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ACT Math and Assessment - Math

Here you will learn some English words related to math, such as "histogram", "theorem", "matrix", etc. that will help you ace your ACTs.

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ACT Vocabulary for Math and Assessment
function
function
[noun]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

a symbol that represents any number between 0 and 9

Ex: In mathematics, figures are used to express numerical values. 
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domain
domain
[noun]

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

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

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

Ex: The function's graph showed a clear linear pattern. 
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diagram
diagram
[noun]

a graphic design intended to explain something

Ex: The teacher used a diagram to explain the structure of the cell. 
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histogram
histogram
[noun]

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

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scatter plot

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

Ex: The scatter plot revealed a positive correlation between hours of study and exam scores. 
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intercept
intercept
[noun]

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

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

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

Ex: In geometry, a plane is defined by three non-collinear points. 
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coordinate

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

Ex: The GPS coordinates 35.6895° N, 139.6917° E lead to Tokyo. 
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line of best fit

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 line of best fit on the scatter plot showed a clear upward trend. 
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to intersect

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

Ex: The two roads intersect at the traffic light. 
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interval
interval
[noun]

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

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

a mathematical function that creates a straight line when graphed

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

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

Ex: To find the vertical asymptotes of a rational function, set the denominator equal to zero and solve for 
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integer constant

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

Ex: In the expression 2x+5, the integer constant is 5. 
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nonlinear
nonlinear
[Adjective]

not following a straight or predictable line, sequence, or pattern

Ex: The growth of the economy is often nonlinear, influenced by numerous factors. 
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to correspond

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

Ex: Each point on the graph corresponds to a pair of values in the equation. 
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term
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: Combining like terms in an algebraic expression simplifies it. 
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axis
axis
[noun]

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

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

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

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

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

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

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

an equation where the highest power of the variable is squared

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

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

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

having equal distances from two or more points

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

having points that lie on the same straight line

Ex: The three points are collinear, forming a straight line on the graph. 
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theorem
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: Mathematicians often prove theorems to establish mathematical truths. 
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period
period
[noun]

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

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

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

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

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

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

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

Ex: When discussing the size of galaxies, astronomers often use scientific notation to represent their vast distances from Earth. 
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matrix
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: A 2x3 matrix represents a collection of numbers organized in two rows and three columns. 
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determinant

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

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

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

Ex: The factorial of 5 is calculated as 5!=5×4×3×2×1=120. 
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vector
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: In physics, force is often represented as a vector, considering both its magnitude and direction. 
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standard coordinate plane

a two-dimensional system used to represent points in space

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

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

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

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

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

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

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