Download Maths Glossary

URRBRAE
AGRICULTURAL
HIGH SCHOOL
YEAR 10
Mathematics
GLOSSARY
A
absolute value
The positive value for a real number, disregarding the sign. Written |x|
e.g. |3| = 3, |-3| = 3.
An angle whose measure is between 0o and 90o
acute angle :
76°
acute triangle :
A triangle with three acute angles.
54°
50°
adjacent angles or sides:
algebraic fractions
Two angles or sides that are next to each other
Normal fraction rules apply .
x 2 x 3x 2 x 5 x




To add or subtract the denominators must be the same.
y 3y 3y 3y 3y
To multiply and divide (invert and multiply to divide).
Cancel and multiply the numerators and denominators (top × top, bottom × bottom).
( 2 x  1 )( x  4 ) ( 3 x  5 )( x  3 ) ( x  4 )( x  3 ) x 2  x  12



( 3 x  5 )( x  7 ) ( 2 x  1 )( x  7 ) ( x  7 )( x  7 )
x 2  49
alternate angles
Two angles that are on opposite sides of the transversal when parallel line are cut by a
transversal. They are between the parallel lines and alternate left and right.
altitude
The perpendicular ( 90 0 ) length from a vertex of a triangle to the opposite side.
altitude
altitude
altitude
base
base
base
angle
angle of elevation
The figure formed by two line segments or rays that extend from a given point.
The amount of turn up from the horizontal
42°
elevation
HORIZONTAL
angle of depression
major
arc
minor
arc
arc
The amount of turn down from the horizontal
depression
area
A part of the circumference of a circle.
The measure, in square units, of the inside of a plane (flat) figure.
Triangle
Square
Rectangle
Triangle
B
a
c
A
sh
2
C
A
b
1
A  ab sin C
2
Circle
Sector
A  S2
Parallelogram
x
Ar
A
2
x
 r2
360
area (composite)
Triangle Rectangle Semi
Circle
average
axis (axes)
B
bar graph
y
3
2
1
-3 -2 -1-1
1 2
-2
-3
Bar Chart
x
3 x
15
A  side  height
A  sh
Trapezium
A  averageof parallel sides  height
A
ab
h
2
The shape must be divided into a combination of the shapes with known formula.
The total area is the sum of the three known shapes.
A=Triangle + Rectangle + Semicircle.
A= sh/2 + l× w + πr2/2
The arithmetic mean. The sum of the values divided by the number of values
The horizontal and vertical lines that form the quadrants of the coordinate plane.
The horizontal axis is called the X-axis. The vertical axis is called the Y-axis.
The point of intersection is called the Origin.
A type of chart used to compare data in which the length of a bar represents the size of
the data. The columns are apart. Used for discrete data or categorical data. (the data is
not connected )
10
5
0
a
base of a triangle
A  length  width
A l  w
A  side  side
b
c
d
e
f
Any side of a triangle. A triangle has three bases and three altitudes.
bearing
Uses NORTH and the amount of clockwise turn in DEGREES. It uses the letter T for
True. Three digits are used for a bearing
0700 T Means face NORTH and turn 70 degrees in a clockwise direction
N
N
W
70
W
147
E
E
318 T
S
N
147 T
1470 T Means face NORTH and turn 147 degrees in a clockwise direction.
S
318
W
E
3180 T Means face NORTH and turn 318 degrees in a clockwise direction
S
BEDMAS
binomial
Order of Operations1. Brackets
2. Exponents
3. Division
4. Multiplication
5. Addition and Subtraction. (Work from left to right, not necessarily addition
before subtraction.)
A polynomial consisting of two terms. e.g. 3x2 - 8
bisector
A line, segment or ray that divides an angle or a line into 2 equal parts.
box-and-whisker plot
A type of graph used in data management showing the spread of the distribution of the
data. Key points are minimum, lower quartile, median, upper quartile, maximum.
f(x)
min
C 2 4
capacity
LQ M
6
UQ
max
8 10 12 14 16 18 20
x
The amount a container holds.
3
1 centimetre
1000 millilitres
1000 Litres
1000 Kilolitres
= 1 millilitre
= 1 Litre
= 1 Kilolitre
= 1 Megalitre
 1 ml
1 cm 3
 1 gram
1000 cm 3  1000 ml  1 Litre
There is a link between the
volume, the capacity and the
mass of water.
1M
3
 1000l
 1 Kilogram
 1 Kilolitre  1 tonne
1 ML
 1000 KL
 1 kilotonne
categorical data
Data classified according to a property or characteristic. (shoe type, hair colour etc)
centi--
Prefix meaning a hundredth part
central angle of circle
An angle subtended by an arc or a chord at the centre of a circle.
x
y
angle at centre
2x
100 cm  1 Metre 1 cm 
1
Metre
100
The angle at the centre is twice the angle at the circumference
2x x
angle at centre
and angle at circumference
chord
A line joining two points on the circumference of a circle.
chord
circle graph / pie chart / sector graph A graph of statistical data where a circle is subdivided into regions that represent the
F
A
percentage of the total (relative frequency) converted to angles.
E
7% 11% The angles are calculated using percentage (as a decimal) of 360 or relative frequency
14%
B
multiplied by 360.
18%
D
23%
C
27%
circum-centre
circumference
C  D
Or C  2  r
circumference angle of a circle
x x
x
2x
The point of intersection of the perpendicular bisectors of each side of a triangle.
It is the centre of the circle that passes through each vertex of the triangle.
The distance around the boundary of a circle. (perimeter).
D is the Diameter r is the Radius
The angle subtended by an arc or chord at the circumference of a circle.
Angles in the same segment or arc are equal.
The angle at the circumference is half the angle at the centre.
Angle at
Equal angles Angle at centre
Circumference
and circumference
coefficient
The numerical factor of a term. e.g. The coefficient of -3x2y is -3. The coefficient of
a3b4c2 is 1. The coefficient of 7p4 is 7.
co-interior angles
On parallel lines co-interior (together-inside) angles are supplementary.
(add up to 1800)
180
collinear points
A
Points that are on the same line. A, B, C are collinear.
B C
It is usually a percentage of sales.
commission
Earnings based on sales.
common denominator
A multiple shared by the denominators of two or more fractions. Common
denominators must be used when adding or subtracting fractions.
Both denominators are the same using equivalent fractions.
(12 is part of both the 3 and 4 times tables).
An easy way to get a common denominator is to multiply the denominators together.
3 1
9
4
 

4 3 12 12
13 N 1

1
12
12
N
compass points.
NW
NNE
NNW
ENE
WNW
W
ESE
WSW
SW
North N, East E, South S, West W, Northeast NE, Southeast SE, Southwest SW,
Northwest NW.
Sometimes a further division is made creating
E
NNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW.
NE
SSE
SSW
SE
S
complementary angles
Two angles whose sum is 90o.
completing the square
x  4   11
Used to solve quadratic equations and finding the turning point of a parabola.
Does not factorise using FOIL backwards. (There are no factors of 5 which add to 8)
Force x2 + 8x to become a perfect square by adding and taking (½ of 8)2 .
Write the perfect square and move the numbers to the right hand side of the equation.
Find the square root of both sides (remember  )
Solve for x by removing the +4
x  4  11
NOTE:- If left in the format y = (x + 4)2 − 11 the Turning Point is (-4,-11)
x  8x  5  0
2
x 2  8 x  16  16  5  0
 x  4 2  11
composite number
A whole number (integer) that has more than 2 different factors. e.g. 18 has factors 1,
18, 2, 9, 3, 6 so it is composite.
compound interest
Compound interest is calculated by adding the interest to the Principal (P) each time
the interest is calculated (the principal grows). The best ways to calculate the amount
is to use the formula, a spreadsheet or a graphics calculator.
A is the final value,
P is the starting amount (Principal.)
i is the rate as a decimal. (6% per year = .06 per year).
If calculated monthly then .06 divided by 12 = .005 per calculation period (monthly)
n is the total number of calculation periods.
It is best to calculate (1+i ) first then raise it to the power of n, then multiply it by P.
A  P ( 1  i )n
(Formulae for finding i or P)
in
A
1
P
P
A
1  i n
concave
A shape that goes in on itself.
A line joining two points inside the shape can go outside the shape.
cone
A cone has a circle as its base and the vertex is directly above or below the centre of
the circle.
congruent
congruent triangles
Figures that have exactly the same size and same shape.
The rules for congruent triangles are.
If three sides of the triangles are equal.
Two sides are equal and the included angle is equal.
Two angles and a corresponding side (same position relative to the angles) are equal.
Right triangles with equal hypotenuses and one other equal side.
SSS.
SAS.
AAS.
RHS.
continuous data
Numerical data with an uninterrupted range of values.
convex
A shape that ‘bulges’ outwards.
Any line joining two points inside the shape remains inside the shape.
coordinate plane
y
9
6
3
-9 -6 -3
-3
-6
-9
3 6 9
x
A plane (flat surface) that is divided into four quadrants by drawing a vertical and a
horizontal line that intersect at a point called the origin. Used for graphing ordered
pairs. The quadrants are numbered 1—4.
y
coordinates
4
2
-4 -2
-2
-4
-6
x
2 4 6
The ordered pair that names the location of a point in the coordinate plane. The first
number in the ordered pair is the x coordinate (horizontal) the second number is the y
coordinate (vertical) ( x, y ) the point (3,-6) is shown
corresponding angles
Angles that have the same relative positions on parallel lines. Above the parallel line
and to the left of the transversal is shown. Corresponding angles are congruent
(equal).
cosine
A trigonometry ratio equal to the adjacent side over hypotenuse. ( CAH)
Used when there is information about the angle, Adjacent side and the Hypotenuse.
adjacent
x
opposite
hypotenuse
cosine rule
c
b
a
adjacent
A

hypotenuse H
H
A
A  H  Cos x angle x  Cos 1 ( A  H )
Cos x
The side a is opposite the angle A and the same pattern for b and B, c and C
c 2  a 2  b 2  2ab cos C (The Cosine of the included angle)
It is used to calculate the third side of a triangle if two sides and the included angle are
known, or to calculate the size of an angle when the lengths of three sides are known.
A
B
Cos x 
C
 a 2  b2  c 2
C  cos  1 

2ab

c  a 2  b 2  2ab cos C




cube
A regular solid figure with six congruent square faces.
cube root
A number that when cubed (index 3) gives the original number.
The cube root of 64 is 4 because 4 3  4  4  4  64
c
cyclic quadrilateral
b
a + c = 180
b + d = 180
a
d
A quadrilateral with all vertices on the circumference of a circle.
Opposite angles of a cyclic quadrilateral are supplementary (add to 180).
cylinder
D
data
A rounded three-dimensional solid that has a flat circular face at each end.
decagon
A polygon with 10 sides
decimal numbers
Addition and Subtraction line up the decimal point.
Multiplication the number of decimal places in the answer is equal to the number of
decimal places in the question. ∙3 × ∙2 = ∙06
Division move the decimal point in the divisor (dividing number) and the question the
same number of places until the divisor is a whole number. ∙126  ∙03 =12∙6  3 = 4∙2
deduct /deduction
Is the same as subtract.
denominator
Facts or opinions from which conclusions can be drawn. (Facts that have been
collected but not yet interpreted)
Numerator
Denominator
density
The name of a fraction. It is below the line. It must be the same for addition and
subtraction but does not get added or subtracted.
Compares the masses of objects and the volume they occupy. The formulae are
m
d
Density 
v
mass
volume
d
m
v
v
m
d
m  d v
In the  cover the one variable and the other two variables are in the correct position
for the formula.
dependent events
Events whose outcomes affect each other.
diagonal
A line segment joining two non-adjacent (not next to each other) vertices of a convex
polygon. It is customary to use n for the number of sides.
n
The formula to calculate the Number of diagonals of a polygon is N  n  3
2
diameter
A chord that passes through the centre of a circle.
difference
The answer to a subtraction problem.
difference of two perfect squares.
This is mainly used in factorisation in algebra but can also be used in number.
a 2  b 2  a  ba  b
directed number
17 2  8 2  17  817  8  9  25  225
16 x 2  49  4 x 2  7 2  4 x  7 4 x  7 
Positive (gain, increase or profit) and negative (loss or decrease) numbers.
direction
1)
N
N
2)
20
W
E
discount
E
Uses the four main directions and the amount of turn away from North and South.
1) N 200 E Means face NORTH then turn 20 degrees towards EAST
2) S 420 W Means face SOUTH then turn 42 degrees towards WEST.
42
S
A percentage or amount taken from the marked price to obtain the actual selling price.
discreet data
Numerical data with exact distinct values.
discriminant
Part of the quadratic formula
= b 2  4ac It determines the number of solutions to
a quadratic equation..
If the answer is Positive 2 solutions, if zero 1 solution, if negative no solutions.
When sketching a parabola it indicates the number (if any) of x intercepts.
distributive law
The formula used to remove brackets a( x  y )  ax  ay  a( x  y )  ax  ay .
Everything in the bracket is multiplied by the outside of the bracket. (sign included)
dodecagon
A polygon with 12 sides.
E
earnings
Money earned as wages, salary, commission or piece work.
Gross Earnings – Income tax = Net Earnings
edge
The line segment where two faces of a polyhedron meet.
equation
A mathematical sentence containing an equal sign.
To solve an algebraic equation whatever changed the pro-numeral (letter) must be
undone by using the mathematical inverse of each operation on both sides.
x35
x2
( 3 ) (  3 )
x 5 7
x  12
( 5 )  5 
x
2
4
x8
5 x  20
x4
( 4 ) (  4 )
( 5 )  ( 5 )
All equations where the pro-numeral occurs once are a combination of the four
mathematical operations.
x
x6
2x  3  7
4 5
3  x  5   24
4
3 3
2x  4
2
2
x2
3
4
4
x
9
3
3 3
x  27
3
3
3
3 3
x58
x  6  12
5
6 6
x  18
5
x3
If the pro-numeral occurs more than once either on the same side of the equal sign or
on opposite sides of the equal sign they must be gathered together first.
5 x  2( 3 x  6 )  10
5 x  6 x  12  10
11 x  12
 10
11 x  22
x2
7 x  4  5x  8
 5x
 5x
2x  4  8
2 x  12
x 6
equiangular
Having equal angles.
equilateral
Having equal sides.
equilateral triangle
A triangle with three equal sides and all angles equal to 60 degrees.
estimation
An approximate amount, value or size of something.
evaluate
To find a numeric answer. The answer is a number.
event
One or more outcomes of a probability experiment.
expand
Multiply factors
3( x  6 )  3 x  18
Distributive Law
experimental probability
( x  4 )( x  3 )  x 2  3 x  4 x  12  x 2  x  12
FOIL
This is determined by observing long term trends e.g. tossing a coin, rolling dice,
picking a card etc.
The experiment must be repeatable and have results which can be listed.
exponent / index
A number that indicates the number of times the base appears as a factor.
63 = 6  6  6 the exponent is 3 and the base is 6. The entire term is called a power.
The index laws are
Add the indices
1. Multiplication a m  a n  a m  n
am  an  amn
2. Division
 
3. Power to a power a m
n
Take the indices
 a mn
Multiply the indices
4. Pr oduct raised to a power ab  a b
m
a
5. Division to a power  
b
6. Index zero
m

m m
am
bm
a0  1
7. Negative Index
am 
Both get index.
Both get index.
Index of 0 answer always = to 1
1
am
Reciprocal index is positive
expression
A group of symbols representing numbers and operations.
exterior angle of a polygon
The angle outside a polygon formed by extending one of its sides.
The sum of all the exterior angles of any polygon is always 360 0
exterior angle of a triangle
y
x
x+y
F
face
Is equal to the sum of the two interior opposite angles
If x is 60 and y is 80 the exterior angle is 140.
60+ 80 = 140 (exterior angle of Δ )
Any of the flat sides of a polyhedron.
factor
One of the numbers that make up a number by multiplication. E.g. 3 is a factor of 6
because 6 = 3×2. ( x  y ) is a factor of x 2  y 2 because ( x  y )( x  y )  x 2  y 2
factorise
Finding the factors is the opposite of expanding.
The factors when multiplied equal the original expression.
10 x  15  5  2 x  5  3  5( 2 x  3 ) (factor is 5 The Distributive law backwards)
x 2  7 x  18  ( x  9 )( x  2 ) (Factors of 18 which differ by +7 FOIL backwards)
factor tree
A diagram representing a systematic way of determining all the prime factors of a
number. e.g. 60  2  2  3  4
a
Any number that can be written in the form
where a and b are integers
b
Addition and Subtraction the denominator must be the same.
fraction
3 3 12 15 27
7
 


1
The denominator is the name and does not get added.
5 4 20 20 20
20
Multiplication: numerator times numerator and denominator times denominator.
3 3
9
 
5 4 20
Division: the fraction (s) immediately to the right of a dividing sign is inverted (turned
upside down) and the dividing sign becomes multiply. 3 3 3 4 12 4
5
frequency
polygon
8
7
6
4

5

3

15

5
A polygon formed by joining the centre of the columns of a histogram.
The polygon must start and finish at zero-----joining the imaginary centres of the zero
columns on either sides.
8
7
6
5
4

5
4
3
2
3
2
1
0
1
0
1 2 3 4 5 6 7 8 9 10 11
1 2 3 4 5 6 7 8 9 10 11
FOIL
F L
F L
(x +3) (x-5)
O
I
I O
A word to help remember how to multiply factors of a quadratic.
( x  3 )( x  5 )  x 2  5 x  3 x  15  x 2  2 x  15
FOIL Multiply the two that are
FIRST in each bracket
x × x = x2
Multiply the two that are on the OUTSIDE of each bracket x × -5 = -5x
Multiply the two that are on the INSIDE of each bracket
+3 × x = +3x
Multiply the two that are
LAST in each bracket.
3 × -5 = -15
formula
A statement expressing the relationship between two or more quantities.
e.g. A   r 2 (area of a circle)
distance= speed × time
H is t o g r a m
H is t o g r a m
frequency diagram /table
Used in statistics as a method of recording the data collected. A tally is often used in
the frequency diagram to keep track of the number of times something occurs. A
graph can then be drawn.
14
12
10
8
6
Cumulative
Frequency
4
Range
2
Tally
Frequency
Relative Frequency
Angle
0
≤5
6 -1 0
1 1 -1 5
≤5
6-10
11-15
16-20
≥21
≥21
1 6 -2 0
4
8
9
12
7
40
Total
function
4/40 =1/10
8/40 = 1/5
4
12
21
33
40
=10%
=20%
9/40
=22∙5%
12/40 = 3/10 =30%
=17·5%
7/40
36
72
81
108
63
360
A set of ordered pairs where each first element is paired with one and only one second
element and no element in either pair is without a partner.
G
gradient /slope
-6 -4 -2
-2
-4
-6
Vertical movement compared to the horizontal movement.
f(x)
6
4
2
f(x)
6
4
2
x
2 4 6 -6 -4 -2
-2
-4
-6
2 4 6
The gradient of a linear function is
rise y move y 2  y1


if 2 points are known.
run x move x 2  x1
The gradient of a linear function is m in the equation y  mx  c (x coefficient)
y =3x+2 gradient is 3 the y intercept is 2. y =x+2 gradient is 1 y intercept is 2
y=x+2
y=3x+2
x
grid/ table/ lattice
A method of listing all possible outcomes in a two stage problem. E.g. two dice
Die 2
H
hectare (hm2)
1
2
3
4
5
6
1
(1,1)
(2,1)
(3,1)
(4,1)
(5,1)
(6,1)
2
(1,2)
(2,2)
(3,2)
(4,2)
(5,2)
(6,2)
Die 1
3
(1,3)
(2,3)
(3,3)
(4,3)
(5,3)
(6,3)
4
(1,4)
(2,4)
(3,4)
(4,4)
(5,4)
(6,4)
5
(1,5)
(2,5)
(3,5)
(4,5)
(5,5)
(6,5)
6
(1,6)
(2,6)
(3,6)
(4,1)
(5,6)
(6,6)
A unit of area that is 100 m by 100 m. It is equivalent to 10 000 m2.
The prefix hecto- means 100 or 102.
height
The perpendicular length from a vertex of a triangle to the line opposite.
The perpendicular distance between two parallel lines is the height of a parallelogram.
is the symbol for perpendicular
heptagon
A polygon with 7 sides.
hexagon
A polygon with 6 sides.
bar gr aph
histogram
14
12
10
8
6
4
2
horizontal
0
A
B
C
dr i nks per
D
E
week
hypotenuse
F
A type of statistical graph that uses bars, where each bar represents a range of values
and the data is continuous. The columns touch each other.
Parallel to the horizon
The side opposite the right angle in a right triangle.
It is always the longest side of the triangle.
I
improper fraction
11
7
The point where all the bisectors of the angles of a triangle intersect.
It is the centre of the circle that has the sides of the triangles as tangents.
A fraction whose numerator is greater than or equal to its denominator. e.g.
y y
z z
x
x
in-centre
index / exponent
A number that indicates the number of times the base appears as a factor.
7 5  7  7  7  7  7 (7 is the base, 5 is the index)
inequality
A mathematical sentence including one of the symbols >,<, or   (greater or less
than, greater or equal to, less than or equal to) the symbol points to the smaller value.
infinitely large
Larger than any integer. Division by zero is an infinitely large and is undefined.
The gradient of a line parallel to the Y axis is infinitely large and undefined.
integer
Any number in the set 0 ,  1,  2 ,  3...........
interior angles of a polygon
interest (Simple)
I
PRT
interest (Compound)
Angles within a polygon formed by the intersection of two sides.
The interior angles of a triangle add up to 1800
The interior angles of a quadrilateral add up to 360 0
The interior angles of an n sided polygon add up to 180(n  2)
(Number of sides minus 2 then multiplied by 180)
Money paid for the use of someone else's money.
Simple Interest is calculated using the formula I  P  R  T (A = P + I)
P = Principal (amount of the loan)
R = Rate is the percentage (as a decimal) per year
T= Time in years.
To change the formula to calculate the Principal, Rate or Time use the SI triangle
cover the one that has to be found and the remainder is the formula required.
n
See compound. A  P(1  i )
interest free
Money borrowed to purchase goods where, for a specified time no interest has to be
paid. If the item is not fully paid by the end of the specified time a high rate of
interest is charged for the full amount for the entire duration of the loan.
inverse operations
Mathematical operations which undo each other.
 and ,  and ,
and squaring ,
3
and cubing etc
invert
Turn upside down.
intersect
To meet or cross.
inter-quartile range
The value of the upper quartile minus the value of the lower quartile.
isosceles
A polygon with two sides equal in length. Refers to either a triangle or a trapezium.
In the triangle the angles opposite the equal sides are equal.
kite
A quadrilateral with two pairs of adjacent sides equal.
To find the area of a kite multiply the diagonals together and divide by two.
The diagonals cut at right angles and the shorter diagonal is bisected.
Prefix meaning thousand.
1000 grams
= 1 kilogram
1000 metres = 1 kilometre
1000 litres
= 1 kilolitre
kilo
L
like terms
Terms that have the same variables (pro-numerals) raised to the same exponent. e.g.
3x2 and -2x2. (in both the variable is x2) Remember that xy is the same as yx.
But 3x 4 and 3x 2 are not the same and cannot be added or subtracted.
A set of connected points without an end.
line
EF
linear equation
F
E
An equation whose graph is a line. The exponents have to be one. e.g. y  2 x  1
(neither x nor y can be squared or cubed etc)
y
4
Slope and Intercept form
2
-4 -2
-2
2 4
x
-4
-6
-8
-10
y  mx  c
m is the gradient (slope) and +c is the y intercept
In y = 2x - 4
The y axis is cut at -4 (y intercept)
y  y1
2 y step
2 up
The gradient is 2 or 
(move from the y intercept)
 2

1 x step x 2   x 1 1 right
The General form
y
4
2
-4 -2
2
-2
-4
4 x
Ax  By  C
In the graph 2x+3y=6 (use the cover up method)
Both the y and x intercepts can be calculated by substituting x = 0 for the y intercept
and y = 0 for the x intercept. y = 0 2x = 6 x=3
x=0 3y =6 y =2
This gives both intercepts which can be used to sketch the graph.
To find the gradient either get y by itself y 
2 x
2
3
Or the gradient can be calculated using the formula
linear growth
2
3
 A 2
M

B
3
gradient =
Linear growth means that a quantity grows by the same amount in each step.
line of symmetry
line segment
M
mean
median
A line that divides a figure into two parts, each the mirror image of the other.
A
AB
B
In statistics, the measure of a central tendency calculated by adding all the values and
dividing the sum by the number of values. (the average.)
The Mean of 3,7,9,2,5,4 = 3+7+9+2+5+4=30 30  6  5
In statistics the middle value when the values are arranged in order of size. If there is
an even number of data items, the median is the average of the middle two.
median
234 579
2,3,4,5,7,9 the middle is half way between the 4 and 5 = 4.5
1 kilometre = 103 metres 1 metre = 102 centimetres 1 centimetre = 101millimetres
metric units of length
y
midpoint
10
B
2
milli
-2
-2
kilometre
1
1
1
103
106
109
metre
length (units1 )
area
(units2 )
volume (units3 )
kilometre
1
1
1
metre
1000
1
1000000
1
1000000000 1
1
1
1
centimetre
102
1
104
1
106
1
millimetre
101
102
103
centimetre
100
1
10000
1
1000000 1
millimetre
10
100
1000
 x1  x 2 y1  y 2   3  7 5  9 
,
,

  ( 5 ,7 )
2
2
2 

  2
M
4
length (units1 )
area
(units2 )
volume (units3 )
The midpoint of a line segment in coordinate geometry is at the average of the x
coordinates and the average of the y coordinates.
8
6
A part of a line with two end points
If A (3, 5) and B (7,9) the mid point is 
A
2 4 6 8 10 x
mixed number
1
Prefix meaning a thousandth part. 1 kilogram =1000 milligrams: 1mg 
Kg
2
1000
A number consisting of a whole number and a fraction. e.g. 3
7
mode
In statistics the value that appears most frequently in a set of data.
2,4,3,5,4,7,4,2,4 the mode is 4.
2, 2, 3, 4, 4, 4, 4, 5, 7 (the 4 occurs more often than any other number)
mutually exclusive
Outcomes which have no common elements e.g. drawing from a deck of cardsdrawing a club is mutually exclusive to drawing a diamond because there are no
‘diamonds-clubs’ cards.
However drawing a club is not mutually exclusive to drawing a king. Because a card
exists that is both a club and a king.
N
net
numerator
A plane figure obtained by opening and flattening a 3-D object.
Numerator
Denominator
The size of the fraction. It is above the line.
O
obtuse angle
An angle whose measure is between 90o and 180o.
obtuse triangle
A triangle with one obtuse angle.
145°
odds
ordered pair
(-4,2)
The ratio of the probability that an event will not occur compared with the probability
of it occurring. (Fail : Success or Loss : Win )
The odds that should be placed on drawing a heart from a deck of cards is 39/13 =3/1.
f(x)
6
4
2
-6 -4 -2
-2
-4
-6
2 4 6
(2,-4)
x
A pair of numbers for which the order is important. e.g. a pair of numbers that gives
the location of a point in a plane such as (-4,2). The order is important because the
point (-4,2) is not the same as (2,-4). It is always ( x, y) (horizontal, vertical)
ordinal data
Based on a characteristic or opinion but can be ranked e.g. Excellent → Very poor.
ordinal numbers
A whole number that indicates position. First, second, third fourth etc
outcome
Results of a probability experiment.
outlier
A data item which is much greater or smaller than the rest of the data. It may be
genuine data and must be included in calculations. It affects the mean and standard
deviation but not the median and inter-quartile range.
P
parabola
y
y
25
20
15
10
5
-4 -2-5
The shape of the graph of a quadratic. y = x2, y = 3x2, y = (x+3)2, y = x2 – 5
y
y = x2 +4x – 5, y = (x+3)2–5
5
y
25
20
15
10
5
2 4
x
y = x2
basic shape
-4 -2-5
2 4
y = 3x2
steeper
x
-8 -6 -4 -2-5
y
y
25
20
15
10
5
2
x
y = (x+3)2
3 to the left
-4 -2-5
y
15
10
5
25
20
15
10
5
2 4
y = x2 – 5
5 down
x
-8 -6 -4 -2
-5
-10
2
25
20
15
10
5
x
-8 -6 -4 -2-5
2
-4 -2
-5
-10
-15
-20
-25
x
y = x2 +4x – 5 y = (x+3)2–5
2 left (-½ x coordinate) 3 left 5 down
2 4
x
y = –x2
inverted
To sketch a Quadratic the following must be listed.
The x intercept/s if they exist. Solve the quadratic for y=0
The y intercept by substituting x = 0
The turning point by
1) Inspection y = (x + 4)2 + 3 TP = (– 4,+3)
2) Using the formula and substitution. y = ax2 + bx + c TP x =
b
2a
For the graph y = x 2 + 8x + 19 (a=1 b=8 c=19)
b 8
x

 4 then by substitution y  ( 4 ) 2  ( 8  4 )  19 y  3 TP  ( 4 ,3 )
2a
2
3) Completing the square
x 2  8 x  19  x 2  8 x  16  16  19   x  4 2  3 TP   4 ,3
parallel lines
Lines in the same plane that are always the same distance apart and never intersect.
parallelogram
A quadrilateral with 2 pairs of parallel sides The properties are
Opposite angles are equal. Opposite sides are equal. Diagonals bisect each other.
pentagon
A five sided polygon.
perimeter
The distance around the boundary of a plane (flat) figure.
Triangle
Square
Rectangle
P  sum of 3 sides
Circle
C  2  r or  D
percentage
P  4  length of side
P  4  l  4l
Parallelogram
P  2 lengths  2 widths
P  2l  2 w
Trapezium
P  2 sides  2 sides
P  2 S1  2 S 2
P  sum of 4 sides
A ratio where the second term is 100. (Hundredths parts) 25% = 25:100
To change a percentage to a decimal or fraction divide the percent by 100.
25%  25 (move the decimal two places to the left ) or
25 1

100 4
To change a fraction or a decimal to a percent multiply by 100.
∙45 = 45 % (move the decimal two places to the right) 1/8 =12½ %
perfect square
A whole number that is the square of an integer.
Perfect squares to know (memorize)
x 2 3 4 5 6 7 8 9 10 11 12 13
x2 4 9 16 25 36 49 64 81 100 121 144 169
In algebra perfect squares to know are
( x  y ) 2  x 2  2 xy  y 2
( x  y ) 2  x 2  2 xy  y 2
Square the first, square the last then double the first times last.
Difference of two perfect squares.
a 2  b 2  a  ba  b
perpendicular
Two lines that intersect to form right angles.
The small box in the corner is the symbol for right angle

Pi
The ratio of the circumference to the diameter of any (every) circle. The approximate
value is 3.142 or
point
22
7
C  D

C
D
An exact location in space represented by a dot. It has no size.
place value
9
8
9×10000
9×104
8×1000
8×103
Digits have a particular value in the number system.
The number 98524∙76831
5
2
4
7
6
8
3
1
5×100
2×10
4
7×1/10 6×1/100 8×1/1000 3×1/10000 1×1/100000
5×102
2×101
4×100
7×10-1
6×10-2
8×10-3
3×10-4
1×10-5
plane
A flat surface that extends infinitely in all directions.
polygon
A closed figure made up of line segments. (no beginning or end)
polyhedron
A 3-D object that has polygons as its faces. The intersection of any two faces forms an
edge.
polynomial
An expression of one or more terms, including some variable(s). e.g. 3 x 2  2 x  1 .
population
In statistics, population refers to the entire group about which data is being collected.
power
A number made up of a base and an index x
prime number
An integer greater than 1 whose only positive factors are itself and one.
The first few are 2,3,5,7,11,13,17,19,23,29,31
prism
A geometric solid with two equal bases that are, parallel polygons and the faces are
rectangles. A prisms is named according to the shape of its bases. e.g. triangular prism
probability
The likelihood of an event occurring.
Experimental probability—an event is repeated many times e.g. tossing a coin 100
53
47
times the results are recorded e.g. H = 53 T = 47
P( H ) 
P( T ) 
100
100
Theoretical probability is based on the outcomes that could occur.
P( ) 
y
35
Number of times the required outcome could occur
1
P( H ) 
Number of all possible outcomes
2
P( T ) 
1
2
If finding the probability of event A or event B add the probabilities.
If finding the probability of event A and event B multiply the probabilities.
P (A or B) =P (A) +P (B)
P (A and B) =P (A) × P (B)
product
The answer to a multiplication problem.
pro-numeral / variable
Usually a lower case letter used to represent numbers. It can be a symbol.
proper fraction
A fraction whose numerator is less than its denominator.
Pythagoras Theorem
In any right angled triangle, the square of the length of the hypotenuse equals the sum
of the squares of the lengths of the other 2 sides.
pyramid
Q
quadrant
c 2  a 2  b2
c  a 2  b2
To find another side
a 2  c 2  b2
a  c 2  b2
A geometric solid with one base that is a polygon and all other faces are triangles with
a common vertex.
Y
2
3
quadrilateral
To find hypotenuse
3
7
1
X
4
When the axes are drawn in a coordinate plane, the plane is divided into 4 sections
called quadrants. They are numbered from 1 to 4.
A four sided figure. (polygon)
Special quadrilaterals with specific properties are
Square Rectangle
Rhombus Kite
Parallelogram
Trapezium
quartile
Any one of the values in a frequency distribution that divides the distribution into four
parts of equal frequency. The first quartile is the number below which ¼ of the values
are found. (1st or lower Quartile, 3rd or upper Quartile the 2nd Quartile is the Median. )
1, 3, 4, 4, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 14, 15.
Min
1
quotient
LQ
5
Median
8.5
UQ
11
Max
15
Five Number
Summary.
The answer to a division problem.
r
radian
radian
r
r
Defined as the angle between 2 radii (radiuses) of a circle where the arc
 radians  1800
between them has length of one radius.
radius (plural: radii)
The distance from the centre of a circle to any point on the circumference of the circle.
range
In statistics, the difference between the least and the greatest values in a set of data.
ratio
A ratio compares two or more quantities of the same kind (units of measure.) 5 : 8
A ratio can be written as a fraction or a decimal.
Because a ratio is really a fraction, equivalent ratios are obtained by dividing or
multiplying all parts of the ratio by the same number.
12 : 15 = 4 : 5 (12÷3 and 15÷3) 3 : 7 = 6 : 14 ( 3×2 and 7×2)
To change a ratio to a fraction or a decimal divide the 1st by the 2nd.
To use a calculator to simplify a ratio either divide the 1st by the 2nd and change the
3
4 55
answer to a fraction or use the fraction button for
2 :3 
 55 : 76
4
5 76
For every ratio question the following information can be written:a 5
b 8

or

b 8
a 5
To calculate a or b knowing a or b
If
a : b  5 : 8 then
5
 b ( a is smaller than b  small number is the numerator . )
8
8
b   a ( b is larger than a  large number is the numerator . )
5
The two shares are 5 and 8  5  8  13 a total of 13 shares
a
To calculate a or b knowing the total
5
8
 Total
b
 Total
13
13
To calculate Total knowing a or b Total is more than a or b therefore use
13  a
13  b
T
T
5
8
a
ratio (decimal)
If a : b  625 then
To calculate a or b knowing a or b
a  625  b ( a is smaller than b  multiply by the decimal to make it smaller )
b  a  625 ( b is larger than a  divide by the decimal to make it larger )
a : b  625 is the same as a : b  625 : 1 The two shares are  625 and 1
 1  625  1  625 a total of 1  625 shares .
 625
1
T
b
T
1  625
1  625
1  625
1  625
To calculate Total knowing a or b T 
a
T
b
 625
1
5
( or enter  625 into the calculator and press  then the S  D button 
)
8
To calculate a or b if you know the Total :  a 
rational number
ray
AB
reciprocals
a
where a and b are integers
b
Half a line (has a beginning but no end) the part of a line on one side of a point
1
1
2
5
Two numbers whose product is one. x and
7 and
and
x
7
5
2
(If the number is a fraction it is turned upside down to get its reciprocal.
Any number that can be written in the form
A
B
rectangle
A parallelogram with four right angles.
All the properties of a parallelogram plus:Diagonals are equal in length and bisect each other.
recurring decimal
A decimal number that contains a digit or digits that repeat. e.g.  33333  3
3
the line above the digits shows which digits recur. 3
 27272727  27
11
An angle whose measure is between 1800 and 3600.
1
195°
reflex angle
300°
regular polygon
A polygon with all sides and all angles equal. An equilateral triangle and a square are
regular polygons.
rhombus
A parallelogram with all sides equal in length.
A rhombus has all the properties of a parallelogram. The extra properties are:Diagonals bisect each other at right angles and bisect the angles of the rhombus.
right angle
Measures exactly 900
right triangle
Triangle with one angle equal to 900
S
sample
In statistics refers to a representative portion of the population from which
information is gathered. It is generally accepted that population  number in sample
The information is used to draw conclusions about the behaviour of the population as
a whole. The sample should be random and representative of the group.
H
H
sample space
T
H
H
T
T
H
H
T
T
H
T
In probability a list of all possible outcomes.
Three coins sample space is HHH , HHT , HTH , HTT , THH , THT , TTH , TTT 
Each branch of the tree diagram is a possible outcome.
T
Scale /(Map or Drawing)
The ratio of a distance measured on a scale drawing to the corresponding distance
measured on the actual object.
scale factor
A scale ratio must be in the same units -- convert to the smaller units.
1cm : 5m = 1 cm : 500 cm
Scale Factor is 500.
Distance on Drawing × Scale Factor = Real Size
Real Size ÷ Scale Factor = Distance on Diagram
scalene triangle
A triangle with all sides of different lengths.
Regent s Scor e
scatter plot
120
100
80
60
40
20
0
0
2
4
6
8
A graphical method used in statistics to show the relationship between two variables.
The values of the two variables form ordered pairs that are graphed on the coordinate
plane. Scatter plots will often show at a glance whether a relationship exists between
two sets of data.
scientific notation
A number written as the product of a number between 1 and 10 and the appropriate
power of ten. (one number to the left of the decimal point) e.g. 118 000 = 1.18 X 105.
secondary data
Data obtained indirectly from sources such as a book or computer database.
sector
Part of a circle bounded by two radii and an arc.
segment
Part of a circle bounded by a chord and an arc.
semi circle
Half a circle
The angle in a semi circle is 900
sign rules
−3 × − 5 = + 15
+3 × + 5 = + 15
−3 × + 5 = − 15
+3 × − 5 = −15
Addition and Subtraction basically common sense is used (no rules.)
− 3 + 5 = +2
−10 + 4 = − 6
− 5 − 7 = −12
+3 + 4 = +7
−
+
Note ( − 5 is the same as (−1 × −5 ) and − 6 is the same as (−1 × +6)
Signs that are next to each other + + − − + − −+ follow the rules for multiplication.
Multiplication and Division (same rules).
If the two signs are the same the answer is positive.
If the two signs are the different the answer is negative.
similar polygons
Polygons that have the same shape but not necessarily the same size.
similar triangles
Similar triangles have the same shape and their corresponding sides are in the same
ratio. Triangles are similar if
Their angles are equal (AAA)
Their corresponding sides are in the same ratio.
Two sides are in the same ratio and an angle in a corresponding position is equal.
18
16
9
35
35
8
simple interest (see interest)
I
PRT
I=PRT
P is the amount borrowed R is percentage as a decimal per year T is time in years.
simplest form (lowest terms)
A fraction is in simplest form if both its numerator and denominator are whole
numbers and their only common factor is 1.
simultaneous equations
Equations with two or more variables that must be true at the same time.
One of the variables must be removed either by substitution or elimination.
SUBSTITUTI ON
2x  y  0
3 x  4 y  11
y  2x
3 x  8 x  11
Substitute
11 x  11
y  2 x  2
x1
( 1 ,2 )
simplify
ELIMINATIO N
2x  y  0
3 x  4 y  11 move under other equation
 4 ( to make the number of y' s equal
8x  4 y  0
2 x  y  0 substitute
3 x  4 y  11 ( add )
2  y0
11 x
 11
y2
x
1
( 1 ,2 )
To make an expression as short or compact as possible. To make it simpler, or to
reduce the number of symbols used.
adjacent
x
sine
opposite
hypotenuse
A
sine rule
b
c
B
square
A trigonometry ratio equal to the opposite side over hypotenuse. SOH
opposite
Sin x 
O  S H
H  O  S x  Sin  1 ( O  H )
hypotenuse
Used if two angles and a side are known or two sides and a
a
b
c


sin A sin B sin C NON included angle are known.
C
a
45
45
45
45
A rhombus with right angles.
A square has all the properties of a parallelogram, rectangle and rhombus.
squaring
Multiplying a number or pro-numeral by itself.
square root
A number that when squared gives the value of the original number. e.g. The square
root of 25 is 5 because 52 = 25.
36   6
symbol can be replaced by using fraction indices.
x
straight angle
180°
tens units
stem-and-leaf plot
1
x2
5
x
1
x5
3
x
2
x 2   x The
x or
x
y
2
x3
An angle whose measure is 180o. (Straight line)
In statistics, a way of recording, organizing and displaying numerical data so that the
original data remains intact. e.g.
In this plot, the last row represents the numbers 90, 92 and 95.
A stem and leaf plot should always be an ‘ordered’ stem and leaf plot.
Mode 75 Median 72 Q1 58+61→119 2 = 59∙5 Q3 = 77+83→1602 = 80
subtend
A line, two points, an arc, a chord, can subtend an angle. i,e. the start and finish of the
angle but not the actual position of the angle.
sum
The answer to an addition problem. The symbol for sum is  .
supplementary angles
Two angles whose measures total 180o.
surd
An irrational number (cannot be written as a fraction.) It exists but is not a precise
number.
It is the square root of a non-perfect square. 7 , 2 There is no exact answer.
To multiply surds
3 2  6
x
y
To divide surds
30
 5
6
x
x
y
y

xy
Surds can only be added or subtracted if they are the same. 2 5  7 5  9 5
Entire surd means everything is under the square root sign
3 7  7  9  63 The 3 goes back under the square root sign as a 32 =9.
To simplify a surd means get as much as possibly from under the square root sign.
Factors that are perfect squares can be moved from underneath the square root sign.
8  4  2  4  2  2 2 The 4 comes out as a 2.
`
The sum of the areas of all the faces, including the bases, of a 3-D object.
surface area
Cube TSA  s 2  6 Six equal squares.
side
altitude
b
base
s
radius
r
Pyramid TSA  b 2 
Cone
TSA   r 2   r s (learn formula)
Sphere TSA  4  r 2
radius
4 ab
 b 2  2ab A square plus 4 equal triangles
2
(learn formula)
Cylinder TSA  2 r 2  Dh
height
circumference
T
tangent
adjacent
x
hypotenuse
tangent
A trigonometry ratio equal to the opposite side over the adjacent side. TOA
opposite
tangent
tangent
Tan x =
opposite
adjacent
OTA
A
O
T
O
x  Tan 1  
 A
A straight line that touches the circumference of a circle at one point.
The tangent is at right angles to the radius at the point of contact.
Two tangents from a common point are equal in length.
A tangent is a straight line that touches a curve once.
term
Any expression written as a product or quotient. e.g. 3xy, 2m3, or -5x3y2z
theoretical probability
Probability that is determined on the basis of reasoning, not through experimentation.
e.g. Since a regular die has 6 sides, the theoretical probability of tossing a 3 is 1 6
time (24 hour clock)
Midnight is 0000 hours. The rest of the time before 12 noon does not change except
four digits must be used and the word hours is used instead of o’clock. E.g.0230 hours
From 12 pm to 12 .59 nothing changes except the word hours is used.
For all other p.m. time 12 hours must be added. 1 pm = 1300 hours.
transversal
A line that intersects 2 or more other lines in the same plane.
transversal
trapezium
180
& are cointerior
A quadrilateral with exactly one pair of parallel sides.
Co-interior angles add up to 180 (parallel lines)
Interior angles add to 360 (quadrilateral)
tree diagram
R
1/2
R
1/2
B
R
1/2
1/2
R
1/2
B 1/2
1/2
B
1/2
R
R
1/2
1/2
1/2
B
R
1/2
B
1/2
B
B
1/2
R
3/5
3/5
R
2/5
B
R
2/5
3/5
B
2/5
3/5
B
2/5
3/5
B
R
2/5
B
R
R
R
3/5
2/5
3/5
B
B
2/5
1/3 R
2/4
R
2/4
B
3/4
R
B
R
1/3
2/3
B
R
1/3
3/3
B
R
1/4 SEB
0/3
U
EN
B
R
3/5
2/5
B
trigonometry
P
HY
OT
37°
ADJACENT
OPPOSITE
2/3
2/3
B
Three marbles 2 black 3 red (replaced).
Two different possible outcomes. P (B) = 2/5. P(R) = 3/5.
P (RRR) = 3/5 × 3/5 × 3/5 = 27/125
P (BRR) = 2/5 × 3/5 × 3/5 = 18/125
P (RRB) = 3/5 × 3/5 × 2/5 = 18/125
P (BRB) = 2/5 × 3/5 × 2/5 = 12/125
3
2
3
18
P (RBR) = /5 × /5 × /5 = /125
P (BBR) = 2/5 × 2/5 × 3/5 = 12/125
P (RBB) = 3/5 × 2/5 × 2/5 = 12/125
P (BBB) = 2/5 × 2/5 × 2/5 = 8 /125
Three marbles 2 black 3 red ( NOT replaced). Dependent events
P (RRR) = 3/5 × 2/4 × 1/3 = 1/10
P (BRR) = 2/5 × 3/4 × 2/3= 1/5
3
2
2
1
P (RRB) = /5 × /4× /3 = /5
P (BRB) = 2/5 × 3/4 × 1/3 = 1/10
P (RBR) = 3/5 × 2/4 × 2/3 = 1/5
P (BBR) = 2/5 × 1/4 × 3/3 = 1/10
3
2
1
1
P (RBB) = /5 × /4 × /3 = /10
P (BBB) = 2/5 × 1/4 × 0/0 = 0
The three trigonometry ratios sine θ, cosine θ, and tangent θ are defined as
follows (the shortened form is written as sin θ, cos θ, and tan θ)
To remember these, use SOH CAH TOA, that is:
Sin θ = Opposite/Hypotenuse, SOH
Cos θ = Adjacent/Hypotenuse, CAH
Tan θ = Opposite/Adjacent
TOA
A
b
c
A diagram representing a systematic way of determining all possible outcomes in a
probability experiment. e.g. if you draw three marbles from a bag:Three marbles 3 black 3 red. (replaced).
Two equally possible outcomes P (B) = ½. P(R) = ½.
P (RRR) = ½× ½ × ½ = 1/8
P (BRR) = ½× ½ × ½ = 1/8
P (RRB) = ½× ½ × ½ = 1/8
P (BRB) = ½× ½ × ½ = 1/8
P (RBR) = ½× ½ × ½ = 1/8
P (BBR) = ½× ½ × ½ = 1/8
P (RBB) = ½× ½ × ½ = 1/8
P (BBB) = ½× ½ × ½ = 1/8
C
a
Area of a triangle is A 
1
ab sin C (the included angle)
2
turn / revolution
U
unit price
A 360 degree angle.
unlike terms
Terms with different variables or the same variables raised to different exponents.
e.g. 4 x 3  3 x 4 .
The price of a single item or the price per kilogram or gram.
V
variable / pro-numeral
venn diagram
A
1
A symbol, usually a small case letter, used to represent numbers. e.g. In the expression
2 x + 3, the variable is x . The 3 is called a constant because its value never changes.
4
2
7 5
6
C
3
vertex (plural: vertices)
B
A diagram to illustrate the relationship between groups. Can be used in probability.
The areas of are 1, 2, 3 members of A, B, C only
1) 1, 2, 3 members of A, B, C only
2) Members of:- A and B but not C (4), B and C but not A (5), A and C but not B (6)
3) A member of A, B and C (7)
The point of intersection of two rays that form an angle, two sides of a polygon or two
edges of a solid.
vertical
At right angles to the horizon.
vertically opposite angles
Two angles formed by the intersection of two lines. They share a common vertex but
no sides or interior points. e.g.
Vertically opposite angles, a and c, are equal and angles b and d, are equal
volume
The amount of space occupied by an object.
Height
Base
Height
Height
Base
Base
height
Base
height
Base
Volume of a prism → Area of the base times height. V= A× H
e.g. Triangle
Rectangular Prism
Irregular Prism
b h
V
H
V  lw H
V  Area of Base  H
2
Volume of a pyramid and cone (pointy shape)
= Area of the base × height ÷ 3.
V
l2  h
3
V
 r2  h
3
Volume of a sphere
Radius
Base
V 
4
 r3
3
Volume of a cylinder (Same idea as a Prism—Area of base × Height)
V   r 2h
height
radius
W
whole number
A number without fractions.