# Week 4 Multiplying and Dividing Radical Expressions

Expand and simplify: (P127)

a) ($\sqrt{3}$ +8) ($2\sqrt[1]{3}$ -1) – $\sqrt{3}$ ($7\sqrt[1]{3}$ -4)

=6-$\sqrt{3}$$16\sqrt[1]{3}$ -8-(21-$4\sqrt[1]{3}$)

=-2 + $15\sqrt[1]{3}$ -21 + $4\sqrt[1]{3}$

=-23+ $19\sqrt[1]{3}$

Firstly, when we solve this type of questions, we need to find the like terms becasue when adding/ substraction, the coefficients are combined when the radicands are the same. For example, in this question, like terms are $\sqrt{3}$$2\sqrt[1]{3}$ and $\sqrt{3}$($7\sqrt[1]{3}$ becasue you can find they all have $\sqrt{3}$, and that means we need to think of a way to combine them together to get a simplified answer.  Secondly, do the calculation carefully and be aware of the like terms. Final step is to check you answer is already simplified  or not.

# Week 3 Simplifying Radical Expressions

$2\sqrt[3]{5}$

=

=$\sqrt{-40}$

When I first do this question,I was confused by the difference of the mixed radical and entire radical. I think the most difficult part is the index part becasue there is a tube and I don’t know how to solve this. And we only learned how to simplify in Grade 10. My  understanding is that when we solve this type of question, we need to multiple all the numbers outside the root, the index and so as the radicand together. When there is a tube (3), just multiple 3, we don’t have to multiple three times becasue that’s not the exact meaning of tube. The most important thing is that we should be careful when we do the calculating.

# Week 2 Geometric Sequence

Determine $S_{10}$ for each geometric series. Give the answer to 3 decimal places. (page 49)

a)0.1+ 0.01+ 0.001+ 0.0001+…

know:$t_{1}$=0.1 ($t_{1}$ means the first one, the first place)

r=0.1( 0.01 divided by 0.1)( each term is multiplied by a constant known as the common ratio) ( to determine the common ratio, divide any  term by the preceding term)

n=10 ( a nautral number and menas the term , for instance, as the question asks to find the 10th term means n= 10)

$S_{10}$

(follow the formula, and use the caluator to caluate the 10th power)

# Notebook

In the movie Notebook, produced by Nicholas Sparks, the first scene focused on an old man. When he opened the book, time flashed back. A poor country boy Noah so desperately fell in love with a rich city girl, Allie. They argued a lot during the whole summer holiday, so Allie left. But they both regret for without saying goodbye to each other. Noah wrote 365 letters to Allie, Allie was terribly tempted to keep thinking about Noah. She wrote the notebook to release her emotion and fortunately, they were reunited years later. Allie remembered less because she got Alzheimer’s disease, but Noah didn’t give up on her. He started to read the notebook to Allie every day for waking up her memory. One day, Allie surprisingly went to Noah’s room because that day was their wedding anniversary. She embraced Noah and gave him a big kiss. She remembered everything and Noah. This movie shows how powerful love can overcome everything, even time and encourage everyone to pursue true love, cherish them for a whole life and believe everlasting love real exists.

(the source of the image:)

# Week 1- My Arithmetic Sequence

1: my own arithmetic sequence: 20，22，24，26，28，30

first five numbers: 20, 22, 24, 26, 28,30

2: $t_{1}+49d=t_{50}$, d=2

20+49×2=t_{50}=118

3: \$latex t_{1}+(n-1)d=t_{n}

=20+(n-1)2

=20+2n-2

=18+2n

4:(sorry Ms Burton, I don’t know how to type the formula, but I post the process oƒ calculating the sum of the 50 terms)