Library

Glossary

220 terms, each explained simply and then precisely, with examples, what not to confuse it with, and the chapters it comes from.

A

abscissa Another name for the x-coordinate
absolute value How far a number is from 0 on the number line, without caring which side
algebra tiles Flat pieces whose areas stand for x², x and 1, used to build rectangles that show how expressions multiply and factorise
algebraic expression A maths phrase made of numbers, letters and operations, like 3x + 5 or a² − 2ab, with no equals sign
algebraic identity An equation that stays true whatever numbers you put in for the letters, like (a + b)² = a² + 2ab + b²
angle The amount of turn between two lines that meet at a point, measured in degrees
angle of depression How far down you tilt your eyes from the horizontal to look at something below you
angle of elevation How far up you tilt your eyes from the horizontal to look at something above you
approximation A value that is close to the true value but not exactly equal to it
arc (major and minor) A curved piece of a circle between two of its points
arc length How long a curved piece of a circle is
area The amount of flat space a shape covers, counted in unit squares
arithmetic progression (AP) A sequence in which you add the same number each time to get the next term
assumed mean (and step deviation) A guessed middle value that makes working out the mean easier; you correct the guess at the end
axis One of the two number lines of the coordinate plane

B

Basic Proportionality Theorem (Thales theorem) A line drawn parallel to one side of a triangle cuts the other two sides in the same ratio
binomial An expression with exactly two terms, like x + 3 or 5x − 2y
Brahmagupta's formula A way to find the area of a four-sided shape whose corners lie on a circle, from its four sides alone

C

Cartesian plane The flat surface with the x-axis and y-axis drawn on it, where every point has a pair of coordinates
centre (of a circle) The fixed point in the middle of a circle; every point of the circle is the same distance from it
chord A straight line segment joining two points on a circle
circle A perfectly round curve
circumcentre The centre of the circle that passes through all three corners of a triangle
circumcircle The circle that passes through all the corners of a triangle (or of any polygon that has such a circle)
circumference The perimeter of a circle
class interval (and class size) A range of values, like 10 to 25, used to group data; its width is the class size
class mark The middle value of a class interval, used to stand for the whole class
coefficient The number multiplying the variable in a term
coincident lines Two lines that lie exactly on top of each other
collinear (points) Points that all lie on one straight line
common difference The fixed amount added each time in an arithmetic progression
common ratio The fixed number you multiply by each time in a geometric progression
complementary events An event and its opposite, "E" and "not E"
composite number A whole number greater than 1 that has more factors than just 1 and itself, like 4, 6, 9 and 15
concyclic (points) Points that all lie on one circle
cone A solid with a circular base that narrows to a point at the top, like an ice-cream cone or a birthday cap
congruent (figures) Exactly the same shape and exactly the same size, so one would fit perfectly on top of the other
consecutive Coming one straight after another, with nothing missed out
consistent pair (of equations) A pair of equations that has at least one solution
constant A term with no variable, so its value never changes, like the 3 in 4x + 5y + 3
converse (of a statement) The statement you get by swapping the "if" part and the "then" part of another statement
coordinates The pair of numbers (x, y) that tells you exactly where a point is
coprime (numbers) Two whole numbers are coprime when the only factor they share is 1
corollary A fact that follows straight away from a result that has just been proved
cosecant, secant and cotangent (the reciprocal ratios) The three ratios you get by turning sine, cosine and tangent upside down
cosine (cos) For an angle in a right triangle, the adjacent side divided by the hypotenuse
cube (of a number) A number multiplied by itself three times
cube root The number that, multiplied by itself three times, gives the number you started with
cubic polynomial A polynomial whose highest power of x is 3, like x³ − 4x or 2x³ − 5x² − 14x + 8
cuboid A box shape with six rectangular faces, like a brick or a matchbox
cumulative frequency A running total of the frequencies, adding each class to all the classes before it
cyclic number A number whose multiples are its own digits turned round in a circle, like 142857, the repeating block of 1/7
cyclic quadrilateral A four-sided shape whose four corners all lie on one circle
cylinder A solid with two equal circles at the ends joined by a curved side, like a tin or a pipe

D

decimal (number) A number written with a decimal point, showing parts smaller than 1 as tenths, hundredths and so on
degree (of a polynomial) The highest power of the variable in a polynomial
denominator The bottom number of a fraction
dense (numbers) Packed with no gaps between
dependent pair (of equations) A pair of equations that are really the same equation, so they have infinitely many solutions
diameter A chord that passes through the centre of a circle; it is the longest chord, and it is twice as long as the radius
difference of two squares One square minus another, which always splits as a² − b² = (a + b)(a − b)
digit One of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 used to write every number
discriminant The number b² − 4ac, which tells you how many real roots ax² + bx + c = 0 has, without solving it
distance formula A rule that gives the straight-line distance between two points from their coordinates
distributive property Multiplying a sum is the same as multiplying each part and then adding
division algorithm (Euclid's division lemma) Any whole number a divided by a whole number b gives a quotient q and a remainder r smaller than b

E

elementary event An event made of just one outcome
elimination method Solving a pair of equations by adding or subtracting them so that one unknown disappears
equally likely (outcomes) Outcomes that each have the same chance of happening
equation A statement that two things are equal, with an equals sign, like 2x + 3 = 11
equiangular triangles Two triangles whose three angles match one for one
estimation Working out a rough answer quickly, with easy nearby numbers, to know roughly what the exact answer should be
event (probability) One outcome, or a group of outcomes, that you are interested in
expansion (of an expression) Opening the brackets
experimental probability A probability worked out from what actually happened when you tried something many times
explicit formula (explicit rule) A rule that gives a term of a sequence straight from its position number, without needing the terms before it

F

factor A number or expression that divides another exactly
factor tree A branching drawing that splits a number into factors, and those into more factors, until only primes are left at the ends
factorisation Writing an expression as a product of simpler ones
fair (unbiased) A coin, die or draw is fair when no outcome is favoured
favourable outcome An outcome that belongs to the event you are asking about
fractal A shape whose small parts look like the whole shape, however far you zoom in
fraction A part of a whole, written as one number over another, like 3/4 (three out of four equal parts)
frequency How many times a value (or a class of values) occurs in the data
Fundamental Theorem of Arithmetic Every whole number greater than 1 can be written as a product of primes in exactly one way, apart from the order

G

gambler's fallacy The wrong belief that after a run of one result, the other result is "due" to happen next
generalisation A result that covers many cases at once, so that an older, narrower result becomes one of its special cases
geometric progression (GP) A sequence in which you multiply by the same number each time to get the next term
grouped data Data sorted into classes (ranges), with a count for each class, instead of listing every value

H

HCF (highest common factor) The biggest number that divides exactly into each of the given numbers
height (altitude) The straight up distance from a base to the opposite corner or side, measured at a right angle to the base
hemisphere Half of a sphere, cut through its centre, like a bowl
Heron's formula A way to find the area of a triangle from its three sides alone, with no height needed
hypotenuse The longest side of a right triangle

I

imaginary number A number built from i, the square root of −1, which has no place on the real number line
impossible event An event that can never happen; its probability is 0
incircle The biggest circle that fits inside a triangle, touching all three sides
inconsistent pair (of equations) A pair of equations with no solution at all
independent events Events where one happening makes no difference to the chance of the other
infinite series A sum that never stops
integer A whole number that can be positive, negative or zero
irrational number A number that cannot be written as a fraction of two integers, like √2 or π

L

law of large numbers The more times you repeat a random experiment, the closer the experimental probability gets to the theoretical probability
LCM (lowest common multiple) The smallest number that each of the given numbers divides into exactly
length of a tangent The distance along a tangent from a point outside a circle to where the tangent touches the circle
line of sight The straight line from your eye to the thing you are looking at
linear decay A quantity that goes down by the same amount every step, like water in a tank falling 0
linear equation in two variables An equation like 3x + 4y = 20 with two unknowns, each only to the power 1; its graph is a straight line
linear growth A quantity that goes up by the same amount every step, like a journey that costs ₹60 more for every extra kilometre
linear polynomial A polynomial of degree 1, like 2x + 3
locus (plural loci) The set of all the points that obey one rule, such as "5 cm from A" or "equally far from A and B"

M

mean (average) The ordinary average
median (of a triangle) A line from a corner of a triangle to the middle of the opposite side
median (of data) The middle value when the data are put in order
midpoint The point exactly halfway between two points
modal class In a grouped table, the class with the largest frequency
mode The value that appears most often
multiple The result of multiplying a number by a whole number

N

natural number The counting numbers
nth term A formula that gives any term of a sequence from its position number n
number line A straight line with 0 marked on it, where every number has its own point
numerator The top number of a fraction

O

one-to-one correspondence Matching the things in one group with the things in another, one with one, so that nothing is left over on either side
opposite and adjacent sides In a right triangle, from one of the sharp angles
ordered pair Two numbers written in brackets in a fixed order, like (2, 5), where swapping them changes the meaning
ordinate Another name for the y-coordinate
origin The starting point of the coordinate plane, (0, 0), where the two axes cross
outcome One possible result of a random experiment

P

pair of linear equations (simultaneous equations) Two linear equations in the same two unknowns, solved together to find values that fit both
parabola The U-shaped curve you get when you draw the graph of a quadratic polynomial
parallel lines Lines that never meet
percentage (per cent) A number out of 100
perfect cube (expression) A number or expression that is something times itself three times
perfect square (expression) A number or expression that is something times itself
perimeter The total length all the way round the border of a shape
perpendicular bisector The line that cuts a line segment into two equal halves and crosses it at a right angle
pi (π) The number you get when you divide the distance round any circle by the distance across it; it is about 3
place value What a digit is worth because of where it stands in a number
point of contact The one point where a tangent touches a circle
points of trisection The two points that cut a line segment into three equal parts
polynomial An expression built from a variable, its whole-number powers, numbers in front of them, and a constant, joined by + and −
population (statistics) The whole group you want to know about, such as every student in a school
power (exponent) A small raised number that says how many times to multiply a number by itself
prime factorisation Writing a number as a product of prime numbers only, like 60 = 2 × 2 × 3 × 5
prime number A whole number greater than 1 whose only factors are 1 and itself, like 2, 3, 5, 7 and 11
probability A number from 0 to 1 that measures how likely something is to happen
probability scale A line from 0 to 1 on which you place events by how likely they are
proof by contradiction A way to prove something by first pretending it is false, then showing that this leads to something impossible
proportion (direct and inverse) When two ratios are equal (2
Pythagoras theorem In a right triangle, the square on the longest side equals the two other squares added together

Q

quadrant One of the four parts the two axes cut the plane into, numbered I to IV, going anticlockwise from the top right
quadratic equation An equation with an x² term and no higher power of x, like 2x² − 5x + 3 = 0
quadratic formula (Śrīdharāchārya's formula) A formula that gives the roots of any quadratic equation ax² + bx + c = 0 straight from a, b and c
quadratic polynomial A polynomial of degree 2, like x² + 5x + 1

R

radius (plural radii) The distance from the centre of a circle to any point on it; also a line segment joining the centre to the circle
random experiment (trial) An action you can repeat, where you know all the results that could happen but cannot know which one will happen this time
randomness Not being able to predict exactly what will happen, even when you know everything that could happen
ratio A way of comparing two amounts by division, written like 3
rational expression A fraction whose top and bottom are algebraic expressions, like (x² − 9)/(x + 3)
rational number Any number you can write as one integer divided by another (not by 0), like 3/4, −2/5 or 7 (which is 7/1)
real number Any number that has a place on the number line
recursive formula (recursive rule) A rule that makes each term of a sequence from the term (or terms) before it, starting from a given first term
reflection A mirror image
reflection symmetry (line symmetry) A shape has reflection symmetry when it can be folded along a line so that the two halves match exactly
relative frequency How often something happened, as a fraction of the total number of tries
repeating decimal A decimal that never ends, where one block of digits repeats forever, like 0
right triangle A triangle with one angle of exactly 90°, a square corner
root (of an equation) A value of x that makes an equation true
rotational symmetry A shape has rotational symmetry when turning it about its centre, by less than a full turn, makes it look exactly the same
rounding Replacing a number with a nearby simpler one, such as the nearest ten, hundred or 2 decimal places

S

sample (statistics) A smaller group chosen from a whole group, studied to learn about the whole group
sample space The list of every possible outcome of a random experiment, written inside curly brackets
scale How a length on a drawing or map compares with the real length, written like 1 cm
scale factor (representative fraction) The number every length is multiplied by when a figure is enlarged or shrunk
secant (a line through a circle) A straight line that cuts a circle at two points
section formula A formula for the point that divides a line segment in a given ratio, such as 3
sector (of a circle) A slice of a circle, like a slice of pizza
segment (of a circle) The part of a circle cut off by a chord
semi-perimeter Half of the perimeter of a shape
semicircle Half of a circle, cut off by a diameter
sequence A list of numbers (or objects) in a fixed order, often following a rule
series The sum you get by adding up the terms of a sequence
Sierpiński triangle A triangle pattern made by cutting out the middle quarter of a triangle, then of each piece left, again and again for ever
similar figures Figures with the same shape but not necessarily the same size, like a photo and its enlargement
similarity criteria (AA, SSS, SAS) Short tests that prove two triangles similar without checking every angle and every side
sine (sin) For an angle in a right triangle, the opposite side divided by the hypotenuse
slant height The length along the sloping side of a cone, from its tip to the edge of its base
slope The a in y = ax + b
special case A narrower result that you get from a general one by adding an extra condition
sphere A perfectly round ball
splitting the middle term A way to factorise x² + bx + c
square (of a number) A number multiplied by itself
square root The number that, multiplied by itself, gives the number you started with
squaring a shape (quadrature) Drawing a square with exactly the same area as a given shape, using only a straight edge and a compass (or a rope and pegs)
stagger (on a running track) The head start given to runners in the outer lanes, so that everyone runs the same distance round the bends
subjective probability A guess at how likely something is, based on a person's own judgement rather than on counting or experiments
subscript (tₙ notation) A small number or letter written low after a symbol, like the 4 in t₄; in a sequence it gives the position of the term
substitution method Solving a pair of equations by writing one unknown in terms of the other, then putting that into the other equation
subtend (an angle) A chord or an arc subtends an angle at a point when the lines from its two ends to that point make that angle
sum and difference of cubes One cube plus or minus another, which always splits into a short bracket times a long one
sure event (certain event) An event that is certain to happen; its probability is 1
surface area (total and curved) The total area of all the outside surfaces of a solid

T

tangent (tan, the ratio) For an angle in a right triangle, the opposite side divided by the adjacent side
tangent (to a circle) A straight line that touches a circle at exactly one point without cutting into it
term One member of a sequence, or one part of an expression joined to the rest by + or −
terminating decimal A decimal that comes to an end, like 0
theoretical probability A probability worked out by counting, when every outcome is equally likely, with no experiment needed
tree diagram A branching picture that shows every possible result of an experiment done in steps
triangular number A number of dots that can be arranged in a triangle
trigonometric identity An equation with trigonometric ratios that is true for every angle, like sin² A + cos² A = 1
trigonometric ratio One of six fractions made from two sides of a right triangle, named after an angle
trigonometry The part of maths about the sides and angles of triangles, used to find heights and distances you cannot measure directly

V

variable A letter, like x or y, that stands for a number that can change
Virahānka-Fibonacci sequence The sequence 1, 2, 3, 5, 8, 13, 21,
volume The amount of space a solid takes up, counted in unit cubes

W

whole number The counting numbers together with zero

X

x-intercept The x-coordinate of a point where a graph crosses (or touches) the x-axis

Y

y-intercept The b in y = ax + b

Z

zero The number for "nothing", written 0; it is neither positive nor negative
zero of a polynomial A number that makes the polynomial equal to 0 when you put it in for x