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SAT Math and Logic - Mathematics

Here you will learn some English words related to mathematics, such as "variable", "histogram", "domain", etc. that you will need to ace your SATs.

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SAT Vocabulary for Math and Logic
intercept
[noun]

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

Ex: The graph clearly shows intercepts where the function crosses the axes .
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plane
[noun]

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

Ex: planes is fundamental to the study of three-dimensional shapes and spaces .
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function
[noun]

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

Ex: Statisticians analyze data functions such as mean , median , and standard deviation to understand distributions and trends .
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to model
[Verb]

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

Ex: modeling the financial system , they were able to predict the economic impact of the policy changes .
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constant
[noun]

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

Ex: In a mathematical formula , constant does not change , unlike a variable .
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a combination of numbers, variables, operations, and grouping symbols that collectively represent a numerical value or relationship

Ex: Euler ’s formula , ( e^{ipi } + 1 = 0 ) , is often cited as a beautiful expression due to its simplicity and depth .
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equivalent
[Adjective]

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

Ex: The decimal 0.75 and the fraction 3/4 equivalent because they represent the same quantity .
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to meet or cross another path, line, etc. at a particular point

Ex: The paths of the two intersected in the dense forest .
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a type of graph used in statistics and data analysis to display and compare two sets of numerical data

Ex: scatter plot helped the scientists visualize the spread of the experimental results .
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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

Ex: The software automatically calculates and displays line of best fit on the graph .
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variable
[noun]

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

Ex: In statistical analysisvariables can be classified as independent or dependent , depending on their role in the study .
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scale
[noun]

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

Ex: The scale is commonly used in surveys to gauge responses .
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figure
[noun]

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

Ex: figure in the article provided a visual representation of the survey results .
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domain
[noun]

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

Ex: The teacher asked the students to identify domain of each function on their homework .
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graph
[noun]

(mathematics) a set of points whose coordinates are in agreement with one another

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histogram
[noun]

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

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interval
[noun]

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

Ex: interval like [ 2 , 2 ] includes only the number 2 , as both endpoints are the same .
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a mathematical function that creates a straight line when graphed

Ex: The relationship between distance and time in uniform motion can be described by a linear function.
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a function that can be expressed as the ratio of two polynomials, where the denominator is not zero

Ex: When graphing a rational function, it's important to identify any asymptotes and intercepts to understand its behavior.
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any set of numbers that represent an exact position on a map or graph

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

Ex: The formula calculates the area of a square by multiplying the length of its side by itself , without needing integer constant.
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an equation that makes a straight line when graphed

Ex: The teacher explained how to convert a standard linear equation to slope-intercept form .
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to have a direct relationship or alignment with something else, such as paired values or elements

Ex: In the table of values , each corresponds to a different solution of the linear equation .
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term
[noun]

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

Ex: Each term in the arithmetic series is obtained by adding a constant difference to the term.
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axis
[noun]

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

Ex: When solving equations, it's common to plot the functions on a graph to visualize their behavior relative to the axes.
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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

Ex: The division algorithm for polynomials allows you to divide one polynomial function by another.
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to fulfill the conditions or requirements of a mathematical statement, equation, or inequality

Ex: The inequality y>2x is satisfied by all points above the line represented by the equation y=2x.
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a numerical or constant factor that multiplies a variable in an algebraic term

Ex: When combining like terms in 3p+2p , coefficients are added to get 5p .
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quadratic
[noun]

an equation where the highest power of the variable is squared

Ex: The roots of the quadratic x2 − 4 = 0 are x=2 and x=−2.
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a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables

Ex: regression can model relationships that are not linear .
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bimodal
[Adjective]

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

Ex: bimodal curve on the graph suggests the presence of two dominant traits in the population .
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equidistant
[Adjective]

having equal distances from two or more points

Ex: The lighthouse was built at equidistant point from the surrounding islands .
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collinear
[Adjective]

having points that lie on the same straight line

Ex: The architect ensured that the columns in the design collinear for aesthetic balance .
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theorem
[noun]

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

Ex: Students often encounter theorems while studying advanced mathematics .
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period
[noun]

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

Ex: In the Fourier series expansion of a function, the period plays a fundamental role in determining the coefficients of the trigonometric terms.
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to find the numerical value of an expression, equation, or function by substituting specific values for the variables

Ex: evaluate the expression 2x+3 when x=5 , substitute x=5 into the expression to get 2(5)+3=13 .
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a way of representing numbers as the sum of each digit multiplied by its place value

Ex: expanded notation, each digit of a number is represented by its place value , such as hundreds , tens , and ones .
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a method of writing numbers as the product of a coefficient and a power of 10

Ex: Engineers scientific notation when describing the dimensions of nanoscale structures in microelectronics and materials science .
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to represent or illustrate something using a drawing, chart, or schematic

Ex: The project diagrammed the timeline to keep everyone on track with deadlines .
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matrix
[noun]

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

Ex: Matrix addition and subtraction are performed element-wise , combining corresponding elements of matrices.
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factorial
[noun]

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

Ex: Factorials are essential in the binomial theorem for expanding expressions .
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vector
[noun]

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

Ex: The force exerted by a tensioned rope can be represented as vector in mechanics .
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a two-dimensional system used to represent points in space

Ex: In physics , vectors are often represented as arrows on standard coordinate plane.
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a mathematical function that relates the angles of a triangle to the lengths of its sides, commonly including sine, cosine, and tangent

Ex: By using the trigonometric function, we can determine the angle from a given ratio of sides .
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a way of representing a system of linear equations in matrix form

Ex: The entries in augmented matrix correspond to the coefficients of the variables and the constants in the system of equations .
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a vector that has a magnitude of 1 and represents direction without regard to scale

Ex: To describe the direction of a force in physics , we often use unit vector representing the direction without considering the magnitude .
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a single number calculated from the elements of a square matrix that indicates important properties, like whether the matrix can be inverted

Ex: In linear algebra , determinant is used to determine the volume scaling factor of the linear transformation described by the matrix .
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