Year 10 vocabulary glossary

upper bound

The upper bound is the largest value a rounded or truncated measurement could actually have been before rounding.

lower bound

The lower bound is the smallest value a rounded or truncated measurement could actually have been before rounding.

error interval

An error interval gives the full range of possible values between the lower and upper bounds of a rounded measurement.

surd

A surd is a root, such as √2 or √5, that cannot be simplified to a whole number or exact decimal.

simplify a surd

To simplify a surd means to rewrite it using the smallest possible number under the root sign, such as √12 = 2√3.

rationalise the denominator

To rationalise the denominator means to rewrite a fraction so that its denominator no longer contains a surd.

irrational number

An irrational number cannot be written exactly as a fraction; its decimal goes on forever without repeating, such as π or √2.

rational number

A rational number can be written exactly as a fraction of two integers, including terminating and recurring decimals.

recurring decimal

A recurring decimal has one or more digits that repeat forever, such as 0.333... (1/3).

terminating decimal

A terminating decimal has a fixed, finite number of digits after the decimal point, such as 0.75.

direct proportion

Two quantities are in direct proportion if, as one increases, the other increases at the same rate, so their ratio stays constant.

inverse proportion

Two quantities are in inverse proportion if, as one increases, the other decreases at a matching rate, so their product stays constant.

proportional

Two quantities are proportional if there is a constant relationship between them, either direct or inverse.

constant of proportionality

The constant of proportionality is the fixed number that links two proportional quantities, such as k in y = kx.

proportionality symbol (∝)

The symbol ∝ means 'is proportional to', such as y ∝ x meaning y is directly proportional to x.

compound measure

A compound measure combines two other measures, such as speed (distance ÷ time) or density (mass ÷ volume).

exponential growth

Exponential growth happens when a quantity increases by the same percentage over equal time periods, growing faster and faster.

quadratic formula

The quadratic formula, x = (-b ± √(b²-4ac)) / 2a, solves any quadratic equation ax² + bx + c = 0.

discriminant

The discriminant, b² - 4ac, shows how many real solutions a quadratic equation has.

completing the square

Completing the square rewrites a quadratic expression in the form (x + p)² + q, useful for solving equations and finding turning points.

perfect square

A perfect square is an expression or number that results from squaring another expression or number, such as (x + 3)² or 49.

simultaneous equations

Simultaneous equations are two or more equations solved together to find values that satisfy all of them at once.

elimination method

The elimination method solves simultaneous equations by adding or subtracting them to remove one unknown.

substitution method

The substitution method solves simultaneous equations by replacing one unknown with an expression from the other equation.

algebraic fraction

An algebraic fraction has an algebraic expression in its numerator, denominator, or both, such as (x+1)/(x-2).

common denominator (algebra)

A common denominator is a shared denominator used to add or subtract algebraic fractions.

optimisation

Optimisation means finding the best possible value, such as a maximum or minimum, for a quantity modelled by an expression.

turning point

The turning point of a quadratic graph is where the curve changes direction, at its maximum or minimum value.

vertex (of a parabola)

The vertex of a parabola is its turning point, the highest or lowest point on the curve.

maximum point

A maximum point is a turning point on a graph where the value is higher than all nearby points.

minimum point

A minimum point is a turning point on a graph where the value is lower than all nearby points.

reciprocal graph

A reciprocal graph, such as y = 1/x, has two curved branches that never touch the axes.

cubic graph

A cubic graph shows a function where the highest power of x is 3, such as y = x³, typically forming an S-shaped curve.

asymptote

An asymptote is a line that a graph gets closer and closer to, but never actually touches.

trigonometry

Trigonometry is the branch of maths dealing with the relationships between angles and side lengths in triangles.

opposite side

In a right-angled triangle, the opposite side is the side across from the angle being considered.

adjacent side

In a right-angled triangle, the adjacent side is the side next to the angle being considered, that is not the hypotenuse.

SOHCAHTOA

SOHCAHTOA is a memory aid for the trigonometric ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

sine rule

The sine rule relates the sides and angles of any triangle: a/sin(A) = b/sin(B) = c/sin(C).

cosine rule

The cosine rule relates the sides and angles of any triangle, used when the sine rule cannot be applied: a² = b² + c² - 2bc·cos(A).

vector

A vector is a quantity with both size (magnitude) and direction, often shown as an arrow or written as a column of numbers.

magnitude (vector)

The magnitude of a vector is its size or length, ignoring direction.

scalar multiplication

Scalar multiplication multiplies every part of a vector by a single number, changing its size but not its direction (unless negative).

resultant vector

A resultant vector is the single vector produced by adding two or more vectors together.

bearing

A bearing is a direction given as an angle measured clockwise from north, always written using three figures, such as 045°.

three-figure bearing

A three-figure bearing always uses three digits, such as 009° or 270°, to avoid confusion with other angle measurements.

histogram

A histogram displays grouped continuous data using bars whose area, not height, represents frequency, for unequal class widths.

frequency density

Frequency density is frequency divided by class width, plotted as the height of bars on a histogram.

box plot

A box plot summarises a data set using its minimum, lower quartile, median, upper quartile and maximum.

quartile

A quartile is one of three values that divide ordered data into four equal parts.

interquartile range

The interquartile range is the difference between the upper quartile and lower quartile, showing the spread of the middle half of the data.

Venn diagram

A Venn diagram uses overlapping circles to show how different sets of data relate to and overlap with each other.

tree diagram

A tree diagram shows the probabilities of combined events using branches, useful for working out probabilities of sequences of events.

conditional probability

Conditional probability is the probability of an event happening given that another event has already happened.

set notation

Set notation uses symbols such as ∪, ∩ and ' to describe and combine groups of items in a Venn diagram.

union (sets)

The union of two sets, shown as A ∪ B, contains every element that is in either set.

intersection (sets)

The intersection of two sets, shown as A ∩ B, contains only the elements that are in both sets.

universal set

The universal set contains every element being considered in a particular problem, usually shown as the rectangle around a Venn diagram.

sampling

Sampling means choosing a smaller group from a population to collect data from, used to represent the whole population.

hypothesis (statistics)

A hypothesis is a statement or prediction that a statistical investigation is designed to test.

stratified sample

A stratified sample divides a population into groups and selects a proportional number from each group, keeping the sample representative.

random sample

A random sample is chosen so that every member of the population has an equal chance of being selected.