•always add up to 360º a + b + c = 180º of a trapezium •add the parallel sides, multiply by...
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Angles on a Point
• Always add up to 360º
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ab
c
a + b + c = 180º
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Area of a Trapezium
• Add the parallel sides, multiply by
the perpendicular height, then
divide by 2. Formula is ½(a+b)h
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a
b
hPerpendicularHeight
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60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
365 days = 1 year
366 days = 1 leap year
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Time
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Metric Measures
10 millimetres = 1 centimetre
100 centimetres = 1 metre
100 metres = 1 Kilometre
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Triangular Numbers
• A number which can be drawn by a triangle of dots. Add 1 to the difference between the last two terms to make the next term.
• 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, . . .
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Corresponding Angles
• Known as “F” angles
• They are always equal
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Inequalities
a > b a is greater than b
a < b a is less than b
a ≥ b a is greater than or equal
to b
a ≤ b a is less than or equal to b
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Circumference of a Circle
• Circumference = pi × diameter
• Circumference = 2 × pi × radius
• C= πd
• C= 2πr
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Diameter
Radius
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Pi = π
• π is a never ending number
that never repeats.
• Pi = 3.1415926535897932384626
4338327950288419716939937510
5820974944592307816406286208
9986280348253421170679821480
8651328230664709384460955058
2231725359408128481117450…..www.mathssite.com
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Imperial Weights
16 ounces (oz) = 1 pound (lb)
14 pounds = 1 stone
112 pounds = 1 hundredweight
2240 pounds = 1 ton
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BEDMAS
B = Brackets
E = Exponents
D = Division
M = Multiplication
A = Addition
S = Subtraction
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Volume of a Sphere
Volume = 4/3 × π × r³
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r
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Shape Names
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Pentagon
5
sidesOctagon
Hexagon
8
sides
6
sides
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External Angles
• The sum of external angles on any
polygon always add up to 360º
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SOH-CAH-TOA
hypotenuse
oppositeSin =θ
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θ
θ
hypotenuse
hypotenuse
oppositeopposit
eadja
ce
nt
adjacent
hypotenuse
adjacent=θcos
adjacent
opposite=θtan
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Cosine Rule
a² = b² + c² - 2bc × CosA
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ab
c
C
BA
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Isosceles Triangle
• 2 Sides are the same
• 2 Angles are the same
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Parallelogram
• Opposite sides are the same
length
• Opposite angles equal
• Opposite sides parallel
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12/24 hour time
0100 = 1.00 am0200 = 2.00 am0300 = 3.00 am0400 = 4.00 am0500 = 5.00 am0600 = 6.00 am0700 = 7.00 am0800 = 8.00 am0900 = 9.00 am1000 = 10.00 am1100 = 11.00 am1200 = 12.00 am
1300 = 1.00 pm1400 = 2.00 pm1500 = 3.00 pm1600 = 4.00 pm1700 = 5.00 pm1800 = 6.00 pm1900 = 7.00 pm2000 = 8.00 pm2100 = 9.00 pm2200 = 10.00 pm2300 = 11.00 pm2400 = 12.00 pm
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Logarithms
logaab = b
loga (bc) = loga b + loga c
loga( ) = loga(b) – loga(c)
loga(bc) = c loga(b)
a
bb
c
ca log
loglog =
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b
a
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Dimensions
Length = units
Area = units²
Volume = units³
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Surface Area of a Sphere
Surface area = 4 × π× r²
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r
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Metric Capacity
1000 millilitres (ml)= 1 litre (l)
1000 cm³ = 1 litre
1000 cc = 1 litre
1000 litres = 1 metre³
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Volume of a Cylinder
Volume = πr²h
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r
h
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Mode
• The number (or data item) that
occurs the most.
• Example : 8 4 8 5 2 9 8
• Answer : The Mode is 8
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Tangent Curve
y=tan(x)
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Negative Numbers
Multiplication
+ × + = +
+ × - = -
- × + = -
- × - = +
Division
+ ÷ + = +
+ ÷ - = -
- ÷ + = -
- ÷ - = +
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Angles Subtended on the
Same Arc
• The angles at
the
circumference
subtended by
the same arc
are equal
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Arc and Sector
• Arc = a part of
the
circumference of
a circle
• The part of a
circle made by
two radii and the
included arc.
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Sector
arc
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GCF
Greatest Common Factor
• This is the biggest number that
goes into two or more numbers
• Example HCF of 12 and 20 is 4
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LCM
Lowest Common Multiple
• This is the smallest number that
two or more numbers go into
• Example LCM of 12 and 20 is 60
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Mass Density Volume
Volume Density Mass ×=
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M
D VDensity
MassVolume =
Volume
MassDensity =
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Similar Shapes
• Shapes are exactly the same, but
are different sizes.
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Compound Interest
• A = Total Amount
• P= Original
Investment
• R= Percentage
Rate per annum
• T= Time in years
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T
100
R1PA
+=
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Inverse Proportion
• As one variable increases, so the other variable decreases.
• As one variable decreases, so the other variable increases.
• If y is inversely proportional to xthen
• k = constant of proportionality
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x
ky
xy =∝ or
1
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Compass Directions
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Box Plots
Minimum (A) = 0
Maximum (B) = 10
Median (C) = 5
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Upper Quartile (D) = 7
Lower Quartile (E) = 3
A E B D B
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Decimals to Percentages
• Multiply the decimal number by
100
0.25 × 100 = 25%
0.5 × 100 = 50%
0.07 × 100 = 7%
1.23 × 100 = 123%
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Bearing
• This is the angle, measured clockwise
from the north. The bearing of B from A
is 230º. The bearing of A from B is 050º.
It always has to have 3 digits.
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N
N
B
A
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Mutually Exclusive Events
• Two events are mutually
exclusive if they cannot occur at
the same time (i.e., you cannot
throw a 4 and a prime number on
a single dice at the same time).
P(A or B) = P(A) + P(B)
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Variance
• Population
variance is where
µ = mean and N =
number of items
• Sample variance
is where M =
mean of sample
N
X∑ −=
22 )( µ
σ
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1
)( 22
−−
= ∑N
MXs
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Systematic Sampling
• This is where you take every nth
one in the list.
• Example : You have 300 names
and you want 30 as your sample.
300÷30 = 10. This means you take
every 10th one.
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Matrix Subtraction
• Matrices of the same dimension
can be subtracted. Subtract the
corresponding elements.
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−−−=
−
51
23
14
65
43
21
14
26
35
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Geometric Formulae
• Find a term use
an = arn-1
• where
a=first term
r=common ratio
n=term needed
• Find a sum use
• where
a=first term
n=term needed
r=common ratio
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r
ras
n
n −−=
1
)1(
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Number Sets
• ℤℤℤℤ is the set of integers, where
– ℤℤℤℤ+ is only the positive integers
– ℤℤℤℤ---- is only the negative integers
• ℕℕℕℕ represents the set of natural
numbersℝℝℝℝ represents the set of real
numbersℚℚℚℚ represents the set of rational
numbers
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Solving Multiplication Equations
• Take the number multiplying the
letter to the other side of the
equation and make it a divide
Example : 2x = 6
x = 6 ÷ 2
x = 3
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