This week in math 10, we learned about arithmetic sequences.
The point of using arithmetic sequences is to find the and to find the .
the is used to find the general form/ the equation that we use to find other terms in the sequence. for example, if we have numbers 16,20,24… the formula can be used to find the 25th term easily with algebra, instead counting each term one by one.
first we need to find the common difference. The common difference between numbers is how much the number adds by or subtracts by from term to term. The common difference is represented as (d). We use the formula down below find the Term N.
in our sequence from before (16, 20, 24…), our first term is 16, and our common difference (d) is +4.
This week in Math 10 we learned about Systems of linear equations.
3 different types of linear equations
– No solutions
– One solution
– Infinite Solutions
First – what is a solution of a linear equation? we can graph all proper linear equations and if we have an equation of y=3x+4 and y=2x+3
The solution – these two equations is the points where both of the lines when graphed touch when graphed.
No Solution – when graphed the lines would be parallel. two parallel lines never touch. You can also tell if two equations have no solution if you only look at the written equation. For example if both equations have the same slope and the y-intercepts are different, this means the equation will have no equation.
^ no solution. If you were to put these two equations into demos, you would end up with two parallel lines.
One Solution – when a linear equation has one solution that means when graphed, somewhere along the graph the two lines will cross, sort of like an X shape. Now when written out, if both linear equations have different slopes than that means they will cross at one point. Even if the y-intercepts are the same it doesn’t matter, only the slopes need to be different.
These two equations are will have at least one solution guaranteed.
Infinite Solutions – So a linear equation with infinite solutions means that when graphed, the two lines will be on top of each other. If written, you can tell two equations will have infinite solutions if the slopes are the same and the y-intercepts are the same.
These two equations will have infinite solutions since they are on top of each other
this week in math 10 – we learned about the method of substitution.
substitution is the algebraic method of finding a solution for a system.
when doing the method of substitution – remember BFSD
B- brackets àexpand
F – Fraction àeliminate fractions
S – Sorting àorganize the numbers and like terms.
D – Divideànumber infant of Y
x + 3y = 19 àrearrange àx = -3y +19
–> 4x- 2y à4(-3y +19) -2y = -12y + 76
= -10y +76
Y = 66
NOW USE Y TO SOLVE FOR X
X + 3y = 19 àx + 3(66) =19
3 x 66 = 198 + x = 19
WEEK 13 – point slope form
This week in math 10 we learned about point slope form. Usually to find the slope formula you use the equation of
m= y1-y2/x1-x2 BUT to find point slope form you switch/move the equation to
m(x1-x2) = y1-y2
a good way to remember what you’re doing in point-slope form is to remember to ‘plug + play’.
That basically means to plug in the numbers into the equation and let algebra take over! Easy!
WEEK 12- slope formula
This week in math 10, we learned about slope formula. Slope formula is equal to
change y/change x
and that is equal to
Example: (3,7) and (-2,11)
Also keep in mind that 5/-4 would be equal to -4/5 , it all depends on how you do your equation
This week in math 10 we learned about graphing! First things first it’s important to understand what a variable is and that there are two types of variables, discrete and continuous. Variables are basically when the data or clues are given to us and it’s our job to find out where they go on a graph to showcase it a different way.
A discrete variable basically means a whole number / a number that you cannot divide. In other words, they don’t have an infinite number of values.A good example to remember this is how many people are in your household? As you cannot divide people in half (I would not like to see it anyway!), it counts as a discrete variable! Or maybe, how many cars sold from a dealership per month. As you cannot sell a fraction of a car, it counts as a discrete variable! When you’re graphing the dots and using a discrete variable, the dots on the graphs are not connected because the space between dots does not have value and there is nothing that is in between the dots on the graph as it cannot be divided.
A continuous variable meansthat there’s, in theory, an infinite number of possibilities. This variable is used to measure things like time, distance, weight, etc.The reason that they qualify as continuous is becausethey are not whole numbers. When you’re graphing the dots and using a continuous variable, the dots on the graphs are connected because the space between dots also has value.
This week in math 10 we learned about functions and relations!
First things first it’s important to know that Relations are 2 things that relate to each other.
Functions are like special relations. Per each input there is only 1 output. A good example to follow that of a mother to multiple children. Each child only has 1 biological mother, that is a function. Whereas a mother who has multiple children doesn’t have the same special relationship as a function (1:1) so it would be classified as relation.
You can see in the photo down below what a visual of relations and functions look like.
This week in math 10 we learned about how to evaluate a notation function. First things first, we need to know the different parts of the function. You can see in the photo below that every part has a label and as this chapter is mostly vocabulary based, it’s important you know what someone could be referencing.
There are a couple different ways that you can show your function, the first one im showing you is called ‘Mapping Notation’. The first thing you need to do is determine the ‘parent function’ aka the simplest form of that type of function, meaning they are as close as they can get to the origin
Next, you ask yourself, what changes in the equation? Or, what type of transformations are taking place in the equation. Let’s take a look at the example down below.
^and as you have the function you can write it in a product of ordered pairs to graph, ex. 2 ~~> (2, 10)
The next type of function notation we learned is simply called ‘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. o evaluate a function, substitute the input (the given number or expression) for the function’s variable. Replace the x with the number/expression. (Function notation is expressed very similarly to mapping notation.)
The last way we are showing is called ‘Equation’. the main part of Equation is that they aren’t names/ labeled so the only was to clearly showcase it is by writing it down visually. also keep in mind that saying ‘Find f (2) when f (x) = 3x, is the same as saying, “Find y when x = 2, for y = 3x.”