Absolute value
How far a number is from zero, ignoring sign.
|−4| = 4 and |4| = 4. The absolute value is always zero or positive. Useful when you care about magnitude rather than direction.
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Acceleration
The rate at which velocity changes.
If a car goes from 0 to 60 mph in 6 seconds, that's 10 mph/s of acceleration. Measured in m/s² in SI units.
See it in actionAcute angle
An angle smaller than 90°.
Sharp angles. The corners of an equilateral triangle (60°) are all acute.
See it in actionAcute triangle
All three angles less than 90°.
Every interior angle is acute.
Addend
Any number being added in a sum.
In 3 + 4 = 7, both 3 and 4 are addends.
Algorithm
A step-by-step recipe for solving a problem.
Long division is an algorithm. So is the way you sort cards into order. Algorithms are the bridge between math and computing.
Angle
The amount of turn between two lines that meet.
Measured in degrees (0° to 360°). A full turn is 360°.
See it in actionArea
How much surface a 2D shape covers.
Measured in square units (cm², m², in²). For a rectangle: width × height.
See it in actionAsymptote
A line a curve gets ever closer to but never touches.
y = 1/x has the x and y axes as asymptotes — it approaches but never reaches them.
See it in actionAverage
A single number that stands in for a set.
Most often means the mean, but median and mode are also kinds of average.
See it in actionAxis
A reference line on a graph.
Most graphs have an x-axis (horizontal) and a y-axis (vertical). They cross at the origin.
Base
The number system's grouping size — usually 10 for us.
Base 10 means each column is 10 times the one to its right. Computers use base 2 (binary). Time uses base 60.
Binary
Base-2 number system.
Uses only 0 and 1. Each place is a power of 2: 1101 = 8 + 4 + 0 + 1 = 13.
See it in actionBisect
To cut into two equal parts.
An angle bisector cuts an angle in half. A perpendicular bisector cuts a line segment in half at right angles.
See it in actionCardinal number
How many — 1, 2, 3.
As opposed to ordinal numbers (1st, 2nd, 3rd), which describe order.
Centroid
The 'centre of mass' of a triangle.
Where the three medians of a triangle meet. Balances the triangle if you pinned it there.
Chord
A straight line joining two points on a curve.
Usually said of a circle. The diameter is the longest possible chord.
See it in actionCircumference
The distance around a circle.
Equal to π × diameter, or 2π × radius. About 3.14× the diameter.
See it in actionCoefficient
The number multiplying a variable.
In 7x, the coefficient is 7. In −y, the coefficient is −1.
See it in actionCoefficient
The number in front of a variable.
In 5x + 3, the coefficient of x is 5.
See it in actionCombination
A selection where order doesn't matter.
Picking 3 students from 10 to form a committee — order doesn't matter, so it's a combination.
See it in actionCommon factor
A number that divides into two or more numbers exactly.
Common factors of 12 and 18: 1, 2, 3, 6. Greatest common factor (GCF): 6.
See it in actionCommon multiple
A number that two or more numbers divide into.
Common multiples of 4 and 6: 12, 24, 36… Least common multiple (LCM): 12.
See it in actionComplementary angles
Two angles that sum to 90°.
If one is 30°, the other is 60°.
See it in actionComposite number
A whole number with more than two factors.
12 is composite (factors: 1, 2, 3, 4, 6, 12). 7 is not — it has only 1 and itself, so it's prime.
See it in actionConcave
Curving inward.
A concave polygon has at least one interior angle > 180°. Imagine a bite taken out.
Congruent
Same shape AND same size.
Two triangles are congruent if you can lay one on top of the other and they match exactly.
See it in actionConjecture
A guess based on patterns, not yet proved.
The Goldbach conjecture says every even number > 2 is the sum of two primes. Believed true; still unproven.
Constant
A value that doesn't change.
In y = 2x + 5, the 5 is a constant. π and e are mathematical constants — fixed for all time.
Coordinate
A pair (or trio) of numbers locating a point.
(3, 4) means x = 3, y = 4 on a 2D grid.
Correlation
How strongly two variables move together.
Measured between −1 and +1. Doesn't imply causation.
See it in actionCosine (cos)
Adjacent over hypotenuse in a right triangle.
cos(θ) = adjacent / hypotenuse. Pairs with sine and tangent — together they're trigonometry.
See it in actionCube
A 3D shape with 6 equal square faces.
Volume = side³. Or, in algebra: cube = raise to the 3rd power.
See it in actionCube root
What number times itself three times equals this?
∛27 = 3 because 3 × 3 × 3 = 27.
See it in actionCylinder
A 3D shape with two parallel circular ends.
Volume = π r² h. A can of soup is a cylinder.
See it in actionDecimal
A number that uses a dot to show parts of a whole.
0.5 is half. 0.25 is a quarter. The columns after the dot are tenths, hundredths, thousandths…
See it in actionDecimal
A number with a decimal point.
0.5, 3.14, 0.001 are all decimals. Each digit's place is a power of ten.
See it in actionDegree (angle)
The unit for measuring an angle.
A full circle is 360°. A right angle is 90°.
See it in actionDegree (polynomial)
The biggest power in a polynomial.
x² + 3x + 7 has degree 2 (it's quadratic). x³ − x has degree 3 (cubic).
See it in actionDenominator
The bottom number of a fraction — total parts.
In 3/4, the denominator is 4. It tells you how many equal pieces the whole is split into.
See it in actionDerivative
The rate of change of a function.
f′(x) tells you the slope of f at the point x. The first major idea of calculus.
See it in actionDiagonal
A line connecting two non-adjacent corners.
A square has 2 diagonals. A pentagon has 5.
Diameter
A straight line across a circle through its center.
Twice the radius. The longest chord of the circle.
See it in actionDilation
Resizing a shape by a scale factor.
Doubling every distance from a centre point. The shape stays similar — same proportions.
See it in actionDistributive law
a(b + c) = ab + ac.
Multiply across the brackets. 3(x + 2) = 3x + 6.
See it in actionDivisor
The number you divide by.
In 20 ÷ 4 = 5, the divisor is 4.
Domain
The set of allowed inputs to a function.
f(x) = √x has domain x ≥ 0 — you can't take a real square root of a negative.
See it in actionDot product
A way to multiply two vectors and get a number.
a · b = a₁b₁ + a₂b₂ + … Tells you about the angle between them.
See it in actionEdge
A line where two faces meet on a 3D shape.
A cube has 12 edges. Edges connect vertices.
Ellipse
An oval — a 'stretched' circle.
All planets orbit the Sun in ellipses, with the Sun at one focus.
Equation
A statement that two things are equal.
Has an equals sign. To solve, do the same operation to both sides until the unknown is alone.
See it in actionEquilateral
All sides equal.
An equilateral triangle has three equal sides — and therefore three 60° angles.
See it in actionEstimation
A sensible guess, fast.
Round to easy numbers, do the easy maths in your head, get an answer that's close enough.
See it in actionEven number
An integer divisible by 2.
0, 2, 4, −6, 100. Easy test: ends in 0, 2, 4, 6 or 8.
Exponent
How many times to multiply a base by itself.
2⁵ = 2 × 2 × 2 × 2 × 2 = 32. The 5 is the exponent.
See it in actionExpression
A math phrase. No equals sign.
3x + 5 is an expression. It has a value once you know x. Add an equals sign and you have an equation.
See it in actionFace
A flat surface of a 3D shape.
A cube has 6 faces. A tetrahedron has 4 (all triangles).
Factor
A whole number that divides another evenly.
12 has factors 1, 2, 3, 4, 6, 12. Prime numbers have only two factors: 1 and themselves.
See it in actionFactorial
n! = n × (n−1) × … × 2 × 1.
5! = 120. Counts arrangements: 5! is the number of ways to order 5 things.
Fibonacci
1, 1, 2, 3, 5, 8, 13… each term is the sum of the previous two.
Shows up in pinecones, sunflowers, and rabbit populations.
See it in actionForce
A push or a pull.
Measured in newtons (N). F = m × a — force equals mass times acceleration.
See it in actionFraction
A part of a whole, written with a top and bottom.
3/4 means three of four equal pieces. The bar is a division — 3 ÷ 4 = 0.75.
See it in actionFraction
A number written as one whole number divided by another.
½, ¾, 7/8. Top is the numerator, bottom is the denominator.
See it in actionFrequency
How often something happens.
In data, the count of each value. In waves, cycles per second (hertz).
See it in actionFunction
A rule that turns one number into another.
Each input gives one output. f(x) = 2x doubles its input.
See it in actionGeometric mean
Multiply n values, take the nth root.
Geometric mean of 2 and 8: √(2 × 8) = 4. Used for growth rates and ratios.
Gradient
Slope of a line — rise over run.
Δy / Δx. Steeper line = bigger gradient.
See it in actionGravity
The force pulling masses toward each other.
On Earth, accelerates falling objects at g ≈ 9.8 m/s².
See it in actionHexadecimal
Base-16 number system.
Digits 0–9 then A–F. Used by programmers because each hex digit packs four binary digits.
See it in actionHexagon
A 6-sided polygon.
A regular hexagon has all sides equal and 120° interior angles. Honeycombs use them.
See it in actionHistogram
A bar chart for grouped continuous data.
Bars touch each other (no gaps), each showing how many values fall into a range.
See it in actionHypotenuse
The longest side of a right triangle.
Across from the right angle. By Pythagoras' theorem, hypotenuse² = leg₁² + leg₂².
See it in actionIdentity
An equation true for every value.
(x + 1)² = x² + 2x + 1 is an identity — both sides are equal for any x.
Inequality
A statement comparing two values.
x > 3 means x is bigger than 3. Symbols: <, >, ≤, ≥, ≠.
See it in actionInfinity (∞)
Bigger than any number.
Not a number itself but a useful idea — for unbounded sets, limits, and the size of the integers.
Inflection
A point where a curve changes its bend.
From curving up (concave up) to curving down (concave down). The second derivative changes sign here.
See it in actionInteger
A whole number — positive, negative, or zero.
…, −3, −2, −1, 0, 1, 2, 3, … No fractions, no decimals.
See it in actionIntegral
An infinite sum that gives an area.
∫ f(x) dx adds up infinitely many infinitely thin strips under the curve y = f(x).
See it in actionInverse
Undoes another operation.
Addition undoes subtraction. Multiplication undoes division. Squaring undoes square-rooting.
Irrational number
A number that can't be written as a/b.
π and √2 are irrational — their decimal expansions go on forever without repeating.
Isosceles
A triangle with two equal sides.
The two angles opposite the equal sides are also equal.
See it in actionKite
A 4-sided shape with two pairs of adjacent equal sides.
Looks like the toy. Diagonals cross at right angles.
See it in actionLimit
What a function heads toward, as x heads toward something.
Even when the function isn't defined at that point, the limit can still exist. The bedrock of calculus.
See it in actionLogarithm
The inverse of an exponent.
log₁₀(1000) = 3 because 10³ = 1000.
See it in actionMagnitude
Size, ignoring direction.
The magnitude of a vector is its length. The magnitude of a number is its absolute value.
See it in actionMatrix
A rectangular grid of numbers.
Used to represent transformations, solve simultaneous equations, and run almost all of modern AI.
Mean
Add them up, divide by how many.
The arithmetic mean is the most common kind of 'average.'
See it in actionMean
The arithmetic average.
Sum the values, divide by how many there are.
See it in actionMedian
The middle value when sorted.
Better than the mean when extreme values would skew things — like income.
See it in actionMode
The value that appears most often.
Datasets can have one mode, several, or none.
See it in actionMode
The most common value.
In 2, 3, 3, 4, 7 — the mode is 3.
See it in actionMomentum
Mass × velocity.
Total momentum is conserved in any closed system. The reason rockets work.
See it in actionNatural number
A counting number: 1, 2, 3…
Sometimes 0 is included, depending on the textbook.
Normal distribution
The bell-shaped curve.
Symmetric, centered on the mean. Heights, errors, exam scores all follow it.
See it in actionNumerator
The top number of a fraction.
In 3/4, the numerator is 3. It tells you how many parts are taken.
See it in actionObtuse angle
An angle bigger than 90° but less than 180°.
Wider than a corner of a square but not a flat line.
See it in actionOctagon
An 8-sided polygon.
Stop signs are octagons. Interior angles of a regular octagon are 135°.
See it in actionOdd number
An integer not divisible by 2.
1, 3, 5, 7, 9… Ends in 1, 3, 5, 7 or 9.
Order of operations
PEMDAS — the rule for what to do first.
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
See it in actionOrigin
The point (0, 0) on a coordinate grid.
Where the x and y axes cross.
Outlier
A value far from the others.
If most data is between 5 and 15 and you see a 100, that 100 is an outlier — worth investigating.
Parallel
Lines that never meet, no matter how far they go.
Parallel lines are everywhere the same distance apart. Train tracks, ruled paper.
Parallelogram
A 4-sided shape with both pairs of opposite sides parallel.
Squares, rectangles and rhombuses are all parallelograms.
See it in actionPentagon
A 5-sided polygon.
A regular pentagon has 108° interior angles.
See it in actionPercentage
A fraction out of 100.
50% = 50/100 = ½. Per-cent literally means 'per hundred'.
See it in actionPerimeter
The total distance around a shape's edge.
An ant walking around the boundary travels the perimeter. For a circle, this is the circumference.
See it in actionPermutation
An arrangement where order matters.
Arranging 3 letters from {A, B, C}: ABC, ACB, BAC, BCA, CAB, CBA — 6 permutations.
See it in actionPerpendicular
At 90° — a right angle.
The corner of a square. Often marked with a small square in diagrams.
Pi (π)
The ratio of any circle's circumference to its diameter.
Approximately 3.14159. Irrational — its decimal goes on forever without repeating.
See it in actionPolygon
A flat, closed shape with straight sides.
Triangles, quadrilaterals, pentagons — all polygons.
See it in actionPolynomial
A sum of terms with whole-number powers.
x³ + 2x² − 5x + 7 is a polynomial. The biggest power is the degree.
See it in actionPower
An exponent.
5² is read 'five to the power of two'.
See it in actionPrime number
A whole number with exactly two factors: 1 and itself.
2, 3, 5, 7, 11, 13, … 1 is not prime. There are infinitely many primes.
See it in actionPrism
A 3D shape with two identical parallel ends and rectangular sides.
A box is a rectangular prism. A toblerone is a triangular prism.
Probability
How likely something is, between 0 and 1.
0 means impossible, 1 means certain, 0.5 means fifty-fifty.
See it in actionPythagoras' theorem
a² + b² = c² for right triangles.
The square on the hypotenuse equals the sum of the squares on the other two sides.
See it in actionQuadratic
An expression where x² appears (and no higher power).
ax² + bx + c. Its graph is a parabola.
See it in actionQuadrilateral
A 4-sided polygon.
Squares, rectangles, rhombuses, parallelograms, trapezoids and kites.
See it in actionQuartile
A value that splits sorted data into quarters.
Q1 (25%), Q2 (median, 50%), Q3 (75%).
See it in actionQuotient
The result of a division.
In 20 ÷ 4 = 5, the quotient is 5.
Radian
An angle unit based on the radius.
One radian is the angle that subtends an arc equal to the radius. 360° = 2π radians.
See it in actionRadius
Distance from the center of a circle to its edge.
Half the diameter. Plural: radii.
See it in actionRange
Largest minus smallest.
A measure of spread. The range of [3, 7, 7, 12] is 9.
See it in actionRange (data)
Largest minus smallest.
Quick measure of spread but easily fooled by outliers.
See it in actionRange (function)
All possible outputs of a function.
f(x) = x² has range y ≥ 0.
See it in actionRate
A ratio comparing two quantities with different units.
Speed is a rate: kilometres per hour. Wages are a rate: dollars per hour.
Ratio
A comparison of two quantities.
Written 2:3 or 2/3. Means '2 of one for every 3 of the other'.
See it in actionRational number
A number that can be written as a/b.
All integers and all fractions are rational. ½, −7, 0.25 are rational.
Reciprocal
1 divided by a number.
Reciprocal of 5 is ⅕. Reciprocal of ⅔ is 3/2. A number times its reciprocal is 1.
Reflection
A flip across a line.
Like a mirror image. Distances from the mirror line are preserved.
See it in actionRhombus
A 4-sided shape with all sides equal.
Like a 'pushed-over' square — opposite sides parallel, but corners not necessarily 90°.
See it in actionRight angle
Exactly 90°.
The corner of a square or a rectangle. Often marked with a tiny square in diagrams.
See it in actionRotation
A turn around a fixed point.
Specified by an angle and a centre. A rotation preserves distances.
See it in actionScalar
A quantity with size only — no direction.
Mass, temperature, time. Compare to vector, which has direction.
Scatter plot
A graph of points showing two variables at once.
Each dot is one data record. Patterns in the cloud reveal correlation.
See it in actionSequence
An ordered list of numbers.
1, 4, 9, 16… (squares). Or 1, 2, 4, 8… (doubling).
See it in actionSine (sin)
Opposite over hypotenuse in a right triangle.
sin(θ) = opposite / hypotenuse. Used everywhere — signal processing, music, orbits.
See it in actionSlope
How steep a line is. Rise over run.
If a line goes up 3 for every 1 across, the slope is 3.
See it in actionSphere
A perfectly round 3D shape.
Every point on its surface is the same distance from the centre. Volume = ⁴⁄₃ π r³.
See it in actionSquare (number)
A number multiplied by itself.
5² = 25. The geometric meaning: the area of a square with that side length.
Square root
A number that, multiplied by itself, gives the original.
√9 = 3 because 3 × 3 = 9. Most square roots are irrational.
Standard deviation
A measure of spread.
Roughly: the typical distance of a value from the mean. Bigger SD = more spread.
See it in actionSum
The result of addition.
The sum of 3 and 4 is 7.
Supplementary angles
Two angles that sum to 180°.
If one is 130°, the other is 50°.
See it in actionSymmetry
Looks the same after a fold, turn, or slide.
A square has 4 lines of reflection symmetry and rotational symmetry of order 4.
See it in actionTangent (line)
A line that just touches a curve at one point.
Same direction as the curve at the point of contact. Slope of the tangent = derivative.
See it in actionTangent (trig)
Opposite over adjacent in a right triangle.
tan(θ) = opposite / adjacent = sin/cos.
See it in actionTranslation
A slide — every point moves the same way.
No turning, no flipping, no resizing.
See it in actionTrapezoid
A 4-sided shape with exactly one pair of parallel sides.
(In British English: trapezium.)
See it in actionVariable
A letter standing in for a number.
Usually x, y or n. The point of variables is to write down a relationship that holds whatever the number is.
See it in actionVector
A quantity with size AND direction.
Often drawn as an arrow. Velocity, force, displacement are vectors.
See it in actionVelocity
Speed with a direction.
60 km/h north and 60 km/h south have the same speed but different velocities.
See it in actionVertex
A corner — where edges meet.
Plural: vertices. A triangle has 3 vertices, a cube has 8.
Volume
How much 3D space something takes up.
Measured in cubic units (cm³, m³). For a box: length × width × height. For a sphere: ⁴⁄₃ π r³.
See it in actionWhole number
Non-negative integer.
0, 1, 2, 3, 4… (Sometimes excludes 0, depending on the textbook.)
X-axis
The horizontal line on a coordinate grid.
Usually represents the independent variable.
Y-axis
The vertical line on a coordinate grid.
Usually represents the dependent variable — the output.
Zero
The number with no quantity.
Acts as the additive identity (n + 0 = n) and breaks division (you can't divide by zero).