Mie Entrance Science flashcards

32 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 solutions are x = [-b ± √(b² - 4ac)] / (2a). The discriminant b² - 4ac determines the number of real roots.

Logarithm product rule

The logarithm of a product equals the sum of the logarithms of the factors: log_a(xy) = log_a x + log_a y, valid for positive x and y and base a > 0, a ≠ 1.

Arithmetic series sum

The sum of the first n terms of an arithmetic sequence with first term a and common difference d is S_n = n/2 [2a + (n - 1)d], equivalently n/2 (first + last).

Geometric series sum

For a geometric sequence with first term a and ratio r ≠ 1, S_n = a(1 - rⁿ)/(1 - r). If |r| < 1, the infinite sum converges to a/(1 - r).

Circle equation

A circle with center (h, k) and radius r has equation (x - h)² + (y - k)² = r². Expanded form x² + y² + Dx + Ey + F = 0 gives center (-D/2, -E/2).

Chain rule

For a composite function y = f(g(x)), the derivative is dy/dx = f'(g(x)) · g'(x). This rule is essential for differentiating nested functions in calculus.

Definite integral

The definite integral ∫_a^b f(x) dx equals F(b) - F(a), where F is any antiderivative of f. It represents the signed area under the curve from x = a to x = b.

Dot product

For vectors a and b, a·b = |a||b|cosθ = a₁b₁ + a₂b₂ + a₃b₃. The dot product is zero when the vectors are perpendicular, and positive when the angle is acute.

Newton's second law

The net force on an object equals its mass times acceleration: F_net = ma. Acceleration is in the same direction as the net force and inversely proportional to mass.

Kinematic equations

For constant acceleration: v = u + at, s = ut + ½at², and v² = u² + 2as. Here u is initial velocity, v final velocity, a acceleration, t time, s displacement.

Conservation of energy

In a closed system with only conservative forces, total mechanical energy (kinetic plus potential) remains constant. Energy can transform between forms but is never created or destroyed.

Ohm's law

For an ohmic conductor at constant temperature, V = IR, where V is voltage, I current, and R resistance. Electrical power is P = VI = I²R = V²/R.

Wave equation

The speed of a wave equals its frequency times its wavelength: v = fλ. For a string, v = √(T/μ), where T is tension and μ is linear mass density.

Snell's law

When light passes between media, n₁ sinθ₁ = n₂ sinθ₂, where n is refractive index and θ is the angle measured from the normal. Higher n means slower light and bending toward the normal.

Ideal gas law

PV = nRT relates pressure, volume, amount in moles, and absolute temperature. R = 8.314 J mol⁻¹ K⁻¹ or 0.0821 L atm mol⁻¹ K⁻¹; temperature must be in kelvin.

Half-life

The time required for half of a radioactive sample to decay. Remaining amount N = N₀(1/2)^(t/T½), and the decay constant λ = ln2 / T½.

Mole concept

One mole contains 6.022 × 10²³ particles (Avogadro's number). The number of moles n = m/M, where m is mass and M is molar mass in g/mol.

Limiting reactant

The reactant that is completely consumed first in a chemical reaction and therefore determines the maximum amount of product formed. Others are in excess.

Molarity

Molarity (M) is the number of moles of solute per liter of solution: M = mol/L. When diluting, M₁V₁ = M₂V₂, since moles of solute remain constant.

pH scale

pH = -log[H₃O⁺]. At 25 °C, pH + pOH = 14. A pH below 7 is acidic, 7 is neutral, and above 7 is basic; each unit represents a tenfold change in hydrogen ion concentration.

Le Chatelier's principle

When a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the equilibrium shifts to counteract the change and restore balance.

Oxidation and reduction

Oxidation is loss of electrons and reduction is gain of electrons (OIL RIG). The oxidizing agent is reduced, and the reducing agent is oxidized in a redox reaction.

Periodic trends

Atomic radius decreases across a period and increases down a group. Electronegativity increases across a period and decreases down a group, reaching a maximum at fluorine.

Bond polarity

Bond polarity depends on electronegativity difference ΔEN: less than 0.4 is nonpolar covalent, 0.4 to 1.7 is polar covalent, and greater than 1.7 is generally ionic.

Cell theory

All living organisms are made of one or more cells, the cell is the basic unit of life, and new cells arise from pre-existing cells through cell division.

Photosynthesis

The process by which plants convert light energy into chemical energy: 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂. Light reactions occur in thylakoids; the Calvin cycle occurs in the stroma.

Cellular respiration

The breakdown of glucose to release ATP: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + ATP. Glycolysis occurs in the cytoplasm; Krebs cycle and electron transport occur in mitochondria.

DNA base pairing

In DNA, adenine pairs with thymine via two hydrogen bonds, and guanine pairs with cytosine via three hydrogen bonds. In RNA, uracil replaces thymine.

Mendel's law of segregation

During meiosis, the two alleles of a gene separate so that each gamete receives only one allele. This explains the 3:1 phenotypic ratio in a monohybrid cross.

Enzyme function

Enzymes are biological catalysts that lower activation energy and speed up reactions without being consumed. Activity depends on temperature and pH; extreme conditions cause denaturation.

Mitosis versus meiosis

Mitosis produces two genetically identical diploid cells for growth and repair. Meiosis produces four genetically distinct haploid gametes, with crossing over occurring in prophase I.

Negative feedback

A homeostatic mechanism in which a change in a variable is detected and a response reverses the change, returning the variable toward its set point. Examples include body temperature and blood glucose regulation.