NSTSE flashcards

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

Newton's second law

The net force on a body equals its mass times its acceleration (F = ma). Doubling the force doubles acceleration; doubling the mass halves it for the same force.

Difference: mass and weight

Mass is the quantity of matter in a body, measured in kilograms and unchanged by location. Weight is the gravitational force mg, measured in newtons, and varies with local gravity.

Ohm's law

At constant temperature, the current through a conductor is directly proportional to the potential difference across it, so V = IR, where R is resistance in ohms.

Resistors in parallel

The reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances. Total resistance is always smaller than the smallest individual resistor in the network.

Archimedes' principle

A body immersed in a fluid experiences an upthrust equal to the weight of fluid it displaces. If that upthrust equals the body's weight, the body floats.

Centripetal force does no work

In uniform circular motion the centripetal force points toward the centre, perpendicular to velocity, so it changes direction but not speed and transfers no energy.

Photosynthesis equation

Carbon dioxide and water, using light energy absorbed by chlorophyll, are converted into glucose and oxygen: 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ inside chloroplasts.

Energy in food chains

Only about ten percent of energy passes to the next trophic level; the rest is lost as heat and in life processes, which limits food chains to roughly four or five levels.

pH scale meaning

A logarithmic scale from 0 to 14 measuring hydrogen ion concentration. Below 7 is acidic, 7 is neutral at 25 °C, and above 7 is basic or alkaline.

Refraction of light

Light bends when passing between media of different optical density because its speed changes. It bends toward the normal entering a denser medium and away from it on leaving.

Quadratic formula

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

Sum of first n naturals

The sum 1 + 2 + 3 + … + n equals n(n+1)/2. For example, the first 10 natural numbers sum to 10 × 11 ÷ 2 = 55.

nth term of an AP

In an arithmetic progression 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 × (first + last).

Pythagorean theorem

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It also tests whether a triangle is right-angled.

Area of a trapezium

The area equals half the sum of the parallel sides multiplied by the perpendicular height between them: A = ½(a + b)h.

Volume of a cone

A cone's volume is one third of the volume of a cylinder with the same base and height: V = ⅓πr²h, where r is base radius and h is perpendicular height.

Simple versus compound interest

Simple interest is PRT/100 and stays constant each year on the original principal. Compound interest is calculated on the growing amount, so it exceeds simple interest after the first year.

Successive percentage change

Two successive changes of x% and y% are not additive; the net change is x + y + xy/100 percent, where the signs of x and y carry the increase or decrease.

Probability complement rule

For any event A, the probability that A does not occur is 1 minus the probability that it does, so P(not A) = 1 − P(A).

Similar figures scaling

When two figures are similar with length ratio k, their areas are in ratio k² and their volumes in ratio k³. Doubling all lengths multiplies volume eightfold.

Mean, median, mode

The mean is the sum divided by the count, the median is the middle value of ordered data, and the mode is the most frequent value. Outliers shift the mean most.

Least common multiple

The smallest positive number divisible by each of the given numbers. For two numbers it equals their product divided by their highest common factor.

Average speed for equal distances

When equal distances are covered at speeds x and y, average speed is the harmonic mean 2xy/(x + y), which is less than the arithmetic average of the two speeds.

Clock hand angle

The minute hand moves 6° per minute and the hour hand 0.5°, so the minute hand gains 5.5° per minute. Hands coincide every 65 5/11 minutes.

Letter position coding

Assign A = 1 through Z = 26. Common codes use fixed shifts, reversal where A pairs with Z, or squares of positions; test the shift on two letters before committing.

Syllogism validity rule

A conclusion follows only if it is true in every possible arrangement satisfying the premises. A conclusion true in just one arrangement is not valid.

Direction displacement

For successive right-angled moves, net displacement from the start is found by Pythagoras on the total east-west and north-south components, with opposite directions subtracting.

Blood relation: uncle

The brother of one's father or mother, or the husband of a parent's sibling, is an uncle. Drawing a generation-level family tree prevents gender and level errors.

Number series strategy

Check successive differences first, then ratios, then alternating subsequences, then squares and cubes. The rule must fit every given term, not only the last two.

Analogy relationship types

Pairs may relate by category, function, part to whole, cause to effect, or degree of intensity. Identify the exact relation in the given pair before matching options.

Odd one out by attribute

Find the property shared by all but one option, such as number type, divisibility, or category. The exception is the answer, so verify the rule against every option.

Seating arrangement basics

Fix one person as reference and place others relative to them. For a circle facing centre, left and right are reversed compared with facing outward.

Calendar odd days

A normal year has 1 odd day and a leap year 2, since 365 = 52 weeks + 1. A century's odd days follow a 400-year cycle of 0.