Category: Math 10

Step 1: See the relationship between the output, or y axis.  In this example, the numbers go up by 3 each time.

Step 2: Take the number that they go up by (in this case it’s three), and incorporate it with the x axis, so it makes 3x.  That’s the first part of the equation.

Step 3: Figure out the rest of the equation by replacing the x with the first number on the x axis.  This might look like 3(1), which is three.  To figure out the rest of the equation, figure out how the product can reach the number across from it on the y axis.  In this example, it’s 6.  So you would have to add three.

Step 4: To prove your point, try it with another example on the list.

3x + 3

3(3) + 3

= 9 + 3 = 12

This week, we studied Difference of Squares.

It’s easy to tell if a question is a Difference of Squares question or not.

You can tell by whether or not it has a subtraction sign, and whether it’s a binomial, meaning there’s two terms.  In the following Difference of Squares equation, we must solve and expand it.

 − 36

We’ll take the and put the individual coefficients in separate brackets like this:

(p  )(p  )

Next, we take 36, and do the square root of it.

= 6

So, we’re left with 6.

Now, we’re going to incorporate the 6 into our new equation.

We need to use zero pairs, so one six is going to be left as a positive, and the other as a negative.

Our final, expanded equation will look like this:

(p – 6)(p + 6)

So when you use the distributive property, or the claw, you’ll get  – 36.

How to Factor GCF:

1. See if you can divide all numbers in the equation with the same number.
2. With the first equation above, we can see that 3, 6, and 9 can all be divided by 3.
3. From there, we put the GCF into the equation.  We put it in front of an open bracket to start off the equation.  Like this: 3(
4. Then, we divide each number by the number we put in front of the open bracket.  3 divided by 3, equals one, so we just place to co-efficient there instead of a 1 in front of it, because the co-efficient by itself indicates that there is a one before it.
5. 9 divided by 3 equals 3, so we replace the 9 with a 3, and now we have 3, plus the co-efficient behind it.
6. 6 divided by 3 equals 2, so we replace the constant, 6, with 2.
7. There we have it, a complete equation.  You can see other examples I’ve created in the picture above.

 

This week, we started talking about polynomials.  I learned how to make equations out of symbols and vice-versa.

First, I wrote out the symbols.  The big, coloured in boxes represent positive x squared.  The white big boxes represent negative x squared.  The long skinny black pieces represent positive x, and the white ones represent negative x.  The small pieces mean a whole number; black meaning positive, and white representing negative.  If we eliminate the zero pairs, we get out equation.  Zero pairs mean there’s a pair of positive and negative symbols.  If we remove them all, we get three big, coloured in squares (3x squared), two white skinny pieces (-2x), and three small white pieces (-3).  So, our equation would look similar to this:

 

This week in Math, I was mostly reviewing for the Unit Test we had this Thursday.  I reviewed big concepts like converting, but what I learned most about in my reviewing, was Pythagorean Theorem.  I’ve always known that a² + b² = c², but I wasn’t sure what to do with it.  For example, I’d do 3² + 6² = 9², but I wasn’t sure just how to calculate it and get the right answer.  So I looked it up, and asked for help from my dad.

 

Here’s how I worked it out:

 

a² + b² = c²

3² + 6² = 9²

9 + 36 = 81

 

Then, I found out that you must find the square root of the answer.

 

The square root of 81 is equal to 9.  Therefore, c² = 9.

This week, we’re transitioning into the measurement unit.  I believe that every unit we do relates to the last unit we did.  At the beginning of the semester, we started with the basics, and we did our numbers unit.  Then, we did exponents, which builds on numbers.  We take some of the concepts, and morph them into the next unit.  I see it kind of like baking a cake.  You take the base from the last unit (the actual cake part), and you add decorations (the new concepts).  Then the next unit, you add another base, but you still have the knowledge of the last unit.  I think that measurement will relate to exponents, in the sense that we’ll use exponents to measure objects and distances.

This week in math 10, we learned the difference between entire radicals and

mixed radicals.  In mixed radicals (example shown below), the 2 is the co-

efficient.  In entire radicals (example shown below), the co-efficient is

invisible.  Really, there’s a 1 as the co-efficient.

 

Mixed Radical:

Entire Radical: