Bulgaria NVO Grade 7 Mathematics key terms

The counting numbers 1, 2, 3, and so on. They are used to count objects and form the starting point for other number sets; some conventions include zero.

A counting number together with zero, giving 0, 1, 2, 3, and so on. Whole numbers contain no fractions, decimals, or negative values.

Any whole number, positive, negative, or zero, such as -7, 0, or 12. Integers contain no fractional or decimal parts and are closed under addition, subtraction, and multiplication.

A number that can be written as a fraction of two integers with a nonzero denominator, such as 3/4, -5, or 0.25. Its decimal form either ends or repeats.

Two numbers the same distance from zero on the number line but on different sides, such as 6 and -6. Their sum is always zero.

The distance of a number from zero on the number line, always zero or positive. Written with vertical bars, so |-9| equals 9 and |9| equals 9.

A straight line with evenly spaced marks labelled by numbers, used to compare values and show operations. Numbers increase to the right and decrease to the left.

A number divisible by each denominator of two or more fractions, allowing them to be added or compared. The smallest one is the least common denominator.

A number written as one integer divided by another, showing parts of a whole. The bottom number names how many equal parts, the top how many are taken.

The number obtained by swapping the numerator and denominator of a fraction. Multiplying a number by its reciprocal gives 1, which makes it useful for division.

A fraction written using place value with a decimal point, such as 0.75 or 2.5. Each digit after the point represents tenths, hundredths, thousandths, and so on.

A short way of writing repeated multiplication, where a base is raised to an exponent. For example, 2 to the fourth power means 2·2·2·2 and equals 16.

The small raised number in a power telling how many times the base is used as a factor. In 5 cubed, the exponent is 3.

A number that, multiplied by itself, gives a stated value. The square root of 49 is 7 because 7 times 7 equals 49; negative numbers have no real square root.

The agreed sequence for evaluating expressions: brackets first, then powers and roots, then multiplication and division left to right, then addition and subtraction left to right.

A single algebraic term formed from numbers and variables joined only by multiplication, such as 7x, -3ab, or 5. It has a coefficient and a degree.

A sum of one or more monomials, such as 4x squared minus 3x plus 2. Polynomials are added, subtracted, multiplied, and sometimes factored.

The numerical factor multiplying the variables in a term. In the term minus 8xy, the coefficient is minus 8; in x, the hidden coefficient is 1.

Terms that have exactly the same variable factors with the same exponents, so they can be combined. For example, 3a and minus 5a combine to give minus 2a.

Rewriting an expression in a shorter equivalent form by combining like terms, removing brackets, and reducing fractions, without changing its value.

An equation that is true for every value of its variables, such as a plus b squared equals a squared plus 2ab plus b squared. Identities are used to expand and factorise.

Writing an expression as a product of simpler expressions. For example, 6x plus 9 becomes 3 times the quantity 2x plus 3, which helps solve equations.

An equation in which each variable appears to the first power only, such as 3x minus 5 equals 10. It usually has exactly one solution, found by balancing both sides.

A value of the variable that makes the equation a true statement. Checking by substitution confirms whether a proposed value is correct.

Equations that have exactly the same solutions, produced by adding, subtracting, multiplying, or dividing both sides by the same nonzero value.

Two or more linear equations in the same variables solved together. A solution must satisfy every equation at once and is often found by substitution or elimination.

A way to solve a system by expressing one variable from one equation and replacing that variable in the other equation, leaving a single-variable equation.

A way to solve a system by adding or subtracting the equations, after suitable multiplication, so one variable cancels and the other can be found.

A statement comparing two expressions with less than, greater than, or their or-equal forms, such as 2x plus 1 is less than 7. Its solutions form a range of values.

The collection of all values of a variable that make an equation or inequality true. For inequalities it is often shown as an interval or on a number line.

A function whose graph is a straight line, written in the form y equals mx plus b. The number m gives the slope and b gives the y-intercept.

A measure of how steep a line is, found as the change in y divided by the change in x between two points. It shows the rate of change.

The point where a graph crosses an axis. The y-intercept is where x equals zero; the x-intercept is where y equals zero.

A grid formed by a horizontal x-axis and a vertical y-axis meeting at the origin. Each point is named by an ordered pair of numbers.

Two numbers written in brackets, x first and y second, locating a point on the coordinate plane. For example, the pair (3, -2) means 3 right and 2 down.

A relationship in which one quantity is a constant multiple of another, so doubling one doubles the other. Its graph is a straight line through the origin.

Figures with exactly the same shape and size, so one can be moved onto the other by sliding, turning, or flipping. Corresponding sides and angles are equal.

Figures with the same shape but possibly different size, whose corresponding angles are equal and corresponding sides are in the same ratio.

The ratio by which a figure is enlarged or reduced to produce a similar figure. Lengths multiply by this factor and areas by its square.

Angles in the same relative position in two figures, or the equal angles formed when a line crosses two parallel lines. They are equal in similar figures.

The total distance around the edge of a plane figure, found by adding the lengths of all its sides. It is measured in units such as centimetres.

The amount of surface a plane figure covers, measured in square units. Formulas differ by shape, for example length times width for a rectangle.

The distance around a circle, calculated as pi times the diameter or twice pi times the radius. It is the circle's perimeter.

The distance from the centre of a circle to any point on its edge, equal to half the diameter. It appears in both circumference and area formulas.

A shape made by joining two or more simple figures, such as rectangles and semicircles. Its area is found by adding or subtracting the parts.

The average found by adding all values and dividing by how many there are. It summarises a data set with one number but is affected by extreme values.

The middle value of a data set arranged in order. With an even count, it is the mean of the two middle values and is less affected by outliers than the mean.

A collection of values or observations gathered about some question. It can be summarised by averages and displayed in tables or charts.

A display using rectangles of different heights to compare counts in categories. The height of each bar shows the frequency of that category.

The number of times a particular value or category occurs in a data set. Frequencies are often shown in tables and used to calculate probabilities.

A number from 0 to 1 measuring how likely an event is, found by dividing favourable outcomes by all equally likely outcomes. Zero means impossible and 1 means certain.

A combination of numbers and operation signs with no equals sign, such as 4 plus 3 times 2. It is evaluated using the order of operations.

A combination of numbers, variables, and operations without an equals sign, such as 5x minus 7. It can be simplified or evaluated for given values.

Translating a real situation into mathematics, such as an equation or formula, solving it, and then interpreting the answer in the original context.