Using the topics listed below answer the following questions. 1. In this unit wh
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Question
Using the topics listed below answer the following questions.
1. In this unit what topics were of most interest and usefulness to you, why? Share a problem from a topic you thought was interesting or useful (Don’t include the solution).
2. In this unit what topics did you find difficult, why? Share an example problem that you struggled with this week (Don’t include the solution).
Unit 6 Topics:
Find Roots without a Calculator
Calculate Roots with a Calculator
Distance Formula
Simplify Using Product and Quotient Rule
Simplify Radical Expressions
Multiply Radical Expression
Divide Radical Expressions
Add, Subtract, and Simplify Radical Expressions
Solve Radical Expressions
Explanation / Answer
It would have been better if you mention the standard, book and topic (Algebra, trigonometry, calculus)
Let's first briefly understand all the topics and their learnings one by one -
Find Roots without a Calculator
Finding the roots of the equation (quadratic, and higher degree polynomials using the initial guess and then division property. Also there are some numerical methods present too in the higher standards to find the roots by converting the equation of f(x) = 0 to x = g(x) and then keep iterating until the change in x is very minimal (it's called fixed point iteration method). Coming back to the topic, it is very useful to find at what points the function/polynomial value is going to be 0 for plotting them and also for analysis)
Calculate Roots with a Calculator
Using a calculator all the coefficients of the polynomials are entered in the calculator function and it provides you the root. Plain and simple. Not miuch effort
Distance Formula
Find the the distance between 2 points on catesian coordinates system (x,y) to understand how far 2 points are situated. This is very important concept applicable in real life. E.g. distance between 2 cities can be calculated and then can be compared to distance between another 2 cities. Or to find out who is closer to person A.
Simplif, Multiply,Divide,Add,Subtrace & solve Radical Expressions
Radical expression are the reality of life. In real life, you don't get the nice simple integers or even rational numbers. So it is important to learn to work with them. Making them simple and then running multiple manipulation on them becomes absolute necessicity in the higher standards.
Considering all the topics, solving the roots without calculator is the most interesting as you don't have calculator everytime with you. In these cases, such techniques becomes important.
Least interesting was multiplying the radical expression, as there was nothing much new to learn. As it is simple multiplication of different exponents.
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