I have learnt a lot from math 10 this semester however, some things were more memorable than others. Here are the top 5 things I learnt in math 10 that I won’t forget quickly:

1. How to find the sine, cosine and tangent in a right triangle.

To find the sine, cosine or tangent of a triangle, you first write out the equation. For example: cos x = but you can replace the cos with sin or tan as well if that’s what you’re trying to find. Next, you need to get x by itself so, you divide cos x by cos to get x by itself.   Now, you need to do the same thing on the other side of the equals sign so we have to divide by cos as well. Then, you move the cosine to the top of the fraction so that you can mulitply it with the fraction which makes it have a negative exponent of -1. Finally, you need to multiply the two together to find x. x = 41.42 (For cosine) x = 45.6 (For sine) x = 35.5 (For tangent)

2. How to find the prime factorization of a number using a factor tree.

First, you find two factors of your number. In this example I’ll use the number 670. The two factors I used were 67 and 10. If one of those numbers is prime, you circle it. 67 is a prime number so it’s circled. Now, you have to find the factors of 10. 5×2=10 so you draw lines under the 10 and write 5 and 2 under each line. If any of those numbers are prime you circle them and that indicates that you can’t find any factors for those ones. 5 and 2 are both prime numbers so you circle them. Finally, you put the numbers that you circled into an equation. () Now, you know the prime factorization of 670.

3. How to solve a system using elimination.

First, the question will give you 2 equations for example: 4x-3y=2 and -4x-y=6. Next, you have to look to see if there are any 0 pairs. Then the next step is to add the two equations together. ([4x-3y=2]+[-4x-y=6]= [-4b=8]) because the 4x and the -4x cancel each other out. Now, you want to get the y by itself. To do that, you divide each side of the equals sign by -4. What’s left is y=-2. Now, you know that the y intercept is (-2) which means you still need to find what the x intercept is to get the full coordinate. To find the x intercept, you rewrite the first or second equation that was at the start and replace the y with (-2).  I’m using the second equation. -4x-(-2)=6 . Now, you multiply everything that needs to be multiplied: -4x+2=6. Next, you want to get x by itself. You move the 2 over to the side that the 6 is on which turns the 2 negative. Then, you add the 6 and the -2 together which equals 4. The equation is written as -4x=4 now. Finally, you divide both sides by -4 to get the x by itself which gives us: x=-1. So finally, you know that the coordinates for this point is (-1,-2) To check that your calculations are right you can add the -1 and -2 back into both equations to see if they’re true.

4(-1)-3(-2)=2:

(-4)+(6)=2

This equation is true so you can move on to check the second equation.

-4(-1)-(-2)=6:

4+2=6

4+2 does equal 6 so you now know for sure that your calculations were right and that the coordinates are (-1,-2)

4. How to change a root number into a radical.

To change a root number (like ) into a radical, you take the base of the exponent (2) as well as the top of the exponent (3) and once you write the 5 into the root sign, you place the 2 on the root sign and the 3 is the exponent next to the 5.  Since a regular square root is when there’s a 2 on it, the 2 becomes invisible when you convert it. ()

5. How to factor an “ugly” trinomial using the box method.

The equation I’m using in this example is 3x^2+8x+4

Your first step is to draw a box and divide it into four parts. Next, you put the 3x^2 in the top left part of the box and the +4 in the bottom right part of the box. Now, you multiply 3x^2 by +4 which equals 12x^2 now, you find the factors of 12. They are: 1\cdot12, 2\cdot6, 3\cdot4 Next, you figure out which of the factors when added together make 8. 1+12=13 so that one can’t be the answer. 3+4=7 so that also isn’t the right one.  That means the only possible answer left is 2+6. 2+6=8 so it’s the right one. If the +4 was actually a -4, you would look to see which factors subtract to the number in the middle of the equation. 8 could not be the middle number in that case however. The number could either be 11, 4 or 1. Now, 2x+6x+8x so we put the 2x in either one of the parts of the box still available and the 6x in the other one. Finally, we find the common factors in all the numbers. In my example, I put the 6x next to the 3x^2. The common factor of the two is 3x. Write that down beside the box. The common factor of 2x and +4 is +2. The common factor of 3x^2 and 2x is x and finally, the common factor of 6x and +4 is +2. Finally, you put all the factors that you just found together to make the factored equation which is (x+2)(3x+2).