Pre-Calc 11 Week #6

This week we learned how to use the quadratic formula and when we should.

In this example I show when we should use the quadratic formula (the first step is to find the discriminant using the formula in the example)

With a discriminant of +24 we know it has 2 roots

if the discriminant was 0 it would have 1 root and if it was negative it would have no root meaning it is unfactorable

In this next example I use the quadratic formula to find an exact answer

With this answer I can then simplify by simplifying the radical and then dividing by a common number in this case 2

Pre-Calc 11 Week #5

This week in Pre-Calc 11 we started learning how to factor and simplify, we learned how to do this using Punnett Squares and using the acronym CDPEU to mean Common, Difference, Pattern, Easy and Ugly respectively. Using CDPEU means looking for what’s common, a difference of squares, a pattern within and if it’s easy or ugly In this example I show how it can be common or how it could be a difference of squares

In this next example I show how to simplify when it’s ugly

Pre-Calc 11 Week #4

This week in pre-calc 11 we learned how to subtract and add radicals
the first step is to simplify the radical like example $sqrt {4}$ would be 2
no matter if the radical is mixed or entire for radicand must be the same
Example: You can’t add $sqrt (2)$ and $sqrt (3)$
In this example I show how when the radicand is the same you can add them $sqrt (2)$ + $sqrt (2)$ = $sqrt (4)$ which equals 2

When the radicand is not the same you have to try to use prime factorization to give the radicand a coefficient which hopefully ends in a radical that has the same radicand

Remember that radicals without a coefficient have a hidden coefficient of 1.

Pre-Calc 11 Week #3

This week we learned about absolute values which is the non-negative value of a number or variable
In this example i show how 2 and -2 have the same absolute value of 2

This is true because the absolute value of -2 can’t be a negative, so it is also 2

There can also be absolute values of variables in which variables turn positive.

In this next example I will show how to do equations that include absolute values, where you have to use the equation as if they’re in brackets before putting whats not in the absolute value into the question after

Pre-Calc 11 Week #2

This week I learned about finite geometric series and how to find the general term ($t_n$) along with how to find the sum of whatever the term number is.

To find $t_n$, you need $t_1$ and the common ratio

In this example I’m looking for $t_{13}$ with a $t_1$ of 5 and a common ratio of 2

And in this next example I show how to find $S_{13}$ with the same numbers.

Pre-Calc 11 Week #1

This week in Pre-Calc 11 we learned how to use the patterns in arithmetic sequences and series to find a number later in the series/sequence.

Basically if $t_1$ is 4 and $t_2$ is 8 we can tell the common difference is +4 using the common difference we can find any number after.

In this example I’ll show how to get $t_{35}$ using the information found