April 10

# Week 8 — Math 10

This week, we began to learn chapter5–Polynomial. I think there are lots of fun to solve the problems of polynomial.

I felt so confused about lots of new words. But now I got those words.

Variable: the letter in a polynomial.

Polynomial: (Note)The exponent of any variable must be a positive integer.

Degree: The degree of a polynomial is the degree of the term with highest degree.

The leading coefficient of a polynomial in a single variable is the coefficient of the term with highest power of the variable.

Zero pair: a pair of terms that combined simplify yo zero.

Distribute: Multiplying a sum or difference by a common number. Used to remove brackets from an expression.

In this week, I also learnt how to use Area Diagram, this really helpful when I am doing those questions.

April 4

# Weekend Bonus Project– Math 10

There is a tree near my house. I measured the length of the shadow is around 2.7m, and the angle between sunlight and ground is 59.6˚. If  we want to know the height of the tree, we need use tan ration. Then, I figure out the hight is around 1.6m.

April 3

# Week 7– Math 10 Trigonometry questions

1. In the picture we can see AC is 50, and we can find out angle ACB is 21˚, we need figure out the length of BC. The angle ACB is the reference angle, so the side AC is the HYP, the side BC is ADJ, so we need use cos ratio. Usually, we around the results to the nearest tenth.

The equation is cos 21˚= $(\frac{x}{50})$ the second step is: Remove X to the left side, so we could get a equation like the picture showing, x=50(cos21˚) then we got the result.

2. In this right triangle PCQ, the angle PCQ is 90 degrees, we already know the side PC is 23, and the side CQ is 40,  we need to figure out the angle CPQ. The angle y is the reference angle, so the side PC is the ADJ, the side CQ is the OPP, so we use tan ratio. And the results we need around to the nearest degrees.

The equation is tan y˚= $(\frac{40}{23})$ And the second step is leave the y alone, the equation must be y˚= $tan^-1\cdot (\frac{40}{23})$ so by the end, we could use calculator to get the result.

3. In this right triangle, the angle NML is 90˚, and the angle MNL is 30˚, we could easily figure out angle MLN is (90˚- 30˚=60˚), so b=60˚. The side ML is 27 and it is OPP side, the side NL is HYP side, so we need use sin ratio. Then the result is 54.

The equation is sin 30˚= $(\frac{27}{a})$ And the second step is to leave the a alone, so I moved the a to the left side and have the equation $(\frac{27}{sin30˚})$ And the last step is using calculator to calculate the results.

March 26

# Week6 — Math 10

This week I learnt Trigonometric Ratios. From the questions on the workbook, I summed up some rules:

Rule I1) sin x˚, sin y˚,  if x>y, so  sin x˚>sin y˚

2) cos x˚, cos y˚, if x>y, so cos x˚<cos y˚

3) tan x˚, tan y˚, if x>y, so tan x˚>tan y˚

4) sin x˚, tan x˚, so sin x˚< tan x˚.

Rule II: sin x˚, cos x˚

1) x<45˚               sin x˚< cos x˚

2) x=45˚              sin x˚= cos x˚

3) x>45˚              sin x˚> cos x˚

There is also a very important rule is cos x˚=sin (90 – x)˚ and sin x˚=cos (90 – x)˚.

March 6

# Week 5 — Math10

The most difficult things I learnt from this week is the “Conversion of Units within the International System of Units (SI)” There are lots of units like feet, inch, yard, etc. I did not learn before. These units always make me confused, and I am a little bit worrying about my next week test.

There is a very difficult question I found in this week. At last, I got it, so it is my Ah-ha moment.

The question is: Convert the following to the indicated measurements using unit analysis.

a)120m/h=____mm/min

When I saw this question I was speechless because I have no idea! But later, I studies the example, and I got a method to solve this question.

Here is my method. Just convert each part of the indicated measurement. And then, just divide 120×10^3mm by 60min, so the answer is 2×10^3mm/min.

February 28

# Week 4– Math 10

These are I learnt new things from this week.

I learnt how to read these pictures. To me it is a new challenge, because I never learnt it in China, and I felt so confused. But now I got it.

The metric reading is easier to read. In the first one, you find the first line in black, that always zero, and points to the whole number part and the first decimal place. So I wrote down 8.6. And then, we need find another black line that looks like connect the white line perfectly. So I wrote down 0.02. At last, you only need to plus them together to get the answer.

The second one, as same as the first one.