Week 18 in math 10 (The Final Post in Math 10)

What we learned Week 18 in Math 10 is just reviewing all units that we have been studying for a semester, for the final exam in Math 10.

The List of Top 5 (The Most Interesting) Things in Math 10


1. About Exponents  (Week 4 in Math 10)

I learned some types of exponents. The steps learning more new information is always interesting, so the first unit of math 10 seemed like the review to me what we learned in grade 9, so, I thought we really began to learn the new information since we learned new types of exponents. I learned about some new types of exponents like fractions and negative numbers, new types of roots (radical signs) like a cube root, and how I can write radicals as a power and a power as a radical. I did not know the existence of cube root before I learnt it.


2. About Measurements  (Week 5 in Math 10)

I could learn about units using to measure a height, a length, and a weight. I have not been using only km, m, cm, and mm for a length and only kg and g for a weight. I leant what k, h, da, d, c, and m are with using king henry doesn’t drink chocolate milk, and more measurements like a foot, an inch, a yard, m, g, µ, and n. In Canada and Korea, people do not use an inch, a foot, and a yard, they were kind of strange to me because I have never used and seen it except when I was reading books of some countries in Europe or American. Also, we learned some geometric formula and how we can use them.


3. About Trigonometry  (Week 7 in Math 10) 

It is the most interesting unit for me because I was fascinated that we can solve every right triangle with just some of the formula. With this unit, I could make math problems fun and interesting. We learnt what and where an opposite, a hypotenuse, and an adjacent, and how I can use them with Sine, Cosine, and Tangent. It was even pretty confusing because it was so easy to misunderstand where the side which we should use is.


4. About Relations and Functions  (Week 13 in Math 10)
We learned what domains, range, relations, and functions are. The domain can be used for the input of the independent variable and the range can be used for the output of the dependent variable. Also, each element of the domain in a range and a function is a special type of relation. I even learned more graphs like a function notion. There are a lot of word problem and I am not comfortable in English yet, so in my opinion, it was the most difficult unit to me in math 10.


5. About Linear Relations

(Week 14 in Math 10)(Week 15 in Math 10)

I learned the slope formula (y1 – y2/x1 – x2) and these three different forms y-intercept form, general form, and point-slope form in linear graphs. The information what I learned in this unit was very useful when we should get the answer in the next unit (The systems of equations). It would keep using when precalculus 11, it might be the most important unit in Math 10.


+) 6. How to Factor Trinomials Easily

Week 10 in Math 10

It was not one of the most interesting or difficult units in Math 10, but I could make the real interest in math. I had already learned about this unit in Korea where is my home country before I came to Canada, so I thought it would be same. However, I learned a new way to factor and simplify them. In South Korea, people just factored to write every single prime number and got the solution, so it was really unfair to people who were weaker about math than other smart people, and I was not so smarter other guys so my friends and I must be a human calculator for the test. But, I could learn there were infinite ways to get an answer as I learned a square of the factoring polynomials. Some of the new mathematical information was not very much like other units, but the interest in math came to me. So, it was not the most interesting unit, but it was the most valuable unit to me because this unit taught me the interest in math.


Week 16 in Math 10

In my opinion, I could learn a lot of information about math, the way to solve many problems, and an interest in math more in this semester. I must quite struggle with math but I could really enjoy math for this semester, and I hope that the information and interests would not be disappeared until I finish studying math.




Week 17 in Math 10

What we learned in math 10 is how to solve systems of equations. It was pretty interesting to me that we can just get the value of the x and y using two equations. There are two ways to get the solution of a pair of equations, Substitution and Elimination.  Substitution is useful when there is a coefficient which value is 1. You can use substitution if you remember how to isolate something on an equation. We should choose the simpler equation (e.g x – 2y = 3) firstly and express one variable in terms of the other. After this step, we need to substitute the expression from the last step into the equation and solve the single variable equation. Lastly, substitute the solution into the equation in the first step to find the value of the other variable. We can solve every single of systems of equations with substitution, but it might be really complicated if there is not a simple equation, so we learned another way, Elimination. I prefer elimination to substitution because I think it is easy for all students in the class unless they do not know how to multiply. Using the method of elimination is very simple. If necessary, multiply each equation by a constant to obtain coefficients for x (or y) that are identical (except perhaps for the sign) and add or subtract the two equations to eliminate one of the variables. After this, solve the resulting equation to determine the value of one of the values. Lastly, substitute the solution the solution into either of the original equations to determine the value of the other variable. We have learned about those ways, However, sometimes, we cannot get a solution of the systems of equations. We must make sure it has zero solution if the slope is same on the equations, and it has infinite solutions if the equations are same.

For examples,

1. A rectangle is to be drawn with perimeter 64 cm. If the length is to be 14 cm more than the width, determine the area of the rectangle.

  • If the width is y and the length is x, the equations are 2x + 2y = 64 and x – y = 14, and the first equation is divided by 2, so the equations are x – y = 14 and x + y = 32 {= (2x + 2y = 64)/2} (it does not really matter to skip dividing steps)
  • Substitution 
  • I am going to isolate y on x + y = 32. x + y = 32 => y = – x + 32. We can just substitute the value of y on one of those equations. x – (– x + 32) = 14 => 2x – 32 = 14 => 2x = 46 => x = 23
  • Elimination 
  • I do not need to multiply any numbers on the equation and just add these two equations. (x + y = 32) + (x – y = 14) => 2x = 46 => x = 23.
  • We can just substitute the value of x on one of those equations. (23) + y = 32 => y = 32 – 23 => y = 9
  • So, the length is 23 cm, and the width is 9 cm.
  • The formula of the area of a rectangle is (length) × (width). (23) × (9) = 207
  • So, the area of the rectangle is 207 cm2


  • The system of equations is 2x – 3y = – 5 and x + y = 5. I got the solutions in two different ways.
  • Substitution
  • I isolated x on the second equation, so the equation is x = – y + 5, and substitute the equation on x of the first equation. 2(– y + 5) – 3y = – 5. – 2y + 10 – 3y = – 5 => – 2y – 3y = – 5 – 10 => – 5y = – 15 => y = 3
  • Elimination 
  • The second equation is multiplied by – 2, – 2(x + y = 5) => – 2x – 2y = – 10, and substract by the first equation. (2x – 3y = – 5) + (– 2x – 2y = – 10) => – 5y = – 15 => y = 3
  • The last step is to substitute 3 on y. x + y = 5 => x + 3 = 5 => x = 5 – 3 => x = 2.
  • So, the solution is (2,3)