Math 10

Math 10 Week #7

alexr2015

We were introduced to the concept of Trigonometry this week. We also learned about three buttons on the calculator. sin, cos, and tan. These words are actually shortened, and they mean “sine, cosine, and tangent”. Trigonometry will usually involve right triangles, but isosceles and scalene triangle are able to be solved through trigonometry. Trig questions usually ask for the length of one side of a triangle, while giving you a reference angle, along with the length of a single side.

How do we solve these? First, each side has a specific name, depending on where the reference angle is. The names are adjacent, opposite, and hypotenuse. The hypotenuse will always be the line opposite from the right angle. The adjacent line is the line closest to the reference angle that is not the hypotenuse. The opposite line is the line farthest from the reference angle that is not the hypotenuse. Got it? Good.

You’ll have to learn the phrase SOH CAH TOA. The beginning of each word represents some specific buttons on the calculator, namely sin, cos, and tan. The last two letters of each word represent the lines of a triangle. You remember “Adjacent, Opposite, and Hypotenuse”, correct? If you have to solve for the length of the opposite line, and are given the length of the hypotenuse along with a reference angle, the question is a sine question. Sine(reference angle)=\frac {O}{H} If say, you were given the length of the opposite line along with a reference angle, but not the length of the hypotenuse, then the question would look like: sine(reference angle)=\frac {O}{H}

The best way to figure out what sort of trig question lays in front of you is to remember the phrase SOH CAH TOA.

Now take a look at some of these questions below. All problems require you to solve for x. The first one is a sine question. How do we know? The opposite line is represented by x, while the hypotenuse is represented by 7. The reference angle is 27. The equation is sin27={x}{7}. We multiply the equation on both sides by 7 to isolate x. The equation now looks like 7(sin27)=x.
7 multiplied by sin27 (approx. 0.454) is 3.2.

The opposite line is 3.2 units long.

Math 10 Week #5

alexr2015

We continued working on the measurement unit this week. One thing we discussed was how to convert metric measurements to inferior–I mean imperial measurements.

How do we convert 250 yards (yds) to meters (m)? Easy!

\frac{250yds}{1}\cdot \frac{0.9144m}{1yds}= \frac{298.6m}{1}

The yds cancel out each other, so you’re left with 250 * 0.9144 = 298.6m!

Math 10 Week #4

alexr2015

Converting metric units to other metric units.

We finished our exponents unit this week, and also started our measurement unit. We talked about metric units, and how to convert metric units to other metric units. We used a number line to help us out, along with the mnemonic “King Henry Doesn’t Usually Drink Chocolate Milk”. to memorise all the metric units.

If we want to convert 3 meters, to millimetres, we would simply start at the m on the number line, and we count how far the units are from each other. Since millimetres are 3 units from the right of meters, we move the decimal three spots to the right. 3m = 3000mm.

Math 10 Week #3

alexr2015

This week we talked about rational exponents. Most of the time, we dealt with negative exponents.

Just about every single number, whenever it contains a negative exponent, the base must be reciprocated.

3^{-3}

Notice the negative exponent? This means the base must be reciprocated. When the base is reciprocated, the negative is removed from the exponent.

\frac{1}{3^3}

Note that for a number such as {2x^-3} the two will stay as a numerator, while the $latex x^{-3

http://www.solving-math-problems.com/negative-exponents.html

}&s=2$ will be “dragged down” into the world of denominators.

\frac{2}{x^3}

Math 10 Week #2

alexr2015

My class learned many things this week. One thing that we learned about was entire radicals and mixed radicals, how to convert one to the other, and vice versa.

 

 

An entire radical is just a square root with no coefficient: \sqrt{75}

A mixed radical is a square root with a coefficient: 5\sqrt{3}

To convert a mixed radical to an entire radical, you need to insert the coefficient into the square root. This is done by simply squaring the coefficient (Multiplying it by itself) and then multiplying it by whatever is inside the square root.

Take the square root 2\sqrt{3} for example. First, we square the coefficient, 2, so it becomes 2^2.

2^2 = 4. This then goes inside the square root and multiply the two numbers together to make \sqrt{12}.

 

 

Math 10 Week #1

alexr2015

This week in Math class, I leaned about different ways to factor. One of these ways was creating factor trees. Here is one below.

https://www.mathsisfun.com/definitions/factor-tree.html

In factor trees, you take a number that you want to find the factors for. Find some factors of that number, than find the factors of the next numbers, until you can’t factor anymore. The numbers that you have left at the bottom are the prime factors of the number at the top.