ENP Alger Access Contest flashcards

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

Quadratic discriminant

For ax² + bx + c = 0, Δ = b² − 4ac. Positive Δ gives two distinct real roots, zero gives one repeated root, negative gives no real roots.

Derivative of sine

The derivative of sin x with respect to x is cos x, valid when x is measured in radians. In degrees the result gains a factor of π/180.

Geometric series sum

For a geometric progression with first term a and ratio r ≠ 1, the sum of n terms is a(1 − rⁿ)/(1 − r). If |r| < 1 the infinite sum is a/(1 − r).

Combinations formula

C(n,k) = n!/(k!(n−k)!) counts the ways to choose k objects from n when order does not matter. Order-sensitive selection uses permutations instead.

Conditional probability

P(A|B) = P(A ∩ B)/P(B), the probability of A given that B occurred, defined when P(B) > 0. It underlies Bayes' theorem and diagnostic testing problems.

Dot product perpendicularity

For vectors u and v, u·v = u₁v₁ + u₂v₂ = |u||v|cos θ. The vectors are perpendicular exactly when the dot product equals zero.

Newton's second law

The net force on a body equals its mass times acceleration, ΣF = ma. The acceleration points in the direction of the net force and is inversely proportional to mass.

Projectile horizontal motion

Ignoring air resistance, horizontal velocity stays constant because no horizontal force acts, while vertical motion accelerates at g. The two components are independent and combine at the end.

Ohm's law

For a conductor at constant temperature, current equals voltage divided by resistance, I = V/R. Electrical power dissipated is P = VI = I²R = V²/R.

Conservation of momentum

In a system with no external net force, total momentum Σmv stays constant before and after a collision. Kinetic energy is conserved only in elastic collisions.

Half-life relation

For radioactive decay N = N₀e^(−λt), the half-life is T½ = ln2/λ ≈ 0.693/λ. After n half-lives the remaining fraction is (1/2)ⁿ.

Ideal gas law

PV = nRT relates pressure, volume, amount in moles and absolute temperature, with R ≈ 8.31 J/(mol·K). Temperature must be in kelvin, never degrees Celsius.

Mole and molar mass

The number of moles equals mass in grams divided by molar mass in g/mol, n = m/M. One mole contains Avogadro's number, about 6.022 × 10²³, of particles.

Molarity definition

Molarity is moles of solute per litre of solution, c = n/V. Diluting a solution keeps solute moles constant, so c₁V₁ = c₂V₂.

pH of strong acid

pH = −log[H₃O⁺]. For a strong monoprotic acid the hydronium concentration equals the acid concentration, so 0.01 M gives pH 2.

Le Chatelier pressure effect

Raising pressure on a gaseous equilibrium shifts it toward the side with fewer gas molecules. Lowering pressure shifts it toward the side with more gas molecules.

Oxidation number change

Oxidation is a rise in oxidation number caused by loss of electrons. Reduction is a fall in oxidation number caused by gain of electrons; both always occur together.

Carboxylic acid group

The functional group −COOH contains a carbonyl carbon bonded to a hydroxyl group. It ionises weakly in water, releasing H⁺ and forming a carboxylate ion.

Photosynthesis equation

6CO₂ + 6H₂O + light energy yields C₆H₁₂O₆ + 6O₂. Light reactions in thylakoids produce ATP and NADPH, used in the stroma to fix carbon.

DNA base pairing

Adenine pairs with thymine through two hydrogen bonds; guanine pairs with cytosine through three. The two strands are antiparallel and complementary in sequence.

Monohybrid cross ratio

Crossing two heterozygotes Aa × Aa gives genotype ratio 1 AA : 2 Aa : 1 aa. When A is fully dominant the phenotype ratio is 3 dominant : 1 recessive.

Enzyme function

Enzymes are biological catalysts that lower activation energy by stabilising the transition state. They are not consumed and each has optimal temperature and pH ranges.

Negative feedback

A control mechanism in which a deviation from a set point triggers a response that reduces the deviation. Insulin lowering high blood glucose is a standard example.

Trophic energy transfer

Only about ten percent of energy at one trophic level passes to the next, the rest being lost mainly as heat through respiration. Food chains therefore rarely exceed five levels.

Transcription versus translation

Transcription copies a DNA template into mRNA in the nucleus. Translation reads mRNA codons at ribosomes, matching each codon to a specific amino acid.

Falsifiability criterion

A scientific hypothesis must make predictions that could be shown wrong by observation. A claim compatible with every possible result cannot be tested scientifically.

Correlation versus causation

An observed association between two variables does not prove one causes the other. A hidden third variable or reverse causation may explain the link.

Significant figures multiplication

When multiplying or dividing measurements, the result keeps the smallest number of significant figures found among the inputs. Addition instead uses decimal places.

Percent error formula

Percent error equals the absolute difference between measured and accepted values, divided by the accepted value, multiplied by 100. It quantifies measurement accuracy.

Graph slope meaning

On a linear graph the slope equals Δy/Δx and carries units of y per x. It expresses the rate at which the dependent variable changes with the independent variable.

Affirming the consequent

From 'if P then Q' and Q, concluding P is a logical fallacy. The valid inference is modus ponens: from 'if P then Q' and P, conclude Q.

Dimensional consistency check

Both sides of a valid physical equation must have identical units. Checking dimensions catches algebraic slips, such as adding a time to a length.