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Browsing category archives: Grade 10

Week 4-Math 10

This week we focused mainly on finding angles in a triangle. This could be the angle of depression, the angle of elevation, or finding out an unknown reference angle.

Reference Angle:

  1. First, we need to start with our triangle and label each side accordingly, since the reference angle is unknown, we have to work backward kind of.
  2.  Second, we need to find out which function we’re using. Listing them off helps (SOH CAH TOA) Since we don’t have the hypotenuse or reference angle, we can’t use sine or cosine. So, tangent is the only choice left. Write out the ratio for the tangent of unknown angle x. 
  3. Third, change tan to the second function on your calculator, and divide the adjacent side by the opposite side.
  4. Lastly, solve the equation by dividing (A/0) and write the final statement. For this question, angle x would equal to be about 61 degrees.

 

The angle of Elevation and Angle of Depression

The angle of Elevation-The angle of elevation is the same as the angle up. To elevate means to lift, so it’s the angle that lifts up.

In this example, the dot on the horizontal line would equal to you, or a person. The dotted line is the sight line up to an object, which ultimately creates an angle of elevation. The object is the other dot, and the angle of elevation is what is created from the horizontal line and the sight line.

 

The angle of Depression-The angle of depression is the same as the angle down. To make a depression means to go down, so it is the angle that is facing downwards if that makes sense.

In this example, the dot on the horizontal line would again equal to you or an observer. The dotted line is, again, the sight line down to an object, which again creates an angle of depression. The only difference between depression to elevation is that one, the depression, is an angle that is diagonally declining down on an angle, while the elevation is inclined on an upward angle. The object is the other dot, which is connected by the sight line.

Week 3-Math 10

Parts of A Triangle and Formulas

Parts-

Hypotenuse-The longest side of a triangle, opposite of the right angle

Reference Angle-Smallest known angle, can be used to measure the other angles

Opposite Side-Side across from Angle A

Adjacent-Side next to Angle A

Formulas- Each formula can be used to find a ratio

 

 

Week 2-Math 10

Exponent Laws and Parts of an Exponent

Parts of an exponent:

There are many parts that make up an exponent, the coefficient, exponential number, and base.  The number in front of the base is the coefficient. The base is often a variable and the exponential number can be positive or negative.

Multiplication:

If the bases are the same, keep the base the same and add the exponents together to get the final product. If the bases are not the same, multiply the bases and then add the exponents together.

Division:

If the bases are the same, then subtract the exponents above the base. If you can reduce the base, do so to simplify it.

Power of a power:

Multiply the exponents inside and outside the bracket and put that answer beside the base as the exponent once more.

All exponents with a value of 0 almost always equal 1. While there may be no copies of the base, there is an invisible coefficient of 1 in front of it, which ends up equaling 1 every time.

 

Week 1-Math 10

How do you find the factors of a large number? These pictures below will help explain how to do so by using both factor trees and division tables.

Factor Trees

First, you have to start with a number, say, 80. Start by writing it at the top of your page. Next, think of any 2 numbers that multiply to equal 80. Maybe 10 and 8? Write these 2 numbers below in a branch-like formation.

Next, think of any 2 numbers that can multiply to equal 10, and 2 numbers that equal 8. For 10, I’m going to use 5 and 2. For 8, I’m going to use 4 and 2. Branch off these numbers out of 10 and 8. Now that those numbers are written down, you have to look and see if you can expand on any numbers.

We can only expand on 4, which goes to 2 and 2. Now, list all the numbers at the bottom of the tree.

Here, we can finally see all the factors that multiply together to equal 80.

Division Tables

First, we’re going to start with a number, 80. Write this down and then draw a little fish hook underneath it.  Write a 2 next to it, and divide 80 by 2.

That equals 40, so write 40 under it. Continue doing this until you eventually cannot divide the number anymore. The list of numbers on the side of the tables are the prime factors in the number. In this case, I only divided by prime numbers.

Racism Then VS Now

The act of racism in a society has been present throughout our history. It has changed from the older days until the present.

Racism then was more focused on work labor and jobs. Back then, a majority of jobs belonged to white men, with the African-American population not having a job to go. Racism rose after the rise of black slavery, they could be bought, traded and mistreated simply if their ‘owners’ wished. Black people were regarded as not being human, and thus, did not have basic human rights.  If a black person was working, they were allowed to be fired merely due to the colour of their skin. White men held most of the power, and made decisions for those who did not share the same skin colour as them. This was an act of clear, apparent racism, and was tolerated back then, but isn’t now.  Anyone who was a person of colour, who tried to speak up against racism, was treated poorly and killed by someone of white skin tone.

Back then, defenceless and innocent black children were being bombarded by police officers on public transit like buses, or even when they were walking through the city. Black people were supposed to give their seat up to white people, and were in trouble if they didn’t.

Now, people with any skin colour are allowed to be hired for any job, and are given equal opportunity to work. Now, people cannot be fired for their skin tone, as discrimination is not allowed in almost all work places. As a comparison from previous years, anyone with any skin tone is allowed to run for power, and can make decisions regarding their race and people.  Slavery is not legal in a numerous amount of places, and almost everyone in the world has some sort of basic human rights. In fact, in Canada, human rights are protected by 3 kinds of laws. There are plenty of people of colour now, who are standing up for further equal rights, and. since we have freedom of speech, are allowed to speak their minds in a way that is true to them.

Compared to back then, black people no longer have to give up their seat on the bus. Defenceless children are no longer allowed to be bombarded by people in the public, and if someone is being racist, so many people speak up to correct and explain why it is now politically incorrect to do so.

Racism has changed from then VS now, and has had a drastic impact upon society and its members. Hopefully, racism will soon be eradicated, but it for sure has had an influential impact. Poverty has also had a large part in racism, but there is always something to improve and work on for the future generations.

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