BMA Long Course cheat sheet

Quadratic formula: for ax² + bx + c = 0, x = [−b ± √(b² − 4ac)] / 2a; discriminant b² − 4ac decides two real, one repeated, or complex roots.

Sum and product of roots: for ax² + bx + c = 0, sum = −b/a and product = c/a.

Arithmetic progression: nth term aₙ = a + (n − 1)d; sum Sₙ = n/2 [2a + (n − 1)d].

Geometric progression: nth term aₙ = arⁿ⁻¹; sum Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1; infinite sum = a/(1 − r) when |r| < 1.

Circle: area = πr², circumference = 2πr; arc length = (θ/360)·2πr for central angle θ in degrees.

Trigonometric identity: sin²θ + cos²θ = 1; also 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ.

Pythagoras theorem: in a right triangle, hypotenuse² = sum of squares of the other two sides (a² + b² = c²).

Probability of an event = favourable outcomes / total equally likely outcomes; P(A ∪ B) = P(A) + P(B) − P(A ∩ B).

Logarithm rules: log(mn) = log m + log n; log(m/n) = log m − log n; log(mⁿ) = n log m.

Newton's second law: F = ma; force is the rate of change of momentum, and 1 N = 1 kg·m/s².

Equations of uniformly accelerated motion: v = u + at; s = ut + ½at²; v² = u² + 2as.

Work = force × displacement in the direction of force; power = work/time; SI unit of power is the watt (J/s).

Kinetic energy = ½mv²; gravitational potential energy near Earth = mgh.

Ohm's law: V = IR; electrical power P = VI = I²R = V²/R.

Density = mass/volume; pressure = force/area; pressure in a liquid at depth h is P = ρgh.

Speed of light in vacuum c ≈ 3 × 10⁸ m/s; sound travels faster in solids than in gases and cannot travel through vacuum.

Law of reflection: angle of incidence equals angle of reflection, both measured from the normal; refraction obeys Snell's law n₁sinθ₁ = n₂sinθ₂.

Universal gravitational force F = Gm₁m₂/r², with G ≈ 6.67 × 10⁻¹¹ N·m²/kg².

Mole concept: 1 mole = 6.022 × 10²³ particles (Avogadro's number) and equals the molar mass in grams of a substance.

Molarity = moles of solute / volume of solution in litres; dilution obeys M₁V₁ = M₂V₂.

pH = −log[H⁺]; pH below 7 is acidic, 7 neutral, above 7 basic at 25 °C.

Acid-base neutralisation: acid + base → salt + water; strong acid with strong base gives pH 7 at equivalence.

Periodic trend: atomic radius decreases across a period and increases down a group; electronegativity increases across a period and decreases down a group.

Oxidation is loss of electrons (increase in oxidation number); reduction is gain of electrons (decrease in oxidation number).

Ideal gas equation PV = nRT, with R ≈ 8.314 J/(mol·K); at STP one mole of ideal gas occupies about 22.4 L.

Common strong acids: HCl, H₂SO₄, HNO₃; common strong bases: NaOH, KOH; weak acids include CH₃COOH and H₂CO₃.

Avogadro's law: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Cell theory: all living things are made of cells, the cell is the basic unit of life, and new cells arise from existing cells.

Mitosis produces two genetically identical diploid cells for growth and repair; meiosis produces four haploid gametes with genetic variation.

Photosynthesis: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂, occurring in chloroplasts with chlorophyll capturing light energy.

Aerobic respiration: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy (about 38 ATP); anaerobic in muscle yields lactic acid.

Human blood groups follow the ABO system: A, B, AB, and O; O is the universal donor and AB the universal recipient for red cells.

DNA is a double helix of nucleotides with bases adenine-thymine and guanine-cytosine paired by hydrogen bonds.

Mendel's law of segregation: the two alleles for a trait separate during gamete formation, each gamete receiving one allele.

Plant tissue types: xylem transports water and minerals upward; phloem transports dissolved sugars in both directions.

Enzymes are protein catalysts that lower activation energy and are denatured by high temperature or extreme pH.

United Nations founded 24 October 1945; headquarters in New York; current membership is 193 member states.

Bangladesh joined the United Nations in 1974; it is a leading contributor to UN peacekeeping missions.

SAARC was founded in 1985 in Dhaka; its secretariat is in Kathmandu, Nepal.

The Nobel Prizes were established by the will of Alfred Nobel; the Peace Prize is awarded in Oslo, other prizes in Stockholm.

World Health Organization headquarters: Geneva, Switzerland; founded 1948.

ASEAN was founded in 1967 in Bangkok with five founding members; its secretariat is in Jakarta.

Sustainable Development Goals: 17 goals adopted by the UN in 2015 with a target year of 2030.

The Olympic Games are held every four years; the modern series began in Athens in 1896.

Bangladesh Liberation War lasted nine months in 1971; victory was achieved on 16 December 1971.

The declaration of independence was broadcast from Chittagong on 26 March 1971, and 26 March is observed as Independence Day.

The 1970 general election gave the Awami League a majority; the resulting political deadlock preceded the 1971 war.

Bangladesh is a unitary parliamentary republic; the Jatiya Sangsad has 350 seats, including 50 reserved for women.

The Constitution of Bangladesh was adopted on 4 November 1972 and took effect on 16 December 1972.

The national anthem 'Amar Shonar Bangla' was written by Rabindranath Tagore; the national poet is Kazi Nazrul Islam.

The Sundarbans, a UNESCO World Heritage Site, is the world's largest mangrove forest and habitat of the Royal Bengal Tiger.

Bangladesh borders India to the west, north, and east, Myanmar to the southeast, and the Bay of Bengal to the south.

The War of Liberation is commemorated at the National Martyrs' Memorial (Jatiya Smriti Saudha) at Savar, near Dhaka.