**GCSE Edexcel Maths Higher Glossary**

The key vocabulary you need to learn for your GCSE Edexcel Maths Higher paper. Find all the terms and definitions you need to understand, from ‘Acceleration’ to ‘Word-based problems’.

##### A (Acceleration to Axes)

**acceleration**

Acceleration is the rate of change of speed, shown by the gradient in a speed-time graph.

**acute angle**

An acute angle is an angle between 0Â° and 90Â°.

**adjacent (trigonometry)**

The adjacent is the side next to the angle Î¸ in a right-angled triangle.

**algebraic method (simultaneous equations)**The algebraic method is a means of solving simultaneous equations using algebra and not a graph. The methods are the elimination method and the substitution method.

**alternate angles**

Alternate angles are on the opposite sides of a transversal line that intersects a pair of parallel lines. Alternate angles are always equal.

**angle**

An angle is the amount of turn, usually from one line to another line connected at a point (vertex).

**arc**

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

**area**

Area is the flat space inside a 2D shape. Typical units are cmÂ² and mÂ²

**arithmetic sequence**

An arithmetic sequence (or linear sequence) is one in which the next term can be found by adding or subtracting the same number each time.

**axis [axes]**

Axes (singular: axis) are lines that cross at 90Â°, used to locate points in a coordinate system.

##### B - C (Bar chart to clockwise)

**bar chart**

Bar charts are used for qualitative (categorical) data. In a bar chart, the height of each bar shows the frequency.

**bar model**

A bar model is a pictorial representation of a mathematical problem where bars are used to represent the known and unknown quantities.

**bearing**

A bearing is an angle in degrees measured clockwise from north that gives a direction of travel. Bearings always have three figures, for example, a bearing of 3Â° is written as 003Â°

**biased (probability)**

Biased means unfair. For example, an unfair coin or spinner or dice is said to be biased.

**biased sample**

A biased sample is a sample that doesnâ€™t represent the population well.

**bisector**

A bisector cuts a line or angle exactly in half.

**box plot **

A box plot is a diagram that shows the median, range and interquartile range of data and is useful for

comparing sets of data.

**calculate**

To calculate is to find the numerical answer.

**capture-recapture**

The capture-recapture method is used to estimate the size of an animal population using the formula \(n=\frac{nK}{k}\) where n = size of sample, K = animals in the first sample that are marked and k = marked animals found in the second sample.

**causation**

Causation between two sets of data when one variable causes the other.

**centre of enlargement**

The centre of enlargement is the point about which a shape is enlarged.

**centre of rotation**

The centre of rotation is the point about which a shape is rotated.

**chord**

A chord is a line segment that joins two points on a circle.

**circumference**

The circumference is the perimeter of a circle.

**clockwise**

Clockwise means the direction in which the hands of clock travel. The opposite direction is anticlockwise.

##### C (Co-interior angles to compound shape)

**co-interior angles**

Co-interior angles are on the same side of a transversal line that intersects a pair of parallel lines. Co-interior angles sum to 180Â°

**coefficient**

A coefficient is the number before a letter in an algebraic term. For example: in the term 5xyÂ², the coefficient is 5

**column vector**

A column vector is a vector whose components are given in a single vertical column.

**commutative**

Commutative means a calculation can be done in any order. For example,

addition and multiplication are commutative:

7 + 4 = 4 + 7Â Â Â Â 8 Ã— 2 = 2 Ã— 8

but subtraction and division are not:

7 â€“ 4 â‰ 4 â€“ 7Â Â Â Â 8 Ã· 2 â‰ 2 Ã· 8

**compass**

A compass shows the direction of magnetic north, east, south and west.

**complement**

The complement of a set is the numbers or objects in the universal set that are not in that set. Aâ€² means the complement of set A (numbers or objects not in set A).

**composite bar chart**

Composite bar charts show two sets of data, stacked in a single bar, on the same bar chart.

**composite function**

A composite function is made when the output from one function is used as the input of another function.

**composite solid**

A composite solid is a 3D shape that is made up of two or more simpler 3D shapes.

**compound interest**

Compound interest is interest calculated on both the original amount deposited and any previous interest payments made.

**compound measure**

A compound measure links two measurements. For example, a rate of pay could be Â£11 per hour and a rate of flow of water could be 3 litres per minute. Speed, density and pressure are also compound measures.

**compound shape**

A compound shape is two or more 2D shapes joined together to create a single shape.

##### C (Conditional probability to cosine (cos))

**conditional probability **

Conditional probability is the probability of one event happening, given that another event has already occurred.

**cone**

A cone is a 3D shape with a circular base and one vertex.

**congruent [congruence]**

Shapes are congruent if all the sides and angles are equal. To be congruent means to be exactly the same size and shape.

**congruent shapes**

Congruent shapes are exactly the same size and shape.

**constant of proportionality**

The constant of proportionality is the ratio between two directly proportional quantities.

**construct**

To construct a shape means to draw it accurately with a ruler and pair of compasses.

**continuous data**

Continuous data is data that can take any value.

**Coordinate [coordinates]**

Coordinates are an ordered pair (x,â€‰y) that locates a point.

**coordinate grid**

A coordinate grid is a grid and a set of axes that you can plot points (coordinates) and lines on.

**correlation**

Correlation describes how data may be related. It can be positive or negative, and range from strong to weak.

**corresponding angles (in parallel lines)**

Corresponding angles are the pair of angles found in the same relative position when a transversal line crosses a pair of parallel lines. Corresponding angles are equal.

**corresponding angles (in similar and congruent shapes)**

Corresponding angles are the pairs of angles that are found in the same relative position in similar and congruent shapes. Corresponding angles are equal.

**corresponding sides (in similar and congruent shapes)**

Corresponding sides are sides in the same relative position in similar and congruent shapes. In congruent shapes, corresponding sides are equal.

**cosine (cos) **

The cosine of an angle in a right-angled triangle is the length of the adjacent side divided by the length of the hypotenuse. \(cos ÆŸ \frac{adjacent}{hypotenuse}\)

##### C (Cosine rule to cylinder)

**cosine rule**

The cosine rule is an extension of Pythagorasâ€™ theorem that can be applied to any triangle. To find a side useÂ

and to find an angle use

**cube**

A cube is a 3D solid with 6 square faces, 8 vertices and 12 edges.

**cube number**

A cubed number is multiplied by itself three times, such as 3 Ã— 3 Ã— 3 = 27. The first three cube numbers are: 1, 8, 27

**cubed**

Cubed means â€˜multiplied by itself and then by itself againâ€™. For example, 5Â³ = 5 Ã— 5 Ã— 5 = 125

**cubic graph**

A cubic graph has an xÂ³ term in its equation. The general equation of a cubic graph is:

y = axÂ³ + bxÂ² + cx + d where a, b, c and d are constants.

**cuboid **

A cuboid is a 3D solid with 6 rectangular faces, 8 vertices and 12 edges.

**cumulative frequency graph **

Cumulative frequency graphs show the total frequency up to each point.

**cyclic quadrilateral**

A cyclic quadrilateral isâ€¯a quadrilateral drawn inside a circle. Every corner of the quadrilateral touches the circumference of the circle.

**cylinder **

A cylinder is a 3D shape with a circular cross-section and a curved surface.

##### D (Data to dual bar chart)

**data**

Data is any information you can collect.

**deceleration**

Deceleration means slowing down; also called negative acceleration.

**decimal**

A decimal is a way of representing a number where the number of tenths, hundredths, thousandths, etc. are written as digits following a decimal point. For example: 1.25, 0.66, â€“9.812

**decimal place**

Decimal place is theâ€¯position of a digit to the right of a decimal point.

**decrease**

To decrease means to reduce.

**denominator**

A denominator is the bottom number in a fraction. For example, the denominator in \(\frac{3}{5}\) is 5

**density**

Density is a compound measure that is calculated using the formula: density =\(\frac{mass}{volume}\). Typical units include kg/mÂ³ and g/cmÂ³

**diameter**

The diameter is the distance across a circle through the centre. The diameter is twice the radius.

**difference of two squares**

The difference of two squares (DOTS) is an expression, such as aÂ² â€“ bÂ², which contains one square number minus another square number. For example, xÂ² â€“ 9 is the difference of two squares.

**digit**

A digit is any one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in the base-ten numbering system.

**direct proportion**

When two values are in direct proportion, they will increase and decrease at the same rate.

**discrete data**

Discrete data is data that can only take specific values or numbers. For example, the number of passengers on a bus.

**dual bar chart**

Dual bar charts show two sets of data, beside each other, on the same bar chart.

##### E (Edge to equidistant)

**edge**

An edge is any straight side of a 2D or 3D shape.

**elevation**

An elevation is the view from the side or the front of an object.

**elimination method (simultaneous equations)**

The elimination method is a way of solving simultaneous equations where you add or subtract the two equations to get rid (eliminate) one of the variables.

**enlargement**

Enlargement is a transformation in which the lengths of the object are multiplied by a scale factor, but the angles are unchanged. An object and its enlargement are similar shapes.

**equation**

An equation is two expressions which are equal in equal in value and connected by an equals sign.

**equation of a graph**

The equation of a graph is a rule that is true for all points on the graph.

**equation of a straight line**

The general equation of a straight line is y = mx + c, where m is the gradient of the line, and c is the y-intercept.

**equidistant**

Equidistant means â€˜the same distanceâ€™.

##### E (Equivalent fractions to extrapolation)

**equivalent fractions**

Equivalent fractions have different denominators but the same value as each other. For example: \(\frac{3}{5}\) and \(\frac{6}{10}\)are equivalent fractions.

**error interval**

Error intervals are inequalities that show possible values of numbers before rounding.

**estimate**

To estimate is to give or find an approximate answer.

**estimation**

Estimation is when we use an easier calculation that is roughly the same to give an approximate answer.

**evaluate (a function) **

You can evaluate a function f(x) by substituting a value in place of x.

**expand**

Expand means to multiply each term inside a set of brackets by the term outside the brackets.

**expected frequency**

The expected frequency of an event is the number of times you expect it to happen. Expected frequency = probability Ã— number of trials

**exponential **

An exponential function is in the form y = \(K^{x} \), where k is a positive constant.

**expression**

An expression is a collection of letters and numbers which cannot be solved (no equal signs). For example,

**exterior angle**

Exterior angles are between a side of the shape and the line extended from the side next to it.

**extrapolation**

Extrapolation is making predictions outside the range of data.

##### F (Face to function)

**face**

The face is a flat surface of a 3D shape.

**factor**

A factor is a positive integer that divides exactly into another integer leaving no remainder.

**factorise [factorising]**

To factorise means to write a number, term or expression as the product of its factors.

**Fibonacci sequence**

A Fibonacci sequence, named after Italian mathematician Fibonacci, is a sequence where you add the previous two terms to get the next term. The â€˜originalâ€™ Fibonacci sequence was: 1, 1, 2, 3, 5, 8, 13, 21, …

**formula**

A formula is an equation which links different variables in a real-life relationship.

**fraction**

A fraction is a number written in the form \(\frac{a}{b}\), where a and b are whole numbers, and b â‰ 0. A fraction also expresses how a whole is divided into parts. For example \(\frac{3}{4}\) means 3 out of 4 parts.

**frequency**

Frequency is the total number of times something happened.

**frequency density **

The frequency density is the frequency divided by the class width.

**frequency polygon **

Frequency polygons represent grouped data. The frequency of each class is plotted against its midpoint, then each point is joined with straight lines.

**frequency tables**

Frequency tables are used to collect data and show how frequently each event or quantity occurs.

**frequency tree**

Frequency trees show the outcomes of two or more events, and the frequencies with which they occur.

**front elevation**

The front elevation is the view of a 3D shape from the front.

**frustrum**

A frustrum is made by removing a small cone from the top of a larger cone.

**function**

Function is a rule that describes the relationship between two variables.

##### G - H (Geometric sequence to hypotenuse)

**geometric sequence**

In a geometric sequence, the next term is found by multiplying or dividing by the same number each time.

**gradient**

The gradient is a measure to describe how steep a line graph is.

**graph**

A graph is produced by using a coordinate grid to plot values of a function. The graph shows the relationship between the variables in a function.

**graphical method (simultaneous equations)**

The graphical method is a way of solving simultaneous equations. Using the graphical method, the solution to a pair of simultaneous equations is the point of intersection of their graphs, the point where the two lines cross.

**grouped (frequency tables)**

Grouped frequency tables are used for continuous quantitative data, such as heights. The data is organised into groups that must not overlap.

**hemisphere **

A hemisphere isâ€¯half a sphere.

**highest common factor (HCF)**

The highest common factor (HCF) of x and y is the biggest number that is a factor of both x and y.

**histogram **

A histogram is used to represent grouped data and can be used when the class widths are different. In a histogram the area of each bar represents the frequency of the data.

**hypotenuse**

The hypotenuse is the longest side of a right-angled triangle.

##### I (Identity to iteration)

**identity**

An identity is an equation that is always true, no matter what the value of the variable is.

**image**

An image is the result after a transformation.

**improper fraction**

In improper fractions, the numerator is greater than the denominator. For example: \(\frac{18}{5}\)

**increase**

To increase means to make larger.

**inequality**

An inequality is a relationship between two expressions which are not equal to one another. The symbols used for inequalities are <, >, â‰¤, â‰¥.

**integer**

An integer is a whole number, such as 1, 73, 946, â€“17

**intercept**

The intercept is the point at which a graph crosses either the x- or y-axis.

**interior angles**

Interior angles are inside a polygon at each vertex

**interquartile range **

The interquartile range is the difference between the upper quartile and lower quartile.

**interpolation**

Interpolation is using the line of best fit to estimate a value within the range of the data.

**intersect**

To intersect is to have a common point or points.

**intersection (set notation)**

The intersection of two sets contains the members that belong to both sets. The intersection of sets A and B is written as A âˆ© B.

**inverse (function) **

The inverse of a function reverses its effect. The inverse of f(x) is written as fâ€“1(x).

**inverse operation**

An inverse operation is an operation that reverses the effect of another operation, such as addition and subtraction.

**inverse proportion**

Two values are in inverse proportion if, when one increases, the other decreases at the same rate.

**irregular polygon**

An irregular polygon is a polygon that is not regular â€“ at least one side or angle is different from the others.

**iteration **

Iteration means repeating a process. It can be used to find an approximate solution to more complex equations.

##### L (Like terms to mutually exclusive events)

**like terms**

Like terms are terms which have the same letters and powers of letters. Order and coefficients do not matter.

**line graph**

Line graphs (or time-series graphs) show how data change over time. Time is always on the horizontal axis.

**line of best fit**

The line of best fit is a straight line drawn on a scatter graph which follows the trend of the data.

**linear equation **

A linear equation is an equation in which the highest power of the variable is 1.

**linear graph**

A linear graph is a set of coordinates that make a straight line when plotted. The line can be horizontal, vertical or sloping.

**line of reflection **

The line of reflection is the line halfway between two mirror images.

**line of symmetry **

A line of symmetry isâ€¯the line that divides a shape or graph into two equal and symmetrical parts.

**loci**

Loci are the sets of points which are all the same distance from a point or a line.

**locus of points**

The path formed by a point which moves according to a rule or property. For example, the locus of points a fixed distance from a point is a circle.

**lowest common multiple (LCM)**

The lowest common multiple (LCM) of x and y is the smallest number that is a multiple of both x and y.

**lower quartile**

The lower quartile (LQ) is the value 25% of the way through a data set.

**magnitude **

Magnitude means size.

**mean**

The mean is the sum of all values divided by the total number of values.

**median**

The median is the middle value when the data is put in order. If there are two middle values, the median is the mean of the two middle values.

**median class**

The median class of grouped data is the class that the middle value lies in.

**member**

The members of a set are numbers or objects that belong to the set.Â x âˆˆ A means x is a member of the set A.

**metric**

The metric system of measurement uses metric units to measure length, mass, volume, etc. Metric units include metre, centimetre, millimetre, kilometre, gram, kilogram, litre and millilitre.

**mixed number **

A mixed number includes a whole part and a fraction part. For example: 10\(\frac{2}{3}\)

**modal class **

The modal class of grouped data is the class with the highest frequency.

**mode**

The mode is the most commonly occurring value. There can be no mode, one mode or multiple modes.

**multiple**

A multiple of a is n Ã— a, where n is any other integer.

**multiplier**

A multiplier is a number, usually a decimal, which is used to calculate a percentage of an amount. For example, to find 82% of an amount, the multiplier is 0.82

**mutually exclusive events**

Mutually exclusive events are events that canâ€™t happen at the same time. For example, a number cannot be both odd and even.

##### N (negative number to outliers)

**negative number**

A negative number is any number less than 0

**net**

A net is a 2D shape that folds up to make a 3D shape.

**non-strict inequality **

Non-strict inequalities (â‰¤ and â‰¥) are represented with closed circles on number lines and solid lines on graphs.

**notation**

Notation is a system of symbols and conventions for writing mathematical terms and expressions.

**nth term**

The nth term is the position-to-term rule for a sequence. You can use it to find any term in the sequence. n is the term number.

**number**

A number is a value representing a quantity and is used in counting and making calculations.

**number line **

A number line is a visual representation of numbers on a straight line.

**numerator**

A numerator is the top number in a fraction. For example, the numerator \(\frac{3}{5}\) is 3

**object**

An object is the original shape, prior to a transformation.

**obtuse angle**

An obtuse angle is an angle between 90Â° and 180Â°

**opposite (trigonometry)**

The opposite is the side across from the angle Î¸ in a right-angled triangle.

**orientation**

Orientation describes how a shape is positioned on a coordinate grid. For example, when you translate a shape, the object and image have the same orientation (unlike rotations and reflections).

**origin**

The origin is the point with coordinates (0,â€‰0)

**outliers**

Outliers are values in a set of data that do not follow the same trend as the rest of the data.

##### P (Pair of compasses to Pi)

**pair of compasses**

A pair of compasses mark the points at a given distance from a fixed point and are used to construct circles and circular arcs.

**pair of simultaneous equations**

A pair simultaneous equation are two equations in two variables that you solve at the same time.

**parallel (graphs)**

Two lines are parallel when they are always the same distance from each other. A pair of parallel lines will have the same gradient.

**parallel lines**

Parallel lines are the same distance from each other. Parallel lines never meet. They are shown on diagrams by arrows on the lines.

**parts (ratio)**

A part is a portion or division of a whole.

**percent**

Percent means â€˜out of 100â€™

**percentage (percentages)**

Percentages are fractions expressed as the number of parts per 100 and recorded using the notation %. For example:

**percentage increase/decrease**

The percentage increase/decrease is percentage change between an original amount and the amount after an increase or decrease. It can be calculated using the formulae: percentage increase/decrease =

**perimeter**

The perimeter is the total distance around the outside of a 2D shape.

**perpendicular**

Perpendicular refers to angles at 90Â° (right angles) to each other.

**perpendicular bisector**

A perpendicular bisector cuts a line exactly in half at right angles.

**perpendicular distance**

The perpendicular distance is the shortest distance from a point to a line.

**perpendicular lines**

Perpendicular lines are lines at 90Â° to each other (at right angles).

**Pi Ï€**Pi (Ï€) is a number that relates the ratio of the circumference of a circle to the diameter. Ï€ = 3.1415, to four decimal places.

##### P (Pictogram to pressure)

**pictogram**

Pictograms are used for qualitative data. They use images to represent the data.

**pie chart**

In a pie chart, the frequency or amount of something is shown as a sector of a circle.

**place value**

Place value is the value of each digit within a number.

**plan**

A plan is a view from directly above an object.

**polygon**

A polygon is a 2D shape with three or more straight sides, called edges.

**polyhedron**

A polyhedron is a solid shape with flat polygonal faces, straight edges and vertices.

**population**

The population is the entire group of things that you can choose from.

**position-to-term rule**

The position-to-term rule is a rule that finds the term based on where it is in the sequence. The position to term rule is always written in terms of n and is also called the nth term.

**positive number**

A positive number is any number greater than 0.

**possibility space**

A possibility spaces (also called a sample space) is a list of all the possible outcomes of two events. You can write a possibility space as a systematic list or in a two-way table.

**power**

A power describes how many times a base number is multiplied by itself, indicated by a small, raised number. For example: with \(5^{4} \), the base is 5 and the power is 4 and \(5^{4} \) = 5 Ã— 5 Ã— 5 Ã— 5

**pressure**

Pressure is a compound measure that is calculated using the formula: pressure = \(\frac{force}{area}\). Typical units include N/mÂ²

##### P (Primary data to Pythagorasâ€™ theorem)

**primary data**

Primary data is data that you collect yourself.

**prime factor**

A prime factor is a factor that is also a prime number.

**prime factor decomposition**

Prime factor decomposition means writing a number as the product of its prime factors. For example, 36 = 2Â² Ã— 3Â³

**prime number**

A prime number is a number with exactly two factors. 1 is not a prime number.

**prism**

A prism is a 3D shape with a polygon as a base and a constant cross section joined by rectangles.

**probability**

Probability is the likelihood that something will happen. It is always a value between 0 and 1. Probabilities can be written as fractions, decimals or percentages.

**probability experiment**

A probability experiment is a test where you carry out trials to estimate the probability of an event.

**probability scale **

A probability scale is a visual representation of probabilities on a number line from 0 (impossible) to 1 (certain).

**product**

The product is the result of multiplication.

**proof **

Proof is a sequence of mathematical statements that follow on logically from each other that shows that something is always true.

**protractor**

The protractor is a tool used to draw and measure angles.

**pyramid**

A pyramid is a 3D shape with a polygon base, and triangular sides that meet at one vertex.

**Pythagorasâ€™ theorem**

Pythagorasâ€™ theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other sides. Often written as aÂ² + bÂ² = cÂ².

##### Q - R (Quadratic expression to ratio)

**quadratic expression**

A quadratic expression is an expression where the highest power of the variable is 2. They are of the form axÂ² + kbx + c, where a, b and c are the coefficients.

**quadratic graph**

The quadratic graph is one with equation: y = axÂ² + by + c, where a, b and c are numbers.

**quadratic sequences**

In a quadratic sequence, the position-to-term rule includes a squared term.

**quadrilateral**

A quadrilateral is a 2D polygon with four sides, four angles, and four vertices. Angles in a quadrilateral add up to 360Â°

**qualitative data**

Qualitative data is non-numerical data; a quality or characteristic. For example, colour of a personâ€™s hair.

**quantitative data**

Quantitative data is numerical data, a quantity or amount. For example, the number of students in a class.

**quotient**

The quotient is the result of division.

**radius**

The radius is the distance of a point on a circle to the centre.

**random sample**

In a random sample, each member of the population is equally likely to be chosen.

**range**

The range of qualitative data is the difference between the largest and smallest values.

**ratio**

A ratio compares two or more quantities in relation to each other. For example, if a bracelet has 2 red beads for every 3 black beads, then the ratio of red to black is 2â€‰:â€‰3

##### R (Real-life-graph to ruler)

**real-life graph**

Real-life graphs are used to represent real-life situations and data.

**reciprocal**

The reciprocal of a number a is \(\frac{1}{a}\). For example, the reciprocal of 4 is \(\frac{1}{4}\). Any number multiplied by its reciprocal is 1

**reciprocal graph**

A reciprocal graph is of the form y=\(\frac{a}{x}\), where a is a constant.

**recurring decimal**

Recurring decimals are numbers with a digit or group of digits that repeat forever. For example:\(\frac{1}{3}\) =0.33333…

**reflection**

Reflections are a type of transformations where a shape is reflected in a line of reflection (also called a mirror line or line of symmetry).

**reflex angle**

A reflex angle is an angle between 180Â° and 360Â°

**regular polygon**

A regular polygon is a polygon with equal sides and equal angles.

**relative frequency**

The relative frequency is the estimated probability of an event, calculated from a probability experiment.

Relative frequency =

**right angle**

A right angle measures exactly 90Â°

**right-angled triangle **

Right-angled triangles are triangles that contain a 90Â° angle.

**roots (used as powers)**

Roots are the inverse of powers. For example, and

**roots (used in equations)**

The roots of an equation means the solutions to the equation. The roots are also the points where a graph crosses the x-axis.

**rotation**

A rotation is a type of transformation where a shape is pivoted around a fixed point (the centre of rotation).

**rounding**

When numbers are rounded, they are written only to a given place value.

**ruler**

A ruler is used to measure straight lines and distances between points.

##### S (Sample to similar shapes)

**sample**

A sample is a smaller set within the population that you can collect data from.

**sample space **

A sample space (also called a possibility space) is a list of all the possible outcomes of an experiment or of combined experiments. You can write a sample space as a systematic list or in a two-way table.

**satisfy **

To satisfy means to fulfil the requirements of a condition such as an equation or inequality.

**scalar**

A scalar is a quantity with just size (no direction). A number is a scalar. Scalars can be used as scale factors or multipliers.

**scale**

Scale is the ratio that defines the relation between a real-life measurement and a scale model. It is used in maps to represent the real-life lengths in smaller units.

**scale drawing **

A scale drawing is a representation of a real-life object with the lengths in proportion to the lengths of the actual object but reduced or enlarged by a scale factor.

**scale factor**

Scale factors indicate the ratio of corresponding lengths in two similar shapes. Scale factor =

**scatter graphs**

Scatter graphs show the relationship between two sets of quantitative data (or variables). Each point represents one individual from the set of data.

**secondary data**

Secondary data is data that someone else collected.

**sector**

A sector is part of the circle formed by two radii and an arc.

**segment**

A segment is the region of a circle formed by a chord and the part of the circumference between the two points.

**semicircle **

A semicircle is half of a circle.

**sequence**

A sequence is an ordered set of numbers or patterns that follow the same rule.

**shape **

A shape is a geometrical figure.

**share**

Share means dividing a quantity evenly.

**side elevation **

The side elevation is the view of a 3D shape from the side.

**significant figures**

Significant figures (s.f.) are digits in a number that contribute to its accuracy.

**similar shapes**

Similar shapes have exactly the same shape, but different sizes.

##### S (Simple interest to surface area)

**simple interest**

Simple interest is calculated only on the original amount deposited.

**simplify**

Simplify means to write or present an expression in the simplest possible way.

**simplify (expression)**

Simplify an expression means to write an expression in its lowest terms by collecting like terms.

**simultaneous equations **

Simultaneous equations are two or more equations that share the same variables that you solve at the same time.

**sine (sin) **

The sine of an angle in a right-angled triangle is the length of the opposite side divided by the length of the hypotenuse

\(sin ÆŸ \frac{opposite}{hypotenuse}\)

**sine rule **

The sine rule can be applied to any triangle. To find a side use and to find an angle use

**sketch **

A sketch is a simplistic drawing of a situation that shows the main features

**solve**

To solve an equation, you need to find the value of the unknown.

**speed**

Speed is a compound measure that can be calculated using the formula speed = \(\frac{distance}{time}\). Speed is shown by the gradient on a distance-time graph.

**sphere**

A sphere is a 3D shape where every point of its surface is the same distance from its centre.

**square numbers**

A square number is multiplied by itself, such as 3 Ã— 3 = 9. The first five square numbers are: 1, 4, 9, 16, 25

**squared**

Squared means â€˜multiplied by itselfâ€™. For example, 5Â² = 5 Ã— 5 = 25

**standard form**

Standard form is when a power of 10 is used to rewrite a very large of very small number. Standard form is written in this way: a Ã— \(10^{n} \), where 1 â‰¤ a < 10 and n is positive or negative integer. For example: 16â€¯000 = 1.6 Ã— \(10^{4} \)and 0.016 = 1.6 Ã— 10â€“2

**strict inequality **

Strict inequalities (< and >) are represented with open circles on number lines and dotted lines on graphs.

**subject of a formula **

The subject of a formula is the letter that is by itself on one side of the equation.

**substitute [substitution]**

Substitution is replacing a letter in an expression with a particular number.

**Substitution method (simultaneous equations) **

The substitution method is a way of solving simultaneous equations where you substitute one variable into another. For example, if one equation has a variable for a subject.

**sum**

The sum is the result of addition.

**surd **

A surd is an irrational square root.

**surface area**

The surface area of a 3D shape is the sum of the area of each face.

##### T (Table of values to translation)

**table of values**

A table of values is a way of writing down the values that satisfy a function or equation.

**tangent**

A tangent is a line that touches the circumference of a circle in exactly one point, and is perpendicular to the radius at the point of contact.

**tangent (tan)**

The tangent of an angle in a right-angled triangle is the length of the opposite side divided by the length of the adjacent \(tan ÆŸ \frac{opposite}{adjacent}\)

**term**

A term is a single number or variable, or numbers and variables multiplied together. For example: 2, x and 5y are all terms.

**term (sequences)**

Terms are the numbers in a sequence. First number = first term, second number = second term â€¦

**term-to-term rule**

The term-to-term is the rule gets you from one term to the next in a sequence.

**theoretical probability**

A theoretical probability, written as P(event), is the probability that an event will happen.

**three-dimensional (3D) shape**

A three-dimension (3D) shape is a solid which is not flat.

**transformation**

A transformation is something that alters a shapeâ€™s position and/or its size.

**translation**

A translation is a type of transformation where a shape is moved to a different position. Translations are often given as column vectors.

##### T (Transversal lines to two-way table)

**transversal lines**

Transversal lines are lines that cross two or more lines. Often parallel lines.

**tree diagram**

A tree diagrams helps you to calculate the probabilities of two or more events. The probability of each outcome is written (or calculated) on each branch.

**triangle**

A triangle is a 2D polygon with three sides, three angles, and three vertices. Angles in a triangle add up to 180Â°

**triangular numbers**

Triangular numbers form a triangular dot pattern. The first four triangular numbers are: 1, 3, 6, 10

**trigonometry**

Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles.

**truncate**

Truncate means removing digits without rounding. 3.7546 truncated to 1 decimal place is 3.7

**turning point**

The turning point represents a maximum or minimum point on a graph.

**two-dimensional (2D) shape**

A two-dimension (2D) shape is any flat shape or picture.

**two-way table**

A two-way table organises data into two categories.

##### U - W (Ungrouped to word-based problem)

**ungrouped (frequency tables)**

Ungrouped frequency tables show the frequency of each data value. They are suitable for discrete data, such as the number of days it rained in one week for a period of 11 weeks.

**union (set notation)**

The union of two or more sets contains the members that belong to either set. A âˆªÂ B means the union of sets A and B.

**unitary method**

Unitary method is a method to solve direct proportion problems. Divide to calculate the value of 1 unit. Multiply, if necessary, to find the value required.

**unit of measurement**

A unit of measurement is a one unit of a quantity. For example, units of measurement for length include metres and centimetres.

**universal set**

The universal set has symbol Î¾ and contains all the elements being considered in the problem.

**unknown**

Unknown is another term for a variable; a letter in an expression or equation.

**upper quartile **

The upper quartile (UQ) is the value 75% of the way through a data set.

**variable **

A variable is a letter whose value can change.

**vector**

A vector is a way of describing movement. Vectors have both direction and magnitude (size).

**Venn diagram**

Venn diagrams use circular regions to show relationships between sets.

**vertex [vertices]**

A vertex is the point where two lines intersect, such as the corner of a shape or the point of an angle.

**vertical line chart**

Vertical line charts are used for qualitative (categorical) data. In a vertical line chart, the height of each line shows the frequency.

**volume**

The volume is a measure of the space inside a 3D shape. Typical units are cmÂ³ and mÂ³.

**word-based problem**

Word-based problems are problems described in words, rather than in mathematical terms. To solve word-based problems, you need to use the information to form equations.