Year 9 vocabulary glossary

standard form

Standard form writes very large or very small numbers as a value between 1 and 10 multiplied by a power of 10, such as 3.2 x 10⁶.

index notation

Index notation writes repeated multiplication using a base number and a power, such as 2⁵ meaning 2 x 2 x 2 x 2 x 2.

index law

An index law is a rule for combining powers, such as adding indices when multiplying powers of the same base.

positive index

A positive index shows a number multiplied by itself that many times, such as the 3 in 4³.

negative index

A negative index means finding the reciprocal of the number raised to the positive version of that power, such as 2⁻¹ = 1/2.

zero index

Any non-zero number raised to the power of zero is equal to 1.

power of ten

A power of ten is 10 raised to a whole-number index, such as 10², used to shift place value in standard form.

repeated percentage change

Repeated percentage change applies the same percentage increase or decrease more than once in a row, such as compound interest over several years.

compound growth

Compound growth is an increase applied repeatedly to an amount that already includes previous increases, so growth speeds up over time.

growth rate

The growth rate is the percentage by which a quantity increases over a given period.

order of magnitude

Order of magnitude describes the approximate size of a number, usually based on its power of 10 in standard form.

scientific notation

Scientific notation is another name for standard form, commonly used in science to write extremely large or small measurements.

double bracket

Expanding double brackets means multiplying two bracketed expressions together, such as (x + 2)(x + 3).

quadratic expression

A quadratic expression contains a term with the unknown squared, such as x² + 5x + 6, and no higher power.

factorise

To factorise means to write an expression as a product of its factors, the reverse process of expanding brackets.

quadratic equation

A quadratic equation is an equation containing a squared term as its highest power, such as x² + 5x + 6 = 0.

x² term

The x² term is the part of a quadratic expression where the unknown is squared, such as the x² in x² + 3x - 4.

inequality

An inequality compares two expressions using symbols such as <, >, ≤ or ≥, showing one is not necessarily equal to the other.

inequality symbol

An inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to) or ≥ (greater than or equal to), shows how two values compare.

linear inequality

A linear inequality is an inequality where the unknown appears only to the power of 1, solved in a similar way to a linear equation.

solution set

A solution set is the full range of values that satisfy an inequality or equation.

number line (inequality)

A number line can show the solution to an inequality using an open circle for < or >, and a closed circle for ≤ or ≥.

quadratic sequence

A quadratic sequence has an nth term containing n², so its term-to-term differences are not constant.

first difference

The first difference is the amount by which each term of a sequence changes from the one before it.

second difference

The second difference is the difference between consecutive first differences; a constant second difference shows a sequence is quadratic.

nth term of a quadratic sequence

The nth term of a quadratic sequence is an expression, involving n², used to find any term directly from its position.

Pythagoras' theorem

Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

hypotenuse

The hypotenuse is the longest side of a right-angled triangle, always opposite the right angle.

right-angled triangle

A right-angled triangle is a triangle with one angle that measures exactly 90 degrees.

congruence condition

A congruence condition is a rule that proves two triangles are congruent by comparing certain sides and angles.

SSS (side-side-side)

SSS is a congruence condition proving two triangles are congruent because all three pairs of corresponding sides are equal.

SAS (side-angle-side)

SAS is a congruence condition proving two triangles are congruent because two sides and the angle between them match.

ASA (angle-side-angle)

ASA is a congruence condition proving two triangles are congruent because two angles and the side between them match.

RHS (right angle-hypotenuse-side)

RHS is a congruence condition proving two right-angled triangles are congruent because their hypotenuses and one other side match.

cylinder

A cylinder is a 3-D shape with two identical circular ends connected by a curved surface.

cone

A cone is a 3-D shape with a circular base that tapers smoothly to a single point, called the apex.

sphere

A sphere is a perfectly round 3-D shape, where every point on its surface is the same distance from the centre.

radius

The radius is the distance from the centre of a circle or sphere to any point on its edge or surface.

circle theorem

A circle theorem is a proven rule about angles, chords or tangents in circles, used to find unknown angles or lengths.

arc

An arc is a curved part of the circumference of a circle.

chord

A chord is any straight line segment joining two points on a circle's circumference, used in several circle theorem proofs.

tangent (circle)

A tangent to a circle is a straight line that touches the circle at exactly one point, at a right angle to the radius there.

similar shapes

Similar shapes have the same angles and are the same shape, but can be different sizes, with sides in the same ratio.

scale factor

A scale factor is the number a shape's lengths are multiplied by to enlarge or reduce it to a similar shape.

corresponding sides

Corresponding sides are sides in the same relative position on two similar or congruent shapes.

exact trigonometric value

An exact trigonometric value is a sine, cosine or tangent ratio for a special angle, such as 30°, 45° or 60°, expressed as a fraction or surd rather than a decimal.

loci

Loci is the plural of locus, meaning all the possible positions of a point that follows a given rule.

locus

A locus is a path or set of points that satisfies a particular rule, such as being a fixed distance from a point.

perpendicular bisector

A perpendicular bisector is a line that crosses another line at a right angle, exactly through its midpoint.

angle bisector

An angle bisector is a line that splits an angle into two equal halves.

plan (view)

A plan is the view of a 3-D shape or object seen from directly above.

elevation

An elevation is the view of a 3-D shape or object seen from the front or side.

frequency polygon

A frequency polygon is a line graph made by joining the midpoints of the tops of bars on a frequency diagram.

cumulative frequency

Cumulative frequency is a running total of frequencies, adding each new frequency to the sum of all before it.

cumulative frequency diagram

A cumulative frequency diagram plots cumulative frequency against value, usually forming an S-shaped curve.

probability

Probability is a measure of how likely an event is to happen, given as a value between 0 (impossible) and 1 (certain).

outcome

An outcome is one possible result of a probability experiment, such as rolling a 4 on a dice.

sample space

The sample space is the set of all possible outcomes of a probability experiment.

sample space diagram

A sample space diagram is a grid or table showing every possible combined outcome of two events.

relative frequency

Relative frequency is the number of times an event happens divided by the total number of trials, used to estimate probability from experiments.

theoretical probability

Theoretical probability is calculated using known, equally likely outcomes, without needing to carry out an experiment.

experimental probability

Experimental probability is found by carrying out trials and recording how often an event actually happens.

trial

A trial is a single instance of carrying out a probability experiment, such as one roll of a dice.

fair (probability)

An object or process is fair if every outcome is equally likely to happen.