# Useful Terms in Maths

Maths is complicated, but a good first step on the road to understanding it is to get to know the most useful terms. There are lists in the front of the Bond books, but here’s my own contribution. I hope it helps!

Algebra: expressions using letters to represent unknown values, eg 2(x + 3) = 16.

Angles: there are three types of angle, depending on the number of degrees.

• acute angles are between 0 and 90 degrees.
• obtuse angles are between 90 and 180 degrees.
• reflex angles are between 180 and 360 degrees.

Arc: part of the circumference of a circle.

Averages: there are three types of average, and they are all useful in different ways.

• The mean is found by adding up all the values and dividing the total by how many there are, eg the mean of the numbers 1-10 is 5.5, as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55, and 55 ÷ 10 = 5.5.
• The mode is the most common value (or values), eg the mode of 1, 2, 2, 3, 4, 5 is 2.
• The median of an odd number of values sorted by size is the one in the middle, eg the median of the numbers 1-5 is 3. The median of an even number of values is the mean of the two numbers in the middle, eg the median of the numbers 1-10 is 5.5, as 5 and 6 are the numbers in the middle, and 11 ÷ 2 = 5.5.

Chord: a straight line drawn between two points on the circumference of a circle.

Circumference: the distance all the way round the edge of a circle.

Congruent: triangles are congruent if they are the same shape and size, eg two right-angled triangles with sides of 3cm, 4cm and 5cm would be ‘congruent’, even if one is the mirror image of the other. You can prove that two triangles are congruent by using any of the following methods: SAS (Side-Angle-Side), SSS (Side-Side-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side) and RHS or HL (Right-angle-Hypotenuse-Side or Hypotenuse-Leg). If all three measurements of the angles and/or sides are equal, the triangles are congruent. You can only create a congruent copy of a triangle by translation, reflection or rotation. (Note: congruence is the same as similarity, except that the triangles have to be the same size.)

Cube: the result of multiplying any number by itself twice, eg 8 is the cube of 2, as 2 x 2 x 2 = 8.

Cube root: the number that has to be multiplied by itself twice to make another number, eg 2 is the cube root of 8, as 2 x 2 x 2 = 8.

Cuboid: a solid with a rectangle for each of the six sides, eg a shoe box.

Denominator: the number on the bottom of a fraction, eg 2 is the denominator of ½.

Diameter: the length of a line drawn across a circle passing through the centre.

Equation: any line of numbers and operators with an equals sign in the middle, showing that the two sides balance, eg 4x + 12 = 34.

Factor: a number that goes into another number evenly, eg 6 is a factor or 12.

Fibonacci series: a sequence of numbers created by adding the previous two numbers together to get the next one, eg 1, 1, 2, 3, 5, 8, 13…

Formula: a way of calculating the answer to a common problem using letters or words, eg the formula for distance is speed x time (or D = S x T).

Highest Common Factor (HCF): the highest number that goes into two other numbers evenly, eg the HCF of 12 and 18 is 6.

Improper fraction: a fraction that is greater than one (in other words, the numerator is greater than the denominator), eg 9/5.

Lowest Common Multiple (LCM) or Lowest/Least Common Denominator (or LCD): the lowest number that is divisible by two other numbers, eg the LCM of 6 and 8 is 24.

Multiple: a number that can be divided evenly by another number, eg 12 is a multiple of 6.

Numerator: the number on the top of a fraction, eg 3 is the numerator of ¾.

Order of operations: the sequence of doing basic mathematical sums when you have a mixture of, say, addition and multiplication. BIDMAS (or BODMAS) is a good way of remembering it, as it stands for:

• Brackets
• Indices/Order (in other words, squares, cubes and so on)
• Division
• Multiplication
• Subtraction

Note that addition doesn’t come ‘before’ subtraction – these operations have to be done in the order in which they occur in the sum, and it makes a difference to the answer, eg 4 – 3 + 2 = 3 if you do the operations in order, which is correct, but you’d get the wrong answer of -1 if you did 3 + 2 first.

Operator: the sign telling you which mathematical operation to do. The most common ones are +, -, x and ÷.

Parallel: two lines are parallel if they will never meet, eg the rails on a railway line.

Perimeter: the distance all the way round the outside of a shape.

Perpendicular: at 90 degrees to each other.

Pi (or π): a constant used to work out the circumference and area of circles, often shown as 22/7 or 3.14 although it’s actually an ‘irrational’ number, which means it goes on for ever.

Prime factors: the lowest prime numbers that can be multiplied together to make a given number, eg the prime factors of 12 are 2² x 3.

Prime numbers: a number that can only be divided by itself and one, eg 2, 3, 5, 7, 11, 13…

Probability: the chance of something happening, calculated as the number of ways of getting what you want divided by the total number of possible outcomes, eg the chance of a coin toss being heads is ½ as there is one ‘heads’ side but two sides in total. To work out the probability of a sequence of events, you have to multiply the individual probabilities together, eg the chance of a coin toss being heads twice in a row is ½ x ½ = ¼

Product: the result of multiplying two numbers together, eg 35 is the product of 5 and 7.

Quadrilateral: a four-sided shape such as the following:

• Kite: a quadrilateral with two pairs of equal sides next to each other (or ‘adjacent’ to each other).
• Parallelogram: a quadrilateral with opposite sides parallel to each other.
• Rectangle: a quadrilateral with two opposite pairs of equal sides and four right angles.
• Rhombus: a quadrilateral with equal sides.
• Square: a quadrilateral with equal sides and four right angles.
• Trapezium (or Trapezoid): a quadrilateral with one pair of parallel sides. (Note: an isosceles trapezium is symmetrical.)

Radius: the distance from the centre of a circle to the circumference.

Range: the highest minus the lowest value in a list, eg the range of the numbers 1-10 is 9.

Regular: a shape is regular if all its sides and angles are equal, eg a 50p piece is a regular (-ish!) heptagon.

Right angle: an angle of 90 degrees.

Sector: a ‘slice’ of a circle in between two radii.

Segment: a part of a circle separated from the rest by a chord.

Shapes: the name of each shape depends on the number of sides. Here are the most common ones.

• Triangles have three sides.
• Pentagons have five sides.
• Hexagons have six sides.
• Heptagons have seven sides.
• Octagons have eight sides.
• Nonagons have nine sides.
• Decagons have 10 sides.
• Hendecagons have 11 sides.
• Dodecagons have 12 sides.

Similar: triangles are similar if they are the same shape, but not necessarily the same size, eg a right-angled triangle with sides of 3cm, 4cm and 5cm is ‘similar’ to a right-angled triangle with sides of 6cm, 8cm and 10cm. (Note: similarity is the same as congruence, except that the triangles don’t have to be the same size.)

Square number: the result of multiplying any number by itself, eg 49 is a square number, as 7 x 7 = 49.

Square root: the number that has to be multiplied by itself to make another number, eg 6 is the square root of 36, as 6 x 6 = 36.

Sum: the result of adding two numbers together, eg 17 is the sum of 8 and 9.

Tangent: either a straight line that touches the circumference of a circle OR the length of the opposite side of a triangle divided by the length of the adjacent side

Transformations: there are three main kinds of transformation: reflection, rotation and translation.

• With reflection, you need to state the formula of the mirror line, eg the shape has been reflected in the line y = 4.
• With rotation, you need to state the number of degrees, the direction and the centre of rotation, eg the shape has been rotated 90 degrees clockwise around the point (4, 3).
• With translation, you need to state the change in the x and y values, eg the shape has been translated four units up and three units to the right.

Triangles: there are four main types, each with different properties.

• equilateral triangles have all three sides the same length and all three angles the same.
• isosceles triangles have two sides the same length and two angles the same.
• scalene triangles have three sides of different lengths with three different angles.
• right-angled triangles have one 90-degree angle.

Variable: an unknown in algebra, eg x or y.

# Parts of Speech

When is a verb not a verb? When it’s a part of speech.

English exams often ask questions about the ‘parts of speech’. This is just a fancy term for all the different kinds of words, but they’re worth knowing just in case. Just watch out for words such as ‘jump’, which can be more than one part of speech!

If you struggle to remember what they all mean, think about the words themselves. Sometimes, there’s a clue in the way they sound, eg adverbs describe verbs, pronoun sounds like noun, preposition contains the word position and a conjunction is the ‘junction’ between two sentences.

## Noun

A noun is a word for a person, place or thing

• abstract noun: a word to describe an idea, eg peace
• common (or concrete) noun: a word for a thing or object, eg table
• proper noun: the name of a person, place etc, eg Nick, London
• collective noun: the name of a group of animals, eg herd or flock

Tip: Make up a phrase or a sentence with ‘the’ in front of the word. If it makes sense, it’s probably a noun, eg He looked at the ______.

An adjective is a word that describes a noun or pronoun, eg green or young

Tip: Make up a phrase or a sentence putting the word between ‘the’ and a noun. If it makes sense, it’s probably an adjective, eg The ______ book lay on the table.

## Verb

A verb is a doing word, eg jumped, was, pays

Tip: Make up a phrase or a sentence putting the word after a pronoun such as ‘he’. If it makes sense, it’s probably a verb, eg He ______ it or He ______ in the garden.

## Pronoun

A pronoun is a word that stands in for a noun

• personal pronoun: a word that shows a person or thing, eg he, she, them
• possessive pronoun: a word that shows the owner of an object, eg his, their
• relative pronoun: a word that ‘relates’ to the subject just mentioned, eg who, that, which

Tip: Make up a phrase or a sentence with a verb after the word (but without ‘the’ or ‘a’ in front of it). If it makes sense, it’s probably a pronoun, eg ______ looked at the wall.

## Article

An article is a word that introduces a noun, ie aan or the.

Strictly speaking, an article is just one kind of ‘determiner’, a word that introduces a noun:

• Articles (indefinite article: a/an, definite article: the)
• Demonstratives (thisthatthesethose)
• Quantifiers (manymuchmoremostsome etc)

Tip: Make up a phrase or a sentence with the word in front of a noun. If it makes sense, it’s probably an article, eg ______ book lay on the table.

An adverb is a word that describes an adjective, adverb or verb, usually ending in -ly, eg really or quickly

Tip: Make up a phrase or a sentence with the word after a verb. If it makes sense, it’s probably an adverb, eg He ran ______ around the garden.

## Preposition

A preposition is a word that shows the position in time or space, eg in, at or after

Tip: Make up a phrase or a sentence about placing something somewhere, putting the word before the location. If it makes sense, it’s probably a preposition, eg She put the book ______ the table.

## Conjunction

A conjunction is a word that connects two sentences together (sometimes called a connective), eg and, but or because.

• Coordinating conjunctions‘ are used to make a ‘compound’ sentence when the clauses are equally important, and the two ‘main clauses’ should always be separated by a comma, eg ‘The sun was warm, but it was cooler in the shade’.
There is a useful way of remembering the coordinating conjunctions, which is to use ‘FANBOYS’. This consists of the first letter of ‘for’, ‘and’, ‘nor’, ‘but’, ‘or’, ‘yet’ and ‘so’.
• Subordinating conjunctions‘ are used to make a ‘complex’ sentence when there is a main clause and a subordinate clause. (Subordinate just means less important.) If the sentence starts with a subordinating conjunction, the clauses need a comma between them, eg ‘Even though it was very hot, he wasn’t thirsty’.
However, if the subordinate clause comes at the end, there is no need for a comma, eg ‘He wasn’t thirsty even though it was very hot’. There are lots of subordinating conjunctions, such as ‘after’, ‘although’ and ‘because’, but the easy way to remember it is to ask yourself if the conjunction is in FANBOYS. If it is, it’s a coordinating conjunction; if it’s not, it’s a subordinating conjunction.
Alternatively, subordinating conjunctions are sometimes known as ‘WABBITS’ because some of the commonest ones start with those letters (when, where, while, after, although, before, because, if, though and since).

Tip: Make up a phrase or a sentence with two clauses joined by the word. If it makes sense, it’s probably a conjunction, eg He looked at the problem ______ decided to do something about it.

## Interjection

An interjection is either an outburst like hey or a word people say when they’re playing for time, eg well or now.

Tip: Make up a phrase or a sentence that someone might say, putting the word at the start, followed by a comma. If it makes sense, it’s probably an interjection, eg ______, can we go to the mall?

## Quiz

You can test yourself by reading any passage in English and going through it word by word, asking yourself what parts of speech they all are.

Why not start with this article? See how fast you can go. If you’re not sure, ask yourself the questions in each of the tips shown above, eg if you think it’s a noun, can you put it into a sentence with ‘the’ in front of it?

Here’s a quick quiz…

1. What are the nine parts of speech? (9 marks)
2. What do they all mean? (9 marks)
3. What are the four different kinds of noun (4 marks)
4. What are the three different kinds of pronoun (3 marks)
5. What are the two kinds of article? (2 marks)
6. What are the two kinds of conjunction? (2 marks)
7. What are the two words that help you remember the different kinds of conjunction? (2 marks)

Total: 31 marks