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.

A "baker's dozen" is 13 (A dozen is 12). In the past a baker could be fined for selling items below weight, so they added one extra "to be sure".

When both sides have the same quantity or mass.
Here "x" is balanced by 4 "1"s, so x must be 4

Banks look after peoples money, give loans and have other financial services. They must be government approved, and must follow special rules set by the government. Banks exist to make a profit for their owners.

When a person can't pay their debts they can be legally declared bankrupt.
A bankrupt person loses everything except some basic things they own, but all the debt will go away. They receive a bad credit record and may not be able to borrow money again for years.
A bankrupt company gets protection from people it owes money to (so they cannot destroy all of the physical capital and goodwill by breaking it apart and moving it away). This gives more time for the business to work out a good solution.

A graph drawn using rectangular bars to show how large each value is.
The bars can be horizontal or vertical.

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle. But the top is also called a base when it is parallel to the bottom!

Definition 1: The number that gets multiplied when using an exponent.
Examples:
1. in 8², 8 is the base, and the result is 8 × 8 = 64
2. in 5³, 5 is the base, and the result is 5 × 5 × 5 = 125

Definition 2: How many digits in a number system.
The decimal number system we use every day has 10 digits {0,1,2,3,4,5,6,7,8,9} and so it is Base 10.
A binary digit can only be 0 or 1, so is Base 2.
A hexadecimal digit can be {0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F}, so is Base 16.

Another name for the decimal number system that we use every day.

A thousand millions.
1,000 x 1,000,000 = 1,000,000,000
Which is a 1 followed by 9 zeros
Using scientific notation: 1 × 109
(In many non-English speaking countries it means a million million, which is a 1 followed by 12 zeros, or 1 × 1012)
Below is a cube made of a million smaller cubes. If each of the small cubes is worth a thousand dollars, then the whole cube is worth a billion dollars.

Binary Numbers use only the digits 0 and 1.

Examples:
• 0 in Binary equals 0 in the Decimal Number System,
• 1 in Binary equals 1 in the Decimal Number System,
• 10 in Binary equals 2 in the Decimal Number System,
• 11 in Binary equals 3 in the Decimal Number System,
• 100 in Binary equals 4 in the Decimal Number System,
• etc.


Also called Base 2

Binary Numbers use only the digits 0 and 1.
Examples: • 0 in Binary equals 0 in the Decimal Number System, • 1 in Binary equals 1 in the Decimal Number System, • 10 in Binary equals 2 in the Decimal Number System, • 11 in Binary equals 3 in the Decimal Number System, • 100 in Binary equals 4 in the Decimal Number System, • etc.
Also called Base 2

An operation that needs two inputs.
A simple example is the addition operation "+":
In 2 + 3 = 5 the operation is "+", which takes two values (2 and 3) and gives the result 5
Subtraction, multiplication and division are also binary operations, and there are many more.
The two inputs are called "operands".
Also, a binary operation should take and return things of the same type! In other words, the operands and the result must belong to the same Set.
An operation that has only one input is called a "unary operation".
Example: the square root function is a unary operation: √(16) = 4 has just one input "16" to produce an output of 4

A polynomial with two terms.
Example: 3x² + 2

To divide into two equal parts.
We can bisect line segments, angles, and more.
The dividing line is called the "bisector"

The line that divides something into two equal parts.
You can bisect line segments, angles, and more.

A single binary digit: 0 or 1
Example: 110100 has 6 bits.
Symbol is b
Example: 1Mb means 1 million bits

A line or border around the outside of a shape. It defines the space or area.

Either of these two:
Lower bound: a value that is less than or equal to every element of a set of data.
Upper bound: a value that is greater than or equal to every element of a set of data.
Example: in {3,5,11,20,22} 3 is a lower bound, and 22 is an upper bound
But be careful! 2 is also a lower bound (it is less than any element of that set), in fact any value 3 or less is a lower bound.
Likewise any value 22 or above is also an upper bound, such as 50 or 1000.
Example: how tall is a human? We may not know the exact shortest human, but we can say that 0 is a lower bound (can't be less than zero in height, right?)

A rectangular shape (in 2 dimensions) Or a "cuboid" (in 3 dimensions)

Another name for Width.
Example: the breadth of the door is 80 cm.

An estimate of income and spending for some period of time.
Example: Sam has a weekly budget to make sure there is enough money at the end of the week for a night out.
Example: HappyPup Ltd has just finished their Yearly Budget and has set aside $20,000 for the local animal shelter.

8 binary digits
A single binary digit (called a "bit") can only be 0 or 1
Example: 1 is a bit
Example: 10110110 is a byte
A bit can have only 2 different values: 0 or 1
A byte can have 2×2×2×2×2×2×2×2 = 256 different values

Symbol is B (and b means bit)
Example: 1MB means 1 million bytes (or 8 million bits)

To work out an answer, usually by adding, multiplying etc.
Example: Calculate the cost of 10 apples when each apple costs 0.50.
Answer: 10 x 0.50 = 5.00

A machine or program used for doing mathematical calculations.

A branch of mathematics that looks at how things change, or how things add up, by breaking them into really small pieces.
Differential Calculus cuts things into small pieces to find how they change, so we can work out slopes, speed, etc
Integral Calculus joins (integrates) the small pieces together to find how much there is, so we can work out areas within curves, volumes, and more.

A diagram that shows what day and month it is.

The amount that something can hold.
Usually it means volume, such as milliliters (ml) or liters (l) in Metric, or pints or gallons in Imperial.
Example: This glass has a capacity of 300 ml (but is actually holding only 160 ml)

Money gained when you sell an asset (such as personal property, real estate, etc) for more than it cost.
Example: Buy a building for $1,000,000, then sell it next year for $1,200,000. The capital gain is $200,000

Money lost when you sell an asset (such as personal property, real estate, etc.) for less than it cost.
Example: Buy a building for $1,000,000, then sell it next year for $950,000. The capital loss is $50,000

Celsius (or "degrees Celsius", or sometimes "Centigrade") is a temperature scale.
It is used to tell how hot or cold something is
It is often written as °C
Water freezes at 0°C and boils at 100°C

The smallest money value in many countries.
100 cents equals one dollar in the US, Canada and Australia.
100 cents equals one euro in Europe.

A measure of length. It is about the width of a fingernail.
There are 100 centimeters in a meter.
The abbreviation is cm
A typical ruler measures up to 30 cm, like the one shown below. It has cm along the top and inches (1 inch = 2.54 cm) along the bottom.

One hundred years.
The 1st Century was from the Year 1 to the Year 100
The 2nd Century was from 101 to 200

The 20th Century was from 1901 to 2000
The 21st Century is from 2001 to 2100


We are currently in the 21st century.

This is a 5 Dollar gold coin from 1855, which is in the 19th Century

A curve that joins up so there are no end points.
Example: an ellipse is a closed curve. So is a circle.

A number used to multiply a variable.
Example: 6z means 6 times z, and "z" is a variable, so 6 is a coefficient.

Variables with no number have a coefficient of 1.
Example: x is really 1x.
Sometimes a letter stands in for the number.
Example: In ax² + bx + c, "x" is a variable, and "a" and "b" are coefficients.

In Finance, collateral is property that a borrower promises to give to a lender if they can't pay back a loan.
Example: you borrow $2,000 and use your car as collateral. If you don't pay back the loan according to the agreement (maybe you miss a monthly payment) they can take your car.

When three or more points lie on a straight line.
(Two points are always in a line.)

An instrument that shows us direction (such as North, South, East and West) by a small magnetic needle that points North/South.

A function made of other functions, where the output of one is the input to the other.Example: the functions 2x+3 and x² together make the composite function (2x+3)²

Composite number has more than two factors. The composite numbers are numbers which are not prime numbers. The number 1 is neither prime nor composite.

Where interest is calculated on both the amount borrowed plus previous interest. Usually calculated one or more times per year.

A machine that can be programmed to do things with data.
Computers can usually:
• "input" data from a mouse, keyboard or touch-screen,
• "process" the data using a CPU and memory, and
• "output" the result onto a screen or save it to disk.

A solid (3-dimensional) object that has a circular base joined to point by a curved side.
The point is called a vertex.

Curved outwards.
Example: A polygon (which has straight sides) is convex when there are NO "dents" or indentations in it (no internal angle is greater than 180°)
The opposite idea is called "concave".

A set of values that show an exact position.
On graphs it is usually a pair of numbers: the first number shows the distance along, and the second number shows the distance up or down.
Example: the point (12,5) is 12 units along, and 5 units up.

In a right angled triangle, the cotangent of an angle is:
The length of the adjacent side divided by the length of the side opposite the angle.
The abbreviation is cot
cot(θ) = adjacent / opposite

A box-shaped solid object that has six identical square faces.

A number multiplied by itself 3 times is called cube numbers.

The cube root of a number is a special value that, when used in a multiplication three times, gives that number.
Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.

A volume that is made by a cube that is 1 meter on each side.
Its symbol is m³
It is equal to 1000 (one thousand) liters.
Example: A box that is 2 meters wide, 2 meters long and 0.25 meters deep has a volume of 2×2×0.25 = 1 m³

A smoothly-flowing line (no sharp changes).
In normal language a curve must bend (change direction), but in mathematics a straight line is also a curve.

A solid object with:
• two identical flat ends that are circular or elliptical
• and one curved side.
It has the same cross-section from one end to the other.

A collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

A Decimal Number is a number that contains a Decimal Point.

A point (small dot) used to separate the whole number part from the fractional part of a number.
Example: in the number 36.9 the point separates the 36 (the whole number part) from the 9 (the fractional part, which really means 9 tenths). So 36.9 is 36 and nine tenths.

The result of subtracting one number from another.

Division is splitting into equal parts or groups. It is the result of "fair sharing".

How much a conic section (a circle, ellipse, parabola or hyperbola) varies from being circular.
A circle has an eccentricity of zero.

Having all sides of equal length.

The numbers that are evenly divided by 2 are called even numbers.

Factorial says to multiply all whole numbers from the chosen number down to 1.
The symbol is "!"
Examples:
4! = 4 × 3 × 2 × 1 = 24
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Fibonacci numbers are created starting with 1 and 1, then get the next number in the list and adds the previous two numbers. Say, 1+1 =2 and then adds 1+2 you get 3, then adds 2+3 gives 5, then 3+5 gives 8 and so on.

Not infinite. Has an end. Could be measured, or given a value.
Example:
There are a finite number of people at a beach.
There are also a finite number of grains of sand at a beach. Hard to count but still finite!
And the length of a beach is also finite.
For infinite or infinity please use search bar or alphabet index above

A Fraction is part of a whole.

The branch of mathematics that deals with points, lines, shapes and space.
• Plane Geometry is about flat shapes like lines, circles and triangles.
• Solid Geometry is about solid (3-dimensional) shapes like spheres and cubes.

Is the number written as 1 followed by 100 zeros:

10,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000

In Scientific Notation it is 1 × 10¹⁰⁰

The greatest number that is a factor of two (or more) other numbers.
When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
Abbreviated "GCF". Also called "Highest Common Factor"
Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest of them.

A Hexadecimal Number is based on the number 16
As well as the familiar digits 0 to 9, there are also the letters A, B, C, D, E and F in place of the decimal numbers 10 to 15.
Example Hexadecimal Number: 82E6B
More Examples:
• 9 in Hexadecimal equals 9 in the Decimal Number System.
• B in Hexadecimal equals 11 in the Decimal Number System.
• 1E in Hexadecimal equals 30 in the Decimal Number System.


Also called Base 16.

The greatest number or Highest Common Factor that is a factor of two (or more) other numbers.
When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor.
Abbreviated "GCF". Also called "Highest Common Factor"
Example: the GCF of 12 and 16 is 4, because 1, 2 and 4 are common factors of both 12 and 16, and 4 is the greatest of them.

An inequality says that two values are not equal.
a ≠ b says that a is not equal to b
There are other special symbols that show in what way things are not equal.
a < b says that a is less than b
a > b says that a is greater than b
(those two are known as strict inequality)
a ≤ b means that a is less than or equal to b
a ≥ b means that a is greater than or equal to b.

A number with no fractional part (no decimals).


Includes:
• the counting numbers {1, 2, 3, ...},
• zero {0},
• and the negative of the counting numbers {-1, -2, -3, ...}
We can write them all down like this: {..., -3, -2, -1, 0, 1, 2, 3, ...}
Examples of integers: -16, -3, 0, 1, 198

The unit of energy, work and heat.
Equal to the work done (or energy transferred) by a force of one newton acting over one meter in the direction of the force.
Its symbol is J, which is also kg m2/s2 (kilogram meter squared per second squared)

A prefix meaning one thousand (1,000 or 10³)

Examples:
• a kilogram is a thousand grams
• a kilometer is a thousand meters
• a kilobyte is a thousand bytes

Symbol is k

Example: 12 km = 12 kilometers = 12 thousand meters (12,000 m)

A Metric measure of mass (which we feel as weight).

The abbreviation is kg.

1 kg = 1000 grams.

1 kg = 2.205 pounds (approximately).

A Metric measure of distance. Equal to 1,000 meters.

The abbreviation is km.

Examples:
• it takes about 12 minutes to walk 1 km
• at highway speed a car goes about 100 km in an hour (100 km/h)

An abbreviation of "kilometers per hour", a metric measure of speed.

This is a sign showing a speed limit of 50 km/h

1 km/h = 0.6 miles per hour approximately

Short for Least Common Multiple.

A value we get closer and closer to, but never quite reach

For example, when we graph y=1/x we see that it gets closer... and closer... to zero but does not ever quite get there.

We then say "As x approaches infinity, then 1/x approaches 0"

A measure of how much matter is in an object.

Suppose a gold bar is quite small but has a mass of 1 kilogram (about 2.2 pounds), so it contains a lot of matter.


Mass is commonly measured by how much something weighs. But weight is caused by gravity, so your weight on the Moon is less than here on Earth, while the mass stays the same.

Mass is measured in grams, kilograms and, tonnes (Metric) or ounces and pounds (US units).

An array of numbers.

They can be added, subtracted, multiplied and more.

There is a whole subject called "Matrix Algebra"

The plural is "matrices".

The number that is to be subtracted from

A number is said to ne 1 (modulo 4 ) number if it leaves a remainder 1 when divided by 4.Similarly, if a number leaves a remainder 3 when divided by 4, it is said to be 3 (modulo 4) number.

Multiplication is (in its simplest form) repeated addition.

A prefix meaning one-billionth (1/1,000,000,000 or 10^-9)

Examples:
• a nanometer is one-billionth of a meter, about the width of DNA (illustrated here)
• a nanosecond is one-billionth of a second

Symbol is n

Example: 12 ns = 12 nanoseconds = 12 billionths of a second (0.000000012 s)

The whole numbers from 1 upwards: 1, 2, 3, and so on ...

Or from 0 upwards in some fields of mathematics: 0, 1, 2, 3 and so on ...

No negative numbers and no fractions.

Less than zero.


(Positive means more than zero. Zero is neither negative nor positive.)

A negative number is written with a minus sign in front

Example: −5 is negative five.

The word "negative" can be shortened to "−ve"

Income after tax and expenses.


For a business: total sales minus all expenses including tax.

Example: Bravedog Inc sells $400,000 of dog biscuits, spending $180,000 making them. Marketing and other costs and tax are $100,000. Bravedog's gross income is $220,000 and its net income is $120,000.

A number used only as a name, or to identify something (not as an actual value or position)

Examples:
· the number on the back of a footballer: "8"
· a zip code: "91210"
· a model number: "380"
· etc

At right angles to, going directly away from.

For a curve imagine a line just touching and matching the slope there (called a "tangent") and draw a line at right angles to it.

Example: a circle's diameter is always normal to its circumference

A number is a count or measurement.

They are really an idea in our minds. We write or talk about numbers using numerals such as "5" or "five". We could also hold up 5 fingers, or tap the table 5 times. These are all different ways of referring to the same number.

There are also different types of numbers, such as
• whole numbers {1,2,3,...}
• decimals (like 1.48 or 50.5)
• fractions (like 1/2 or 3/8)
• and more.

A person's ability to use and understand numbers:

· knowing their relative values,
· how to use them to make judgments,
· how to use them in flexible ways when adding, subtracting, multiplying or dividing
· how to develop useful strategies when counting, measuring or estimating.

A symbol or name that stands for a number.

Examples: 3, 49 and twelve are all numerals

An 8-sided polygon (a flat shape with straight sides).

An Octal Number uses only these 8 digits: 0, 1, 2, 3, 4, 5, 6 and 7

Examples:
• 7 in Octal equals 7 in the Decimal Number System
• 10 in Octal equals 8 in the Decimal Number System
• 11 in Octal equals 9 in the Decimal Number System
• 167 in Octal equals 119 in the Decimal Number System

Also called Base 8

The numbers that are not evenly divided by 2 are called odd numbers.

The vertical ("y") value in a pair of coordinates. How far up or down the point is.

Always written second in an ordered pair of coordinates such as (12,5).

In this example, the value "5" is the ordinate

A Percentage is parts per 100. The symbol is %

The ratio of a circle's circumference to its diameter

In other words: all the way around a circle divided by all the way across it.

The symbol is π

No matter how large or small the circle, its circumference is always π times its diameter.

π = 3.14159265358979323846... (the digits go on forever without repeating)

A rough approximation is 22/7 (=3.1428571...), but that is not accurate.

If a number has only two factors: 1 and the number is called prime numbers

Income minus all expenses.

Example: Sam's Bakery received $900 yesterday, but expenses such as wages, food and electricity came to $650. So the Profit was $900 − $650 = $250.


But if the income is LESS THAN the expenses it is called a "Loss".

Example: Two days ago Sam's Bakery received $480, but expenses were $520.
$480 − $520 = −$40, which is a $40 Loss

How much there is of something.

Example: What is the quantity of rice?
• We can say "a handful"
• Or use a measuring cup and say "40 milliliters"
• Or we can count them and say "1562"

The answer after we divide one number by another.

dividend ÷ divisor = quotient.

Example: in 12 ÷ 3 = 4, 4 is the quotient.

The angle made by taking the radius and wrapping it round the circle.

One Radian is (180/π) degrees, which is about 57.2958 degrees.

A ratio shows the relative sizes of two or more values.

Ratios can be shown in different ways:
• using the ":" to separate example values
• using the "/" to separate one value from the total
• as a decimal, after dividing one value by the total
• as a percentage, after dividing one value by the total

Example: if there is 1 boy and 3 girls you could write the ratio as:

1:3 (for every one boy there are 3 girls)
1/4 are boys and 3/4 are girls
0.25 are boys (by dividing 1 by 4)
25% are boys (0.25 as a percentage)

The price after the original price has been reduced by a discount.

The sale price here is $8.00

If the discount is a percentage we must first work out the discount amount:
• discount amount = original price × discount rate
• then subtract that from the original price

Example: the shirt shop is having a 10% discount sale
The t-shirt's normal price is $23
• discount amount = $23 × 10% = $2.30
• then $23 - $2.30 = $20.70 (the Sale Price)

Half a circle (made by a diameter and the connecting arc)

Its area is half of a circle's area: πr²/2
Its perimeter is half of a circle's perimeter plus the diameter: πr + 2r

A collection of "things" (objects or numbers, etc).

Here is a set of clothing items.

Each member is called an element of the set.

A set has only one of each member (all members are unique).

Example: {1,2,3,4} is the set of counting numbers less than 5

Interest calculated as a percent of the original loan.

Example: a 3-year loan of $1,000 at 10% costs 3 lots of 10%
So the interest is 3 × $1,000 × 10% = $300

(Simple interest is almost never used in the real world, with compound interest being preferred.)

A device for measuring and displaying speed.

A 3-dimensional object shaped like a ball.

Every point on the surface is the same distance from the center.

A number multiplied by itself is called square numbers

A square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.

Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16.

The symbol is √ which always means the positive square root.

Example: √36 = 6 (because 6 x 6 = 36)

A measure of how spread out numbers are.

It is the square root of the Variance,
and the Variance is the average of the squared differences from the Mean.

Part of another set.

A is a subset of B when every member of A is a member of B.

Example: B = {1,2,3,4,5}
Then A = {1,2,3} is a subset of B
Other subsets of B include {2,3} or {1,4,5} or {4} etc...
But {1,2,6} is NOT a subset of B as it has 6 (which is not in B)

Subtraction is taking one number away from another.

The number that is to be subtracted.

A 3-sided flat shape with straight sides. It is a polygon.

A number is said to be triangular number, when that number of pebbles can be arranged in a triangle using one pebble at the top, two pebbles in next row, three pebbles in next row and so on.

Trigonometry is the study of triangles: their angles, lengths and more.

(The name comes from Greek trigonon "triangle" + metron "measure").

Not equal.

Example: 7 and 5 are unequal.

The symbol is ≠ (the "not equal" symbol).

Example: 7 ≠ 5

The set made by combining the elements of two sets.

So the union of sets A and B is the set of elements in A, or B, or both.

The symbol is a special "U" like this: ∪

Example:
Soccer = {alex, hunter, casey, drew}
Tennis = {casey, drew, jade}
Soccer ∪ Tennis = {alex, hunter, casey, drew, jade}
In words: the union of the "Soccer" and "Tennis" sets is alex, hunter, casey, drew and jade

Velocity is speed (how fast something is moving) with a direction.

Saying that Ariel the Dog is running 3 km/h Westwards is a velocity.

(But saying just 3 km/h is a speed.)

A point where two or more line segments meet. A corner.

Examples:
• any corner of a pentagon (a plane shape)
• any corner of a tetrahedron (a solid)

(The plural of vertex is "vertices".)

Payment for work based on hours worked (or sometimes per day or per amount of work done).

Can be paid weekly, two-weekly, or monthly.

Example: Alex earns $20 per hour, and worked 40 hours last week so earned an $800 wage.

You often get paid extra for overtime work.

How heavy something is. The downward force caused by gravity on an object.

Weight and Mass are different things, but weighing scales are designed to estimate the mass sitting on them and so (instead of units of force) it is common to use units of mass like these:
• grams, kilograms and tonnes (in Metric)
• ounces, pounds and tons (in US units)

All of something. Complete.

Any of the numbers {0, 1, 2, 3, ...} etc.

There is no fractional or decimal part. And no negatives.

Example: 5, 49 and 980 are all whole numbers.

The distance from side to side.

Example: the width of this door is 80 cm.

The letter "x" is often used in algebra to mean a value that is not yet known.

It is called a "variable" or sometimes an "unknown".

In x + 2 = 7, x is a variable, but we can work out its value if we try!

A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

The line on a graph that runs horizontally (left-right) through zero.

It is used as a reference line so you can measure from it.

The horizontal value in a pair of coordinates: how far along the point is.

The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5).

In this example, the value "12" is the X Coordinate.

Also called "Abscissa"

The line on a graph that runs vertically (up-down) through zero.

It is used as a reference line so you can measure from it.

The vertical value in a pair of coordinates. How far up or down the point is.

The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5).

In this example, the value "5" is the Y Coordinate.
Also called "Ordinate"

How many standard deviations a value is from the mean.

In this example, the value 1.7 is 2 standard deviations away from the mean of 1.4, so 1.7 has a z-score of 2.
Similarly 1.85 has a z-score of 3.

So to convert a value to a Standard Score ("z-score"):
· first subtract the mean,
· then divide by the standard deviation

A prefix meaning one-sextillionth (1/1,000,000,000,000,000,000,000 or 10^-21)

The same as multiplying by 10^-21 (which is 0.000 000 000 000 000 000 001)

Prefix is z

Example: 12 zg = 12 zeptograms = 0.000 000 000 000 000 000 012 g

The mass of 1 single molecule of glucose (a simple sugar found in many foods) is 0.3 zg

The whole number between −1 and 1, with the symbol 0

Shows that there is no amount.

Example: 6 − 6 = 0 (the difference between six and six is zero)


Zero is not positive and is also not negative.

When we add zero to a number the result is just the number, unchanged.
When we multiply a number by zero we get zero.


Zero is also used as a "place-holder" so that you can write a numeral properly.

Example: 502 (five hundred and two) could be mistaken for 52 (fifty two) without the zero in the tens place.