AP SSC General Science (BSEAP) cheat sheet

Concave and convex mirrors are spherical mirrors; the reflecting surface is part of a sphere whose centre is C and radius of curvature R.

Principal axis passes through pole P and centre of curvature C; focal point F lies midway, so f = R/2 for small-aperture mirrors.

Mirror formula: 1/v + 1/u = 1/f, with sign convention: distances measured from pole, along incident light positive, against it negative.

Magnification m = h'/h = -v/u; negative m means real inverted image, positive m means virtual erect image.

Concave mirror: object beyond C gives real, inverted, diminished image between F and C; object between F and P gives virtual, erect, enlarged image.

Convex mirror always forms a virtual, erect, diminished image behind the mirror between P and F; f and R are positive by convention.

Ray rules: a ray parallel to the axis reflects through F; a ray through F reflects parallel to the axis; a ray through C retraces its path.

Uses: concave mirrors in torch reflectors, shaving mirrors, dentist mirrors; convex mirrors as rear-view and security mirrors for wider field.

A chemical equation must be balanced to satisfy conservation of mass: atoms of each element equal on both sides.

Combination: A + B → AB; Decomposition: AB → A + B (thermal, electrolytic, or photolytic).

Displacement: more reactive element displaces less reactive one, e.g. Fe + CuSO4 → FeSO4 + Cu.

Double displacement: ions exchange, e.g. AgNO3 + NaCl → AgCl↓ + NaNO3; precipitation indicated by ↓.

Oxidation is loss of electrons/gain of oxygen; reduction is gain of electrons/loss of oxygen; both occur together in redox reactions.

Exothermic reactions release heat (respiration, combustion); endothermic absorb heat (decomposition of CaCO3).

Rusting of iron needs both oxygen and moisture; galvanisation or painting prevents it.

State symbols (s), (l), (g), (aq) and conditions above the arrow make an equation more informative.

Arrhenius acid releases H+ in water; base releases OH−; strong acids (HCl, H2SO4, HNO3) ionise completely, weak acids (CH3COOH, H2CO3) partly.

pH scale 0–14: pH < 7 acidic, pH = 7 neutral, pH > 7 basic; pH decreases as H+ concentration increases.

Litmus: acids turn blue litmus red; bases turn red litmus blue; phenolphthalein is colourless in acid, pink in base.

Neutralisation: acid + base → salt + water, e.g. HCl + NaOH → NaCl + H2O.

Metal + acid → salt + hydrogen gas; carbonate/bicarbonate + acid → salt + water + CO2 (lime water turns milky).

Water of crystallisation: CuSO4·5H2O blue crystals turn white on heating, regaining blue on adding water.

Baking soda is NaHCO3, washing soda Na2CO3·10H2O, bleaching powder Ca(OCl)Cl, plaster of Paris CaSO4·½H2O.

pH in daily life: tooth decay below pH 5.5; antacids neutralise excess stomach HCl; acidic soil treated with lime.

Refraction is bending of light when it passes from one transparent medium to another due to change in speed.

Laws: incident ray, refracted ray, and normal at the point of incidence are coplanar; sin i / sin r = constant (Snell's law).

Refractive index n = speed of light in vacuum / speed in medium = sin i / sin r (from air into medium).

Light bends toward the normal when entering a denser medium and away from the normal when entering a rarer medium.

Total internal reflection occurs when light travels from denser to rarer medium and angle of incidence exceeds critical angle C, where sin C = 1/n.

Applications of TIR: optical fibres, endoscopes, mirage, sparkling of diamond, totally reflecting prisms in periscopes.

Lateral displacement occurs when a ray passes through a parallel-sided glass slab; emergent ray is parallel to incident ray.

Real depth and apparent depth relation: n = real depth / apparent depth; a pool looks shallower than it is.

Eye parts: cornea refracts most light, iris controls pupil size, crystalline lens fine-focuses, retina has rods (dim light) and cones (colour).

Accommodation is change of lens focal length by ciliary muscles; near point ≈ 25 cm for a normal adult eye.

Myopia (short-sight) corrected by concave lens; hypermetropia (long-sight) corrected by convex lens; presbyopia by bifocal lens.

Dispersion of white light by a prism gives spectrum VIBGYOR because each colour has a different refractive index.

Rainbow forms by refraction, dispersion, and total internal reflection inside water droplets, with sun behind the observer.

Atmospheric refraction causes twinkling of stars and apparent flattening of the Sun at sunrise and sunset.

Scattering of shorter wavelengths makes the sky blue and sunsets red; Tyndall effect shows scattering by colloidal particles.

Colour blindness results from defective cones; cataract is clouding of the lens, treated by surgery with lens implant.

Subatomic particles: electron (charge −1, mass ≈ 1/1836 u), proton (+1, 1 u), neutron (0, 1 u).

Atomic number Z = number of protons; mass number A = protons + neutrons; isotopes have same Z, different A.

Bohr model: electrons orbit in fixed shells K, L, M, N with 2n² maximum capacity; energy is quantised.

Valence shell electrons determine chemical properties; octet rule describes stable 8-electron configuration.

Electronic configuration follows Aufbau order 1s 2s 2p 3s 3p 4s 3d, with Hund's rule and Pauli exclusion principle.

Rutherford's alpha-scattering experiment showed a small, dense, positively charged nucleus with mostly empty space.

Isotopes: protium, deuterium, tritium of hydrogen; 35Cl and 37Cl of chlorine; used in medicine and dating.

Valency = number of electrons needed, gained, lost, or shared to complete an octet; noble gases have valency zero.

Mendeleev arranged elements by increasing atomic mass and predicted gaps; anomalies led to atomic number as the basis.

Modern periodic law: properties are a periodic function of atomic number; there are 7 periods and 18 groups.

Across a period (left to right), atomic radius decreases, nuclear charge increases, metallic character decreases.

Down a group, atomic radius and metallic character increase; ionisation energy and electronegativity decrease.

Group 1 alkali metals are highly reactive with water; Group 17 halogens are reactive non-metals; Group 18 noble gases are inert.

Metals lie on the left and centre, non-metals on the upper right, metalloids along the dividing line (B, Si, Ge, As).

Ionisation potential and electron affinity rise across a period; reactivity of metals falls across a period.

Position predicts valency: group 1 and 2 give 1 and 2; groups 13–17 give valence electrons 3–7.

Ionic (electrovalent) bond forms by transfer of electrons between metal and non-metal, e.g. Na+Cl−; high melting point, conduct when molten.

Covalent bond forms by sharing electron pairs between non-metals, e.g. H2, Cl2, H2O, CH4; single, double, triple bonds possible.

Lewis dot structures show valence electrons; octet completion explains most stable molecules.

Polar covalent bonds arise from electronegativity difference, e.g. HCl; non-polar when difference is zero, e.g. Cl2.

Coordinate (dative) bond: one atom donates both electrons, as in NH4+ or H3O+.

Metallic bond involves a lattice of positive ions in a sea of delocalised electrons, explaining conductivity and malleability.

Properties: ionic compounds are crystalline and soluble in water; covalent compounds are usually poor conductors and have lower melting points.

Electron dot diagram of MgCl2 shows Mg losing two electrons to two Cl atoms, forming Mg2+ and two Cl−.

Ohm's law: V = IR at constant temperature; resistance R = ρL/A, so longer or thinner wires have greater resistance.

Series: same current, total R = R1 + R2 + R3; Parallel: same voltage, 1/R = 1/R1 + 1/R2 + 1/R3.

Electric power P = VI = I²R = V²/R; energy in kWh = power in kW × time in hours.

Heating effect: H = I²Rt (Joule's law); used in electric iron, heater, fuse; fuse wire has low melting point.

Magnetic effect: current-carrying conductor produces a magnetic field; field lines around a straight wire are concentric circles.

Right-hand thumb rule gives field direction; Fleming's left-hand rule gives force on a conductor in a magnetic field (motor principle).

Electromagnetic induction (Faraday): changing magnetic flux induces EMF; Fleming's right-hand rule gives induced current direction (generator).

A solenoid with a soft iron core is an electromagnet; AC changes direction periodically, DC does not.

Ores are minerals from which metal is extracted economically; gangue is unwanted impurity (sand, clay).

Concentration removes gangue: froth flotation for sulphide ores, magnetic separation for magnetic ores, gravity separation for oxide ores.

Roasting heats sulphide ore in excess air to oxide (ZnS → ZnO); calcination heats carbonate in limited air (CaCO3 → CaO).

Reduction converts oxide to metal using carbon, CO, or reactive metals; thermite reaction uses Al to reduce Fe2O3.

Highly reactive metals (K, Na, Ca, Al) are extracted by electrolysis of molten salts; aluminium by Hall–Héroult process.

Refining: electrolytic refining gives pure metal at cathode; zone refining and liquation are other methods.

Flux combines with gangue to form slag, which is removed; e.g. CaCO3 is flux in iron extraction.

Corrosion of metals is prevented by painting, oiling, galvanising, alloying, or cathodic protection.

Carbon shows tetravalency and catenation, forming a huge number of compounds; allotropes include diamond, graphite, fullerene.

Saturated hydrocarbons (alkanes) have single bonds; unsaturated (alkenes, alkynes) have double or triple bonds and are more reactive.

Homologous series: same functional group, successive members differ by CH2 and 14 u, e.g. CH4, C2H6, C3H8.

Functional groups: alcohol –OH, aldehyde –CHO, ketone –CO–, carboxylic acid –COOH, ester –COO–, halo –X.

Ethanol (C2H5OH) reacts with sodium to give hydrogen; with carboxylic acid and acid catalyst gives ester (sweet smell).

Ethanoic acid (CH3COOH) is a weak acid; reacts with carbonate to give CO2 and turns blue litmus red.

Combustion of saturated hydrocarbons gives clean blue flame; unsaturated give sooty flame; incomplete combustion gives CO.

Soaps are sodium/potassium salts of fatty acids; micelles trap oil in water; hard water forms scum with soap.

Heredity is transmission of characters from parents to offspring; genes are units of inheritance located on chromosomes.

Mendel's laws: dominance, segregation, and independent assortment; monohybrid F2 ratio 3:1, dihybrid 9:3:3:1.

Genotype is genetic makeup (TT, Tt, tt); phenotype is observable trait; dominant allele masks recessive.

Sex determination in humans: XX female, XY male; father's sperm determines the child's sex.

Variation arises from sexual reproduction, mutation, and recombination; it is the raw material of evolution.

Evolution evidence: fossils, homologous and analogous organs, vestigial organs (appendix, wisdom teeth).

Natural selection (Darwin): individuals with favourable variations survive and reproduce, changing populations over time.

Speciation occurs when populations are reproductively isolated; human evolution traced through fossil hominids.

Digestion: mouth (salivary amylase on starch) → stomach (HCl, pepsin on protein) → small intestine (bile, pancreatic and intestinal enzymes).

Villi of small intestine increase surface area for absorption; large intestine absorbs water and salts.

Respiration: alveoli provide large surface area for gas exchange; oxygen diffuses into blood, CO2 out.

Blood transport: arteries carry blood away from heart, veins toward it; capillaries allow exchange; valves prevent backflow.

Excretion: nephrons in kidneys filter blood, reabsorb glucose and water, and form urine; urine passes ureter → bladder → urethra.

Nervous coordination: neuron carries impulses; reflex action is a quick involuntary response through the spinal cord.

Hormones are chemical messengers: insulin (pancreas) lowers blood glucose; thyroxine regulates metabolism; adrenaline prepares for emergency.

Plants coordinate with auxins for growth and stomata for gas exchange; xylem carries water, phloem carries food.

Asexual reproduction: binary fission (Amoeba), budding (Hydra, yeast), fragmentation (Spirogyra), regeneration (Planaria), vegetative propagation in plants.

Sexual reproduction involves gamete formation and fusion (fertilisation), producing genetic variation.

Flower parts: sepals, petals, stamens (anther, filament), carpel (stigma, style, ovary); pollination transfers pollen.

Double fertilisation in angiosperms gives zygote (2n) and endosperm (3n); ovule becomes seed, ovary becomes fruit.

Human male reproductive system: testes produce sperm and testosterone; vas deferens, seminal vesicles, prostate add secretions.

Human female system: ovaries release ova; fallopian tube is site of fertilisation; uterus supports embryo; placenta provides exchange.

Menstrual cycle about 28 days; ovulation near day 14; fertilisation forms zygote, which implants in the uterus.

Contraception methods include barrier (condom), hormonal pills, IUDs, and surgical tubectomy/vasectomy; STDs include gonorrhoea and syphilis.

Natural resources are classified as renewable (sunlight, wind, water, forests, soil) and non-renewable (coal, petroleum, minerals).

The atmosphere is layered: troposphere (weather), stratosphere (ozone layer), mesosphere, thermosphere, exosphere.

Ozone (O3) in the stratosphere absorbs harmful UV radiation; CFCs deplete it.

Soil formation is a slow process; soil erosion by wind and water is checked by contour ploughing, terracing, and planting cover crops.

Water cycle: evaporation, condensation, precipitation, runoff, and groundwater recharge; rainwater harvesting conserves water.

Deforestation causes soil erosion, floods, loss of biodiversity, and increased CO2; afforestation and social forestry counter it.

Fossil fuels are finite; burning them releases CO2, SO2, and oxides of nitrogen causing acid rain and global warming.

Biodiversity hotspots and wildlife sanctuaries protect species; sustainable use balances human need with conservation.

Ecosystem components: biotic (producers, consumers, decomposers) and abiotic (light, temperature, water, soil).

Food chain transfers energy; only about 10% passes to the next trophic level (10% law), so food chains are short.

Food web is a network of interconnected food chains; removal of one species affects many others.

Energy flow is unidirectional from Sun to producers to consumers; nutrients cycle (carbon, nitrogen, oxygen cycles).

Biodegradable wastes (paper, food) are broken down by microbes; non-biodegradable (plastics, DDT) persist and accumulate.

Biomagnification is increase in concentration of harmful chemicals at higher trophic levels, e.g. pesticides in birds.

Ozone depletion by CFCs allows more UV to reach Earth, causing skin cancer and crop damage.

Waste management: reduce, reuse, recycle; segregation at source; composting of biodegradable waste.