Mathematical Formulas for 8th Grade Exam

This page presents a comprehensive collection of wzory matematyczne egzamin ósmoklasisty (mathematical formulas for the 8th-grade exam), focusing on powers, roots, and plane geometry. These formulas are essential for students preparing for their egzamin ósmoklasisty 2023.

Powers (Potęgi)

The section on powers includes several key formulas:

Example: 2⁹ · 2³ = 2¹²

This example demonstrates the rule for multiplying powers with the same base.

Definition: a^m · a^n = a^(m+n)

This formula shows how to multiply powers with the same base by adding the exponents.

Other important power formulas include:

• (a · b)² = a² · b²
• (a^b)^c = a^(b·c)
• a^0 = 1 (for any non-zero a)

Highlight: Understanding these power rules is crucial for simplifying complex expressions and solving equations efficiently.

Roots (Pierwiastki)

The document provides essential formulas for working with roots:

Example: √(ab) = √a · √b

This formula demonstrates how to simplify the square root of a product.

Other root formulas include:

• ∛(a³) = a
• √(a²) = |a|

Vocabulary: The symbol "√" represents the square root, while "∛" represents the cube root.

Plane Geometry (Geometria płaska)

This section covers formulas for various geometric shapes, including:

1. Square (Kwadrat):

   • Area: P = a²
   • Diagonal: d = a√2
   • Perimeter: Ob = 4a

2. Rectangle (Prostokąt):

   • Area: P = a · b
   • Perimeter: Ob = 2a + 2b

3. Rhombus (Romb):

   • Area: P = e · f / 2 (where e and f are diagonals)
   • Perimeter: Ob = 4a

4. Parallelogram (Równoległobok):

   • Area: P = a · h
   • Perimeter: Ob = 2a + 2b

5. Equilateral Triangle (Trójkąt równoboczny):

   • Area: P = (a² · √3) / 4
   • Height: h = (a · √3) / 2
   • Inradius: r = a · √3 / 6
   • Circumradius: R = a · √3 / 3

Highlight: These geometria płaska WZORY are essential for solving problems related to areas, perimeters, and other geometric properties of shapes.

The page includes clear diagrams for each shape, making it easier for students to visualize and understand the formulas. This visual representation is particularly helpful for grasping concepts in plane geometry.

Quote: "W-zaznaczone wysokości 'h'" (Height marked as 'h')

This note on the diagram helps students identify the height in various shapes, which is crucial for area calculations.

Overall, this page serves as an excellent quick reference guide for students preparing for the egzamin ósmoklasisty, covering key wzory matematyczne szkoła podstawowa PDF that are likely to appear on the exam.