Standard unit

A **standard unit** is a formal unit from a system of units which is comprehensive and is used to define other units or combinations of units. For example, in the metric system, the standard units for *length*, *mass* and *time* are respectively, *metre*, *kilogram* and *second*. The standard units are described in the International System of Units (SI). Related formal, units are:

*centimetre* = metre × 1/100*
tonne* = kilogram × 1 000

minute =

Other non-standard formal units are, for example, carat, gallon, hour and knot.

Stem-and-leaf plot (stemplot)

A **stem-and-leaf plot **is a method of organising and displaying numerical data in which each data value is split in to two parts, a ‘stem’ and a ‘leaf’. Stem plots provide a visual indication of spread. For example, the stem-and-leaf plot below displays the resting pulse rates (in beats per minute) of 19 students.

**Key** : 11|0 = 110 beats per minute

In this plot, the stem unit is ‘10’ and the leaf unit is ‘1’. The top row in the plot, 6 | 8 8 8 9, displays pulse rates of 68, 68, 68 and 69.

A **back-to-back stem-and-leaf** **plot** is a method for comparing two data distributions by attaching two sets of ‘leaves’ to the same ‘stem’ in a stem-and-leaf plot. For example, the stem-and-leaf plot below displays the distribution of pulse rates of 19 students before and after gentle exercise.

Straight angle

A **straight angle **is the angle formed by taking a ray and its opposite ray. A straight angle is half of a revolution, and so has size equal to 180° or π radians.

*See also: Radian, Degree.*

Subitising

The capacity to visually recognise the size of a small set of objects without counting.

Subset

A **subset** is a set of elements *A* all contained within some larger set *B*. *A* is a subset of *B* if and only if every element of *A* is also an element of *B*, expressed . The subset *A* in this situation may also coincide with the set *B* itself, that is, .

*A* is a **proper** subset of *B* (written ) if all elements of *A* are contained within *B *but* A* *excludes* at least one element of *B,* so that it cannot coincide with *B *itself. If *A* is not a subset of *B*, it is expressed . For example, for the sets , and

, while .

*See also: inclusion, set.*

Subtraction

**Subtraction** is one of the basic operations of arithmetic and algebra and involves the combination of two or more quantities using the operator.

For example, , , , .

Subtraction is the **inverse operation** to addition and can be defined in terms of addition, such that if then and . For example, if 13 = 9 + 4 then 13 – 9 = 4 and 13 – 4 = 9.

Subtraction may be defined more formally depending on the context. For example:

- Subtraction of real numbers may be modelled using lengths of joined line segments on a number line.
- The addition of two fractions is defined by introducing a common denominator, that is:

.

*See also: addition, inverse operation.*

Sum

A **sum** is the result of adding several numbers or algebraic expressions. For example,

are sums.

The symbol å can be used to indicate a sum where each term can be described by an algebraic expression. For example, the mean (average) defined as:

can also be written using sum notation as:

*See also: addition.*

Supplementary angles

Two adjacent angles that form a straight angle are said to be **supplementary angles**. The sum of the angle measures in degrees of supplementary angles is 180° (a straight angle). An example of two supplementary angles is below:

*See also: complementary angles.*

Surd

A **surd** is a numerical expression involving one or more irrational roots of numbers. Examples of surds include , and .

*See also: irrational number.*

Surface area

Surface area is the measure of the total area of the surface(s) of a three-dimensional shape or object. For example, the surface area of a cube with side length units is square units. The surface area of a sphere with radius units is square units.

Symbolic

Using marks or symbols that have a meaning particular to mathematical language, for example, the written statement ‘two is less than 3’ can be written symbolically as ‘’.

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Symmetry (and asymmetry)

**Symmetry** is a visual property of regularity in shape by, for example, reflection or rotation. The letter **T** is symmetrical by reflection, the letter **Z** is symmetrical by rotation, the letter **H** is symmetrical by both reflection and rotation, but the letter **R** is *not* symmetrical.

A plane figure *F* has line symmetry in a line if the image of *F* under the reflection in is *F *itself. The line is called the axis of symmetry.

A plane figure *F* has **rotational symmetry **about a point *O* if there is a non-trivial rotation such that the image of *F* under the rotation is *F* itself.

A rotation of 120o around *O *maps the equilateral triangle onto itself.

Shapes which are not symmetrical are said to be **asymmetrical**. The human body is asymmetrical with respect to an imaginary line down the middle. *See also: rotation, reflection.*

T

Tangent (geometry)

A **tangent** to a curve at a point is a line that touches but does not cut a curve at that point. Two tangents are shown in the following diagram:

In the special case of a circle, a tangent is a line that intersects a circle at just one point. It touches the circle at that point of contact but does *not* pass inside it. A tangent to a circle is perpendicular to the diameter which contains the point, as show below:

*See also: circle, diameter.*

Tangent (ratio)

In any right-angled triangle, where

*See also: trigonometry.*

Tangram

A Chinese puzzle formed by a square cut into several pieces that are then rearranged to create other shapes. An example of an uncut tangram is below:

Image from: https://www.mathsisfun.com/definitions/tangram.html

Term

A **term** is a product of a constant (coefficient) and variables raised to positive integer powers. For example, is a term (variables and , coefficient ).

*See also: coefficient.*

Terminating decimal

A **terminating decimal** is a decimal that contains only finitely many non-zero decimal digits.

Every terminating decimal represents a rational number where the denominator is a power of . For example, is the decimal representation of

*See also: rational number.*

Tessellation (tiling)

A **tessellation** is a repeated pattern in the plane or on a surface where shapes completely fill all of the space around a given point where their boundaries meet. For example, a honeycomb is a tessellation using hexagons. Tiling patterns are tessellations using rectangular tiles or brick pavers in paths, mosaics in buildings, quilts and art.

A **regular tessellation **is created by tessellating regular polygons. If more than one regular polygon is used, it is a **semi-regular tessellation**. Examples of a regular tessellation of hexagons, and a semi-regular tessellation of triangles, hexagons and squares, are below:

Images from: https://www.mathsisfun.com/geometry/tessellation.html

*See also: polygon.*

Theorem

A mathematical statement which has been shown to be true by proof is called a **theorem**.

*See also: proof.*

Three-dimensional

An object with width, height and depth is three-dimensional. A solid is any three-dimensional geometric object (such as the Platonic solids). *See also: two-dimensional.*

Transformation

A transformation is a map of the plane onto itself. The transformations included in this glossary are enlargements or scaling (dilations), reflections, rotations and translations. These are one-to-one transformations of the plane onto itself.

A transformation is said to be an **isometry** if it leaves lengths, area and angles unchanged. Reflections, rotations and translations are isometries, dilations are not isometries.

*See also: enlargement, scale, reflection, rotation, translation, correspondence.*

Translation

Shifting a figure in the plane without turning it is called translation. Translations can be specified as a combination of a horizontal shift and a vertical shift.

*See also: transformation.*

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Transversal

A **transversal **is a line that intersects two other lines obliquely.

*See also: corresponding angle, co-interior angle, alternate angle.*

Trapezium

A **trapezium** is a quadrilateral with one pair of opposite sides parallel.

A **right-trapezium** has two right angles. The following are examples of a right-trapezium:

*See also: quadrilateral, parallel.*

*Source: *https://victoriancurriculum.vcaa.vic.edu.au/LearningArea/LoadFile?learningArea=mathematics&subject=mathematics&name=Mathematics%20Glossary.docx&storage=Glossary

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