Mathematics glossary
Absolute value
How far a number is from zero, ignoring the sign.
The magnitude of a real number, written |x|.
|−7| = 7.
Used in: Fractions, Decimals and IntegersAdditive inverse
The opposite of a number.
The number that adds to a given number to make zero.
The additive inverse of −6 is 6.
Used in: Operations with Rational NumbersAmbiguous case
When the sine rule gives two possible triangles.
The SSA situation where two angles share the same sine value.
θ and 180° − θ both fit.
Used in: Sine Rule, Cosine Rule and SolidsAngle of elevation
The angle you look up from level ground.
The angle between the horizontal and an upward line of sight.
32° up to the top of a tower.
Used in: Right-Triangle Trigonometry and Coordinate GeometryCoefficient
The number in front of a variable.
The numerical factor multiplying a variable in a term.
In 3d, the coefficient is 3.
Used in: Expressions, Equations and InequalitiesCombination
A selection where the order does not matter.
nCr = n!/(r!(n − r)!).
Choosing 3 students from 10 gives 120 ways.
Used in: Probability Rules, Counting and the Normal DistributionComposition
Doing one function and then another.
(f ∘ g)(x) = f(g(x)).
Convert miles to km, then km to m.
Used in: Transformations, Inverses and CompositionCompound interest
Interest earned on your interest as well as your original money.
A = P(1 + r)ᵗ, where interest is added to the principal each period.
10 000 at 6% for 4 years grows to 12 624.77.
Used in: Exact Values and Financial MathematicsConditional probability
The chance of something happening given that something else already has.
P(A | B) = P(A and B) ÷ P(B).
The chance of rain given that clouds are present.
Used in: Data Analysis, Regression and Conditional ProbabilityCongruent
Same shape and same size.
Related by a sequence of rigid motions, so all corresponding parts are equal.
Two triangles proved equal by SAS.
Used in: Congruence Proof and Similar FiguresConstant of proportionality
The fixed number you multiply x by to get y.
The value k in the relationship y = kx.
If y = 2.5x, then k = 2.5.
Used in: Proportional Relationships and the Constant of ProportionalityCorrelation coefficient
A number showing how closely points follow a straight line.
r, a value from −1 to 1 measuring linear association strength and direction.
r = −0.85 is a strong negative relationship.
Used in: Data Analysis, Regression and Conditional ProbabilityCosine rule
A formula linking three sides and one angle in any triangle.
c² = a² + b² − 2ab·cos C.
Used when you know two sides and the included angle.
Used in: Sine Rule, Cosine Rule and SolidsCross section
The shape you see when you slice a solid.
The intersection of a plane with a three-dimensional figure.
Slicing a cube parallel to a face gives a square.
Used in: Scale Drawings and Triangle ConstructionsCube root
The number that gives your value when multiplied by itself three times.
The value x such that x³ equals the given number.
∛64 = 4.
Used in: Rational, Irrational Numbers and Exponent LawsDepreciation
The loss of value of something over time.
Exponential decay modelled by A = P(1 − r)ᵗ.
A car losing 15% of its value each year.
Used in: Exact Values and Financial MathematicsDifference of two squares
A pattern where one square is subtracted from another.
a² − b² factorises as (a − b)(a + b).
x² − 25 = (x − 5)(x + 5).
Used in: Expression Structure, Equations and SystemsDilation
An enlargement or reduction from a centre point.
A transformation multiplying all distances from a centre by a scale factor k.
A factor of 2 doubles every length.
Used in: Transformations, Congruence and SimilarityDiscriminant
The part of the quadratic formula that tells you how many solutions there are.
The value b² − 4ac.
A negative discriminant means no real roots.
Used in: Quadratic Equations and Their GraphsDistance formula
A way to find how far apart two points are on a grid.
d = √((x₂ − x₁)² + (y₂ − y₁)²), derived from the Pythagorean theorem.
From (1, 2) to (4, 6) the distance is 5.
Used in: The Pythagorean Theorem and Curved SolidsDomain
All the inputs a function is allowed to take.
The set of values for which a function is defined.
Time cannot be negative, so the domain starts at 0.
Used in: Functions, Sequences and Exponential GrowthElimination
Adding or subtracting equations to remove one variable.
A solution method that cancels one variable by combining equations.
Adding x + y = 7 and x − y = 1 gives 2x = 8.
Used in: Systems of Linear EquationsEquivalent ratios
Ratios that describe the same relationship.
Ratios related by multiplying or dividing both terms by the same non-zero number.
3:18 and 6:36 are equivalent.
Used in: Ratios, Rates and Unit RatesExtraneous solution
An answer that appears during solving but does not really work.
A solution introduced by an operation that is not reversible, failing the original restrictions.
x = 3 in an equation where x − 3 is a denominator.
Used in: Polynomials and Rational ExpressionsFactorise
To rewrite a sum as a product.
To express an expression as a product of its factors.
6x + 9 = 3(2x + 3).
Used in: Linear Expressions, Equations and InequalitiesFeasible region
The area on a graph where all conditions are satisfied.
The set of points satisfying every inequality in a system.
The overlap of shaded regions.
Used in: Expression Structure, Equations and SystemsFunction
A rule giving exactly one output for each input.
A relation in which every element of the domain maps to exactly one element of the range.
y = 2x + 3 is a function.
Used in: Functions: Rules, Graphs and ModelsGeometric sequence
A list where each term is multiplied by the same number.
A sequence with a constant ratio r between consecutive terms.
3, 6, 12, 24 with r = 2.
Used in: Functions, Sequences and Exponential GrowthHypotenuse
The longest side of a right triangle.
The side opposite the right angle.
In a 3-4-5 triangle the hypotenuse is 5.
Used in: The Pythagorean Theorem and Curved SolidsInequality
A statement that one amount is bigger or smaller than another.
A relation using <, >, ≤ or ≥ describing a set of values.
x > 20 includes every number greater than 20.
Used in: Expressions, Equations and InequalitiesInitial value
The starting amount before any change.
The output of a function when the input is zero.
In y = 40 − 3x the initial value is 40.
Used in: Functions: Rules, Graphs and ModelsInscribed angle
An angle with its point on the circle.
An angle whose vertex lies on the circle and whose arms are chords.
An inscribed angle is half the central angle on the same arc.
Used in: Circle Theorems, Arcs and SectorsInterquartile range
The spread of the middle half of the data.
The difference between the upper and lower quartiles, Q3 − Q1.
If Q1 = 12 and Q3 = 20, the IQR is 8.
Used in: Statistical Questions and DistributionsInverse function
A function that undoes another one.
f⁻¹ such that f⁻¹(f(x)) = x for all x in the domain.
The inverse of 3x − 7 is (x + 7)/3.
Used in: Transformations, Inverses and CompositionIrrational number
A number that cannot be written as a fraction.
A real number whose decimal expansion neither terminates nor repeats.
√2 ≈ 1.41421356…
Used in: Rational, Irrational Numbers and Exponent LawsLeast common multiple
The smallest number both values divide into.
The smallest positive integer that is a multiple of each given integer.
The LCM of 6 and 8 is 24.
Used in: Fractions, Decimals and IntegersLike terms
Terms with exactly the same variable part.
Terms that differ only in their numerical coefficient.
5x and 2x are like terms; 5x and 5 are not.
Used in: Linear Expressions, Equations and InequalitiesLine of best fit
A straight line drawn to follow the trend of the points.
A linear model summarising the relationship in bivariate data.
Used to predict a score from study hours.
Used in: Scatter Plots, Trend Lines and Two-Way TablesLogarithm
The exponent you need to reach a number.
logₐb is the power to which a must be raised to give b.
log₃81 = 4.
Used in: Quadratic and Exponential ModelsMean absolute deviation
The average distance of values from the mean.
The mean of the absolute differences between each value and the mean.
A small MAD means the data is consistent.
Used in: Statistical Questions and DistributionsMultiplier
The single number you multiply by to apply a percent change.
The factor (1 ± p/100) that produces a percent increase or decrease.
A 25% discount uses the multiplier 0.75.
Used in: Percent and Unit ConversionNet
A flat pattern that folds into a solid.
A two-dimensional representation of all the faces of a polyhedron.
A cube net has six squares.
Used in: Area, Volume and Surface AreaOrder of magnitude
A rough size in powers of ten.
The exponent of ten nearest the size of a quantity.
A number near 10⁶ is one order of magnitude larger than one near 10⁵.
Used in: Scientific Notation and Orders of MagnitudeOrigin
The point where both axes cross.
The point (0, 0) on the coordinate plane.
Every proportional graph passes through the origin.
Used in: Proportional Relationships and the Constant of ProportionalityOutlier
A value that sits far away from the rest.
An observation markedly distant from the overall pattern of the data.
One student with 12 study hours and a low score.
Used in: Scatter Plots, Trend Lines and Two-Way TablesPercent
A number out of one hundred.
A ratio with denominator 100, written with the % symbol.
25% means 25 out of every 100.
Used in: Percent and Unit ConversionPercent error
How far a measurement is from the true value, as a percent.
|measured − actual| ÷ actual × 100.
Measuring 98 cm instead of 100 cm is a 2% error.
Used in: Percent Change: Tax, Discount, Interest and ErrorPi
The number you get when you divide any circumference by its diameter.
The constant ratio of a circle's circumference to its diameter, ≈ 3.14159.
C = πd.
Used in: Circles, Angles and Composite MeasurementPopulation
The whole group you want to know about.
The complete set of individuals under study.
All 900 students in the school.
Used in: Random Sampling and Comparing PopulationsRandom sample
A sample where everyone has an equal chance of being picked.
A subset selected so that every member of the population is equally likely to be chosen.
Drawing 60 names from a hat.
Used in: Random Sampling and Comparing PopulationsRatio
A way of comparing two amounts by division.
A multiplicative comparison of two quantities, written a:b or a/b.
The ratio of 3 notebooks to 18 riyals is 3:18.
Used in: Ratios, Rates and Unit RatesRationalising
Removing a root from the bottom of a fraction.
Rewriting an expression so the denominator is rational.
3/√2 = 3√2/2.
Used in: Radicals, Rational Exponents and PrecisionReciprocal
The fraction turned upside down.
The multiplicative inverse of a non-zero number.
The reciprocal of 2/5 is 5/2.
Used in: Fractions, Decimals and IntegersRelative frequency
How often something actually happened, as a fraction of trials.
The number of successes divided by the number of trials.
54 heads in 100 tosses gives 0.54.
Used in: Probability Models and Compound EventsRepeating decimal
A decimal with digits that go on in a pattern forever.
A decimal expansion in which a block of digits repeats indefinitely.
1/3 = 0.333…
Used in: Operations with Rational NumbersRigid motion
A move that does not change size or shape.
A transformation preserving distance and angle measure.
Translations, reflections and rotations.
Used in: Transformations, Congruence and SimilaritySample space
A list of everything that could happen.
The set of all possible outcomes of an experiment.
For two coins: HH, HT, TH, TT.
Used in: Probability Models and Compound EventsScale factor
The number every length is multiplied by.
The ratio of corresponding lengths between two similar figures.
A 1:50 plan uses a scale factor of 50.
Used in: Scale Drawings and Triangle ConstructionsScientific notation
Writing a number as one digit, a decimal part and a power of ten.
A number expressed as a × 10ⁿ where 1 ≤ a < 10 and n is an integer.
150 000 000 = 1.5 × 10⁸.
Used in: Scientific Notation and Orders of MagnitudeSector
A slice of a circle between two radii.
The region bounded by two radii and the arc between them.
A 60° sector is one sixth of the circle.
Used in: Circle Theorems, Arcs and SectorsSimilar
Same shape, possibly different size.
Related by a dilation and rigid motions, with equal angles and proportional sides.
Two triangles with the same three angles.
Used in: Congruence Proof and Similar FiguresSimple interest
Interest calculated only on the original amount.
I = Prt, where P is principal, r the rate and t the time.
5000 at 4% for 3 years earns 600.
Used in: Percent Change: Tax, Discount, Interest and ErrorSlope
How steep a line is.
The constant rate of change (y₂ − y₁)/(x₂ − x₁) of a linear function.
A ramp rising 1 m over 8 m has slope 0.125.
Used in: Linear Equations, Slope and y = mx + cStandard deviation
A measure of how spread out data is around the mean.
The square root of the average squared deviation from the mean.
About 68% of normal data lies within one standard deviation.
Used in: Probability Rules, Counting and the Normal DistributionStatistical question
A question whose answers vary.
A question that anticipates variability in the data used to answer it.
How tall are Grade 6 students? is statistical.
Used in: Statistical Questions and DistributionsSurd
A root that cannot be simplified to a whole number.
An irrational root expressed exactly in radical form.
√50 = 5√2.
Used in: Radicals, Rational Exponents and PrecisionSurface area
The total area of all the outside faces.
The sum of the areas of every face of a three-dimensional figure.
A 2×3×4 prism has surface area 52 square units.
Used in: Area, Volume and Surface AreaSystem of equations
Two or more equations that must be true at the same time.
A set of equations whose common solutions satisfy every equation.
y = 2x and y = x + 3 meet at (3, 6).
Used in: Systems of Linear EquationsTangent ratio
Opposite divided by adjacent in a right triangle.
tan θ = opposite ÷ adjacent, a fixed ratio for a given angle.
tan 45° = 1.
Used in: Right-Triangle Trigonometry and Coordinate GeometryUnit rate
How much you get for exactly one of something.
The value of a/b for the ratio a:b, expressed per one unit.
56 riyals for 10 notebooks is a unit rate of 5.60 per notebook.
Used in: Ratios, Rates and Unit RatesVariable
A letter that stands for a number.
A symbol representing an unknown or varying quantity.
In 3d + 10, d is the variable.
Used in: Expressions, Equations and InequalitiesVertex
The highest or lowest point of a parabola.
The turning point of a quadratic function, on its axis of symmetry.
y = (x − 3)² − 4 has vertex (3, −4).
Used in: Quadratic Equations and Their GraphsVertex form
A way of writing a quadratic that shows its turning point.
y = a(x − h)² + k with vertex (h, k).
y = (x − 4)² − 5.
Used in: Quadratic and Exponential ModelsVertical angles
Opposite angles formed when two lines cross.
A pair of non-adjacent angles formed by two intersecting lines; they are equal.
If one is 65°, the opposite one is also 65°.
Used in: Circles, Angles and Composite Measurementy-intercept
Where the line crosses the vertical axis.
The value of y when x = 0, written c in y = mx + c.
In y = 3x + 5 the y-intercept is 5.
Used in: Linear Equations, Slope and y = mx + cZero of a function
An input that makes the output zero.
A value x for which f(x) = 0, corresponding to a factor.
x = 2 is a zero of (x − 2)(x + 1).
Used in: Polynomials and Rational Expressions