ACCUPLACER QAS key terms

A comparison of two quantities by division, often written as a to b, a:b, or a/b. It tells how many times one amount contains another and can be scaled up or down proportionally.

An equation stating that two ratios are equal, such as a/b = c/d. Solving one usually means cross-multiplying to find an unknown value that keeps the relationship consistent.

A rate expressed so the second quantity equals one, such as miles per single hour or price per single item. It makes comparisons between different-sized offers or speeds straightforward.

A ratio comparing two quantities with different units, such as kilometers per liter or dollars per hour. Rates describe how one measured amount changes relative to another measured amount.

A ratio comparing a number to 100, so 35% means 35 out of every 100. Percents convert to decimals by dividing by 100 and to fractions by placing over 100.

The difference between a new value and an original value, divided by the original value, then written as a percent. It measures increase or decrease relative to where you started.

The starting amount before a change, discount, markup, or growth is applied. Percent change problems divide by this value, so identifying it correctly is essential for an accurate answer.

An amount added to a cost or price to reach a selling price, often stated as a percent of cost. It increases the price a buyer pays compared with the seller's original cost.

A reduction subtracted from an original price, frequently given as a percent off. The sale price equals the original price minus the discount amount.

A letter or symbol standing for an unknown or changing number in an expression or equation. Variables let you write general relationships and solve for values that satisfy conditions.

The numerical factor multiplied by a variable in a term, such as the 7 in 7x. It tells how many of that variable are being combined.

A mathematical phrase combining numbers, variables, and operations without an equals sign, such as 3x + 5. It can be simplified or evaluated but not solved for a value.

A statement that two expressions are equal, joined by an equals sign. Solving it means finding values of the variable that make the statement true.

An equation in which every variable appears to the first power only, graphing as a straight line. Standard forms include slope-intercept and point-slope, and they have at most one solution per variable.

The measure of a line's steepness, calculated as the change in y divided by the change in x between two points. It describes how much the output rises or falls per unit of input.

The point where a graph crosses the vertical axis, occurring where x equals zero. In a linear equation written as y = mx + b, it is the value b.

A statement comparing two expressions using symbols like less than, greater than, or not equal to. Its solution is a range of values, and multiplying or dividing by a negative reverses the symbol.

The collection of all values that satisfy an equation or inequality. For a single linear equation it may be one number, while for an inequality it is typically an interval of numbers.

To rewrite an expression in a more compact equivalent form by combining like terms, reducing fractions, or applying order of operations. The value stays the same while the appearance changes.

Terms that have identical variable parts, such as 4x and 9x, so their coefficients can be added or subtracted. Terms with different variables or exponents cannot be combined this way.

A single part of an expression separated by plus or minus signs, made of a coefficient and variable factors. For example, 3x + 5 has two terms: 3x and 5.

A small raised number showing how many times a base is multiplied by itself, as in 2 to the fourth power. It is not the same as multiplying the base by the exponent.

In an exponential expression, the number being repeatedly multiplied, such as the 3 in 3 squared. In other contexts, it can also mean the reference value in a percent problem.

A number that, when multiplied by itself, produces a given value, such as 6 for 36. Every positive number has two square roots, one positive and one negative.

The distance of a number from zero on the number line, always nonnegative. It strips away sign, so the absolute value of both 8 and negative 8 is 8.

A whole number that may be positive, negative, or zero, with no fractional or decimal part. Integers include values like negative 5, 0, and 12 but not 3.5.

A number that can be written as a fraction of two integers, where the denominator is not zero. This includes terminating and repeating decimals as well as all whole numbers.

A real number that cannot be written as a simple fraction of two integers, with a decimal that never terminates or repeats. Familiar examples include pi and the square root of 2.

The arithmetic average found by adding all data values and dividing by how many there are. It is sensitive to extreme values, which can pull it up or down.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It is less affected by extreme values than the mean.

The value or values that appear most often in a data set. A set may have no mode, one mode, or several modes if multiple values tie for highest frequency.

The difference between the largest and smallest values in a data set. It gives a quick but rough sense of spread because it depends only on the two extreme values.

A data value far from the rest of the group, either unusually large or small. Outliers can strongly distort the mean and range while leaving the median nearly unchanged.

A measure of how spread out data values are around the mean, roughly the typical distance from average. A small value means values cluster tightly; a large value means they are widely scattered.

An average in which each value is multiplied by a weight reflecting its importance or frequency, then divided by the total weight. It differs from a simple mean when some values count more than others.

The count of how many times a particular value or category appears in a data set. Frequencies are often displayed in tables or bar heights and are used to compute averages and probabilities.

The proportion of observations in a category, found by dividing that category's count by the total number of observations. It is often expressed as a percent and estimates probability.

A number from 0 to 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be computed from equally likely outcomes or estimated from data.

The likelihood of an event estimated from actual trials, calculated as favorable outcomes divided by total trials. It may differ from theoretical probability, especially with few trials.

The set of all outcomes in which a given event does not happen. The probability of an event plus the probability of its complement always equals 1.

Two events whose outcomes do not influence each other, so the chance of both equals the product of their separate probabilities. A coin flip followed by a die roll is a classic example.

A technique for solving proportions in which you multiply the numerator of one ratio by the denominator of the other. Setting the two products equal isolates the unknown value quickly.