Mathematics Dictionary of Mathematics Definitions

An abacus has beads that slide on rods. It can be used to count, add, subtract, multiply and more.

The horizontal ("x") value in a pair of coordinates. How far along the point is.
Always written first in an ordered pair of coordinates such as (12,5).
In this example, the value "12" is the abscissa.
(The second value "5" shows how far up or down and is called the Ordinate)

The difference between the actual and measured value.
Shown as a positive value.
Example: When your instrument measures in "1"s, then any value between 6½ and 7½ is measured as "7", so the absolute error is ½.

How far a number is from zero.
Examples: 6 is 6 away from zero, so the absolute value of 6 is 6 −6 is 6 away from zero, so the absolute value of −6 is 6
In other words it is the magnitude of a number, no negatives allowed.
The symbol "|" is placed either side to mean "Absolute Value", so we write: |−6| = 6

How fast velocity changes.
Usually measured as m/s² ("meters per second squared").
Example: going from 5 m/s (5 meters per second) to 6 m/s in exactly one second is an acceleration of 1 meter per second per second.
And two lots of "per second" becomes "per second squared".
So the acceleration is 1 m/s².

How close a measured value is to the actual (true) value.

A US Standard Unit of area, usually used to measure land.
1 acre = 4,840 square yards.
1 acre is about 0.4 hectares in the Metric system, or exactly 4,046.8564224 square meters.

An angle less than 90° (90° is called a Right Angle)

A triangle that has all angles less than 90° (90° is a Right Angle)

The numbers to be added together are called the "Addends"

Addition is bringing two or more numbers (or things) together to make a new total.

The "Additive Identity" is 0, because adding 0 to a number does not change it: a + 0 = 0 + a = a

Lying next to each other.

Two angles that have a common side and a common vertex (corner point), and don't overlap.

Algebra uses letters (like x or y) or other symbols in place of values, and then plays with them using special rules.
Example: x + 3 = 7 "x" is used in place of a value we don't know yet and is called the "unknown" or the "variable".
In this case the value of "x" can be found by subtracting 3 from both sides of the equal sign like this:
Start with: x + 3 = 7 Subtract 3 from both sides: x + 3 − 3 = 7 − 3 Calculate: x + 0 = 4 Answer: x = 4

A step-by-step solution.
Each step has clear instructions. Like a recipe.
Example: one algorithm for adding two digit numbers is: 1. add the tens 2. add the ones 3. add the numbers from steps 1 and 2
So to add 15 and 32 using that algorithm: 1. add 10 and 30 to get 40 2. add 5 and 2 to get 7 3. add 40 and 7 to get 47
Long Division is another example of an algorithm: when you follow the steps you get the answer.
Computers use algorithms all the time.
"Algorithm" is named after the 9th century Persian mathematician Al-Khwarizmi.

When two lines are crossed by another line (the Transversal), a pair of angles • on the outer side of those two lines • but on opposite sides of the transversal are called Alternate Exterior Angles.

When two lines are crossed by another line (the Transversal), a pair of angles • on the inner side of each of those two lines • but on opposite sides of the transversal are called Alternate Interior Angles.

An infinite series where the terms alternate between positive and negative.
Example: 1/2 − 1/4 + 1/8 − 1/16 + ... = 1/3

The height of an object or place above sea level.

Generally: another word for height.
For Triangles: a line segment leaving at right angles from a side and going to the opposite corner.

The height from the center line to the peak (or trough) of a periodic function. Or we can measure the height from highest to lowest points and divide that by 2.

Something physical with continuous change.

The amount of turn between two lines around their common point (the vertex).

A line that splits an angle into two equal angles.
("Bisect" means to divide into two equal parts.)

The "upwards" angle from the horizontal to a line of sight from the observer to some point of interest.If the angle goes "downwards" it is called an Angle of Depression.

Something that happens once a year.
Example: Christmas is an annual festival.

The percentage cost of borrowing per year, including interest, fees, etc.
Example. A $1000 loan repaid after one year with $80 interest plus a $10 service fee, has a total finance charge of $90, and so has an APR of 9%.

The annual rate of return on an investment.
Example: A $1,000 investment at 10% per year earns $100 in one year, and has an APY of 10%.
Example: A $1,000 investment at 5% per half-year earns $102.50 in one year, and has an APY of 10.25%.

Moving in the opposite direction to the hands on a clock.

Also called Counterclockwise (US English).

Angles are usually measured anticlockwise.

The point (vertex) furthest from the base of an object.

The distance from the center of a regular polygon to the midpoint of a side.

Part of the circumference of a circle. Or part of any curve

The size of a surface. The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle or circle, or surface of a solid (3-dimensional) object.

An input to a function: a variable that affects a functions result.
Example: imagine a function that works out the height of a tree:
h(year) = 20 × year,
then "year" is an argument of the function "h".

The basic calculations we make in everyday life: addition, subtraction, multiplication and division. The subject also includes fractions and percentages (related to division), and exponents (related to multiplication).

Another name for Arithmetic Sequence

A sequence made by adding the same value each time.Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, ... (each number is 3 larger than the number before it)

Any of the two lines that form the angle.

Items (such as objects, numbers, etc.) arranged in rows and/or columns.

Arranged from smallest to largest. Increasing.
Example: 3, 9, 12, 55 are in ascending order.

Something you own that has value.
Specially if it helps you make money, but it doesn't have to.

Examples: personal property, real estate, stocks/shares, bank accounts

When adding it doesn't matter how we group the numbers (i.e. which we calculate first).
Example addition: (6 + 3) + 4 = 6 + (3 + 4) Because 9 + 4 = 6 + 7 = 13
Also when multiplying it doesn't matter how we group the numbers.
Example multiplication: (2 × 4) × 3 = 2 × (4 × 3) Because 8 × 3 = 2 × 12 = 24

Asymmetry means "no symmetry". Something without symmetry is asymmetrical. It is also possible to be symmetrical in one way and asymmetrical in another.

A line that a curve approaches, as it heads towards infinity.

A property of an object or person etc. Something you can say it has (such as size or color).
Example: The attributes of a dog include height, speed and color.

Average (Mean) is the sum divided by the count.

Plural of Axis.
Pronounced "ak-seez".
Axes often means the "x" and "y" lines that cross at right angles to make a graph.