Armenia Mathematics Unified Exam key terms

The property that one integer can be divided by another with zero remainder. Written a | b when b = a·k for some integer k.

The integer left over after division when the divisor does not divide evenly. For a = bq + r, the remainder r satisfies 0 ≤ r < |b|.

The largest positive integer that divides each of two or more given integers without a remainder. Often denoted gcd(a, b).

The smallest positive integer that is a multiple of each of two or more given integers. Often denoted lcm(a, b).

An integer greater than 1 whose only positive divisors are 1 and itself, such as 2, 3, 5, 7 and 11.

The unique expression of an integer greater than 1 as a product of prime numbers, usually written with powers, for example 360 = 2³·3²·5.

A statement that two integers leave the same remainder when divided by a fixed positive integer m, written a ≡ b (mod m).

An expression formed by adding and multiplying constants and non-negative integer powers of a variable, such as 3x² − 5x + 2.

The largest exponent of the variable that appears with a nonzero coefficient in a polynomial written in standard form.

Rewriting an expression as a product of simpler expressions, for example turning x² − 9 into (x − 3)(x + 3).

An equation of the form ax² + bx + c = 0 with a ≠ 0. Its real solutions are found using the discriminant and the quadratic formula.

The quantity b² − 4ac of a quadratic equation ax² + bx + c = 0. Its sign tells whether there are two, one, or no real solutions.

A value of the variable that makes the equation a true statement when substituted into it.

A statement comparing two expressions with one of the symbols <, >, ≤ or ≥, for example 2x + 1 ≤ 7.

The distance of a real number from zero on the number line, written |x|. It equals x when x ≥ 0 and −x when x < 0.

A shorthand for describing sets of real numbers using brackets and parentheses, such as [2, 5) for all numbers from 2 up to but not including 5.

A rule that assigns to each input value from a set exactly one output value. Written f(x) for input x.

The set of all input values for which a function is defined and produces a real output.

The set of all output values that a function actually takes as the input varies over its domain.

An input value x for which f(x) = 0. On a graph these are the points where the curve meets the horizontal axis.

The measure of steepness of a line, equal to the change in y divided by the change in x between two points on it.

A function of the form f(x) = kx + b, whose graph is a straight line with slope k and vertical intercept b.

A sequence in which each term after the first is obtained by adding a fixed constant, the common difference, to the previous term.

The constant amount added to each term of an arithmetic progression to obtain the next term, usually denoted d.

A sequence in which each term after the first is obtained by multiplying the previous term by a fixed nonzero constant, the common ratio.

The fixed nonzero factor by which each term of a geometric progression is multiplied to obtain the next term, usually denoted q or r.

The total of the first n terms of a geometric progression, equal to a₁(1 − qⁿ)/(1 − q) when the common ratio q is not 1.

Ratios of side lengths in a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

An equation involving trigonometric functions that holds for every value where both sides are defined, such as sin²x + cos²x = 1.

The circle of radius 1 centred at the origin. A point on it at angle θ has coordinates (cos θ, sin θ).

A unit of angle measure defined so that a full turn is 2π radians. One radian corresponds to an arc equal in length to the radius.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

Triangles whose corresponding angles are equal, so their corresponding side lengths are in the same fixed ratio.

The measure of the region enclosed by a triangle, given by half the product of a base and the height drawn to that base.

The amount of three-dimensional space enclosed by a solid, measured in cubic units such as cubic centimetres.

The total area of all the faces or the curved boundary of a three-dimensional solid, measured in square units.

An arrangement of objects in which order matters. The number of orderings of n distinct objects is n factorial.

A selection of objects from a group in which order does not matter, counted by n! divided by k!(n − k)!.

The product of all positive integers from 1 up to a given positive integer n, written n!. By convention 0! equals 1.

A number between 0 and 1 measuring how likely an event is, computed as favourable outcomes divided by all equally likely outcomes.

Two events whose occurrence does not affect each other. Their joint probability equals the product of their individual probabilities.

The arithmetic average of a data set, found by adding all values and dividing by the number of values.

The middle value of a data set arranged in order; if there is an even number of values, it is the average of the two middle ones.

The instantaneous rate of change of a function, defined as the limit of the difference quotient as the change in input approaches zero.

The value that a function's output approaches as its input approaches a specified point, whether or not the function is defined there.

A quantity representing accumulated change, computed as the limit of sums of small products; the definite integral gives signed area under a curve.

The property of a function whose graph has no breaks at a point: the limit there exists and equals the function's value.