A |

**acute-angled triangle:**

A triangle with three internal angles, each less than 90°, is called an acute-angled triangle.

**alternate angles:**

Alternate angles are created when a transversal or line segment intersects two other lines or line segments.

Angles*d*and

*f*are alternate angles. If the two intersected lines are parallel, then the alternate angles are equal. They are also known as 'Z' angles.

**alternate interior angles:**

Interior angles on alternate sides of a line intersecting two others are called alternate interior angles.

**amplitude:**

The amplitude of a wave is half the vertical distance from a crest to a trough.

**angle:**

An angle is a measure of turning. Angles are measured in degrees. The symbol for an angle is .

**angle of rotation:**

Under a rotation about a centre, C, an original point, A, will produce the image, A', with angle ACA' being the angle of rotation.

**ASA:**

ASA stands for angle-side-angle and refers to the known details of a possible triangle.

B |

**back-bearing:**

A back-bearing provides a return direction for a given bearing, e.g. 080° is the back-bearing of 260°.

**bearing:**

A bearing is the direction (as an angle measured clockwise from north) that a point lies from a given location. It is usually given as a three-figure bearing, e.g. 087°.

**bisect:**

To bisect something is to cut it in half. In mathematics, lines and angles are often bisected.

C |

**Cartesian coordinate system:**

Two axes that intersect at right angles are used to identify points in a plane. Conventionally, the horizontal axis is labelled
as the *x* axis and the vertical axis as the *y* axis. This creates a numbered grid on which points are defined by an ordered pair of numbers (*x*, *y*). The system is named after the French scholar, René Descartes.

**centre of rotation:**

Under a rotation, an original point, A, and its image, A', are always the same distance away from the centre of rotation, C. The angle ACA' is the angle of rotation.

**chord:**

A straight line segment joining two points of a circle (or any curve).

**circumscribe:**

A circle is circumscribed about a shape if each vertex of the shape lies on the circumference of the circle. The shape is said to be inscribed in the circle.

**closed:**

A closed curve is one that is continuous and that begins and ends in the same place.

**coefficient:**

A numerical value which multiplies a term of an expression is called a coefficient. For example, the coefficient of *x* in the expression is 4.

**common factor:**

A factor that is shared by two or more different numbers is called a common factor.

**complementary angles:**

If two angles sum to 90 then they are complementary angles.

**concave:**

A polygon is concave if one or more of its interior angles is greater than 180.

**cone:**

A solid with a circular base. All points on the circumference of the base are joined to a vertex in a different plane than the base.

**congruence;congruent:**

Two shapes are congruent if their lengths and angles are identical (i.e. if one can 'fit' exactly over the other). Mirror images, for example, are congruent.

**constant:**

A constant is a quantity (such as a number or symbol) that has a fixed value, in contrast to a variable.

**constant difference:**

The difference between consecutive terms of a linear sequence is called the constant difference.

**coordinates:**

A pair of numbers that determine the location of a point on *x*-*y* plane are called coordinates.

**coplanar:**

Any set of points, lines, curves and/or shapes are coplanar if they exist in the same plane.

**corresponding angles:**

Corresponding angles are created when a transversal or line segment intersects two other lines or line segments.

Angles*a*and

*e*are corresponding angles. If the two intersected lines are parallel, then the corresponding angles are equal. They are also known as 'F' angles.

**counting number:**

A counting number is a positive whole number greater than zero: 1, 2, 3,… Counting numbers are also called counting natural numbers.

**cube root:**

The cube root of a number yields that number when multiplied by itself three times – that is, when it is cubed. For example, 2 is the cube root of 8.

**cylinder:**

A solid with a circular base and a parallel circular top whose every parallel slice in between is also a congruent circle.

D |

**d.p.:**

This is the standard abbreviation for decimal places – the number of digits that appear after the decimal point in a decimal number

**decimal number:**

A decimal number is a number that includes tenths, hundredths, thousandths and so on, represented by digits after a decimal point.

**decimal places:**

Decimal places are the digits representing tenths, hundredths, thousandths and so on that appear after the decimal point in a decimal number.

**diameter:**

A straight line segment joining two points on the circumference of a circle and passing through its centre (or the length of this line). Equal to twice the radius length.

**digit:**

One of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Numbers are made up of one or more digits. For example, the number 72 has 2 digits and the number 1.807 has 4 digits.

E |

**enlargement:**

An enlargement is a type of transformation in which lengths are multiplied whilst directions and angles are preserved. The transformation is specified by a scale factor of enlargement and a centre of enlargement. For every point in the original shape, the transformation multiplies the distance between the point and the centre of enlargement by the scale factor.

**equation:**

An equation is a mathematical statement that two expressions have equal value. The expressions are linked with the 'equals' symbol (=).

**equidistant:**

Items that are at an equal distance from an identified point, line or plane are said to be equidistant from it.

**equilateral triangle:**

An equilateral triangle has three sides of the same length and hence three angles of 60°.

**equivalent fraction:**

A fraction with the same value as another fraction is called an equivalent fraction.

**evaluate:**

To evaluate a numerical or an algebraic expression means to find its value.

**exponent:**

The number written as a superscript above another number is called the exponent. It indicates the number of times the first number is to be multiplied by itself. This is also known as the index or the power of the first number.

**expression:**

In mathematics, an expression is combination of known symbols including variables, constants and/or numbers. Algebraic equations are made up of expressions. Examples of expressions include : , , and .

**exterior angle:**

When the side of a convex polygon is produced (lengthened), the exterior angle is the angle between this line and an adjacent side.

F |

**factor:**

A factor is any of two or more numbers (or other quantities) that are multiplied together. For example, 2 and 5 are factors of 10.

**formula:**

A formula is a general equation that shows the algebraic connection between related quantities.

H |

**HCF:**

This is the standard abbreviation for the highest common factor – the factor of highest value that is shared by two or more different numbers.

**highest common factor:**

The factor of highest value that is shared by two or more different numbers is called the highest common factor. This is often abbreviated to HCF.

**horizontal:**

A horizontal line runs parallel to the Earth's surface and at right angles to a vertical line. The horizontal axis of a graph runs from left to right.

**hypotenuse:**

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

I |

**index:**

The number written as a superscript above another number is called the index. It indicates the number of times the first number is to be multiplied by itself. This is also known as the exponent or the power of the first number.

**index notation:**

Index notation is a shorthand way of writing a number repeatedly multiplied by itself. For example, can be written as (in words: 3 to the power 4).

**inscribe:**

A shape is inscribed within a circle if each vertex of the shape lies on the circumference of the circle. The circle is then said to be circumscribed about the shape.

**integer:**

An integer is any of the natural numbers plus zero and the negative numbers: …,-3, -2, -1, 0, 1, 2, 3,…

**intercept:**

In the Cartesian coordinate system, an intercept is the positive or negative distance from the origin to the point where a line or curve cuts a given axis.

**interior angle:**

An interior angle is the angle between adjacent sides at a vertex of a polygon.

**intersect:**

To intersect is to have a common point or points. For example, two lines intersect at a point and two planes intersect at a straight line. The point at which two or more lines intersect is called a vertex.

**irrational number:**

Any number that cannot be expressed as the ratio of two integers is an irrational number. For example, the square root of 2 and are both irrational numbers.

**isosceles triangle;isosceles:**

An isosceles triangle is one that has two sides of equal length and hence two angles of equal size.

J |

K |

L |

**latitude:**

The lattitude measurement of a point on the Earth's surface is the angular distance north or south of the Equator.

**LCM:**

This is the standard abbreviation for the least common multiple – the smallest-value multiple that is shared by two different numbers.

**least common multiple:**

The smallest-value multiple that is shared by two different numbers is called the least common multiple. This is often abbreviated to LCM.

**line segment:**

A line segment is the set of points on the straight line between any two points, including the two endpoints themselves.

**linear sequence:**

In a linear sequence, consecutive terms of the sequence are generated by adding or subtracting the same number each time.

**locus:**

A locus is a set of points that all satisfy a particular condition. For instance, the two-dimensional locus of points equidistant
from two points *A* and *B* is the perpendicular bisector of the line segment *AB*.

**longitude:**

The longitude measurement of a point on the Earth's surface is the angular distance measured east to west from the zero line at Greenwich, England.

**lowest common denominator:**

The lowest common multiple of the denominators of two or more fractions is called the lowest common denominator.

M |

**multiple:**

A multiple of an integer is the product of that number and another integer.

N |

**natural number:**

A natural number is a positive whole number greater than zero: 1, 2, 3,… Natural numbers are also called counting numbers.

**net:**

A net is a flat pattern of polygons which, when folded up, creates a polyhedron (a many-sided solid).

**notation:**

Mathematical notation is a convention for writing down ideas in mathematics. Some examples are fraction notation, vector notation and index notation.

O |

**obtuse-angled triangle:**

A triangle with one internal angle of between 90° and 180° is called an obtuse-angled triangle.

**opposite angles:**

Opposite angles are formed when two lines intersect.

Angle*a*is opposite angle

*c*and angle

*b*is opposite angle

*d*. Opposite angles are always equal.

**origin:**

The origin is the point of intersection of the *x* axis and the *y* axis. It has the coordinates (0,0).

P |

**parallel:**

Two lines, curves or planes are said to be parallel if the perpendicular distance between them is always the same.

**parallelogram:**

A parallelogram is a quadrilateral with two sets of parallel sides.

**perfect square:**

A perfect square is a natural number which is equal to the square of another natural number. For example, 4, 9 and 16 are perfect squares as they are equal to 2, 3 and 4 squared respectively.

**perimeter:**

The perimeter of a shape is the total length of its outside edge(s).

**period:**

A function has a period, *p*, if for all values of *x*. So the period of the cosine function is 360° since .

**periodic function:**

A periodic function is one for which for all values of *x* (for some particular value of *p*). For instance is a periodic function since , for all values of *x*.

**perpendicular:**

Two lines or planes are perpendicular if they are at right angles to one another.

**perpendicular bisector:**

A perpendicular bisector is a line that cuts in half a given line segment and forms a 90° angle with it.

**pi:**

The irrational number pi represents the ratio of the lengths of the circumference to the diameter of a circle. It has the approximate value 3.14159265 and is always written using the symbol .

**plane:**

A plane has position, length and width but no height. It is an object with two-dimensions.

**point:**

A point has no properties except position. It is an object with zero dimensions.

Points in the *x*-*y* plane can be specified using *x* and *y* coordinates.

**power:**

A number is raised to a particular power when it is multiplied by itself that number of times. Powers are written as a superscript above the number that is multiplied by itself. For example means 3 to the power of 4 or .

**prime factor:**

Any factor of a number that is a prime number is called a prime factor.

**prime number:**

A prime number is a positive integer that has exactly two factors: itself and 1.

**prism:**

A solid whose ends are two parallel congruent polygons. Similar points in each shape are joined by a straight line.

**proof:**

A proof is an argument consisting of a sequence of justified conclusions that is used to universally demonstrate the validity of a statement.

**pyramid:**

A pyramid has a polygon as a base and one other vertex in another plane. This vertex is joined to each of the polygon's edges by a triangle.

**Pythagoras' theorem:**

Pythagoras' theorem states that, for any 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 two sides.

**Pythagorean triple:**

A Pythagorean triple is a set of three positive integers where the square of the largest is equal to the sum of the squares of the other two numbers. Such a set of numbers conform to Pythagoras' theorem and could therefore be the lengths of the sides of a right-angled triangle. An example of a Pythagorean triple is (3, 4, 5).

Q |

**quadrants:**

A plane is divided into quarters called quadrants by the axes in a Cartesian coordinate system. The quadrants are numbered first, second, third and fourth in an anticlockwise direction starting in the upper right quadrant.

**quadratic:**

A quadratic equation has the general form , where *a*, *b* and *c* are constants.

R |

**radius:**

A straight line segment joining the centre of a circle with a point on its circumference (or the length of this line).

**ratio:**

A ratio compares two quantities. The ratio of *a* to *b* is often written *a*:*b*. For example, if the ratio of the width to the length of a swimming pool is 1:3, the length is three times the width.

**rational number:**

Any number that can be written as the exact ratio of two integers is a rational number. For example, -5, 12 and are all rational numbers.

**ray:**

A ray is the set of all points lying on a given side of a certain point on a straight line.

**reciprocal:**

The reciprocal of a number is 1 divided by that number. For example, is the reciprocal of 3. The product of any number and its reciprocal is always 1.

**recurring decimal:**

A decimal number with an infinitely repeating digit or group of digits is called a recurring decimal. The repeating group is indicated by a dot above the first and last digit. For example, means 3.125125125125…

**reflection:**

A 2-D transformation in the coordinate plane. A line of reflection must be specified and then an image is created for each point in a shape.

The line segment joining each point with its image is perpendicular to the line of reflection and bisected by it.**regular polygon:**

A regular polygon has sides of equal length and interior angles of the same size.

**remainder:**

The amount left over when an integer is divided by another integer is called the remainder. If an integer is divided by one of its factors, then the remainder is zero.

**right pyramid:**

A right pyramid has a regular polygon as its base and its vertex is directly over the centre of the base.

**right-angled triangle:**

A triangle with one internal angle of 90° is called a right-angled triangle.

**rule:**

In general, a rule is a procedure for performing a process. In the context of sequences, a rule describes the sequence and can be used to generate or extend it.

S |

**s.f.:**

This is the standard abbreviation for significant figures – digits used to write a number to a given accuracy, rather than to denote place value.

**SAS:**

SAS stands for side-angle-side and refers to the known details of a possible triangle.

**scale factor:**

The scale factor is the ratio of distances between equivalent points on two geometrically similar shapes.

**scalene triangle:**

A scalene triangle is one with no equal-length sides and therefore no equal-size angles.

**sector:**

The region of a circle bounded by an arc and the two radii joining its end points to the centre.

**segment:**

The region of a circle bounded by an arc and the chord joining its two end points.

**sequence:**

A sequence is a set of numbers in a given order. All the numbers in a sequence are generated by applying a rule.

**significant figures:**

Significant figures are the digits used to write a number to a given accuracy, rather than to denote place value.

**similar:**

Two shapes are similar if one is congruent to an enlargement of the other. All squares are similar, as are all circles.

**simplify (a fraction):**

Simplifying a fraction means to rewrite it so that the numerator and denominator have as small a value as possible.

**sphere:**

A sphere is a ball-shaped solid whose points are all equidistant from a central point.

**square number:**

A square number is a natural number which is equal to the square of another natural number. For example, 4, 9 and 16 are square numbers as they are equal to 2, 3 and 4 squared respectively.

**square root:**

A square root is a number whose square is equal to the given number. For example, 2 is the square root of 4.

**SSA:**

SSA stands for side-side-angle and refers to the known details of a possible triangle.

**SSS:**

SSS stands for side-side-side and refers to the known details of a possible triangle.

**straight line:**

A straight line is a set of points related by an equation of the form *y = ax + c*. It has length and position, but no breadth and is therefore one-dimensional.

**substitute:**

In algebra, to substitute means to replace a given symbol in an expression by its numerical value. For example, substituting
5 for *n* in the expression *x* = 3*n* gives *x* = 3 × 5 = 15. .

**subtend;subtended:**

An angle is subtended by a line, *A*, if the lines forming the angle extend from the endpoints of line *A*.

**supplementary angles:**

If two angles sum to 180 then they are supplementary angles.

**symbol:**

A letter or other mark that represents a quantity. The symbol *x* is often used to denote a variable quantity, while other letters are used to represent constant numbers.

**symmetry:**

A plane figure has symmetry if the effect of a reflection or rotation is to produce an identical-looking figure in the same position.

T |

**tangent:**

For any right-angled triangle, the tangent ratio for an angle of *x*° is:

A line that touches a circle or curve at only one point.

**term:**

Each of the numbers in a sequence is called a term. In the sequence 3, 6, 9,... 6 is the second term and 9 is the third term.

**terminating decimal:**

A decimal number that has a finite number of digits is called a terminating decimal. All terminating decimals can be expressed as fractions in which the denominator is a multiple of 2 and/or 5.

**transformation:**

A transformation on a shape is any operation which alters the appearance of the shape in a well defined manner.

**translation:**

Geometric translation is a transformation on the coordinate plane which changes the position of a shape while retaining its lengths, angles, and orientation.

**trapezium:**

A trapezium is a quadrilateral with one set of parallel sides and one set of non-parallel sides.

**trigonometric formulae:**

For any right-angled triangle, these are:

for an angle of *x*°.

**trigonometric ratios:**

For any right-angled triangle, these are:

for an angle of *x*°.

**turning point:**

A turning point on a curve is a point at which the gradient is 0 but the points either side have a non-zero gradient. So a quadratic curve always has a minimum or maximum point which is a turning point.

U |

**unitary fraction:**

A fraction in which the numerator is equal to 1 is called a unitary fraction.

V |

**variable:**

A variable is a non-specified number which can be represented by a letter. The letters *x* and *y* are commonly used to represent variables.

**vertical:**

A vertical line runs at a right angle to a horizontal line. The vertical axis of a graph runs from top to bottom of a page.

W |

X |

**x-y plane:**

The *x*-*y* plane is a dimensional grid on which points and curves can be plotted. The *x* axis is normally the horizontal axis and the *y* axis the vertical one.

Y |

Z |