TG POLYCET flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, the roots are x = [−b ± √(b² − 4ac)] / 2a. The discriminant b² − 4ac decides whether roots are real, equal, or non-real.

Sum and product of roots

For ax² + bx + c = 0 with roots α and β, α + β = −b/a and αβ = c/a. A quadratic built from given roots is x² − (α+β)x + αβ = 0.

Arithmetic progression sum

For an AP with first term a and common difference d, the nth term is a + (n−1)d and the sum of n terms is (n/2)[2a + (n−1)d], also written as n times the average of first and last term.

Geometric progression sum

For a GP with first term a and ratio r, the sum of n terms is a(rⁿ − 1)/(r − 1) when r ≠ 1. The infinite sum a/(1 − r) exists only if |r| < 1.

Pythagorean trigonometric identities

sin²θ + cos²θ = 1 always holds. Dividing it by cos²θ gives 1 + tan²θ = sec²θ, and dividing by sin²θ gives 1 + cot²θ = cosec²θ.

Distance and section formula

Distance between (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)² + (y₂−y₁)²]. A point dividing the join in ratio m:n has coordinates ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).

Volume of solids

Cylinder volume is πr²h, cone is (1/3)πr²h, and sphere is (4/3)πr³. A hemisphere is half a sphere, so its volume is (2/3)πr³.

Probability complement rule

Probability equals favourable outcomes divided by total equally likely outcomes, so it always lies between 0 and 1. P(E) + P(not E) = 1, so the chance of an event not happening is 1 − P(E).

Equations of motion

For constant acceleration a, v = u + at, s = ut + ½at², and v² = u² + 2as. In free fall, a equals g, about 9.8 m/s² downward, if air resistance is ignored.

Newton's second law

Force equals mass times acceleration, F = ma. The same law in momentum form says force equals rate of change of momentum, which explains impulse as force multiplied by time.

Kinetic and potential energy

Kinetic energy of a moving body is ½mv², and gravitational potential energy gained near Earth is mgh. Their sum, mechanical energy, stays constant when only gravity does work.

Ohm's law and resistance

At constant temperature, V = IR across a conductor. In series resistances add directly; in parallel the reciprocals add, so total resistance is less than the smallest individual resistance.

Electrical power formulas

Power dissipated in a circuit is P = VI, which becomes I²R or V²/R using Ohm's law. Energy consumed equals power multiplied by time, and one kilowatt-hour equals 3.6 × 10⁶ joules.

Snell's law

For light crossing between media, n₁ sin i = n₂ sin r, where angles are measured from the normal. Refractive index n = c/v, the ratio of light speed in vacuum to that in the medium.

Lens formula and power

For a lens, 1/v − 1/u = 1/f with signs per convention. Power P = 1/f when f is in metres; the unit is the dioptre, positive for converging and negative for diverging lenses.

Wave equation

Wave speed equals frequency multiplied by wavelength, v = fλ. Frequency is set by the source and stays constant across media, so wavelength changes when speed changes.

Mole concept

One mole contains 6.022 × 10²³ particles and equals the molar mass in grams. One mole of any ideal gas occupies 22.4 litres at standard temperature and pressure.

Molarity

Molarity is the number of moles of solute dissolved per litre of solution, not per litre of solvent. Diluting a solution decreases molarity while the amount of solute stays unchanged.

pH scale

pH = −log[H⁺]. Values below 7 are acidic, 7 is neutral, and above 7 is basic. A change of one pH unit means a tenfold change in hydrogen ion concentration.

Oxidation and reduction

Oxidation is loss of electrons and a rise in oxidation number; reduction is gain of electrons. The oxidising agent accepts electrons and is itself reduced in the reaction.

Periodic trends

Across a period atomic radius decreases while ionisation energy and electronegativity increase. Down a group radius increases and ionisation energy decreases because outer electrons are farther from the nucleus.

Types of chemical bonds

Ionic bonds arise by transfer of electrons from metals to non-metals. Covalent bonds arise by sharing electrons between non-metals, and metallic bonds involve delocalised electrons shared among metal cations.

Common gas tests

Carbon dioxide turns lime water milky, oxygen relights a glowing splint, and hydrogen burns with a pop. Moist blue litmus turning red shows an acidic gas such as hydrogen chloride.

Photosynthesis

Green plants make glucose from carbon dioxide and water using light energy and chlorophyll, releasing oxygen. Light reactions occur in the grana and the Calvin cycle in the stroma of the chloroplast.

Cellular respiration

Respiration breaks glucose with oxygen to release carbon dioxide, water and energy. Glycolysis happens in the cytoplasm, while the Krebs cycle and electron transport occur in mitochondria.

Human blood circulation

Deoxygenated blood enters the right atrium, goes to the right ventricle and lungs, returns to the left atrium, and is pumped by the left ventricle into the aorta for the body.

Mendelian ratios

A monohybrid cross of heterozygotes gives an F₂ phenotype ratio of 3:1 and genotype ratio 1:2:1. A dihybrid cross of heterozygotes gives the F₂ phenotype ratio 9:3:3:1.

DNA base pairing

DNA is a double helix of two antiparallel strands joined by hydrogen bonds. Adenine pairs with thymine using two bonds, and guanine pairs with cytosine using three bonds.

Nephron function

Each kidney nephron filters blood at the glomerulus, then reabsorbs glucose, amino acids and most water in the tubules. The remaining fluid becomes urine, which passes to the bladder.

Mitosis versus meiosis

Mitosis gives two diploid cells identical to the parent, for growth and repair. Meiosis gives four haploid gametes with new gene combinations, providing variation in sexual reproduction.

ABO blood group inheritance

Alleles I^A and I^B are codominant and i is recessive. A parent with I^A i and another with I^B i can have an O child because both may pass on the recessive i allele.

Enzyme action

Enzymes are protein catalysts whose active site binds a specific substrate. Activity peaks at an optimum temperature and pH, and high temperature denatures the enzyme by destroying the active site shape.

Energy flow in ecosystems

Producers capture solar energy, consumers eat other organisms, and decomposers break down dead matter. Only about ten percent of energy passes to the next trophic level, the rest being lost mainly as heat.