Bulgaria NVO Grade 7 Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate in this order: brackets, then powers and roots, then multiplication and division from left to right, then addition and subtraction from left to right.

Absolute value

The distance of a number from zero on the number line, always non-negative. For example |−7| = 7 and |4| = 4.

Reciprocal of a fraction

The reciprocal of a/b is b/a, obtained by swapping numerator and denominator. Dividing by a fraction means multiplying by its reciprocal.

Power rules

For a ≠ 0: a^m·a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, and a^(−n) = 1/a^n.

Like monomials

Monomials with exactly the same variables raised to the same powers, such as 3x²y and −5x²y. Only their coefficients are added when simplifying.

Difference of squares

The identity a² − b² = (a − b)(a + b), used both to expand products of a sum and difference and to factor expressions such as x² − 25.

Square of a binomial

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b². The middle term is twice the product of the two terms.

Factoring by common factor

Writing an expression as a product by taking out the greatest common factor of all terms, for example 6x³ + 9x² = 3x²(2x + 3).

Equivalent equations

Equations with the same solution set. Adding, subtracting, multiplying, or dividing both sides by the same nonzero number produces an equivalent equation.

Inequality sign reversal

When both sides of an inequality are multiplied or divided by a negative number, the direction of the inequality sign must be reversed.

System with no solution

A system of two linear equations whose graphs are parallel lines. The coefficients of the variables are proportional but the constants are not.

Slope of a line

For a line through points (x₁, y₁) and (x₂, y₂), slope k = (y₂ − y₁)/(x₂ − x₁). It measures the change in y per unit change in x.

Direct proportionality

A relationship y = kx with constant k ≠ 0, whose graph is a straight line through the origin; the quotient y/x is the same for all points.

y-intercept

The y-coordinate of the point where a graph crosses the y-axis, found by setting x = 0. For y = kx + m the intercept is m.

Parallel lines condition

Two non-vertical lines are parallel exactly when their slopes are equal. Distinct parallel lines never meet, so their equations have no common solution.

Triangle angle sum

The three interior angles of any triangle add up to 180°. This determines the third angle when the other two are known.

Isosceles triangle property

A triangle with two equal sides has equal angles opposite those sides. Conversely, equal base angles imply that the opposite sides are equal.

Congruent triangles

Triangles with equal corresponding sides and angles, proved by SSS, SAS, ASA/AAS, or hypotenuse–leg for right triangles. Their areas are equal.

Similarity ratio

The constant ratio between corresponding sides of similar figures. Perimeters share this ratio, while areas are multiplied by its square.

Parallelogram properties

Opposite sides are equal and parallel, opposite angles are equal, consecutive angles sum to 180°, and the diagonals bisect each other.

Polygon interior angle sum

For a polygon with n sides, the interior angles sum to (n − 2)·180°. For example, a pentagon has 3·180° = 540°.

Triangle area formula

Area equals one half of a base multiplied by the height drawn to that base: S = (1/2)·a·h. The height must be perpendicular to the base.

Circle circumference and area

For radius r: circumference C = 2πr and area S = πr². The diameter d = 2r, so C = πd as well.

Trapezoid area

Area equals half the sum of the two parallel bases multiplied by the height: S = ((a + b)/2)·h, where h is perpendicular to the bases.

Pythagorean theorem

In a right triangle with legs a and b and hypotenuse c: a² + b² = c². It is used to find a missing side or a distance.

Scaling of area

If all lengths of a figure are multiplied by factor k, then perimeters are multiplied by k and areas by k².

Arithmetic mean

The sum of all data values divided by how many values there are. Extreme values strongly influence it, unlike the median.

Median of a data set

The middle value after arranging the data in order; with an even number of values, it is the mean of the two middle ones.

Probability of an event

The number of favourable outcomes divided by the number of equally likely outcomes, always between 0 and 1 inclusive.

Complementary probability

The probability that event A does not occur equals 1 − P(A). For example, if P(A) = 0.3, then P(not A) = 0.7.

Percent change

Increase by p% multiplies a quantity by (1 + p/100); decrease by p% multiplies it by (1 − p/100).

Counterexample

A single case that contradicts a general statement, which is enough to prove that statement false. One example never proves a statement true.