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Matematika a Logika SAT - Mathematics

Zde se naučíte některá anglická slova související s matematikou, jako "proměnná", "histogram", "doména" atd., která budete potřebovat k úspěšnému složení SAT.

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SAT Vocabulary for Math and Logic
intercept
intercept
[Podstatné jméno]

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

průsečík, intercept

průsečík, intercept

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

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

rovina, plochý povrch

rovina, plochý povrch

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

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

funkce

funkce

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

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

modelovat, reprezentovat

modelovat, reprezentovat

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

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

konstanta

konstanta

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

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

výraz, vzorec

výraz, vzorec

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

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

ekvivalentní

ekvivalentní

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

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

protínat se, křížit se

protínat se, křížit se

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

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

bodový graf, rozptylový diagram

bodový graf, rozptylový diagram

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

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

přímka nejlepšího přizpůsobení, regresní přímka

přímka nejlepšího přizpůsobení, regresní přímka

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

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

proměnná

proměnná

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

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

stupnice, gradace

stupnice, gradace

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

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

obrázek, graf

obrázek, graf

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

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

definiční obor, doména

definiční obor, doména

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

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

graf, křivka

graf, křivka

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

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

histogram, sloupcový graf

histogram, sloupcový graf

interval
interval
[Podstatné jméno]

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

interval, mezera

interval, mezera

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
[Podstatné jméno]

a mathematical function that creates a straight line when graphed

lineární funkce, lineární zobrazení

lineární funkce, lineární zobrazení

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

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

racionální funkce, racionální zlomek

racionální funkce, racionální zlomek

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

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

souřadnice, zeměpisné souřadnice

souřadnice, zeměpisné souřadnice

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

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

celočíselná konstanta, konstanta celého čísla

celočíselná konstanta, konstanta celého čísla

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

an equation that makes a straight line when graphed

lineární rovnice, rovnice přímky

lineární rovnice, rovnice přímky

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

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

odpovídat, mít přímý vztah k

odpovídat, mít přímý vztah k

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

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

termín, prvek

termín, prvek

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

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

osa, referenční čára

osa, referenční čára

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

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

polynomiální funkce, mnohočlenná funkce

polynomiální funkce, mnohočlenná funkce

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

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

splnit, uspokojit

splnit, uspokojit

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
[Podstatné jméno]

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

koeficient, násobitelný faktor

koeficient, násobitelný faktor

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

an equation where the highest power of the variable is squared

kvadratická rovnice

kvadratická rovnice

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

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

regrese

regrese

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

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

bimodální, s dvěma režimy

bimodální, s dvěma režimy

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

having equal distances from two or more points

stejně vzdálený, ve stejné vzdálenosti

stejně vzdálený, ve stejné vzdálenosti

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

having points that lie on the same straight line

kolineární, ležící na stejné přímce

kolineární, ležící na stejné přímce

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

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

věta

věta

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

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

perioda, interval

perioda, interval

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

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

vyhodnotit

vyhodnotit

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

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

rozvinutý zápis, numerický rozklad

rozvinutý zápis, numerický rozklad

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

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

vědecká notace, vědecký zápis

vědecká notace, vědecký zápis

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

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

diagramovat, schematizovat

diagramovat, schematizovat

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

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

matice, tabulka

matice, tabulka

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

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

faktoriál, faktoriál

faktoriál, faktoriál

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

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

vektor, vektor

vektor, vektor

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

a two-dimensional system used to represent points in space

standardní souřadnicová rovina, standardní kartézská rovina

standardní souřadnicová rovina, standardní kartézská rovina

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

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

trigonometrická funkce

trigonometrická funkce

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

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

rozšířená matice, augmentovaná matice

rozšířená matice, augmentovaná matice

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
[Podstatné jméno]

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

jednotkový vektor, vektor o velikosti 1

jednotkový vektor, vektor o velikosti 1

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

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

determinant

determinant

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