Closed-Ended Questions (Zadania Zamknięte)

This section presents five multiple-choice questions covering various mathematical concepts relevant to the matura rozszerzona matematyka.

The first question deals with comparing the values of different mathematical expressions, including logarithms and trigonometric functions. Students must determine the correct order of these values.

Question 2 involves geometry, specifically a square inscribed in a circle. Students need to calculate the side length of the square given the radius of the circle.

Definition: Inscribed square - A square that fits inside a circle with all four vertices touching the circle's circumference.

The third question focuses on sequences and limits, asking students to determine the limit of a given sequence as n approaches infinity.

Question 4 deals with function analysis, requiring students to identify properties of a given rational function, such as its behavior and extrema.

The final closed-ended question is a probability problem involving the selection of three-digit numbers. Students must calculate the probability of selecting a number divisible by either 3 or 7.

Highlight: This section tests students' ability to quickly analyze and solve diverse mathematical problems, a crucial skill for the matura matematyka rozszerzona.

Open-Ended Questions (Zadania Otwarte)

This section contains eight open-ended questions that require detailed solutions and explanations, mimicking the format of the matura rozszerzona matematyka 2024.

Question 6 asks students to prove a logarithmic identity involving multiple variables. This problem tests students' understanding of logarithm properties and algebraic manipulation.

Example: The question requires proving that log(ab) = (x+1)y / (y+1), given certain conditions for a, b, c, x, and y.

Question 7 involves geometry, specifically an equilateral triangle with parallel lines drawn inside it. Students must prove a relationship between the area of a smaller triangle formed within the larger one and the given dimensions.

Question 8 presents a cubic equation where the coefficients form a geometric sequence. Students need to solve this equation using their knowledge of polynomial factoring and geometric sequences.

Vocabulary: Geometric sequence - A sequence where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Zadania otwarte - część szósta

Ostatnia strona zawiera zadanie z geometrii płaskiej dotyczące równoległoboku.

Highlight: Zadanie 13 wymaga obliczenia pola równoległoboku, znając długości jego boków i kąt między przekątnymi.

Example: Wykorzystanie wzoru na pole równoległoboku P = ab sin α, gdzie α jest kątem między bokami.

Vocabulary: Przekątna równoległoboku - odcinek łączący przeciwległe wierzchołki równoległoboku.