Category: Math 11

Week 12 – Pre Calculus 11 – Adding and Subtracting Rationals

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This week in pre-calculus 11 we learned about adding unsubtracting rational expressions. I’m going to go over some basics before we get into some more complicated examples.

When adding and subtracting fractions or denominator must be the same. So in this example..

The denominator is x on one and the other is 5. To get a common denominator we must multiply. Whatever you do to the top you do to the bottom.

Now they have a common denominator so we can simplify it. In this example are two numerators cannot be simplified any further because one has a variable and the other doesn’t.

last thing you need to do is find the non- permissible values.  Non permissible  values are a value for the variable and the denominator that would cause the denominator to equal zero. So in this example if we substituted X to be zero that would cause the denominator to be 5(0) = 0. So we would write…

Now that we have a basics covered we can move onto a more complicated example.

Repeat the same steps:

1- get a common denominator

2- simplify (divide)

3- Final answer

4-Non-permissible values

 

Week 11 – Pre Calculus 11 – Maximum and Minimum

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This week in pre-calculus 11 we went over maximum and minimum within a parabola. Today I will show you how to find them and where to find them on a graph.

What is max and min? 

The maximum and minimum are the highest or lowest point of the graph which is also known as the vertex.

How do you know if it is a max or a min? 

If the parabola is pointing upwards then the vertex is the lowest point which is the minimum.

If the parabola is pointing downwards than the vertex is at the highest point meaning it is the maximum.

Finding the min and max is very important because this will help you graph the rest of the parabola. The line of symmetry crosses through the vertex (max/min) meaning that you can graph both sides because you know the LOS.

Week 10 – Precalculus 11 – Graphing parabola/ finding vertex and intercepts

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And this week in Precalculus 11 we  went over vertex and finding X and Y intercepts .  I learned how to find the vertex and X and Y intercept when given a vertex form quadratic equation.

Vertex:  The vertex is either at the highest or lowest (max/min)  there’s also the point where the middle of the parabola  is.

For first example I’m going to give you a graph and we will find the All 3 of the things I listed. Will start with the graphed equation.

we can see in this parabola contacts is (-3,4).

The X intercepts are when the parabola crosses over our X axis. (-5,0) (-1,0)

Y intercept is when the parabola crosses over the Y axis. (0, -5)

Now we will graph an equation (if you are slightly confused go to my week 9 blog post, it explains what each part does)

review week 9:

graph:

As from our week 9 lesson we know that the parabola will move 4 to the left and 1 down. The stretch remains the same as there is no coefficient.


Week 9 – Pre calculus 11 – parts of vertex form

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Week 9 of pre-calculus 11 we went over the vertex form also known as standard form. This form is a type of quadratic and it gives us the vertex. Different parts of the vertex form tell you different things which is what I will be going over today.

This is how vertex form looks like:

Now that you know how it looks I will show you what each part does to the  parabola.

REFLECTION (open up/down)– if there is a negative in front of the coefficient that means the parabola open downwards, if it is positive the parabola will open upwards

STRETCH (slim/wide) – if there is a coefficient this tells us if our parabola will be wider or skinnier (congruent in is something you get from this as well)

HORIZONTAL TRANSLATION (left/right) –  if the number inside the bracket it’s negative it goes to the right, if you if the number in the bracket is positive then it goes to the left (opposites)

VERTICAL TRANSLATION (up/down) – The number is positive at the end it goes up, if the  Number at the end is negative it goes down.

In this example we know that our parabola will be opening down and it will be slimmer. The parabola will move three to the right and seven up. So we know that the vertex will be (3,7)!

Questions: 

– Why is it slimmer if there’s a number?

First need to know how our parent function looks like. A parent function is the original  parabola before we start to change things. 

Now in the example we did before it had a coefficient of three which means the partent function is multiplied by three.

Week 4 – Pre Calculus 11 – simplifying with variables radicands

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This week we went over over simplifying expressions with variable radicands.i found many things that help me understand how to simplify expressions with variables that I would like to share.

To add radicals they must have like terms such as in this example:

Step 1: identify if radicals have the same base

Step 2: if they have the same base add or subtract depending on the sign.

Now the way understand the concept of adding like terms we can move onto once with variable radicands.

Tip: if an radicand is factorable turn it into a mixed radical ( you can factor the number of variables as well!)

Step 1:
turn into mixed radicals (if you don’t know how to do this look at my week 2 blog post)
first thing you wanna do is make a factor tree and find perfect squares go from an entire radical to a mixed radical.

Step 2: multiply your coefficients ( coefficients are the numbers in front of the radical sign)

Step 3: Now that you have completed turning them into mixed radicals you can add them together because they have the same base.

Week 8 – Pre-Calculus 11 – Quadratic equation

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Week eight of precalculus 11  we learned our third method of finding or X values. This is my favourite method for it works every time even though it requires a lot of steps. Today I will show you the equation, how to fill it out, and how to use the formula.

The quadratic equation: 

Step 1- find the values of A B and C

Step 2- slot in the values into the quadratic equation

Step 3- Multiply

Step 4-Subtract (or add depending on the question) the radicand

Step 5- if possible square root of the Radicand (if not leave it as a square root or turn into a mora radical)

Step 6-  solve your two possible answers if needed

Step 7-  answer 

Week 7 – Pre – Calculus 11 – completing the square

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Week seven precalculus 11 we worked on completing the square. I found this technique difficult at first but now I understand how to do it and I would like to share that.

step 1:  Divide middle term by two and  Square it

step 2: in the numbers you got into equation by adding it and subtracting it

 

step 3: you now have a factorable part. Factor and add like terms together.

 

step 4: Isolate the X

step 5: answer

Week 6 – precalculus 11 – factoring trinomials

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This week in precalculus 11 we reviewed how to factor a trinomial.  when factoring a trinomial‘s do you want to bring the trinomial back to its state before you used foil. Before we remove the brackets now we put the brackets back.

Step 1- Find the product 

First thing you do is find factors of the last number.List all the possible ones on the side (product is what the answer is called two numbers are multiplied)

Step 2- Find the sum 

Look at the list that you’ve created for factors and find one that one added have the sum of our second number. (Sum is what the answer is called when two numbers are added)

Step 3- 

no that was a factor pair we will be using, insert them into the equation. (In this example there were no negatives)

Check your answer-  Use Foil 

when you want to check your answer you can use foil. If your final answer is the same as the equation we started with you are correct.

FOIL-

Week 3 – Precalculus 11 – Fractional exponents

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This week in three calculus 11 we worked on fractional exponents. One thing I learned was how to solve fractional exponents. I will explain 2 examples and share some tips I learned in class that help me remember what to do.

Example 1:

Step 1-


first thing you want to do is to know where all the number are going to go. Something I learned was flower power. The root of the flower is in the ground so the root is going to be the denominator of the fractional exponent.

Step 2-

Now that you know where everything has to go place it in its correct places and turn it into a root.

Step 3-

Something that helps me when solving is to write down perfect cubes and squares. Look at the list you have written and find it. (If it not on your list then it will be a decimal)

Step 4-

Once you have found the perfect cube write down your final answer.

Example 2:

Step 1-

Like last example we are going to use flower power. Root on the bottom.

Step 2-

next is the same thing. Turn the fractional exponent into a root.

Step 3-

Write down your perfect squares and cubes and search for your number. (I advise to  memorize perfect squares 1-15 and perfect cubes 1-8)

Step 4-

Now because the power on our answer is not one we should solve it. When a number has a power it is saying how many times you multiply that number by itself.

Step 5-

And you have your final answer!

Week 2 – Precalculus 11 – Entire radicals to mixed radicals

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This week in precalculus 11 we worked on our unit about radicals.  I learned how to change an entire radical into a mixed radical.I will give an example on how to convert a entire radical into a mixed radical. First I will explain how to identify a mixed and entire radical

Now that you know how to identify both radicals let’s move onto an example.

Step 1:

The first step you want to write all the prime factors (it makes it much easier).

Step 2:

Next you’re going to write those prime factors under a radical. This equation we’re dealing with square root so you’ll be grouping them in pairs.

Step 3:

step three are you going to want to place the same pairs into the same radical. Any numbers without a pair will be put separately into its own radical. This will help us for our next step.

Step 4:

after that you’re going to want to simplify the pairs within the radicals.

Step 5:

step five you’re going to solve for the square roots that are a perfect square.

Step 6:

lastly you’re going to simplify once again and you’ve got your answer!