Hey guys! Preparing for your Mala Matura and feeling swamped by all those math formulas? No worries, I’ve got your back! This guide is designed to be your one-stop-shop for all the essential math formulas you'll need to ace that exam. We'll break it down, make it easy to understand, and hopefully, even a little bit fun. Let’s dive in!

Brojevi i Operacije (Numbers and Operations)

Okay, let's start with the basics – numbers and how we play around with them. This section is all about understanding the fundamental rules that govern arithmetic, which are super crucial for solving more complex problems later on.

Osnovne računske operacije (Basic Arithmetic Operations)

This is where it all begins! You absolutely need to be rock solid on addition, subtraction, multiplication, and division. Remember the order of operations (PEMDAS/BODMAS)? It's your best friend! Also, understanding how these operations interact with negative numbers, fractions, and decimals is absolutely key.

• Addition (+): Combining two or more numbers to find their sum. Pretty straightforward, right? But make sure you're comfortable adding different types of numbers (integers, fractions, decimals).
• Subtraction (-): Finding the difference between two numbers. Watch out for those negative signs!
• *Multiplication (x or ): Repeated addition. Knowing your times tables is a massive time-saver.
• Division (÷ or /): Splitting a number into equal parts. Remember long division? It might come in handy.

Keywords to remember: Sum, difference, product, quotient, integers, fractions, decimals, PEMDAS/BODMAS.

Stepenovanje i Korenovanje (Exponents and Roots)

Exponents are a shorthand way of writing repeated multiplication, while roots are the inverse operation. Mastering these concepts opens the door to algebra and more advanced math.

• Stepenovanje (Exponents): A number raised to a power indicates how many times to multiply the number by itself. For example, 2³ (2 cubed) = 2 * 2 * 2 = 8. Understand the rules of exponents, like when you multiply powers with the same base, you add the exponents. Also, remember that any number raised to the power of 0 is 1!
• Korenovanje (Roots): Finding the number that, when multiplied by itself a certain number of times, equals the given number. The square root (√) is the most common. For example, √9 = 3 because 3 * 3 = 9. Make sure you understand how to simplify radicals.

Keywords to remember: Base, exponent, power, square root, cube root, radical, index.

Deljivost (Divisibility)

Knowing the divisibility rules for common numbers (2, 3, 4, 5, 6, 9, 10) can save you tons of time when simplifying fractions or factoring numbers. Practice these rules until they become second nature!

• Divisible by 2: The last digit is even (0, 2, 4, 6, 8).
• Divisible by 3: The sum of the digits is divisible by 3.
• Divisible by 4: The last two digits are divisible by 4.
• Divisible by 5: The last digit is 0 or 5.
• Divisible by 6: Divisible by both 2 and 3.
• Divisible by 9: The sum of the digits is divisible by 9.
• Divisible by 10: The last digit is 0.

Keywords to remember: Divisor, multiple, factor, divisibility rules.

Algebra

Algebra is like a puzzle where you use letters to represent unknown numbers. Don't let it intimidate you! Once you grasp the basic principles, it becomes a powerful tool for solving a wide range of problems.

Izrazi i Jednačine (Expressions and Equations)

Understanding the difference between expressions and equations is fundamental. An expression is a combination of numbers, variables, and operations, while an equation states that two expressions are equal.

• Izrazi (Expressions): A mathematical phrase that contains numbers, variables, and operators (like +, -, *, /). Examples: 3x + 2, a² - b². You can simplify expressions, but you can't "solve" them.
• Jednačine (Equations): A statement that two expressions are equal. It contains an equals sign (=). Examples: 2x + 5 = 11, y = mx + b. Your goal is usually to find the value of the variable that makes the equation true.

Keywords to remember: Variable, constant, coefficient, term, expression, equation, solve.

Linearne Jednačine (Linear Equations)

Linear equations are equations where the highest power of the variable is 1. They are relatively simple to solve and have many practical applications.

• Solving for x: The goal is to isolate the variable (usually 'x') on one side of the equation. Use inverse operations (addition/subtraction, multiplication/division) to undo the operations that are being performed on the variable. Remember to do the same thing to both sides of the equation to keep it balanced!
• Example: 3x + 7 = 16 * Subtract 7 from both sides: 3x = 9 * Divide both sides by 3: x = 3

Keywords to remember: Slope, intercept, linear function, solving equations.

Sistemi Jednačina (Systems of Equations)

Sometimes you'll have two or more equations with two or more variables. To solve these systems, you need to find values for all the variables that satisfy all the equations simultaneously. Common methods include substitution and elimination.

• Substitution Method: Solve one equation for one variable, then substitute that expression into the other equation. This will give you a single equation with one variable, which you can solve. Then, substitute the value you found back into either of the original equations to find the value of the other variable.
• Elimination Method: Multiply one or both equations by a constant so that the coefficients of one of the variables are opposites. Then, add the equations together. This will eliminate one of the variables, leaving you with a single equation with one variable.

Keywords to remember: System of equations, simultaneous equations, substitution, elimination.

Geometrija (Geometry)

Geometry is the study of shapes, sizes, and positions of figures. This section covers the basic geometric concepts you'll need for the Mala Matura.

Površina i Obim (Area and Perimeter)

Understanding how to calculate the area and perimeter of different shapes is essential. Make sure you know the formulas for squares, rectangles, triangles, circles, and parallelograms.

• Square: * Area: A = side * side = s² * Perimeter: P = 4 * side = 4s
• Rectangle: * Area: A = length * width = l * w * Perimeter: P = 2 * (length + width) = 2(l + w)
• Triangle: * Area: A = 1/2 * base * height = 1/2 * b * h * Perimeter: P = side1 + side2 + side3 = a + b + c
• Circle: * Area: A = π * radius² = πr² * Circumference (Perimeter): C = 2 * π * radius = 2πr
• Parallelogram: * Area: A = base * height = b * h * Perimeter: P = 2 * (side1 + side2) = 2(a + b)

Keywords to remember: Area, perimeter, circumference, length, width, base, height, radius, π (pi).

Zapremina (Volume)

Volume is the amount of space a three-dimensional object occupies. You should be familiar with the formulas for calculating the volume of cubes, rectangular prisms, and cylinders.

• Cube: * Volume: V = side * side * side = s³
• Rectangular Prism: * Volume: V = length * width * height = l * w * h
• Cylinder: * Volume: V = π * radius² * height = πr²h

Keywords to remember: Volume, length, width, height, radius, π (pi).

Uglovi (Angles)

Understanding different types of angles (acute, obtuse, right, straight) and their relationships is important for solving geometry problems. Also, remember the angle sum properties of triangles and quadrilaterals.

• Types of Angles: * Acute Angle: Less than 90 degrees. * Right Angle: Exactly 90 degrees. * Obtuse Angle: Greater than 90 degrees but less than 180 degrees. * Straight Angle: Exactly 180 degrees.
• Angle Sum Properties: * Triangle: The sum of the angles in a triangle is always 180 degrees. * Quadrilateral: The sum of the angles in a quadrilateral is always 360 degrees.

Keywords to remember: Acute, obtuse, right, straight, angle, degree, triangle, quadrilateral.

Razlomci i Procenti (Fractions and Percentages)

Fractions and percentages are used to represent parts of a whole. Being comfortable with converting between fractions, decimals, and percentages is crucial for many real-world applications.

Razlomci (Fractions)

Make sure you know how to add, subtract, multiply, and divide fractions. Also, remember how to simplify fractions to their lowest terms.

• Addition/Subtraction: You need a common denominator. Find the least common multiple (LCM) of the denominators, then rewrite the fractions with the common denominator. Add or subtract the numerators, keeping the denominator the same.
• Multiplication: Multiply the numerators and multiply the denominators.
• Division: Invert the second fraction (the one you're dividing by) and multiply.

Keywords to remember: Numerator, denominator, proper fraction, improper fraction, mixed number, LCM.

Procenti (Percentages)

Percent means "out of 100." To convert a fraction or decimal to a percentage, multiply by 100. To convert a percentage to a fraction or decimal, divide by 100.

• Finding a Percentage of a Number: Multiply the number by the percentage (as a decimal).
• Example: What is 25% of 80? 0.25 * 80 = 20

Keywords to remember: Percent, percentage, decimal, fraction.

Statistika i Verovatnoća (Statistics and Probability)

This section introduces you to the basics of collecting, organizing, and interpreting data, as well as the concepts of probability.

Srednja Vrednost (Mean), Medijana (Median), Mod (Mode)

These are measures of central tendency that describe the "average" value of a dataset.

• Mean: The sum of the values divided by the number of values. (Average).
• Median: The middle value when the values are arranged in order. If there are two middle values, the median is the average of those two values.
• Mode: The value that appears most frequently in the dataset.

Keywords to remember: Mean, median, mode, average, dataset.

Verovatnoća (Probability)

Probability is the chance that a particular event will occur. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

• Calculating Probability: Probability = (Number of favorable outcomes) / (Total number of possible outcomes).

Keywords to remember: Probability, event, outcome, favorable outcome, possible outcome.

Okay guys, that's a wrap! This guide covers the key math formulas and concepts you'll need for your Mala Matura. Remember to practice, practice, practice! The more you work through problems, the more comfortable you'll become with these formulas. Good luck, and I know you'll do great!**