FRNSW Cognitive Test flashcards

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

Valid vs sound argument

A valid argument's conclusion must follow from its premises whatever their truth; a sound argument is valid and has actually true premises.

Contrapositive equivalence

If P then Q is logically equivalent to If not Q then not P. The converse and inverse forms are not equivalent to the original statement.

Distributed middle term

A valid categorical syllogism must have its middle term distributed in at least one premise, meaning the premise speaks about every member of that class.

Meaning of only

In logic, Only A are B means all B are A. It does not mean all A are B, so reversing the terms produces an invalid conclusion.

Unless translation

The statement A unless B is equivalent to If not B then A. It sets B as the sole exception to A, not as a second sufficient condition.

Negative premise rule

Two negative premises yield no valid conclusion; with exactly one negative premise, any valid conclusion must itself be negative.

Necessary assumption

An unstated premise the argument requires: if it is false, the conclusion no longer follows. Negating it is the standard test.

Scope of some

Some A are B asserts at least one member exists in both classes. It does not establish that any A falls outside B.

Reverse percentage

To recover an original amount before a percentage change, divide by the multiplier: after a 15% discount, original = final / 0.85.

Successive percentage multipliers

Chain percentage changes by multiplying factors: 1.20 then 0.90 gives 1.08, an overall rise of 8%, not 10%.

Combined work rate

If two workers need a and b hours alone, their combined time is ab/(a+b) hours, because their rates add rather than their times.

Harmonic mean speed

For equal distances travelled at speeds x and y, average speed is 2xy/(x+y), which is lower than the arithmetic mean of the speeds.

Ratio sharing formula

To divide total T in ratio a:b:c, sum the parts (a+b+c) and give each share T multiplied by its part over the sum.

km/h to m/s

Multiply kilometres per hour by 1000/3600, equivalently divide by 3.6. So 72 km/h equals 20 m/s.

Scaling of area and volume

If lengths scale by factor k, areas scale by k squared and volumes by k cubed; doubling a shape's sides multiplies volume eightfold.

Percentage change formula

Percentage change equals (new value minus old value) divided by old value, multiplied by 100, with sign showing increase or decrease.

Cube net opposite faces

In a valid cube net, two faces are opposite when exactly one square lies between them along a straight line of squares.

Mirror versus water image

A mirror image reverses left and right about a vertical axis; a water image reverses top and bottom about a horizontal axis.

Reflection versus rotation

A reflected figure cannot be produced by rotating the original in the plane; reflections reverse the handedness of the shape.

Painted cube two-face count

On an n by n by n cube painted on all outer faces, cubes with exactly two painted faces number 12(n-2), along the twelve edges.

Painted cube corner count

Exactly three painted faces occur only at the eight corners of a painted cube, regardless of the cube's size when n is at least 2.

Fold and punch doubling

Each fold of paper doubles the number of holes produced by one punch; unfold by reflecting the pattern across fold lines in reverse order.

Forty-five degree rotation cycle

Rotating a figure in 45-degree steps returns it to the original orientation after eight steps; 90-degree steps need four.

Matrix rule direction

In figure matrices, test rules across rows before columns; typical rules are element addition, subtraction, or movement by a fixed step.

Lever balance equation

About the fulcrum, effort times effort arm equals load times load arm. Lengthening the effort arm reduces the force required.

Lever classes

Class 1 has fulcrum between effort and load; class 2 has load in the middle; class 3 has effort in the middle and gives advantage below one.

Movable pulley advantage

With n rope segments supporting the load, ideal effort equals load divided by n. A single movable pulley therefore halves the effort.

Meshed gear ratio

Gears in mesh rotate in opposite directions, with speeds inversely proportional to tooth count: rpm A times teeth A equals rpm B times teeth B.

Pressure and area

Pressure equals force divided by area, so the same force concentrated on a smaller area produces greater pressure and deeper penetration.

Pascal hydraulic principle

Pressure applied to a confined fluid transmits equally throughout, so output force equals input force times the ratio of piston areas.

Archimedes buoyancy

Buoyant force equals the weight of fluid displaced. An object floats when its average density is less than the surrounding fluid's density.

Friction behaviour

Friction opposes relative motion and grows with surface roughness and normal force; wheels and lubrication reduce it, converting motion energy to heat.