ORELA Mathematics (NT304) key terms

The counting numbers 1, 2, 3, and so on. Some textbooks include 0 in this set, so check the convention a problem uses before answering questions about divisibility or closure.

The set of nonnegative counting numbers: 0, 1, 2, 3, and so on. It differs from the natural numbers only by including zero, a distinction tested in set and number-sense items.

All positive and negative counting numbers together with zero, extending infinitely in both directions. The set is closed under addition, subtraction, and multiplication, but not under division unless the divisor divides evenly.

Any number expressible as a fraction of two integers with a nonzero denominator. Decimal expansions either terminate or repeat, which is the quickest way to identify a rational value on the exam.

Real numbers that cannot be written as a ratio of integers, such as the square root of 2 or pi. Their decimal expansions never terminate and never repeat, so no fraction equals them exactly.

The complete set of points on the number line, including both rational and irrational values. Every real number is either rational or irrational, and the set is closed under the four basic operations except division by zero.

The distance of a number from zero on the number line, always nonnegative. Written with vertical bars, it turns negatives positive and leaves positives unchanged, and appears in distance and inequality problems.

A straight line with evenly spaced points labeled by real numbers, increasing to the right. It visually represents order, opposites, absolute value, and the solutions of inequalities.

The value a digit has because of its position in a numeral, such as the 3 in 3,500 meaning three thousands. Understanding place value underlies regrouping, rounding, and decimal comparison.

Replacing a number with a nearby value of a chosen precision, decided by looking at the next digit. If that digit is 5 or more, round up; otherwise keep the digit unchanged.

Finding a value close enough to the exact answer for a stated purpose, often by rounding or using compatible numbers. It checks reasonableness and supports mental computation in everyday problem solving.

A whole number greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 5, and 7. The number 1 is neither prime nor composite.

A whole number greater than 1 with at least one positive divisor besides 1 and itself, such as 4, 9, or 12. Every composite number can be broken into a unique product of primes.

Writing a composite number as a product of prime factors, for example 60 equals 2 squared times 3 times 5. It is used to find greatest common factors, least common multiples, and simplify radicals.

The largest positive integer that divides two or more given numbers without a remainder. It is found by multiplying shared prime factors and is used to reduce fractions to lowest terms.

The smallest positive integer that is a multiple of two or more given numbers. It is used to find common denominators and to solve problems about events repeating on different cycles.

Numbers that represent part of a whole or a ratio, written as one integer over another nonzero integer. Equivalent fractions, simplification, and common denominators are core skills for operations with them.

A base-ten numeral using a point to separate whole-number places from fractional places. Each place to the right is one tenth the value of the place before it, linking decimals directly to fractions and place value.

A ratio comparing a number to 100, so 45 percent means 45 per hundred or 0.45. Percents convert easily to decimals and fractions and appear in discount, tax, and interest problems.

A comparison of two quantities by division, often written as a to b or a:b. Ratios can compare parts to parts or parts to a whole and are scaled by multiplying both quantities by the same factor.

An equation stating that two ratios are equal, solved by cross-multiplying. It models scaling, percent problems, and similar figures where corresponding quantities grow at the same rate.

A rate expressed per one unit of a second quantity, such as miles per hour or cost per ounce. It is found by dividing and allows direct comparison of different-sized offers or speeds.

The agreed sequence for evaluating expressions: grouping symbols, exponents, multiplication and division left to right, then addition and subtraction left to right. Following it prevents ambiguity and produces one correct value.

A small raised number showing how many times a base is used as a factor, so 2 cubed means 2 times 2 times 2. Rules for multiplying, dividing, and raising powers to powers apply.

A number that, when multiplied by itself, gives a specified number, so the square root of 49 is 7. The radical symbol denotes the nonnegative root, and perfect squares give whole-number results.

A compact way to write very large or small numbers as a number between 1 and 10 multiplied by a power of ten. The exponent records how many places the decimal point moved.

A letter or symbol standing for an unknown or changing number in an expression or equation. Variables let rules be stated generally and are manipulated using the properties of operations.

A combination of variables, numbers, and operation symbols without an equals sign, such as 3x plus 5. It can be simplified, evaluated for given values, or factored but not solved.

A statement that two expressions have equal value, connected by an equals sign. Solving means finding values of variables that make the statement true, using inverse operations to isolate them.

A statement comparing expressions with symbols such as less than, greater than, or not equal. Solutions form a range of values, graphed on a number line with open or closed endpoints.

Multiplying a sum by a factor gives the same result as multiplying each addend by the factor and adding, so a times (b plus c) equals ab plus ac. It justifies expanding and factoring expressions.

The steepness of a line, computed as the change in y divided by the change in x between two points. It appears as the coefficient of x in slope-intercept form and describes constant rate of change.

The point where a graph crosses the vertical axis, occurring where x equals zero. In a linear model it often represents a starting value before any change occurs.

A function whose graph is a straight line and whose rule can be written as y equals mx plus b. It changes at a constant rate, making it the basic model for proportional and steady-growth situations.

A function of the form y equals ax squared plus bx plus c, whose graph is a parabola. Its highest or lowest point is the vertex, and its real roots are where the graph meets the x-axis.

Rewriting an expression as a product of simpler expressions, such as turning x squared minus 9 into (x minus 3)(x plus 3). It solves quadratic equations when one side equals zero.

The turning point of a parabola, where the graph reaches its minimum or maximum value. Its coordinates can be found from the equation and mark the axis of symmetry.

A rule assigning exactly one output value to each input value in its domain. Passing the vertical line test confirms that a graph represents a function.

Having exactly the same size and shape, so one figure can be moved onto the other by rigid motions. Corresponding sides and angles of congruent figures are equal.

Figures with the same shape but not necessarily the same size, having equal corresponding angles and proportional corresponding sides. The scale factor compares their lengths.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. It finds a missing side and also tests whether a triangle is right-angled.

A change in a figure's position or size, including translations, rotations, reflections, and dilations. The first three preserve congruence, while dilations preserve only shape.

The number of square units needed to cover a two-dimensional region. Formulas for rectangles, triangles, circles, and composite shapes depend on the dimensions and the shape's structure.

The total distance around the boundary of a two-dimensional figure, found by adding side lengths. For a circle this distance is called the circumference.

The amount of space a three-dimensional solid occupies, measured in cubic units. It is computed by multiplying base area by height or by using formulas specific to each solid.

The total area of all faces or curved surfaces of a three-dimensional solid. Nets help visualize each face, and the result is reported in square units.

The arithmetic average, found by adding all data values and dividing by how many there are. It is affected strongly by extreme values, unlike the median.

The middle value of a data set arranged in order, or the average of the two middle values when the count is even. It resists distortion by outliers.

The value or values that appear most often in a data set. A set may have one mode, several modes, or none, and the mode is the only average usable with categorical data.

A number from 0 to 1 expressing how likely an event is, often as favorable outcomes divided by total equally likely outcomes. It underpins predictions and expected-value reasoning.

The set of all possible outcomes of a probability experiment, such as the six faces of a die. Listing it completely is the first step in computing probabilities.

Events whose outcomes do not affect each other, so the probability of both equals the product of their individual probabilities. Drawing with replacement produces independent events.