All SAT Math Terms

Definition:

Distance from zero. The absolute value can never be negative.

Example:

“|-17| = 17 and |42| = 42”

Definition:

A portion of the circumference of a circle. If the circle was a pizza, your slice would be a sector, and the crust on your slice would be an arc.

Example:

“The curved edge of a pizza slice”

Definition:

The bottom (and sometimes the top) of a 3-D geometric figure.

Example:

“The base of a cylinder is a circle”

Definition:

A 3-D figure with a length, width, and height, and where all the angles are right. This is also called a rectangular prism, and, if the three dimensions are all equal, it is a cube.

Example:

“A shoebox or dice”

Definition:

The set of all points in a plane that are equidistant from a given point (aka, the center). A point is on the circle if it is on the circumference. A point is in the circle if it is in the area enclosed by the circumference.

Example:

“A perfect round shape”

Definition:

The point from which all points on a circle are equidistant. The center is in the circle, but not on the circle. All the radii start at the center, and the center is the midpoint of every diameter.

Example:

“The middle point of a circle”

Definition:

A number that is a mix of the real and the imaginary. It is given in the form a + bi, where a is the real part and bi is the imaginary part.

Example:

“3 + 4i”

Definition:

A 3-D shape with a circular base on the bottom and a point on the top. A right circular cone means the point is directly above (or directly below) the center of the circular base.

Example:

“An ice cream cone”

Definition:

A way to describe the level of uncertainty when a statistic about a population is being estimated by a sampling from that population. The confidence interval gives an upper and lower boundary between which you are a certain percent sure the true value falls.

Example:

“Amy polled 100 people and asked them how they would vote in next week's election. 52% of them said they would vote for her. As a result, she is 90% sure that she will get between 47% and 57% of the vote on election day.”

Definition:

Two binomials in the form (a + b)(a - b). When you multiply conjugates, you will get a difference of squares. When you multiply complex conjugates (a + bi)(a - bi), you will magically turn something imaginary into something real!

Example:

“(x + 3)(x - 3) = x² - 9”

Definition:

In a row, without skipping over any items.

Example:

“14, 15, and 16 are consecutive integers; 19, 21, and 23 are consecutive odd integers”

Definition:

(1) The term of a polynomial that doesn't have a variable at all. (2) A parameter in a function that will always hold the same value, even for different points on the function.

Example:

“In the polynomial 15x² - 19x + 7, the constant is 7. In y = 5x - 9, the constants are 5 and -9.”

Definition:

A way to describe the trend in bivariate data. If the line of best fit has a positive slope, there is a positive correlation, and if the line of best fit has a negative slope, there is a negative correlation.

Example:

“Strong positive correlation between study time and test scores”

Definition:

In a right triangle, the ratio between the side adjacent to a given angle and the hypotenuse.

Example:

“cos x = adjacent/hypotenuse”

Definition:

A 3-D geometric figure with two circular bases. It looks a lot like a soda can.

Example:

“A soda can or pipe”

Definition:

Getting smaller. A function is decreasing when, if you trace along the function from left to right, you are going in a downward direction.

Example:

“A downward sloping line”

Definition:

(1) A way to describe a polynomial by giving the highest exponent. (2) A unit used to measure an angle.

Example:

“15x⁷ - 12x⁴ + 3x - 1 is a 7th degree polynomial. A right angle has 90°.”

Definition:

The amount of money put into a bank account. This does not include any interest earned on that money.

Example:

“Jack opens up a new bank account and makes an initial deposit of $100.”

Definition:

The longest distance from one side of a circle to another. The diameter is twice the radius and will always go through the center of its circle.

Example:

“The width of a circle”

Definition:

All the values of x you can use in a function. Most functions have an infinite domain; the exceptions are rational functions, where you have to make sure the denominator will not be zero, and radical functions, where you have to make sure the value under the square root is ≥ 0.

Example:

“The domain of f(x) = -7x² - 4 is infinite because you can plug in any x value at all and get an answer.”

Definition:

The individual items in a set

Example:

“The set {-7, 7} has two elements.”

Definition:

A mathematical statement that includes an equal sign.

Example:

“2x + 3 = 7”

Definition:

Equal to, or the same as.

Example:

“½ = 0.5 = 50%”

Definition:

Something that is getting smaller at an ever decreasing-rate. This is represented by a curve that starts off with a steep drop, but eventually levels off.

Example:

“Starting with a value such as 300 and cutting it in half over and over. The function f(x) = 300(0.5ˣ) models this situation.”

Definition:

Something that is growing at an ever-increasing rate. This is represented by a curved line that starts off almost flat, but eventually gets very steep.

Example:

“Starting with the number 5, and doubling it over and over. The function f(x) = 5(2ˣ) models this example.”

Definition:

A mathematical statement consisting of numbers, variables, and/or operations that does not have an equal sign or inequality. Expressions cannot be solved; they can only be simplified.

Example:

“3x + 2y - 7”

Definition:

An acronym that describes the process of multiplying two binomials. It stands for Firsts, Outers, Inners, Lasts.

Example:

“(x² + 3)(2x - 5) = 2x³ - 5x² + 6x - 15”

Definition:

A mathematical description of the relationship between two variables. Typically, x is the input, and f(x) is the output. For a relation to be a function, there must be exactly one value of f(x) for each value of x.

Example:

“f(x) = 2x - 1 is an example of a linear function”

Definition:

A visual representation of the relationship between two variables. On the SAT, you will be analyzing graphs of functions and relations that are shown on the xy-plane.

Example:

“A line, curve, or other shape plotted on coordinate axes”

Definition:

The measurement from the bottom to the top, along a vertical line.

Example:

“The height of a building”

Definition:

The side of a right triangle that is opposite the right angle. It will always be the longest side of the right triangle.

Example:

“The longest side in a right triangle”

Definition:

The value that is equal to √-1 and is represented in math as i. In the real world, you can't take the square root of -1. When you're taking the SAT, make sure you know that i² = -1.

Example:

“i, 2i, 3 + 4i”

Definition:

Getting larger. A function is increasing when, if you trace along the function from left to right, you are going in an upward direction.

Example:

“An upward sloping line”

Definition:

A statement describing the relationship between two expressions. There are 5 inequalities in math: <, ≤, >, ≥, and ≠.

Example:

“x > 5, y ≤ 10”

Definition:

All whole numbers and their opposites. Integers can be positive or negative, but cannot be fractions or have decimals.

Example:

“5, -15, 92, and 0 are all integers. However, ½, 5.692, and √2 are not integers.”

Definition:

The points at which the graph of a function crosses over one of the axes. The y-intercept will have coordinates (0,y) and the x-intercept, (x, 0).

Example:

“The y-intercept of y = 2x + 3 is (0, 3)”

Definition:

The money a bank will give you as a 'thank you' for saving your money at their institution. Simple interest is money given to you rather than deposited back into your account. Compounded interest is when the interest you earn is deposited into your account, and you start to gain interest on that interest.

Example:

“5% annual interest on a $1000 savings account”

Definition:

A triangle with two equal sides. Isosceles triangles will have two congruent base angles and one different vertex angle. Isosceles right triangles will be 45-45-90 triangles.

Example:

“A triangle with two sides of length 5 and one side of length 3”

Definition:

A geometric figure that extends infinitely in two directions and does not change direction.

Example:

“A straight line that goes on forever”

Definition:

A line drawn on a scatterplot to show the general trend of the data. The slope of your line of best fit would tell you if there is a positive or negative correlation to the data.

Example:

“A line that best represents the trend in scatterplot data”

Definition:

A relationship that has a constant slope. Equations in the form y = mx + b are linear.

Example:

“y = 2x + 3”

Definition:

A way to describe the level of uncertainty when a statistic about a population is being estimated by a sample from that population. The margin of error can be easily converted to a confidence interval, and vice versa.

Example:

“Amy polled 100 people and asked them how they would vote in next week's election. 52% of them said they would vote for her. So, she estimates she will get 52% of the vote with a margin of error of ±5%.”

Definition:

(1) The largest value in a set of data. (2) The y-value of the highest point in a function.

Example:

“The maximum value in {1, 5, 3, 9, 2} is 9”

Definition:

A statistic calculated by adding up all the numbers in a set and dividing by how many values were in that set. The mean is also called the average and describes the center of the data.

Example:

“The mean of {2, 4, 6, 8} is (2+4+6+8)/4 = 5”

Definition:

A statistic arrived at by putting the data in ascending order and selecting the middle number. If there are an even number of data points, the median is calculated by adding the two numbers in the center and then dividing by two.

Example:

“The median of {1, 3, 5, 7, 9} is 5. The median of {1, 3, 5, 7} is (3+5)/2 = 4”

Definition:

(1) The smallest value in a set of data. (2) The y-value of the lowest point in a function.

Example:

“The minimum value in {1, 5, 3, 9, 2} is 1”

Definition:

A mathematical equation that describes how variables relate to each other in the real world.

Example:

“The model H = 1.88L + 32.02 can be used by archeologists to estimate a person's total height (H) from the length of the femur (L), where H and L are both in inches.”

Definition:

A number or numbers in a set that just don't seem to belong with all the other numbers because they are much larger or much smaller than the rest of the group.

Example:

“In the set {5, 7, 52, 58, 59, 62, 71, 80}, 5 and 7 are outliers.”

Definition:

The 'U' shaped curve that results from graphing a quadratic function.

Example:

“The graph of y = x²”

Definition:

In geometry, two lines in the same plane that will never intersect. In coordinate geometry, two lines that have equal slopes. In a system of equations, two lines that have no solution.

Example:

“Railroad tracks”

Definition:

The expression of a decimal or fraction as a number out of 100.

Example:

“0.5 is the same thing as ½, which are both the same thing as 50%.”

Definition:

In geometry, two lines in a plane that meet at a right angle. In coordinate geometry, two lines whose slopes are opposite reciprocals.

Example:

“The corner of a square”

Definition:

A number in math that represents the ratio between the circumference of a circle and its diameter. It is an irrational number, but we usually round it to 3.14 or use the fraction 22/7.

Example:

“π ≈ 3.14159...”

Definition:

All of the elements in a group.

Example:

“The USA has a population of approximately 329 million people.”

Definition:

The result of multiplication

Example:

“The product of 5 and 6 is 30.”

Definition:

A 3-D geometric shape that has a polygonal base and comes to a point at the top. The sides are all triangles.

Example:

“The Great Pyramid of Giza”

Definition:

An equation relating the three sides of a right triangle. Specifically, it is a² + b² = c² where a and b are the legs and c is the hypotenuse.

Example:

“In a 3-4-5 triangle: 3² + 4² = 5², so 9 + 16 = 25”

Definition:

Sets of three integers that satisfy the Pythagorean theorem. The triples you should know for the SAT are 3-4-5 and 5-12-13.

Example:

“3-4-5, 5-12-13, 8-15-17”

Definition:

The result of division

Example:

“The quotient of 20 and 5 is 4. (Note that order is important. The quotient of 5 and 20 is ¼.)”

Definition:

A unit of measurement for angles. A right angle is π/2 radians, a straight angle is π radians, and a whole circle is 2π radians.

Example:

“Imagine there is a circle painted on the ground that has a radius of 4 feet. If you were to start at one point on the circle and walk along the circumference for 4 feet, then you will have walked along one radian, or about 57.3°, of the circle.”

Definition:

The distance between the center of any circle and any point on that circle. The radius is half of the diameter.

Example:

“The distance from the center of a circle to its edge”

Definition:

(1) A statistic calculated by subtracting the smallest value from the largest value. (2) All possible y-values for a given function.

Example:

“The range of f(x) = x² + 7 is from 7 to positive infinity.”

Definition:

A way to describe the comparison of two separate measurements, such as in miles per hour, dollars per gallon, or pages per minute.

Example:

“60 miles per hour, $3.50 per gallon”

Definition:

A comparison of two numbers, usually written as a fraction or in the form a:b.

Example:

“If there are 2 watermelons and 15 pumpkins in a field, then the ratio of watermelons to pumpkins is 2:15.”

Definition:

Any number that can be located on a number line. All positives, negatives, decimals, and zero are real numbers. The only numbers that aren't real are imaginary numbers.

Example:

“5, -3, 0.5, √2, π”

Definition:

A 4 sided figure with 4 right angles. Find the perimeter by adding up the 4 sides, and find the area by multiplying length by width.

Example:

“A door or window”

Definition:

A geometric shape where all the sides are equal, and all the angles are equal. A regular triangle is an equilateral triangle. A regular quadrilateral is a square.

Example:

“A square, equilateral triangle, regular pentagon”

Definition:

The number 'left over' when you divide two numbers.

Example:

“When you divide 13 by 5 you get 2 with a remainder of 3. (5×2=10, plus 3 more to get to 13.)”

Definition:

An angle of exactly 90°, or a shape that includes an angle of 90°.

Example:

“The corner of a square”

Definition:

(1) A number that when multiplied by itself a certain number of times results in the given value. (2) Another word for the zeros or x-intercepts of a polynomial function.

Example:

“The square root of 100 is 10 and the 5th root of 32 is 2.”

Definition:

A subset of a population.

Example:

“Makenzie wants to know how the kids in her school feel about wearing uniforms, so she talks to a sample of 20 students randomly selected from the student body.”

Definition:

The process a researcher uses to collect data from a portion of a population. This could be accomplished by making observations, running an experiment, or conducting a survey.

Example:

“Random sampling, stratified sampling, cluster sampling”

Definition:

Causes an equation to be true

Example:

“The value of x that satisfies 3x + 9 = 12 is 1.”

Definition:

A method of displaying bivariate data by graphing each pair of numbers as a point with an x and y coordinate.

Example:

“If you gathered information on how much time your classmates spent studying for a math quiz and each one's grade on the quiz, you could then graph your data on an xy-plane.”

Definition:

A portion of the area of a circle. If the circle was a pizza, your slice would be a sector, and the crust on your slice would be an arc.

Example:

“A pizza slice”

Definition:

Two triangles that are the same shape, but not necessarily the same size. Their angles will be equal, but their sides will be proportional.

Example:

“Two triangles with the same angles but different sizes”

Definition:

In a right triangle, the ratio between the side opposite a given angle and the hypotenuse.

Example:

“sin x = opposite/hypotenuse”

Definition:

A mnemonic to help you remember three important formulas in trigonometry. sin x = opposite/hypotenuse, cos x = adjacent/hypotenuse, and tan x = opposite/adjacent.

Example:

“SOH: Sine = Opposite/Hypotenuse, CAH: Cosine = Adjacent/Hypotenuse, TOA: Tangent = Opposite/Adjacent”

Definition:

(1) The value of a variable that makes an equation true. (2) The point(s) at which the graphs of two or more functions cross.

Example:

“The solution of 5x - 7 = -2 is x = 1.”

Definition:

All possible values of the variable

Example:

“If |x| = 7, then x can equal 7 or -7, and the solution set is {-7, 7}.”

Definition:

Triangles with angles of 30°-60°-90° or with angles of 45°-45°-90°. These triangles are special because if you are given the length of any one of the sides, you can figure out the other two sides.

Example:

“A 30-60-90 triangle with sides in the ratio 1:√3:2”

Definition:

The set of all points in 3-D space that are equidistant from a given point. That given point is the center of the sphere.

Example:

“A basketball or globe”

Definition:

A statistic that describes how spread out the data is. A low standard deviation means the data are gathered close to the mean, while a high standard deviation means that there are data points pretty far to the left and the right of the center.

Example:

“Data with values {1, 2, 3, 4, 5} has a lower standard deviation than {1, 1, 1, 5, 5, 5}”

Definition:

The result of adding two or more values.

Example:

“The sum of 1 and 1 is 2.”

Definition:

Multiple equations for which there are multiple unknown variables. For instance, if x and y are both unknowns, you need to have two equations to solve for them.

Example:

“2x + 3y = 7 and x - y = 1”

Definition:

Data that is organized into rows and columns.

Example:

“A spreadsheet or data chart”

Definition:

(1) In a right triangle, the ratio between the side opposite a given angle and side adjacent to that angle. (2) A line that touches a circle but doesn't go inside the circle.

Example:

“tan x = opposite/adjacent”

Definition:

A quadrilateral with exactly one pair of parallel sides, called the bases. If one of the sides is perpendicular to the bases, it is a right trapezoid. If the two non-parallel sides are congruent, it is an isosceles trapezoid.

Example:

“A shape like a table with one pair of parallel sides”

Definition:

A 2-D shape with three sides and three angles. The three angles will always add up to 180°.

Example:

“Any three-sided shape”

Definition:

This is what we say when someone tries to divide by zero or tries to describe the slope of a vertical line.

Example:

“The slope of a vertical line is undefined”

Definition:

The set of elements that are in either one of two given sets.

Example:

“The union of {1, 2, 3} and {3, 4, 5} is {1, 2, 3, 4, 5}”

Definition:

Numbers that the variable is able to represent.

Example:

“The values of x that satisfy x² = 9 are 3 and -3.”

Definition:

An easy way to tell if a graph is a function. If you can draw a vertical line that passes through the graph in more than one place, then it's not a function.

Example:

“A circle fails the vertical line test because a vertical line can pass through it twice”

Definition:

A measurement of how much space is inside a 3-D figure. The units that describe volume will be cubic (in³, ft³, cm³) or volume specific (gallon, Liter).

Example:

“The volume of a box is length × width × height”

Definition:

An object's mass times the acceleration due to gravity. Common units for weight are pounds (lbs) and Newtons (N).

Example:

“A person's weight on Earth vs. the Moon”

Definition:

The horizontal baseline in the coordinate xy-plane.

Example:

“The horizontal line on a graph”

Definition:

A two dimensional system in which the exact location of any point can be described by giving its distance from the baseline horizontal and vertical axes.

Example:

“A coordinate plane with x and y axes”

Definition:

The vertical baseline in the coordinate xy-plane.

Example:

“The vertical line on a graph”

Definition:

Another word for the roots or x-intercepts of a polynomial function. Find the zeros by setting the function equal to zero and solving.

Example:

“The zeros of f(x) = x² - 4 are x = 2 and x = -2”