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Maths Cheat Sheet by [deleted]

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Probab­ility Terms

Sample space
The set of all possible outcomes (e.g 1,2,3,­4,5,6 on a normal dice)
Equally likely outcomes
A situation in which all outcomes have the same chance of occuring
Mutually exclusive events
These events have no outcomes in common
Non mutually exclusive events
These events have at least one outcome in common
Probab­ility can be expressed in fraction, decimal or percentage form.

Comple­mentary Events

Luke's chance of clearing the high jump is 7/10. Luke's chance of not clearing the high jump is?
1 (10) - 7/10 = 3/10 P(not clearing the high jump)
We have a bag with 9 red marbles, 2 blue marbles, and 3 green marbles. What is the probab­ility of not selecting a blue marble?
Number of total marbles = 14
Blue marbles = 2
1 (14) - 2 = 12/14 P(non blue marbles)

Time Zones

What is the time in London, when it is 9am in Sydney? (Sydney is 10 hours ahead)
London time = Sydney time - 10 hours
9am - 10h = 11pm in London
What is the time in Sydney, when it is 9am in London? (London is 10 hours behind)
Sydney time = London time + 10 hours
9am + 10h = 7pm in Sydney

Volume of Prisms

Rectan­gular prisms
Length x Width x Height
Triangular prisms
Area of triangle x Height
Any other prism
Area x Height (area of the cross section and height is the height of the prism)
If the question tells you to, find the area of the shape's cross section and then times the amount by the height to get the volume.

Remember to add cubed units to the answer.

Probab­ility Inform­ation

A "­sta­nda­rd" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Clubs (black suite), Hearts, and Diamonds (red suite). Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Ace may or may not be higher than King.

To convert 12 hour time to 24 hour time follow these rules. For AM times, leave the times the same except for single digit hours in which a 0 is written at the front. For PM times, add 12 to the hour digits.
 

Index Notation

m x m
m2
5 x n x n x n
5n3
When a pronumeral is multiplied by itself a number of times we can simplify the expression using index notation.

Remember to substitute if necessary.

Dividing Algebraic Terms

30a / 2a
Divide the numbers first, so 30 / 2 = 15.
Next, cancel out the pronum­erals. A goes into A, which gives us just 15.
12ab / 6a2
Divide the numbers first, so 12 / 6 equals 2. Next, cancel out the pronum­erals. A goes into A but B does not go into A. This gives us 2b / a.
Remember to always write the dividing algebraic terms in fraction form.

Factor­ising Algebraic Terms

3a + 12
3 x a + 3 x 4 is the expanded form.
The factorised form is 3(a + 4).
6m + 9
First, find the HCF. In this case, it is 3.

Put the HCF out the front of a pair of brackets. Find what the HCF is multiplied by to get each term.

So we end up getting 3(2m + 3)
Factor­ising is the reverse form of expanding. A good way to check your factor­isation is by expanding your answer it to see if you get the original expression

Conver­sions

Area of Plane Shapes

Rectangle
Width x Height (or wh)
Square
a² (a = length of side)
Triangle
1/2 x Base x Height (or bh)
Trapezium
1/2 x (side a+ side b)
Parall­elogram
Base x Height (or bh)
Rhombu­s/Kite
Side A x Side B / 2
For a composite shape, split the shape into already known shapes and use their respective methods to find the area (add the areas together).

Remember to add squared units with the answer.

Volume and Capacity Conver­sions

Cubic Millimetres
mm³
Cubic Millimetres
cm³
1cm³ = 1000m³
Cubic Metres
1m³ = 1000 000 cm³
Mililitre
mL
1mL = 1cm³
Litres
L
1L = 1000ml = 1000cm³
Kilolitres
kL
1kL = 1000L = 1m3
Megalitres
ML
1ML = 1000kL = 1000 000L
 

Adding and Subtra­cting Like Terms

5x - 2y - 3x + 7y
Move the terms with the same pronumeral next to each other. So we get 5x - 3x - 2y + 7y

Simplify and you get 2x + 5y
7ab - 3bc + 2ab
Move the terms with the same pronumeral next to each other. So we get 7ab + 2ab - 3bc

Simplify and you get 9ab - 3bc
Only like terms can be added or subtracted together.

Multip­lying Algebraic Terms

10 x 3n
10 x 3 = 30
30 x n = 30n
20n x 3mn
20 x 3 = 60
60 x n x n x m = 60n2m
Remember to multiply the numbers first, then multiply the pro numerals (or add it to the end of the product).

Negative and positive rules also apply to any problems.

Negative and Positive Rules

Expanding Algebraic Terms

5(y + 3) + 2y
5 x y = 5y
5 x 3 = 15
5y + 2y = 7y
Expanded form is 7y + 15
3(a + 4) + 2(5 - a)
3 x a = 3a
3 x 4 = 12
2 x 5 = 10
2 x a = 2a
3a +- 2a = a
12 + 10 = 22
Expanded form is a + 22
To write an expression without grouping symbols, multiply each term inside the grouping symbols by the term outside.

Watch out for expres­sions that have negative signs outside the grouping symbols

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