This week we learned the last unit：Systems of Linear Equations. I think this can be a relatively simple unit compared to other units. Except for the occasional numbers that are a bit tricky and painstakingly cumbersome, the overall picture is fairly straightforward. Simple questions, this time you can find a simple solution to the problem, this will reduce the trouble of computing, the answer is accurate! In this unit, we solve problems that involve systems of linear equations in two variables, graphically, and algebraically using the method of substitution and the method of elimination. An alternative approach is to solve the system algebraically.There are two algebraic methods: substitution & elimination. Elimination is particularly useful when the equations involve fractions.
Numbers of Solutions:
Lines intersect at one point，1 solution
Lines are parallel, no solution
Lines are coincident, infinitely many
This week we are still studying Equations of Linear Relations Lesson. After studying the fourth lesson: Slope-Point Form. Let my memory not only stay in this lesson but also recall the knowledge of the first few lessons.
The point-slope form of the equation of a line is y-y1=m(x-x1), where m is the slope of the line, and (x1,y1)represents a point on the line. To determine the equation of a line in higher grade math courses, the point-slope equation, y-y1=m(x-x1), is used more frequently than the slope-y-intercept equation,y=mx+b.
#Note: The slope-point equation is used when we have the slope of a line and the coordinates of any point on the line. When using this method to determine the equation slope-y-intercept form, y=mx+b.
Here is the question that Hard to solve by me 😂，However, after the explanation of the teacher and classmates, he suddenly realized that such a simple question
This week, we ended the seventh unit, ushered in the eighth unit.At the end of unit seven, we learned about how to use Function Notation to solve problem.From Lesson 9, we knew that Values of the independent variable represent the inputs of a function and are shown on the horizontal axis.Values of the dependent variable represents the outputs of a function and are shown on the vertical axis. And why I wrote something about horizontal axis and vertical axis,that is because Unit eight : Characteristics of linear relations lesson need to use these knowledge. What is a linear relation? A linear relation is a relation whose graph is represented by a straight line.The line can be infinite or finite depending the domain and range of the linear relation. In some cases we are only interested in a portion of a line. This portion is called a line segment.And from lesson 4, we learned slope of a line segment. The slope of a line segment is a measure of the steepness of the line segment.It is the ratio of rise (the change in vertical height between the endpoints) over run (the change in horizontal length between the endpoints).
This week, we learned Relations and Functions Lesson #2~#9, I think this is a fun but very hard unit. Because there are many new proper nouns and the need to remember 😂.
Relation:A relation is a set of inputs and outputs, often written as ordered pairs (input, output)
Functions:A function is a relation in which each input has only one output.
When representing a relation, we often regard the values of the independent variable as the input and the values of the dependent variable as the output.
The input values make up the domain of the relation ,and the output values make up the range of the relation.
The domain of a relation is the set of all possible values which can be used for the input of the independent variable(x)
The range of a relation is the set of all possible values of the output of the dependent variable.(y)
The following is a question I made when I first started to do a question(How to answer it is also written on the paper)
This is the last week to study Factoring Polynomial Expressions Lesson.At this week, we review about Polynomial Operations Lesson and Factoring Polynomial Expressions Lesson. We did two classes’ prastice text. And after Finished found that some defects exist. Let me know, this unit is a very living unit, learning points of knowledge can be combined with the knowledge of the first few units,so not only review the knowledge of this unit point, but also indirectly review the knowledge of the first few units.This also sounded the alarm for the review of my midterm test,Review is not a unit or two things, but all the knowledge points learned before. So to review the comprehensive words, you should then sort through the knowledge of previous learning points, and to do the same mistakes before doing the same, let your brain start to recall those points of knowledge.Here are some of the questions I did not quite understand, did wrong and hesitated when I did my review exercises on Friday.
This week we learned factoring Polynomial Expression Lesson.Listen to the name to know the content of the previous unit to learn, because the last unit called Polynomial Operations Lesson.This unit compared to the previous unit, the difference is not not particularly large, but added some new knowledge in it.
I think this module is mainly to test the common factor of our previous study,having mastered this is the same calculation as the previous one. And I learned something new .
Notice that :
1) If the product is positive then the two integers must be either both positive or both negative.
2) If the product is negative, then one integer is positive and the other is negative.
3) In a prefect square trinomial, the first and last terms must be perfect squares and the middle term must be twice the product of the square roots of the first and last terms.
4) The method of factoring by splitting the value of b into two integers whose product is ac and whose sum is b is called the method of decomposition.
This week we learned something about Polynomial Operations Lesson, This is a week of challenges and fun.
Say he is mainly fun to use different drawing methods to solve and confirm the accuracy of the answer or not.Say he has the challenge mainly lies in the back to the more complicated questions we want to calculate, almost the things we just learned are concentrated in a problem, so the operation will be more prone to deviation.
The following is a post-experience for me:When doing the questions do not worry about removing the brackets, especially in the face of the square and the cubic power of the demolition of the brackets as soon as possible, will affect the accuracy of the back of the operation.So if you want to calculate the square or cubic can be written as the following form:(?x-?)(?x+?) or (?x-?)(?x-?)(?x-?),instead of directly into(?x2-?x+?x….) ,this will make it clear that you know what to do next. However, if this is done, there are still discrepancies with the answer, it is quite possible that even if the calculation is not passed, so my small solution can not be guaranteed.
(This is where I made the question is wrong, I hope this kind of question is not very clear or troublesome students help). # The picture write by myself and choose on the math book.
This week we use knowledge about Trigonometry to solving triangles and problems.During I solving problems , I have a little trouble on it. Here is a question I will not do. I think I will do it, but my answer is inconsistent with the correct answer later. I really have no clue, so I raised the question. After teaching the students to explain, I know how to do it.So I used to do wrong because I used 9 years of age on the vertex, as well as parallel theory, so the answer is very different from the true answer In fact this question or should be used Trigonometry to solve the problem.When he explained half of the time he re-painted a triangle and just the answer we had just written, I was very puzzled. He explained to me that the original is not every question of the map is accurate. So when faced with such a type of problem, in order to do the problem can be re-painted, so that will not be due to the number of too many wrong.I think his little trick is good, so I think when I encounter a similar problem the next time you can also use this trick.
And here is question which I have a little problem on it.