Državna Matura Math A key terms

Any number that can be placed on the number line, including rational and irrational values. It excludes imaginary numbers, and it is the basic setting for almost every task on this exam.

The distance of a number from zero on the number line, always non-negative. Written with vertical bars, it turns negative inputs positive and is used when solving equations and inequalities involving distance.

A number expressible as a fraction of two integers with a non-zero denominator. Its decimal form either terminates or repeats, which helps when deciding whether a value is rational or irrational.

A real number that cannot be written as a fraction of integers, so its decimal expansion never terminates and never repeats. Familiar examples are square roots of non-squares and the constants pi and e.

A set of real numbers lying between two endpoints, written with brackets or parentheses to show whether endpoints are included. Union and intersection of intervals describe solution sets of inequalities.

A notation showing repeated multiplication of a base, where the exponent counts how many factors appear. Rules for multiplying, dividing and raising powers to powers underpin most algebraic simplification.

A value that, raised to a given power, produces the radicand. The n-th root is written with a radical sign and can be rewritten as a fractional exponent, linking roots to powers.

Rewriting a fraction so that no root remains in the denominator, usually by multiplying numerator and denominator by a suitable radical or conjugate. The value is unchanged, but the form becomes easier to compare and simplify.

A combination of numbers, variables and operations without an equality sign. Simplifying, expanding and factoring such expressions is a routine first step before solving equations.

Writing an expression as a product of simpler factors, for example by taking out a common factor or using a difference of squares. It is the main tool for solving polynomial equations and simplifying rational expressions.

A statement that two expressions are equal, true only for certain values of the variable. Solving means finding all such values, and the solution set may be empty or contain several numbers.

A statement comparing two expressions with less-than, greater-than or related symbols. Solving gives a set of values, often an interval, and multiplying or dividing by a negative number reverses the sign.

If a product of factors equals zero, then at least one factor must be zero. This justifies solving factored equations by setting each factor to zero separately.

A value produced during solving that does not actually satisfy the original equation, often arising after squaring or multiplying by an expression that can be zero. Such values must be checked and discarded.

A rule assigning exactly one output value to each input from a specified set. The domain lists allowed inputs, the range lists resulting outputs, and the graph shows all input-output pairs.

The set of all input values for which a function is defined. Restrictions come from division by zero, even roots of negatives and logarithms of non-positive numbers, so it must be checked before analysis.

The set of all output values a function actually produces. It is found from the graph or by analysing the function's behaviour, and it differs from the codomain, which is only the declared target set.

A function that undoes another, sending each output back to its original input. It exists only when the original function is one-to-one, and its graph is the reflection in the line y equals x.

Applying one function to the result of another, written as f of g of x. Order matters, and the domain of the composite excludes inputs where the inner function is undefined or the outer one rejects its output.

A function of the form a x squared plus b x plus c with a non-zero. Its graph is a parabola opening upward or downward, with a vertex giving the minimum or maximum value.

The turning point of a parabola, where the function reaches its minimum or maximum. Its coordinates can be read from the completed-square form or computed from the coefficients.

The vertical line through a parabola's vertex that divides the graph into two mirror-image halves. Its equation is x equals minus b over 2a for a quadratic written in standard form.

The quantity b squared minus 4ac in a quadratic equation. Its sign tells whether there are two, one or no real solutions, so it reveals how many times the parabola meets the x-axis.

A function where the variable sits in the exponent, written as a times b to the x with positive base b. It grows or decays by a constant factor and has a horizontal asymptote.

The exponent to which a base must be raised to produce a given number. Logarithms reverse exponentials, turn products into sums, and obey rules for products, quotients and powers.

The logarithm with base e, written ln. It appears in continuous growth models and calculus, and its derivative is one over x for positive x.

A line that a graph approaches ever more closely without necessarily meeting. Horizontal and vertical asymptotes describe end behaviour and points of unbounded growth in rational, exponential and logarithmic functions.

A function given as one polynomial divided by another. Its domain excludes zeros of the denominator, and these often produce vertical asymptotes or removable holes in the graph.

An expression built from a variable using only non-negative whole-number powers and constant coefficients. Its degree, leading coefficient and roots determine the shape and end behaviour of its graph.

Shifting, stretching, compressing or reflecting a graph by changing its formula. Adding outside the function moves it vertically, adding inside moves it horizontally, and negatives reflect across an axis.

The U-shaped curve that is the graph of a quadratic function. It has a vertex, an axis of symmetry and, depending on the sign of the leading coefficient, opens upward or downward.

A curve obtained by cutting a cone with a plane: circle, ellipse, parabola or hyperbola. Each has a standard equation whose parameters reveal centre, axes and eccentricity.

The set of points at a fixed distance from a centre point. Its equation in the plane follows from the distance formula, and the fixed distance is the radius.

A conic section consisting of two separate branches, defined by a constant difference of distances to two foci. Its standard equation has a minus sign between the squared terms.

A quantity with both magnitude and direction, represented by an arrow or by coordinates. Vectors can be added, subtracted and multiplied by scalars, and the dot product measures alignment.

A way of combining two vectors to get a number, equal to the product of their magnitudes and the cosine of the angle between them. It is zero exactly when the vectors are perpendicular.

A straight set of points extending without end, described by an equation such as y equals m x plus c. The slope m measures steepness and the intercept c gives where it crosses the y-axis.

The expression for the distance between two points in the plane, derived from the Pythagorean theorem. It generalises to the length of a vector and to the equation of a circle.

A sequence in which each term after the first is obtained by adding a fixed difference. Its n-th term is linear in n, and its partial sums form a quadratic pattern.

A sequence in which each term after the first is obtained by multiplying by a fixed ratio. Terms grow or decay exponentially, and infinite sums converge only when the ratio is smaller than one in size.

The sum of the terms of a sequence, often written with sigma notation. Partial sums may approach a finite limit, in which case the infinite series is said to converge.

The value a function or sequence approaches as its input or index gets arbitrarily close to a target. Limits underlie continuity, asymptotes, derivatives and convergence of series.

The instantaneous rate of change of a function, equal to the limit of difference quotients. Geometrically it gives the slope of the tangent line at a point.

A line touching a curve at a point with the same slope there. Its slope equals the derivative at that point, and for a circle it is perpendicular to the radius.

A quantity accumulating infinitely many infinitesimal contributions, interpreted as signed area under a curve. Definite integrals are computed using antiderivatives via the fundamental theorem of calculus.

A ratio of two sides of a right triangle, such as sine, cosine or tangent of an acute angle. These ratios extend to all angles through the unit circle and connect geometry with periodic functions.

For an acute angle in a right triangle, the ratio of the opposite side to the hypotenuse. On the unit circle it equals the y-coordinate of the corresponding point.

For an acute angle in a right triangle, the ratio of the adjacent side to the hypotenuse. On the unit circle it equals the x-coordinate, and it appears in the dot product formula.

The circle of radius one centred at the origin. Angles measured from the positive x-axis give points whose coordinates are the cosine and sine of that angle.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. It underlies the distance formula and the basic trigonometric identity.

An arrangement of objects in which order matters. Counting permutations uses factorials and falling products, and it differs from combinations, where order is irrelevant.

A selection of objects in which order does not matter, counted with binomial coefficients. It appears in the binomial theorem and in counting favourable outcomes for probability.

A number between zero and one measuring how likely an event is, computed as favourable outcomes divided by all equally likely outcomes. Complementary and independent events obey simple rules.

A measure of how spread out data are, equal to the square root of the variance. A small value means values cluster near the mean, while a large value means wide dispersion.

The arithmetic average of a data set, found by adding all values and dividing by their count. It is sensitive to extreme values, unlike the median.

The middle value of an ordered data set, or the average of the two middle values when the count is even. It resists distortion by outliers and pairs with quartiles in box plots.