Expected Value

 This week in maths we talked about expected value. 

If we repeat something equally likely outcomes a large number of times, we can work out how many time we would expect each outcome to occur.

Eg. You roll a die 50 times. How many do you expect?

Expected value= 1/6 x 50= 8.3

Tree Diagrams

 Last week in maths we have learnt about Tree Diagrams. Tree Diagrams can be used to show the different possibilities and calculate probabilities.

Learning Reflection || Math

This week in Maths, we started another topic for this term and we have been learning about Probability. In Probability, we also learnt about Relative Frequency.

Introduction
Probability is all about using Maths to predict how likely a future event is to occur. 

Relative Frequency
We can use a frequency table of past events to estimate how likely that event is to occur again and compare it to other events.

Kinematics

In maths, we have been focusing on Kinematics. This week we have lean about Acceleration, Newton's 3 Laws and Mass and Weight.

Acceleration
The following equation links the acceleration of an object, it's change in speed and the time taken. 

The formula that is used to find the acceleration is;

a=Δv ➗ t

Eg. A runner accelerates from 0m/s to 8m/s in 10s.

a=Δv ➗ t
  = 8➗10

  = 0.8 m/s2

Newton's 3 Laws

• An object will either remain at rest or moving with constant speed if no unbalanced force acts on it.
• If an unbalanced force acts on an object it will accelerate.
• Every action has an equal and opposite reaction.

Mass and Weight

An object's mass and its weight are two different things. Mass is the amount of matter in an object, measured in kg. We often (mistakenly) call this our weight. Weight is a force of gravity which acts on an object, measured in N.

Formula:                                                          

Fw = mg 

Where: Fw is the weight force of an object (in N)

             m is the mass of the object (in kg)

             g is the acceleration due to gravity (10 m/s2)

Eg. A car with mass 1500kg accelerates at 7m/s2.

      F= ma

        = 1500 x 7

        = 10 500N

 

Algebra

Substitution

Substitution into an equation replacing a variable with a number when it is known, and then evaluating that equation (calculating the value of the result). It is always important to remember the following.

- Always use the correct order of operation - BEDMAS
- One or more variables or the number next to each other (such as 3a or pqr) means to multiply them
- A fraction represents division (top ➗ bottom)

- Don't forget to replace a variable with its value every time it appears in a formula.

Example: If a= 2 b=4 c=5

5c = [5x5 = 25]

6a-2 = [6x2 - 2 = 10]

Using Formulae

We often use formulae to represent practical situations. For example, the formulae for the area of a triangle is:

A=½bh     

Where: b= base

            h = height

Financial Literacy

In Maths we have been learning about Financial Literacy and for this week we talked about Percentages and Increases/Decreases.

Percentage
- To calculate a certain percentage of an amount, use this rule:
[percentage ➗ 100 x amount]

Eg.1 
10% of $150 = $15
(10 ➗ 100 x 150 = 15)

26% of $451= $117.26
(26 ➗ 100 x 451 = 117.26)

Eg.2 
A store has a hoodie, normal price $66, on sale for 25% off.

a) How much is the discount?
    25➗100x$66 = $16.50

b) What is the sale price?
    $66 ➖ $16.50 = $49.50

Increases/Decreases
- Often we need to increase or decrease an amount by a certain percentage (eg. discount, mark-up etc).

For these types of calculation, do the following:

1. Calculate the "percentage of" the amount (percentage ➗ 100 x amount)

2. Add it (for an increase) or subtract (for a decrease) from the original amount.

Eg.1
Increase $80 by15%
(15% ➗ 100 x 80 = 12)
($80 ➕ $12 = $92)

Earning Incomes

In Maths we have been learning about Financial. This week we have talked about two main ways you can earn money by getting a wage or a salary. We also learned how they get paid and how much I will get paid once I work overtime.

Wages: Is a paid as a certain amount of money per hours worked.

[hours x money]

Salary: Is a fixed amount per year. This usually occurs in jobs where the hours are flexible, so you are paid for the work being done rather than the time taken to do it. 

[salary ➗ week per year]

Overtime:  To avoid employees being forced to do unfair hours of work employers must pay their employees extra, depending on particular conditions and legal requirements. This will usually be for doing over a certain number of hours in a day. This extra pay is called overtime pay. It is calculated on the extra hours done.

Overtime pay is calculated by multiplying the hourly wage by a particular number.

Time and a half: multiply by the wager rate by 1.5.

Double time: multiply the wage rate by 2

Example: 

Ordinary Time: 8 x $16.20 = $129.60

Overtime Pay: 3 x $16.20 x 1.5 = $72.90

Total pay: $129.60 + $72.90 = $202.50

Measurement || Perimeter/Area/Volume

In Math, this past few days we have been learning about "Measurements".

Area;
The area of a shape is a measure of the amount of 2-dimensional surface the shape covers.
Faces; are the flat surfaces of the shape.
Edges; are the lines between faces.
Verticles; are the corners.

Rectangle: 
Area = length x width
Triangle:
Area = 1/2 x base x height
Parallelogram:
Area = base x height
Trapezium:
Area = 1/2 x (a+b) x height

Net
A net of a 3D shape is a plan draw in a 2D that could be cut out and folded up to make that shape.

Perimeter
The perimeter of a 2-dimensional shape is the distance around the outside. Because it is a distance, it is measure in mm, cm, m, or km.

Perimeter = a+a+a+a

Circles
The perimeter of a circle is called the circumference.

If you know the radius: C =2 x π x r
If you know the diameter: C = π x d

- The formula for the area is:
Area = π x radius squared

Calculating Volume
The volume of a 3-dimensional shape is a representation of the amount of space inside it or the amount of 'stuff' that could fit inside the shape.

Cuboid (Volume)
A cuboid is a box shape with all 6 faces being rectangles. This also includes cubes with all faces being square.
The volume of a cuboid is calculated using the rule:
Volume = length x width x height


Prisms
A prism is a shape in which there are at least one directions you would slice the shape, that would create the same cross-sectional area anywhere in the direction. Usually, you need yo calculate the cross-sectional area first.

The volume of a prism is calculated using the rule:
Volume = cross-sectional area x length

Pyramids
A pyramid is a shape that has a particular shape base (often a square) and then all sides face come together to a point. Also, you will usually need to calculate the base area first.

The volume of a pyramid is calculated using the rule:
Volume = 1/3 x base area x height

Spheres
A sphere is a perfectly round solid such as a ball.

The volume of a sphere is calculated using the rule:
Volume = 4/3 x π x radius cube

Maths Pattern

In maths, we have been studying patterns. Math patterns are in orders that repeat base on a rule and the rule is a set way to calculate or solve a problem.

1.) 2,7,12,17,22,27,32 - added by 5
2.) 5,16,27,38,49,60,71 - added by 11
3.) 2, 3.5, 5, 6.5, 8, 10.5, 12 - added by 1.5
4.) 13, 9, 5, 1, -3, -7,-11 - subtracted by 4
5.) -20, -17, -14, -11, -8, -5, -2 - subtracte by 3