ACT Math: Foundation Concepts and Complexity Management

Ratio

A comparison of two quantities, usually written as a:b or a/b.

Proportion

A statement that two ratios are equal.

Part-to-Part Ratio

A ratio comparing individual parts of a whole.

Part-to-Whole Ratio

A ratio comparing a part to the total of the whole.

Direct Variation

A relationship where one variable is a constant multiple of another, expressed as y = kx.

Unit Rate

Describes how many units of the first quantity correspond to one unit of the second quantity.

Density

A measurement defined as mass (or count) per volume (or area), expressed as Density = Mass / Volume.

Basic Percent Formula

Part = Percent (as decimal) × Whole.

Percent Change Formula

Percent Change = (New Value - Old Value) / Old Value × 100.

Sequential Percent Change

Calculating changes in multiple steps rather than additive; affects overall percentage.

Dimensional Analysis

A method to convert units using multiplication by conversion factors that equal one.

Chain Method

A method for converting units by multiplying by conversion factors to cancel out unwanted units.

Mean

The average, calculated as the sum of terms divided by the number of terms.

Median

The middle value in an ordered list of numbers.

Mode

The value that appears most frequently in a data set.

Range

The difference between the maximum and minimum values in a data set.

Weighted Average

Averages calculated for groups of differing sizes, using the formula (AvgA × SizeA + AvgB × SizeB) / (SizeA + SizeB).

Rectangle Area Formula

Area = length × width (A = lw).

Triangle Area Formula

Area = 1/2 × base × height (A = 1/2 bh).

Circle Area Formula

Area = π × radius² (A = πr²).

Volume of Rectangular Prism

Volume = length × width × height (V = lwh).

Scientific Notation

A way to express numbers as a × 10^n, where 1 ≤ |a| < 10.

Greatest Common Factor (GCF)

The largest number that divides evenly into two or more numbers.

Least Common Multiple (LCM)

The smallest number that is a multiple of two or more numbers.

Unit Blindness

Failing to account for the units in a problem, leading to errors.

Radius vs. Diameter Error

Confusing the units needed for calculations when the given measurement is in different terms.

Average Rate Trap

Misunderstanding average rate calculations, especially in regards to different speeds.

Distribution of Negatives

Failing to correctly apply a negative when simplifying expressions, leading to incorrect results.