Math 10 Week 18

The top 5 things that I find important for math 10.

  1. BEDMAS

it stands for: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.

It is essential to know for when attempting any question because it is the order of how to solve something.

2: the exponent rule

exponents are weird, and have a different way of being solved.

ex: 5 to the power of 4 times 5 to the power of 9. You would think that it would equal 5 to the power of 36 but it is not. when exponents are multiplied or divided, it is like addition or subtraction. only when there are exponents on the of brackets, then you can multiply or divide: (5 to the power of 7) to the power of 4 = 5 to the power of 28. It is handy to know this so you don’t go making mistakes with exponents

3: Pythagoras theorem

this is handy to know if you are doing anything with triangles. It can find a missing side of you have 2 of the 3 sides. a2 + b2 = c2     

4: radicals and mixed radicals:

knowing how to convert radicals to mixed radicals and mixed radicals to radicals can be useful. eample: √96 

to turn this into a mixed radical you need to split 96 into 2 numbers: ex: √16 and √6.

this would equal 4√6.

to get back to a radical, you need to put the 4 back under the root sign. this would need 2 4’s. so now you have √4x4x6, which would equal √96

 

5: KHDUDCM

for measurement, this acronym is very hand for memorizing all the conversions.

this is the acronym: King Henry Doesn’t Usually Drink Chocolate Milk

what it actually stands for: Kilo, Hecto, Deca, Unit, Deci, Centi, Milli

Math 10 Week 17

This week in math I have learned how to solve and sub with linear equations.

ex: y=3x-7 and y=-x+9

first, I would sub in -x+9 for y of y=3x-7
-x+9=3x-7

next I would subtract 9 from each side
-x+9=3x-7
-9       -9

then I would subtract 3x from each side

-x=3x-16
-3x -3x

Then I would divide each side by -4

-4x/-4=-16/-4

Which would make x=4. Now I would imput 4 into y=-x+9

Now to solve for y

y=-x+9

y=-(4)+9

y=5.

to double check my answer I would do the same with the other question:

y=3x-7

y=3(4)-7

y=12-7

y=5

That is how you do it.

Math 10 Week 16

this week in math I have learned how to convert slope intercept forum(y=mx+b) to  general forum (Ax+By+C=0).

example:

(3,-7) and (-5,9)

first, you find the slope, y1-y2/x1-x2.

> m= -7-9/3-(-5)

> m= -16/8

-16/8 can be reduced to -2 by dividing both sides ny 8.

now, so far we have y=-2x+b. to find b, we will need to put in x and y values from one of the points:

> (-7)= -2(3) + b

> -7= -6 + b.  next we move everything but b to the other side of the equation. So we will have to add 6 to both sides

>6 – 7=b, -1 = b. Now that we have found b, we can put it back into y= -2x -1. We now need to move -2x and -1 to the other side, so we will need to add 2x and 1 to each side

this will result in 2x + y+ 1=0

that is how you convert slope intercept forum into general forum

 

Math 10 Week 15

This week in math I’ve learned how to use the slope formula to calculate the slope of a line segment.

This is how you do it:

ex: C(36,-41) and D(-20,-27)

to make the equation, you do rise1 – rise2 over run1 – run2. This is where C(run1,rise1) and D(run2,rise2). You start by subtracting -41 from -27 which equals -14, and then subtract 36 from -20 which equals 56. The product should be -14/56 which could be reduced to -2/8 and then to -1/4

 

Math 10 Week 14

This week in math I learned how to find the length of a line segment using points.

example: A(2,7) to B(5,7)

For this, I know that the points are ordered (x,y), so the y value does not change. The x value however, is not the same in both points.
For point A, x=2, and for point B, x=5. The length of the line is 3.

A more complex example would be; P(-6,6), Q(-6,-10), and R(8,-10).

this is what it would look like on a grid.

If you were going to have to find the distance from P to R, you will need to fine the other 2 lines, Q to R and P to Q in order to find the distance from P to R.
You can get PQ and QR from looking at the graph, with the length of PQ being 16 and QR being 14. Next, to find the distance from P to R you would use Pythagoras theorem. 16 squared is 256, and 14 squared is 196. 256+196=452. the square root of 452 is 21.260. But if the question is asking for an exact value that wont work. so you will need to factor 452.

 

that is what PR would equal as an EXACT value.

Math 10 Week 11

LCM (lowest common multiple) and GCF (greatest common factor) are very important for deciphering some equations.

The GCF is the greatest factor that divides two numbers. to factor this polinomial, you would need the GCF:

The greatest common factor would be 2x.

 

The LCM is the smallest integer that is evenly divisible by both a and b. For example,LCM (2,3) = 6 and LCM (6,10) = 30.

the LCM is 75n to the power of 4