phototropism$
Higher auxin on shaded side ⇒ shoot bends towards light.
5.Feedback Regulation of Hormones
$Level high \to Gland stops secretion; Level low \to Gland secretes$
Homeostasis. Example: TSH regulates thyroid, thyroid regulates TSH.

1.Ploidy Change During Reproduction★
$Gamete (n) + Gamete (n) \to Zygote (2n)$
Meiosis halves chromosome number (2n → n); fertilisation restores diploidy.
2.Binary Fission
$1 parent \to 2 daughters$
Amoeba, bacteria, paramecium. Simple division into two.
3.Multiple Fission
$1 parent \to many daughters$
Plasmodium (malaria parasite). Nucleus divides multiple times before cytoplasm.
4.Budding
$Parent \to Parent + Bud (offspring)$
Yeast, Hydra. Small outgrowth develops into a new organism.
5.Menstrual Cycle★
$Duration \approx 28 days; Ovulation \approx day 14$
Cycle: menstruation (1–5), follicular (6–14), ovulation (~14), luteal (15–28).
6.Gestation Period (Human)
$\approx 40 weeks or 9 months$
From fertilisation to birth. Foetus develops inside the uterus.

1.Cell Theory★
$All living things are made of cells; cells arise from pre-existing cells.$
Schleiden, Schwann and Virchow. Foundational statement of biology.
2.Bacterial Growth
$N = N_{0} \times 2^{n}$
Bacteria divide by binary fission. n = number of generations, N₀ = starting count.
3.Doubling Time
$N = N_{0} \times 2^{t / T_{d}}$
T_d = doubling time (~20 min for E. coli under ideal conditions).
4.Cell Size and SA:V Ratio★
$\frac{S A}{V} = \frac{3}{r} (sphere)$
Smaller cells have higher SA:V — better diffusion of nutrients and wastes.
5.Mitosis Chromosome Behaviour
$2 n \to 2 n$
Mitosis: parent cell (2n) divides into two identical daughter cells (each 2n). No change in chromosome number.
6.Meiosis Chromosome Behaviour★
$2 n \to n$
Meiosis: parent cell (2n) divides into four gametes, each with n chromosomes (haploid).
7.Number of Cells after m Mitotic Divisions
$N = 2^{m}$
Starting with 1 cell, after m divisions you get 2ᵐ cells.