24-hour clock
A way of writing times with four digits, from 00:00 at midnight to 23:59.
Notes: Time calculations
Maths terminology
Every key term, with its definition and a picture where one helps. Tap a bold word in the notes to see it there too.
289 terms
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A
Acceleration
How quickly velocity changes; the gradient of a velocity–time graph.
Adjacent
In a right-angled triangle, the side next to the angle you're using that isn't the hypotenuse.
Notes: Right-angled trigonometry
Algebraic fraction
A fraction with algebra in the numerator or denominator, such as (x − 3)/(x + 2).
Notes: Algebraic fractions
Alternate angles
Equal angles on opposite sides of a line crossing two parallel lines, between them.
Angle of depression
The angle measured downwards from the horizontal.
Notes: Right-angled trigonometry
Area
The amount of space inside a 2D shape, measured in square units.
Notes: Distance–time and velocity–time graphs · Perimeter and area · Circles, arcs and sectors · Sine and cosine rules · Histograms
Area of a triangle
½ab sin C, using two sides and the angle between them.
Notes: Sine and cosine rules
ASA
A condition for congruent triangles: two angles and a corresponding side are equal.
Notes: Congruence and similarity
Asymptote
A line that a graph gets closer and closer to but never touches.
Notes: Quadratic, cubic and reciprocal graphs · Circle and trigonometric graphs
B
Back bearing
The bearing of the return direction: 180° more or less than the original bearing.
Notes: Scale drawings and bearings
Bar chart
A chart that shows the frequency of each category as a bar, with gaps between the bars.
Notes: Charts and diagrams
Base
The number or letter being raised to a power: in x⁴, the base is x.
Notes: Powers, roots and index laws
Bearing
A direction given as a three-figure angle measured clockwise from north.
Notes: Scale drawings and bearings
Best buy
The option that gives the most for your money, found by comparing the cost of the same amount of each.
Notes: Money and best buys
Bias
When a sample or method is unfair, so the results don't represent the population.
Notes: Types of data and sampling
Biased
Some outcomes are more likely than others.
BIDMAS
The order of operations: brackets, indices, division and multiplication, addition and subtraction.
Box plot
A diagram showing the minimum, lower quartile, median, upper quartile and maximum.
C
Cancel
To divide the top and bottom of a fraction by the same factor.
Notes: Fractions · Algebraic fractions
Circle theorem
A rule about angles and lines in circles, used as a reason in angle problems.
Notes: Circle theorems
Co-interior angles
Angles on the same side of a line crossing two parallel lines, between them; they add up to 180°.
Coefficient
The number in front of a letter: in 3x, the coefficient is 3.
Column method
A written method that adds or subtracts digit by digit, with the place values lined up.
Notes: Written calculation methods
Column vector
A vector written as two numbers: the movement across, then up.
Notes: Transformations · Vectors
Common denominator
A denominator that two or more fractions share, so they can be added or subtracted.
Notes: Algebraic fractions
Common factor
A number or letter that divides into every term, such as 4xy in 8x²y − 12xy².
Completing the square
Writing a quadratic as (x + p)² + q.
Composite bar chart
A bar chart with each bar split into parts, stacked on top of each other.
Notes: Charts and diagrams
Compound interest
Interest worked out on the new amount each year, so it grows faster than simple interest.
Notes: Compound growth and decay
Compound measure
A measure made from two others, such as speed (distance and time).
Notes: Compound measures
Conditional probability
The probability of an event, given that another event has happened.
Constant of proportionality
The number k in a proportion equation, such as y = kx.
Continuous data
Data that can take any value in a range, usually measured.
Notes: Types of data and sampling
Conversion factor
The number you multiply or divide by to change from one unit to another.
Notes: Units and conversion graphs
Conversion graph
A straight-line graph used to change between two units.
Coordinates
A pair of numbers (x, y) giving a point's position: across, then up.
Notes: Coordinates and midpoints
Corresponding angles
Equal angles in the same position where a line crosses two parallel lines.
Cross-section
The shape you see when you cut straight across a 3D shape.
Notes: Volume and surface area
Cube number
A number made by multiplying a whole number by itself three times, such as 1, 8, 27 and 64.
Cubic graph
The graph of an equation with an x³ term and no higher power.
Cyclic quadrilateral
A quadrilateral with all four corners on the circumference of a circle.
Notes: Circle theorems
D
Decimal hours
A time written as a decimal number of hours, such as 2.4 hours for 2 hours 24 minutes.
Notes: Time calculations
Decimal place
A column after the decimal point; 7.47 has 2 decimal places.
Notes: Written calculation methods · Rounding and estimating
Denominator
The bottom number of a fraction: how many equal parts the whole is split into.
Notes: Fractions
Dependent events
Events where the outcome of one changes the probabilities for the other.
Notes: Tree diagrams
Depreciation
A fall in value over time, often by the same percentage each year.
Notes: Compound growth and decay
Diameter
A straight line across a circle through its centre; twice the radius.
Notes: Circles, arcs and sectors
Difference of two squares
An expression of the form a² − b², which factorises to (a + b)(a − b).
Notes: Factorising quadratics
Direct proportion
When one quantity is multiplied by a number, the other is multiplied by the same number.
Discrete data
Data that can only take certain values, usually counted.
Notes: Types of data and sampling
Discriminant
The part b² − 4ac; if it is negative, the equation has no solutions.
Dual bar chart
A bar chart with two bars side by side for each category, to compare two sets of data.
Notes: Charts and diagrams
E
Eliminate
To get rid of one letter by adding or subtracting the equations.
Notes: Simultaneous equations
Enlargement
A transformation that makes a shape bigger or smaller by a scale factor from a centre.
Notes: Transformations
Equation
Two expressions that are equal for particular values, such as 3x + 2 = 11.
Notes: Simplifying and forming expressions · Transformations
Equation of a circle
x² + y² = r² for a circle with centre (0, 0) and radius r.
Equilateral triangle
A triangle with all three sides equal and all three angles 60°.
Notes: Properties of 2D shapes
Error interval
The range of values a rounded or truncated number could have been, such as 7.35 ≤ l < 7.45.
Notes: Error intervals and bounds
Estimate
A rough answer found by rounding the numbers first, used to check a calculation.
Notes: Order of operations and calculators · Rounding and estimating
Expand
To multiply out brackets, so the expression has no brackets.
Expected outcome
The number of times you'd expect an event to happen: probability × number of trials.
Notes: Relative frequency
Exponential graph
The graph of y = kˣ, which grows (or decays) more and more quickly.
Expression
Terms added or subtracted, with no equals sign, such as 3x + 2y.
Exterior angle
The angle between one side of a polygon and the next side extended.
Notes: Angles in polygons
Extrapolation
Estimating a value outside the range of the data, which is less reliable.
Notes: Scatter graphs
F
f(x)
Function notation: the output of a function for an input x, so y = f(x) can stand for any graph.
Notes: Functions · Graph transformations
Factorise
To write an expression as a product, by taking common factors out into brackets.
Notes: Expanding and factorising brackets · Factorising quadratics
Formula
A rule that links quantities, such as A = lw.
Notes: Simplifying and forming expressions · Compound measures
Frequency
How many times a value or group appears.
Notes: Frequency tables and estimating the mean · Charts and diagrams
Frequency polygon
A graph of grouped data, with frequencies plotted at class midpoints and joined by straight lines.
Notes: Charts and diagrams
Frequency tree
A diagram showing how a group of people or things splits into smaller groups.
G
Geometric sequence
A sequence where each term is the one before multiplied by the same number.
Notes: Sequences
Gradient
How steep a line is: the change in y divided by the change in x.
Notes: Straight-line graphs · Parallel and perpendicular lines · Distance–time and velocity–time graphs
Grid method
Multiplying by splitting each number or bracket into parts in a grid, multiplying the parts and adding the results.
Notes: Written calculation methods · Expanding and factorising brackets
H
Highest common factor (HCF)
The biggest number that divides exactly into two or more numbers.
Notes: Prime factors, HCF and LCM
Histogram
A chart for continuous data where the area of each bar shows the frequency.
Notes: Histograms
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle.
Notes: Constructions and loci · Pythagoras' theorem · Right-angled trigonometry
I
Identity
A statement that is true for every value of its letters, shown with ≡.
Imperial units
Older units such as inches, miles, pounds and gallons.
Notes: Units and conversion graphs
Improper fraction
A fraction whose numerator is bigger than its denominator, such as 11/4.
Notes: Fractions
Index form
Repeated factors written as powers, such as 2 × 2 × 2 = 2³.
Notes: Prime factors, HCF and LCM
Indices
Powers, such as the 2 in 5²; roots count as indices too.
Notes: Order of operations and calculators · Powers, roots and index laws
Inequality
A statement that one amount is bigger or smaller than another, using <, >, ≤ or ≥.
Notes: Linear inequalities
Integer
A whole number, which can be positive, negative or zero.
Notes: Types of numbers and place value · Linear inequalities
Interquartile range
The upper quartile minus the lower quartile: the spread of the middle half of the data.
Inverse operation
The operation that undoes another: + undoes −, and × undoes ÷.
Notes: Solving linear equations
Inverse proportion
When one quantity is multiplied by a number, the other is divided by it.
Isosceles triangle
A triangle with two equal sides and two equal angles.
Notes: Properties of 2D shapes
Iteration
Repeating a calculation, using each answer as the input to the next.
Notes: Iterative methods
Iteration formula
A rule, such as xₙ₊₁ = ∛(4xₙ + 2), that gives the next value from the current one.
Notes: Iterative methods
K
Kite
A quadrilateral with two pairs of equal adjacent sides. Its diagonals cross at right angles.
Notes: Properties of 2D shapes
L
Like terms
Terms with exactly the same letters and powers, such as 5a and −2a.
Line graph
A graph of points joined by straight lines, often showing how something changes over time.
Notes: Real-life graphs
Line of best fit
A straight line drawn through the middle of the points on a scatter graph.
Notes: Scatter graphs
Line of symmetry
A mirror line that splits a shape or graph into two matching halves. For a quadratic graph, the vertical line through its turning point.
Linear
Making a straight-line graph; a linear equation has no x² or higher powers.
Notes: Straight-line graphs
Long division
A written method for dividing by a number with two or more digits, writing out each step.
Notes: Written calculation methods
Lowest common multiple (LCM)
The smallest number that two or more numbers all divide into exactly.
Notes: Prime factors, HCF and LCM
M
Mean
The total of the values divided by the number of values.
Notes: Averages and range · Frequency tables and estimating the mean · Charts and diagrams
Median
The middle value when the data is in order.
Notes: Averages and range · Cumulative frequency and box plots
Metric units
Units based on powers of 10, such as millimetres, grams and litres.
Notes: Units and conversion graphs
Midpoint
The point exactly halfway along a line segment. In a grouped frequency table, the value halfway between the ends of a class.
Notes: Coordinates and midpoints · Constructions and loci · Frequency tables and estimating the mean · Charts and diagrams
Multiple
A number in another number's times table.
Multiplier
The number you multiply by to make a percentage change, such as 1.15 for a 15% increase.
Notes: Percentages
N
Negative reciprocal
A number flipped and with its sign changed: the negative reciprocal of 2/3 is −3/2.
nth term
A rule that gives any term of a sequence from its position n, such as 4n + 3.
Notes: Sequences
O
Open circle
On a number line, a circle that isn't filled in: that end is not included.
Notes: Linear inequalities
Opposite
In a right-angled triangle, the side opposite the angle you're using.
Notes: Right-angled trigonometry
Order of rotational symmetry
How many times a shape looks the same in one full turn.
Notes: Properties of 2D shapes
Ordinary number
A number written out in full, such as 206 000, rather than in standard form.
Notes: Standard form
Original amount
The amount before a percentage increase or decrease.
Outlier
A value that is much bigger or smaller than the rest of the data.
Notes: Averages and range · Scatter graphs
Overestimate
An estimate that is bigger than the real answer.
Notes: Rounding and estimating · Distance–time and velocity–time graphs
Overtime
Hours worked beyond the normal hours, often paid at a higher rate.
Notes: Money and best buys
P
Parallel
Lines that run in the same direction and never meet; they have the same gradient.
Notes: Parallel and perpendicular lines · Vectors
Percentage
A number out of 100; 35% means 35/100.
Percentage change
How much an amount has changed, as a percentage of the original amount.
Notes: Percentages
Period
How often a repeating graph repeats: 360° for sin and cos, 180° for tan.
Perpendicular
Meeting at a right angle; perpendicular gradients multiply to −1.
Notes: Parallel and perpendicular lines · Perimeter and area · Circle theorems
Perpendicular bisector
A line that cuts another line in half at right angles.
Notes: Parallel and perpendicular lines · Constructions and loci
Pictogram
A chart that uses symbols to show frequencies, with a key to say what each symbol stands for.
Notes: Charts and diagrams
Pie chart
A circle split into sectors, with each sector's angle showing its share of the total.
Notes: Charts and diagrams
Place value
What a digit is worth because of the column it is in.
Plane
A flat surface that goes on in every direction, such as the base of a shape.
Point of intersection
The point where two lines or curves cross; it fits both equations.
Power
How many times a number is multiplied by itself; also called an index. In 2⁵ the power is 5.
Notes: Powers, roots and index laws
Power of 10
10 multiplied by itself a number of times, such as 10³ = 1000; 10⁻³ = 0.001.
Notes: Standard form
Probability
How likely something is to happen, from 0 (impossible) to 1 (certain).
Notes: Probability basics · Relative frequency
Prove
To show that a statement is true in every case, using algebra.
Notes: Algebraic proof · Congruence and similarity
Pythagoras' theorem
In a right-angled triangle, a² + b² = c², where c is the hypotenuse.
Notes: Pythagoras' theorem
Q
Quadratic
An expression or equation whose highest power of x is x², such as x² + 7x + 12.
Notes: Factorising quadratics · Sequences
Quadratic equation
An equation whose highest power of x is x², such as x² + 2x − 15 = 0.
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a, which solves ax² + bx + c = 0.
Quadratic graph
The graph of an equation with an x² term and no higher power: a U or ∩ shaped curve.
Quadratic inequality
An inequality with an x² term, such as x² − x − 6 < 0.
Quartiles
The values a quarter (lower quartile) and three quarters (upper quartile) of the way through the data.
R
Radius
The distance from the centre of a circle to its edge.
Rate
How one quantity changes for each unit of another, such as £1.50 per mile.
Notes: Real-life graphs · Money and best buys
Rearrange
To change the subject of a formula by doing the same to both sides.
Reciprocal
1 divided by a number; a number times its reciprocal is 1.
Notes: Types of numbers and place value · Powers, roots and index laws
Reciprocal graph
The graph of y = k/x: two curves that never touch the axes.
Recurring decimal
A decimal with a digit or block of digits that repeats forever, such as 0.333…
Reflection
Flipping a graph or shape over a mirror line, such as the x-axis or the y-axis.
Notes: Graph transformations · Transformations
Region
The part of a graph where every point satisfies a set of inequalities.
Regular polygon
A polygon with all its sides equal and all its angles equal.
Notes: Angles in polygons
Relative frequency
How often an event happened in an experiment, divided by the number of trials.
Notes: Relative frequency
Reverse percentage
Finding an original amount from the amount after a percentage change.
Notes: Reverse percentages
Rhombus
A quadrilateral with four equal sides and opposite sides parallel. Its diagonals cross at right angles.
Notes: Properties of 2D shapes
RHS
A condition for congruent right-angled triangles: the right angle, the hypotenuse and one other side are equal.
Notes: Congruence and similarity
Root
A solution of an equation, where its graph crosses the x-axis. Also the number that gives a value when raised to a power, such as √36 = 6.
Notes: Types of numbers and place value · Powers, roots and index laws · Solving quadratics by factorising · Iterative methods · Turning points and roots · Solving equations with graphs
S
SAS
A condition for congruent triangles: two sides and the angle between them are equal.
Notes: Congruence and similarity
Scalar
An ordinary number, with size but no direction, that a vector can be multiplied by.
Notes: Vectors
Scale
How lengths on a drawing or map compare to real lengths, such as 1 cm to 2 m.
Notes: Scale drawings and bearings
Scale factor
How many times bigger one shape is than a similar shape.
Notes: Congruence and similarity · Transformations
Scatter graph
A graph that plots pairs of values as points, to show whether two variables are correlated.
Notes: Scatter graphs
Second difference
The difference between consecutive first differences of a sequence. If the second differences are all the same, the sequence is quadratic.
Notes: Sequences
Secondary data
Data that someone else has collected, such as from a website or a census.
Notes: Types of data and sampling
Segment
The part of a circle between a chord and an arc.
Notes: Circles, arcs and sectors · Circle theorems
Set notation
Writing a set with braces, such as {x : x ≥ 3}, meaning all x such that x ≥ 3.
Short division
The bus stop method: dividing digit by digit and carrying each remainder to the next digit.
Notes: Written calculation methods
Significant figure
A digit counted from the first non-zero digit of a number.
Notes: Rounding and estimating
Similar
The same shape but not necessarily the same size: angles equal, sides in the same ratio.
Notes: Congruence and similarity
Simple interest
Interest that is the same each year, worked out on the original amount only.
Notes: Compound growth and decay
Simultaneous equations
Two equations, with two unknowns, that are both true at the same time.
Notes: Simultaneous equations · Solving equations with graphs
SOH CAH TOA
A way to remember the trigonometric ratios: sin θ = O/H, cos θ = A/H and tan θ = O/A.
Notes: Right-angled trigonometry
Solution
A value of x that makes an equation true; for a quadratic, also called a root.
Solve
To find the value of the letter that makes an equation true.
Notes: Solving linear equations · Functions
Space diagonal
A line through the inside of a 3D shape, joining two opposite corners.
Speed
How far something travels per unit of time; the gradient of a distance–time graph.
Notes: Distance–time and velocity–time graphs · Compound measures
Square number
A number made by multiplying a whole number by itself, such as 1, 4, 9, 16 and 25.
Standard form
A number written as A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number.
Notes: Standard form
Standing charge
A fixed charge on a bill, paid whatever the amount used, on top of the cost per unit.
Notes: Money and best buys
Stationary
Not moving; shown by a flat line on a distance–time graph.
Stem-and-leaf diagram
A way of showing ordered data, with the tens as stems and the units as leaves.
Notes: Averages and range
Subject
The letter on its own on one side of a formula: in v = u + at, v is the subject.
Substitute
To replace a letter with a number or an expression.
Notes: Substitution and rearranging formulae · Simultaneous equations
T
Tangent
A straight line that touches a circle or curve at one point without crossing it. On a graph, it has the same gradient as the curve there.
Notes: Circle and trigonometric graphs · Distance–time and velocity–time graphs · Circles, arcs and sectors · Circle theorems
Term
One part of an expression, such as 3x or −5, including its sign.
Notes: Simplifying and forming expressions · Solving linear equations · Factorising quadratics · Sequences
Tetrahedron
A 3D shape with four triangular faces: a triangular-based pyramid.
Notes: Properties of 3D shapes
Translation
Sliding a graph or shape without turning or resizing it.
Notes: Graph transformations · Transformations
Trapezium
A quadrilateral with one pair of parallel sides.
Tree diagram
A diagram of branches showing the outcomes of events, one after another, with their probabilities.
Notes: Tree diagrams
Truncate
To cut a number off after a certain digit without rounding it.
Notes: Error intervals and bounds
Two-way table
A table that sorts data by two features, with totals for each row and column.
U
Underestimate
An estimate that is smaller than the real answer.
Notes: Rounding and estimating · Distance–time and velocity–time graphs
Unitary method
Finding the value of one unit first, then multiplying.
Universal set
The set of everything being considered, written ξ: the rectangle round a Venn diagram.
Upper bound
The value a rounded number must be less than; it is half a unit above the rounded value.
Notes: Error intervals and bounds · Cumulative frequency and box plots
V
VAT
Value Added Tax, usually 20%, added to the price of many goods and services.
Notes: Reverse percentages · Money and best buys
Venn diagram
A diagram of overlapping circles that sorts things into sets.
Vertically opposite angles
The equal angles opposite each other where two straight lines cross.
X
Y
y-intercept
Where a graph crosses the y-axis; in y = mx + c, it is c.