Download Formulas, Units and Shape Facts

Dyffryn School
Ysgol Y Dyffryn
Mathematics Faculty
Formulae and Facts
Booklet
Foundation Tier
Number Facts
Sum
Difference
Product
Share
Prime number
Square number
Cube number
Factor
Common factor
Highest Common Factor
Multiple
Common Multiple
Lowest Common Multiple
This means add.
This means take away.
This means multiply.
This means divide.
A number that has only two factors and can only be
divided by itself and one. (1, 9, 21, 27 are not prime numbers.)
The answer to when a number is multiplied by itself.
The answer to when number is multiplied by itself 3 times.
A number that can divide into another number e.g. the factors of
6 are 1, 2, 3 and 6
A number that can divide into two or more other numbers
The largest common factor.
A number that another number can divide into e.g. Multiples of
10 are 10, 20, 30 …
A number that two or more numbers can divide into
The smallest common multiple
Averages
Mean – Total divided by the amount of numbers.
Median – Middle number of an arranged set.
Mode – The most common number.
Range – The difference between the largest and smallest numbers.
Area
Square = (length)2
Rectangle = Length × Width
Triangle = Base × Height
2
Parallelogram = Base × Height
Trapezium = (a + b) × height
2
Compound/composite shapes – Split these up into known shapes and add up the areas.
Circle
Diameter is the distance across the centre of a circle
Radius = ½ diameter
Area of a circle =  × radius2
Circumference of a circle =  × diameter
For a semi-circle find the area as normal then half the answer
Volume
Volume of any prism = cross sectional area (Face area) × length
Cube = (length)3
Cuboid = length × width × height
Density
Density = Mass
Volume
M
D
Average Speed
Average speed = Distance
Time
V
D
S
T
Pythagoras’ Theorem
c2 = a2 + b2
or a2 + b2 = c2 (The hypotenuse is the longest side and is opposite the right angle)
Foreign Exchange
To convert from the original money to new money multiply
To convert back divide
Scale drawing
To go from scale to real life multiply
To go from real life to scale divide
Bearings
Bearings are always measured from the North and are measured in a clockwise direction. If a
bearing is bigger than 180o, measure anticlockwise and subtract from 360.
Estimated Mean
Estimated mean = (Total frequency x midpoint)  Total frequency
or
total f × x
Total f
Grouped frequency diagram – Bar chart with a proper scale
Frequency polygon – plot across to the midpoint and up to frequency. Join the points plotted
in order with a ruler.
Units (You have to know these)
1cm = 10mm
100cm = 1m
1000m = 1km
1g = 1000mg
1kg = 1000g
1 litre = 1000cm3
1 litre = 1000 millilitres
1 litre = 100 centilitres
1 mile  1.6 km
1m3 = 1000 litres
1ml = 1cm3
1 gallon = 4.5 litres
1 inch  2.5 cm
Converting squared or cubed units
cm2
mm2 × 102 or 100
2
m
cm2 ×1002 or 10000
3
m
cm3
× 1003 or 1000000
2
2
mm
cm
 102 or 100
cm2
m2
 1002 or 10000
3
3
cm
m
 1003 or 1000000
Metric Units
Weight
Grams (g)
Kilograms (kg)
Tonnes
Length
Millimetres (mm)
Centimetres (cm)
Metres (m)
Kilometres (km)
Grams are used for the weight of small items, for example the
weight of a pound coin or the weight of an exercise book.
Kilograms are used for the weight of heavy items,
for example, the weight of a sofa or the weight of a person.
Tonnes are used for the weight of very heavy items, for example
The weight of an aeroplane.
Millimetres are used for very small lengths, for example
the width of a finger nail.
Centimetres are used for small lengths, for example
the length of an exercise book.
Metres are used for distances such as the length of a room,
the height of a person or the height of a door.
Kilometres are used for long lengths such as the distance
between Swansea and Cardiff.
Volume
Millilitres (ml)
Millilitres are used for small volumes, for example the volume
water in a teaspoon.
Centilitres can be used to measure liquid in a glass.
Litres are used for larger volumes, for example the volume of
petrol in a tank.
Centilitres (cl)
Litres (l)
Angle Facts
Angles on a straight line add up to 180o
Angles round a point add up to 360o
Angles in a triangle add up to 180o
Angles in a quadrilateral add up to 360o
Vertically opposite angles are equal
Corresponding angles (F) formed in parallel lines are the same
Alternate angles (Z) formed in parallel lines are the same
Interior angles (C) formed in parallel lines add to 180
Polygons
The angle facts here are for regular polygons
Polygon
No of sides
Sum of angles
Triangle
3
180o
Quadrilateral
4
360o
Pentagon
5
540o
Hexagon
6
720o
Interior angle
60o
90o
108o
120o
Exterior angle
120o
90o
72o
60o
The sum of the exterior angles in any polygon is 360o
Shape Facts
Triangle
Types
Equilateral
Isosceles
Right angle
Scalene
All sides are the same length, all angles are 60o
Two sides the same length, two angles the same
Triangle with a right angle in it
All sides have different lengths
Quadrilateral
Types
Square
Rectangle
Rhombus
All sides the same length, all angles are 90o
Opposite sides are the same length, all angles are 90o
All sides are the same length, opposite sides are parallel, opposite
angles are the same
Parallelogram Opposite sides are parallel and equal in length, opposite angles are the
same
Trapezium
One set of parallel sides
Kite
Two sets of equal sides, two horizontal angles are the same
3D Shapes
Cube
Cuboid
Triangular prism
Square based pyramid
Tetrahedron
Percentage Change
% change = change/original × 100
All faces are congruent, this means the same (square)
Either all faces are rectangles or 4 are rectangles and 2 are
squares
2 faces are triangles and 3 are rectangles
5 vertices (corners), 4 faces are triangles and 1 is a square
All faces are equilateral triangles.