Year 11 vocabulary glossary

exact value

An exact value is a precise answer given as a fraction, surd or multiple of π, rather than a rounded decimal.

truncate

To truncate a number means to cut off its digits after a certain point without rounding, such as truncating 3.789 to 3.78.

degree of accuracy

The degree of accuracy states how precisely a number has been given or should be rounded, such as to 2 decimal places or 3 significant figures.

appropriate accuracy

Appropriate accuracy means rounding an answer to a sensible level of precision for the context of the question, not more or less than needed.

growth and decay

Growth and decay describe quantities that repeatedly increase or decrease by the same percentage over equal time periods.

compound measure

A compound measure combines two other measures, such as speed, density or pressure, calculated by dividing one quantity by another.

rearrange a formula

To rearrange a formula means to change its subject, using inverse operations to isolate a different letter on its own.

efficient method

An efficient method solves a problem correctly using the fewest, most direct steps, valued especially under exam time pressure.

algebraic proof

An algebraic proof uses algebra to show that a mathematical statement is always true, using expressions such as 2n for any even number.

identity

An identity is a statement, shown with the symbol ≡, that is true for every value of the variable, unlike an equation which is only true for certain values.

prove

To prove a statement means to show, using logical algebraic steps, that it is true in every case, not just checked with examples.

expression is always positive/negative

Showing an expression is always positive (or negative) usually involves completing the square to reveal a squared term that cannot be negative.

iteration

Iteration is the process of repeating a calculation, using each output as the next input, to get closer and closer to a solution.

iterative formula

An iterative formula, such as xₙ₊₁ = f(xₙ), generates the next approximation to a solution from the previous one.

converge

A sequence of iterations converges when its values settle closer and closer towards a single solution.

function notation

Function notation, such as f(x), names a function and shows what value of x is being substituted into it.

inverse function

An inverse function, written f⁻¹(x), reverses the effect of the original function, taking an output back to its input.

composite function

A composite function applies one function to the result of another, written fg(x), meaning 'do g first, then f'.

enlargement

An enlargement is a transformation that changes the size of a shape by a scale factor, from a fixed centre of enlargement.

centre of enlargement

The centre of enlargement is the fixed point that a shape is enlarged or reduced from.

vector proof

A vector proof uses vector addition and scalar multiples to show geometric facts, such as that two lines are parallel or that points lie on a straight line.

collinear

Points are collinear if they all lie on the same straight line.

position vector

A position vector describes the position of a point relative to a fixed origin.

parallel vectors

Two vectors are parallel if one is a scalar multiple of the other, meaning they point in the same or exactly opposite direction.

angle of elevation

The angle of elevation is the angle measured upwards from the horizontal to a point above, such as looking up at a tower.

angle of depression

The angle of depression is the angle measured downwards from the horizontal to a point below, such as looking down from a cliff.

similar triangles

Similar triangles have exactly the same angles and sides in the same ratio, though they may be different sizes.

mutually exclusive events

Mutually exclusive events cannot happen at the same time, so their probabilities can simply be added together to find the probability of either happening.

independent events

Independent events do not affect each other's probability, so the probability of both happening is found by multiplying their individual probabilities.

AND rule (probability)

The AND rule multiplies probabilities to find the chance of two independent events both happening.

OR rule (probability)

The OR rule adds probabilities to find the chance of one mutually exclusive event or another happening.

expected frequency

Expected frequency is the number of times an outcome is predicted to occur, found by multiplying probability by the number of trials.

two-way table

A two-way table organises data by two categories at once, in rows and columns, making it easy to read off combined totals.

frequency tree

A frequency tree shows actual counts, rather than probabilities, branching out to show how a sample splits across combined events.

product rule for counting

The product rule for counting multiplies the number of choices at each stage to find the total number of possible combined outcomes.

modal class

The modal class is the class interval with the highest frequency in a set of grouped data.

estimate the mean (grouped data)

To estimate the mean of grouped data, use the midpoint of each class interval multiplied by its frequency, since the exact values are unknown.

skewed distribution

A skewed distribution is not symmetrical, with data bunched more towards one end and a longer 'tail' at the other.

statistical inference

Statistical inference means drawing conclusions about a whole population based on evidence from a sample.

comparing distributions

Comparing distributions means using measures such as the median and interquartile range to judge how two data sets differ in centre and spread.