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SAT Math and Logic - Arithmetic and Statistics

Here you will learn some English words related to arithmetic and statistics, such as "divisible", "range", "median", etc. that you will need to ace your SATs.

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SAT Vocabulary for Math and Logic
mixed number

a combination of a whole number and a proper fraction

Ex: When working with measurements, such as lengths or amounts, we often encounter mixed numbers instead of whole numbers. 
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prime number

a number greater than 1 with only two devisors which can be itself or 1

Ex: 7 is a prime number because its only divisors are 1 and 7. 
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rational number

a number that can be written as a fraction, where both the top and bottom are whole numbers, and the bottom is not zero

Ex: 3/4 is a rational number because it can be written as a fraction of two integers. 
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irrational number

a number incapable of being expressed as a ratio of two integers

Ex: The square root of 2 is an irrational number. 
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complex number

a number that has both a real part and a part involving a unit that, when squared, gives a negative result

Ex: Multiplying a complex number by its conjugate results in a real number. 
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real number

any number that can be found on the number line, including both positive and negative numbers, zero, and fractions

Ex: The number 5 is a real number because it can be located on the number line. 
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whole number

any positive number without fractions or decimals, including zero

Ex: The numbers 0, 1, 2, 3, and so on are all whole numbers. 
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integer
integer
[noun]

any number without fractions or decimals, including positive numbers, negative numbers, and zero

Ex: The numbers -3, 0, and 7 are all integers. 
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fraction
fraction
[noun]

a number obtained by dividing one integer or rational number by another, typically written in the form a/b

Ex: One-half (1/2) is a simple fraction. 
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decimal
decimal
[noun]

(mathematics) a number less than one, called a fraction, that is represented as a period followed by the number of tenths, hundredths, etc.

Ex: In mathematics, decimals are a way to represent fractions or portions of a whole using a decimal point. 
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improper fraction

a fraction where the the top number is greater than or equal to the equal to the bottom number

Ex: To compare improper fractions, you can convert them to decimal form. 
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mean
mean
[noun]

(mathematics) the average value of a set of quantities calculated by adding them, and dividing them by the total number of the quantities

Ex: To find the mean of 4, 6, and 8, add them together and divide by 3. 
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divisible
divisible
[Adjective]

having the quality of being divided, especially by a number

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root
root
[noun]

a value that, when multiplied by itself a specified number of times, results in the given number

Ex: The square root of 16 is 4. 
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range
range
[noun]

the difference between the highest and lowest values in a set of numbers

Ex: The range of exam scores in the class was 40 points, from a low of 55 to a high of 95. 
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square
square
[noun]

the second exponent of any given number produced when multiplied by itself

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average
average
[Adjective]

calculated by adding a set of numbers together and dividing this amount by the total number of amounts in that set

Ex: His average score in math class is 85%. 
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solution
solution
[noun]

a correct answer to a problem in mathematics or a puzzle

Ex: After careful analysis, she found the solution to the complex algebraic equation. 
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product
product
[noun]

the result of multiplying two or more numbers or quantities together

Ex: The product of 3 and 4 is 12. 
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quotient
quotient
[noun]

the result obtained by dividing one quantity or number by another, expressed as the outcome of a division operation

Ex: In the division problem 12 ÷ 4, the quotient is 3. 
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factor
factor
[noun]

(mathematics) one of the numbers that another number can be divided by

Ex: A factor of a number divides it evenly without leaving a remainder. 
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value
value
[noun]

(mathematics) an amount that is shown by a sign or letter

Ex: In algebra, variables represent unknown values that can be determined through equations. 
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inequality

a statement that compares two quantities, expressions, or values and indicates their relative sizes

Ex: The inequality x>5 represents all real numbers greater than 5. 
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equation
equation
[noun]

(mathematics) a statement indicating the equality between two values

Ex: In algebra, solving equations involves finding the values of variables that satisfy the equality stated. 
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minimum
minimum
[noun]

the lowest amount, degree, or extent there is or is possible, allowed or required

Ex: We need to keep disruptions to a minimum during the construction process. 
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exponential

a mathematical expression where a number is multiplied by itself a certain number of times determined by a variable

Ex: In population studies, the growth can often be modeled by an exponential. 
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linear
linear
[Adjective]

related to equations that create straight lines when graphed, indicating a constant rate of change

Ex: In this math problem, we need to solve a set of linear equations to find the values of x and y. 
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common ratio

the constant ratio between consecutive terms

Ex: In the geometric sequence 2, 6, 18, 54, ..., the common ratio between consecutive terms is r=3. 
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common multiple

a number that is a multiple of two or more given numbers

Ex: The smallest common multiple of 4 and 5 is 20. 
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common factor

a number that divides exactly into two or more given numbers without leaving a remainder

Ex: The common factors of 12 and 18 include 1, 2, 3, and 6. 
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common denominator

(mathematics) a number divisible by all the numbers that are below the line in a set of fractions

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least common denominator

the smallest positive integer that is a common multiple of the denominators of two or more fractions

Ex: Finding the least common denominator is a crucial step in solving problems that involve multiple fractions. 
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probability

(mathematics) a number representing the chances of something specific happening

Ex: The probability of rolling a six on a fair die is one-sixth. 
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to estimate

to guess the value, number, quantity, size, etc. of something without exact calculation

Ex: I estimate that there are about 100 people at the party. 
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arithmetic sequence

a sequence of numbers in which the difference between any two consecutive terms is constant

Ex: In the arithmetic sequence 2, 5, 8, 11, 14, ..., each term increases by 3, which is the common difference. 
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frequency
frequency
[noun]

the number of times a particular event occurs within a specific period or among a set of observations

Ex: The frequency of heads in 100 coin flips was 52. 
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distribution

(statistics) an arrangement of values of a variable showing how often each occurs, either observed or theoretical

Ex: The histogram shows the distribution of exam scores. 
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median
median
[noun]

a statistical measure that represents the middle value of a data set when the values are arranged in ascending or descending order

Ex: In the set {2, 5, 8, 10, 12}, the median is 8, as it is the middle value when arranged in ascending order. 
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mode
mode
[noun]

the value that appears most frequently in a data set

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bimodal
bimodal
[Adjective]

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

Ex: The bimodal distribution of exam scores indicated two groups of students with different performance levels. 
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standard deviation

a measure of how much the values in a set typically differ from the average

Ex: A low standard deviation indicates that the data points are close to the mean. 
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margin of error

the range within which the true value is expected to fall, accounting for potential inaccuracies in measurement or sampling

Ex: The poll results have a margin of error of ±3%, indicating the possible range of true public opinion. 
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random
random
[Adjective]

occurring in such a way that each possible outcome has a certain probability of occurring, but the specific outcome cannot be predicted with certainty

Ex: A random sample is selected from the population in such a way that each member has an equal chance of being chosen. 
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trend line

a straight line drawn through a set of data points on a graph to represent the general direction or pattern of the data

Ex: The trend line on the stock chart indicates a steady increase in prices over the past year. 
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dot plot
dot plot
[noun]

a type of statistical chart consisting of dots that represent individual data points

Ex: The teacher used a dot plot to show the distribution of test scores in the class. 
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linear model

a mathematical representation that describes the relationship between two or more variables using a linear equation

Ex: The linear model y=2x+3 suggests that for every unit increase in x, y increases by 2. 
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