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Matematyka i Logika SAT - Mathematics

Tutaj nauczysz się niektórych angielskich słów związanych z matematyką, takich jak "zmienna", "histogram", "dziedzina" itp., które będą Ci potrzebne do zdania SAT.

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SAT Vocabulary for Math and Logic
intercept
intercept
[Rzeczownik]

the point where a line, curve, or surface crosses an axis on a graph

punkt przecięcia, przechwytywanie

punkt przecięcia, przechwytywanie

Ex: The y-intercept of the line is where it crosses the y-axis at 
plane
plane
[Rzeczownik]

a flat, two-dimensional surface that extends infinitely in all directions

płaszczyzna, płaska powierzchnia

płaszczyzna, płaska powierzchnia

Ex: In geometry, a plane is defined by three non-collinear points. 
function
function
[Rzeczownik]

(mathematics) a quantity whose value changes according to another quantity's varying value

funkcja

funkcja

Ex: In calculus, a function represents a relationship between input and output variables, often denoted as f(x). 
to model
to model
[Czasownik]

to make a representation of something, especially one based on mathematics

modelować, reprezentować

modelować, reprezentować

Ex: Economists model supply and demand to understand market trends and make forecasts. 
constant
constant
[Rzeczownik]

a quantity or value that remains the same and does not change in a specific mathematical context

stała

stała

Ex: Pi is a mathematical constant approximately equal to 3.14159. 
expression
expression
[Rzeczownik]

a combination of numbers, variables, operations, and grouping symbols that collectively represent a numerical value or relationship

wyrażenie, formuła

wyrażenie, formuła

Ex: The algebraic expression ( 2x + 3 ) represents a linear equation when set equal to zero. 
equivalent
equivalent
[przymiotnik]

(of mathematical expressions or quantities) having the same value or function, even if they appear in different forms

równoważny

równoważny

Ex: The fractions 1/2 and 2/4 are equivalent because they represent the same value. 
to intersect
to intersect
[Czasownik]

to meet or cross another path, line, etc. at a particular point

przecinać się, krzyżować się

przecinać się, krzyżować się

Ex: The two roads intersect at the traffic light. 
scatter plot
scatter plot
[Rzeczownik]

a type of graph used in statistics and data analysis to display and compare two sets of numerical data

wykres rozrzutu, diagram punktowy

wykres rozrzutu, diagram punktowy

Ex: The scatter plot revealed a positive correlation between hours of study and exam scores. 
line of best fit
line of best fit
[Rzeczownik]

a straight line drawn through the center of a group of data points on a scatter plot representing the best approximation of the relationship between the variables being studied

linia najlepszego dopasowania, linia regresji

linia najlepszego dopasowania, linia regresji

Ex: The line of best fit on the scatter plot showed a clear upward trend. 
variable
variable
[Rzeczownik]

(mathematics) a quantity that is capable of assuming different values in a calculation

zmienna

zmienna

Ex: In algebra, variables such as x, y, and z represent quantities that can vary or change in value. 
scale
scale
[Rzeczownik]

a system of numerical values used to quantify and compare levels, degrees, or values

skala, stopniowanie

skala, stopniowanie

Ex: The earthquake's intensity was measured on the Richter scale. 
figure
figure
[Rzeczownik]

a diagram or illustration that is used to show or explain something, such as a chart, graph, or drawing

rysunek, wykres

rysunek, wykres

Ex: The report included several figures to make the data easier to understand. 
domain
domain
[Rzeczownik]

the set of all possible input values for which a given function is defined

dziedzina, zbiór definicji

dziedzina, zbiór definicji

Ex: To find the domain of a rational function, exclude any values that make the denominator zero. 
graph
graph
[Rzeczownik]

(in mathematics) a set of points with coordinates that satisfy specific relationships

wykres, krzywa

wykres, krzywa

Ex: The function's graph showed a clear linear pattern. 
histogram
histogram
[Rzeczownik]

a diagram consisting of bars with different heights that represent the amount of a variable

histogram, wykres słupkowy

histogram, wykres słupkowy

interval
interval
[Rzeczownik]

a set of real numbers that includes all the numbers between any two specified numbers within the set

przedział, interwał

przedział, interwał

Ex: The interval (a, b), where a and b are real numbers, represents all numbers between a and b but excludes the endpoints. 
linear function
linear function
[Rzeczownik]

a mathematical function that creates a straight line when graphed

funkcja liniowa, odwzorowanie liniowe

funkcja liniowa, odwzorowanie liniowe

Ex: In economics, supply and demand can often be modeled using linear functions to predict market behavior. 
rational function
rational function
[Rzeczownik]

a function that can be expressed as the ratio of two polynomials, where the denominator is not zero

funkcja wymierna, ułamek wymierny

funkcja wymierna, ułamek wymierny

Ex: To find the vertical asymptotes of a rational function, set the denominator equal to zero and solve for 
coordinate
coordinate
[Rzeczownik]

any set of numbers that represents an exact position on a map or graph

współrzędna, współrzędne geograficzne

współrzędna, współrzędne geograficzne

Ex: The GPS coordinates 35.6895° N, 139.6917° E lead to Tokyo. 
integer constant
integer constant
[Rzeczownik]

a fixed numerical value that is a whole number, either positive, negative, or zero

stała całkowita, stała liczby całkowitej

stała całkowita, stała liczby całkowitej

Ex: In the expression 2x+5, the integer constant is 5. 
linear equation
linear equation
[Rzeczownik]

an equation that makes a straight line when graphed

równanie liniowe, równanie prostej

równanie liniowe, równanie prostej

Ex: To solve a linear equation, you need to isolate the variable on one side of the equation. 
to correspond
to correspond
[Czasownik]

to have a direct relationship or alignment with something else, such as paired values or elements

odpowiadać, mieć bezpośredni związek z

odpowiadać, mieć bezpośredni związek z

Ex: Each point on the graph corresponds to a pair of values in the equation. 
term
term
[Rzeczownik]

a single number, variable, or the product of numbers and variables in an expression or equation, separated by addition or subtraction operators

termin, element

termin, element

Ex: Combining like terms in an algebraic expression simplifies it. 
axis
axis
[Rzeczownik]

a reference line used in coordinate systems to provide a framework for locating points

oś, linia odniesienia

oś, linia odniesienia

Ex: When graphing functions, it's essential to label the axes to provide context for the plotted points. 
polynominal function

a mathematical function that can be expressed as a sum of terms, where each term is a constant multiplied by a variable raised to a non-negative integer power

funkcja wielomianowa, funkcja polinomalna

funkcja wielomianowa, funkcja polinomalna

Ex: In algebra, students learn how to add, subtract, multiply, and factor polynomial functions. 
to satisfy
to satisfy
[Czasownik]

to fulfill the conditions or requirements of a mathematical statement, equation, or inequality

spełniać, zaspokajać

spełniać, zaspokajać

Ex: In order to prove the conjecture, we must find an example that satisfies all given conditions and demonstrates the truth of the statement. 
coefficient
coefficient
[Rzeczownik]

a numerical or constant factor that multiplies a variable in an algebraic term

współczynnik, czynnik mnożnikowy

współczynnik, czynnik mnożnikowy

Ex: The coefficient matrix in the linear system helps to simplify solving for the variable values. 
quadratic
quadratic
[Rzeczownik]

an equation where the highest power of the variable is squared

równanie kwadratowe

równanie kwadratowe

Ex: Factoring is one method to solve a quadratic, provided it can be easily factored. 
regression
regression
[Rzeczownik]

a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables

regresja

regresja

Ex: Linear regression is used to find the best-fitting line through a set of data points. 
bimodal
bimodal
[przymiotnik]

having or involving two distinct modes, peaks, or most frequent values

bimodalny, z dwoma modami

bimodalny, z dwoma modami

Ex: The bimodal distribution of exam scores indicated two groups of students with different performance levels. 
equidistant
equidistant
[przymiotnik]

having equal distances from two or more points

równoodległy, w równej odległości

równoodległy, w równej odległości

Ex: The point is equidistant from both the x-axis and the y-axis in the coordinate plane. 
collinear
collinear
[przymiotnik]

having points that lie on the same straight line

współliniowy, leżący na jednej prostej

współliniowy, leżący na jednej prostej

Ex: The three points are collinear, forming a straight line on the graph. 
theorem
theorem
[Rzeczownik]

a statement or proposition that has been proven to be true based on previously established axioms, definitions, and other theorems within a particular mathematical or logical system

twierdzenie

twierdzenie

Ex: Mathematicians often prove theorems to establish mathematical truths. 
period
period
[Rzeczownik]

a recurring interval or length associated with a mathematical function or pattern

okres, przedział

okres, przedział

Ex: The period of a trigonometric function is the length of the interval over which the function repeats its values. 
to evaluate
to evaluate
[Czasownik]

to find the numerical value of an expression, equation, or function by substituting specific values for the variables

oceniać

oceniać

Ex: Evaluating complex mathematical expressions often involves breaking down the problem into simpler steps. 
expanded notation
expanded notation
[Rzeczownik]

a way of representing numbers as the sum of each digit multiplied by its place value

zapis rozszerzony, rozkład liczbowy

zapis rozszerzony, rozkład liczbowy

Ex: Students learn expanded notation to better understand the structure and value of numbers. 
scientific notation

a method of writing numbers as the product of a coefficient and a power of 10

notacja naukowa, zapis naukowy

notacja naukowa, zapis naukowy

Ex: When discussing the size of galaxies, astronomers often use scientific notation to represent their vast distances from Earth. 
to diagram
to diagram
[Czasownik]

to represent or illustrate something using a drawing, chart, or schematic

diagramować, schemtyzować

diagramować, schemtyzować

Ex: The engineer diagrammed the new circuit design on the whiteboard. 
matrix
matrix
[Rzeczownik]

a rectangular array of numbers or symbols organized in rows and columns, commonly used in linear algebra for representing equations, transformations, and vector operations

macierz, tabela

macierz, tabela

Ex: A 2x3 matrix represents a collection of numbers organized in two rows and three columns. 
factorial
factorial
[Rzeczownik]

the product of all positive whole numbers from 1 to a given number

silnia, faktoryczna

silnia, faktoryczna

Ex: The factorial of 5 is calculated as 5!=5×4×3×2×1=120. 
vector
vector
[Rzeczownik]

an ordered set of numbers that describes both magnitude and direction, commonly used to represent quantities like displacement, velocity, or force in physics and engineering

wektor, wektor

wektor, wektor

Ex: In physics, force is often represented as a vector, considering both its magnitude and direction. 
standard coordinate plane

a two-dimensional system used to represent points in space

standardowa płaszczyzna współrzędnych, standardowa płaszczyzna kartezjańska

standardowa płaszczyzna współrzędnych, standardowa płaszczyzna kartezjańska

Ex: The standard coordinate plane provides a visual representation of mathematical relationships between variables in two dimensions. 
trigonometric function

a mathematical function that relates the angles of a triangle to the lengths of its sides, commonly including sine, cosine, and tangent

funkcja trygonometryczna

funkcja trygonometryczna

Ex: The sine and cosine trigonometric functions are fundamental in calculating wave patterns. 
augmented matrix
augmented matrix
[Rzeczownik]

a way of representing a system of linear equations in matrix form

macierz rozszerzona, macierz uzupełniona

macierz rozszerzona, macierz uzupełniona

Ex: To solve a system of linear equations using the method of Gaussian elimination, we first write the system in augmented matrix form. 
unit vector
unit vector
[Rzeczownik]

a vector that has a magnitude of 1 and represents direction without regard to scale

wektor jednostkowy, wektor o długości 1

wektor jednostkowy, wektor o długości 1

Ex: A unit vector is often employed in mathematics to define orthonormal bases and to describe geometric transformations. 
determinant
determinant
[Rzeczownik]

a single number calculated from the elements of a square matrix that indicates important properties, like whether the matrix can be inverted

wyznacznik

wyznacznik

Ex: If the determinant of a matrix is zero, the matrix is singular and does not have an inverse. 
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