Mathematics Review - 8th Grade Curriculum

A comprehensive set of vocabulary flashcards covering mathematics topics including powers, roots, algebraic expressions, number sets, geometry (Pythagorean theorem, circles, cylinders), and geometric loci.

Power (Mocnina)

A shortened notation for the repeated multiplication of the same number.

Second Power ($a^2$)

The multiplication of a number by itself, represented as $a^2 = a \times a$. For a negative number, the result is always positive.

Third Power ($a^3$)

The multiplication of a number by itself three times, represented as $a^3 = a \times a \times a$. The sign of the result remains the same as the original number.

Square Root ($\sqrt{a}$)

The inverse operation of the second power; it finds a number that, when squared, equals the given number. It does not exist for negative numbers in the set of real numbers.

Cube Root ($\sqrt[3]{a}$)

The inverse operation of the third power; it finds a number that, when raised to the third power, equals the given number. Unlike the square root, it can be calculated for negative numbers.

Natural Exponent

A positive integer ($n$) in the expression $a^n$, where $a$ is the base and $n$ is the exponent.

Product of Powers Rule

When multiplying powers with the same base, the exponents are added: $a^m \times a^n = a^{m+n}$.

Quotient of Powers Rule

When dividing powers with the same base, the exponents are subtracted: $a^m : a^n = a^{m-n}$.

Power of a Power Rule

When raising a power to another exponent, the exponents are multiplied: $(a^m)^n = a^{m \times n}$.

Power of a Product Rule

The power of a product is equal to the product of the individual powers of the factors: $(ab)^n = a^n \times b^n$.

Power of a Quotient Rule

The power of a quotient is equal to the quotient of the individual powers: $(a/b)^n = a^n / b^n$.

Negative Exponent Rule

A negative exponent denotes the reciprocal of the corresponding positive power: $a^{-n} = \frac{1}{a^n}$, valid as long as the base is not equal to zero.

Algebraic Expression

A mathematical notation composed of numbers, variables, and arithmetic operations.

Factoring by Grouping (Vytýkání)

The transformation of an expression into a product by identifying common factors, for example: $8x + 16 = 8(x + 2)$.

Natural Numbers ($N$)

The set of numbers $0, 1, 2, 3...$ used primarily for counting.

Integers ($Z$)

The set containing all natural numbers and their negative counterparts.

Rational Numbers ($Q$)

Numbers that can be expressed in the form of a fraction.

Irrational Numbers ($I$)

Numbers that cannot be written as a fraction, such as $\pi$ or $\sqrt{2}$.

Real Numbers ($R$)

The set encompassing all rational and irrational numbers.

Linear Equation

An equation containing one unknown raised to the first power, solved by isolating the variable on one side.

Linear Inequality Sign Rule

When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign ($>, <, \text{or} \neq$) must be reversed.

Pythagorean Theorem

A law applicable only to right-angled triangles stating that the sum of the squares of the legs equals the square of the hypotenuse: $a^2 + b^2 = c^2$.

Circle (Kružnice)

A set of all points in a plane that are at the same fixed distance (radius) from a central point.

Disk (Kruh)

The portion of a plane bounded by a circle.

Circumference ($o$)

The distance around a circle, calculated as $o = 2 \times \text{π} \times r$ or $o = \text{π} \times d$.

Area of a Disk ($S$)

The space inside a circle, calculated using the formula $S = \text{π} \times r^2$.

Number $\text{π}$ (Pi)

A mathematical constant approximately equal to $3.14$.

Cylinder (Válec)

A 3D geometric solid consisting of two circular bases and a mantle.

Volume of a Cylinder ($V$)

Calculated as the area of the base times the height: $V = \text{π} \times r^2 \times v$, where $v$ is the height.

Surface Area of a Cylinder ($S$)

The total area of the two bases and the mantle: $S = 2 \times \text{π} \times r^2 + 2 \times \text{π} \times r \times v$.

Locus of Points (Množina všech bodů dané vlastnosti)

A set of all points that satisfy a specific geometric condition.

Perpendicular Bisector (Osa úsečky)

A set of all points that are at the same distance from both endpoints of a line segment.

Angle Bisector (Osa úhlu)

A set of all points that are equidistant from the two rays (arms) of an angle.

Perpendicular Lines

Lines that intersect at a right angle of $90^\text{o}$.

Parallel Lines

Lines within the same plane that never intersect.