# Week 17 – Math 10

This week in math 10, we learned Arithmetic Sequences. An arithmetic sequence is a list of numbers with a definite pattern.

Let’s say we have to determine $t_n$ and $t_30$

We can know that d is 2. And then, we can figure $t_n$ out using it.

After that, we can find $t_30$ using $t_n$ =$t_1$+(n-1)(d)

We should put 10 in $t_n$, 30 in n and, -2 in d.

Now, we can get $t_30$= 10+(30-1)(-2) and, $t_30$=48

# Week 16 – Math 10

This week in math 10, we were focused on solving problem application of systems such as number, money, mixtures, distance, and speed.

Therefore, today I am going to show you how to solve money problems.

Example 1. Four pencils and two erasers cost $3 .50. At the same prices, two pencils and five erasers cost$3. 17. Determine the cost of one eraser.

# Week 15 – Math 10

This week in math 10, we learned solving systems of linear equations. We can solve systems by Graphing, Substitution and Elimination.

So, I am going to show you how to solve systems by Elimination that is my favourite method. In the elimination method you either add or subtract the equations to get an equation in one variable.

Example

3x+6y=4

5x-6y=6

We can eliminate the x-variable by addition of the two equations.

3y+2x=6
5y2x=18
⎯⎯⎯⎯⎯⎯⎯
8y=24, y=3
The value of y can now be substituted into either of the original equations to find the value of x.
9+2x=6, 2x=-3
x=-3/2
So the solution of the linear system is (-3/2, 3)

# Math 10 – Week 14

This week in math 10, we started unit 9 and learned about system of equations. A system of equations is a collection of two or more equations with a same set of unknowns.

Example: two equations that share the variables x and y

x + y = 6

2x + y =8

Those two equations are shown in this graph:

So you can know that the solution for this example is where the lines cross at (2,4)

# Math 10 – Week 13

This week in math 10, we learned about how to do Point-Slope Form.

The point-slope form is  y − y1 = m(x − x1)

Example:

Slope “m” = 5/2.5 = 2

We know m, and also know that (x1, y1) = (6,6), and so we have y-6 = 2(x-6)

We can simplify it:

y-6 = 2(x-6)

= y-6 = 2x-12

= y = 2x-6

# Week 12 – Math 10

This week, we learned about Slope and how to find it.

Slope is

Rise changes to y, and Run changes to x.

Example.  Find the slope of the line that passes through A (3,2) and B (6,4).

y1 = 2, y2 = 4, x1= 3, x2 = 6. You can find the slope using them. So the slope is 2/3.

# Week 11 – Math 10

This week in math 10, we learned about characteristics of linear relations.

If you know the location of two points ( A and B ) like here, You could get the distance between them.

1. Make a right angled triangle.

2. Using the Pythagoras c² = a² + b², you can get the distance of c.

# Week 10 – Math 10

This week in math 10, we learned about function notation. I learned that we can use Mapping Notation and Function Notation to express a function.

Function Notation:

Function Notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation.

Mapping Notation:

Mapping Notation isa  way that we can express any kind of transformation in the geometric plane.

# Week 9 – Math 10

This week in math 10, we learned what a function is.

what is a function?  : a special relation from a set of inputs to a set of possible outputs where each input(x) is related to exactly one output(x).

The set of allowable inputs to a given function is called the domain of the function.

The set of possible outputs is called the range of the function.

Examples :