Mathematics 8

A perfect square is a whole number times itself once (n × n = n²), like 6 × 6 = 36. It's the area of an n-by-n square.

A percent above 100% means more than the whole original amount — 150% of a value is the whole value plus half again.

A rate compares two different units (km/h, $/kg); a ratio compares two quantities of the same kind (3 red : 5 blue).

Adding and subtracting fractions requires a common denominator; multiplying fractions multiplies across (numerator × numerator, denominator × denominator); dividing by a fraction means multiplying by its reciprocal.

A perfect cube is a whole number times itself twice (n × n × n = n³), like 4 × 4 × 4 = 64. It's the volume of an n-by-n-by-n cube.

A discrete linear relation changes by the same fixed amount (the rate of change) each step — that amount can now be negative (a decrease) or a large number.

A variable stands in for a number that can change; an expression combines variables, numbers, and operations to describe a situation (like 25 + 0.10n).

A two-step equation needs two inverse operations to isolate the variable — typically undo addition/subtraction first, then multiplication/division.

The relation can be shown three connected ways: a table of input/output pairs, a graph of separate (discrete) points, and a rule like 'output = 2 × input − 3'.

Evaluating an expression means substituting a specific number in for the variable and simplifying using order of operations.

Surface area is the total area of all the outside faces added together — unfold the solid (its net) to see and add up each flat face.

For any right triangle, a² + b² = c², where a and b are the two legs and c is the hypotenuse (the longest side, opposite the right angle).

A 3D object can be described by its top view, front view, and side view — three flat 2D drawings that together capture its shape.

Volume is how much space fits inside, found for a prism or cylinder as (area of the base) × (height).

To find a missing leg, rearrange the formula: a² = c² − b².

The mean (average) is the sum of all values divided by how many values there are.

Two events are independent when the outcome of one does not affect the outcome of the other (like a coin flip and a die roll).

The median is the middle value when the data is ordered from least to greatest (average the two middle values if there's an even count).

The theoretical probability of two independent events both happening is found by multiplying their individual probabilities: P(A and B) = P(A) × P(B).

The mode is the value that appears most often; a data set can have one mode, more than one, or none — and an extreme outlier can pull the mean away from what feels 'typical'.

Unit price is the cost per single unit (per item, per 100 g, per litre) — dividing total price by total quantity.

A 'best buy' is the option with the lowest unit price, not necessarily the lowest total price or the biggest discount percentage.

Sale signs (like '20% off') and bulk packaging can be misleading — always check the actual unit price to compare fairly.