This past week in Pre Calculus 11 we finished unit 3: Solving Quadratic Equations. We learned how to determine the discriminant and what the purpose of finding it is. The discriminant tells me how many roots each equation has. You use the formula b^2 -4ac=0 and solve.
This past week in Pre-Calculus I learned that when a equation is irrational and comes to the square root at the end it must have a + and – sign with it. This represents that there are 2 possible answers, one with either a positive root sign and the other with a negative root sign. This is an example of what an equation would look like:
If the equations at the end were put into a calculator solved they would give the points at which the parabola will cross the x-axis.
The week in pre calculus we learned how to add, subtract, multiply and divide radical expressions. Something I learned this week was how to rationalize a denominator. When a denominator is not a whole number and it is in radical form you need to get it to a rational number so you are able to divide. To do so you multiply the radical by itself, example:
Here I have made the denominator rational.
This past week in Pre Calculus we finished unit 1-Sequences and Series and then we started unit 2-Absolute Value and Radicals. We learned what absolute value was and what the symbol to represent it looks like.
Absolute value is the distance of any number to 0. Example is 4 is 4 numbers away from 0 so it would be written as .
If the number is negative like it must be changed to a positive to .
Last week in Pre Calculus 11 we learned about Arithmetic Series and Sequences where the common difference is always added, this week we learned about Geometric Series and Sequences where instead of adding, you multiplied. Something I struggled with this week was putting the correct numbers into the correct spots where the variables were. I chose to make my blog post about how to use the geometric sequence formula which is:
Using this formula you will be able to find how much any term is equal to.
Sequence: 1, 5, 9, 13, 17
= + (n – 1)(d)
= 1 + (50 – 1)(4)
= 1 + (49)(4)
Finding the sum of the first 50 terms:
= ( + )
= (1 + 197)
In the first week of Pre-Calculus 11 we started unit 1 – Sequences and Series. Something I learned this week was what an arithmetic sequence is and what it does or the purpose of it. In my own definition, an arithmetic sequence is a series of numbers that have the same difference between each number. An example of this would be -3, 0, 3 ,6… is an arithmetic sequence because the difference between each number is 3 and its always 3. The numbers 1, 4, 6, 10… is not an arithmetic sequence because the difference between 1 and 4 is 3 but the difference between 4 and 6 is 2 so it changed and didn’t always have the same difference.
We learned this week what an arithmetic sequence is but also what the purpose of it is. If I wanted to know what the 45th term in the series that might be challenging to find out but using the formula = + (n-1)d I can solve and find out the 45th term much easier than I would have if I did all the work and counted by 3, 45 times.
After filling in the formula and solving you will get the 45th term in the series which is 129.