Monthly Archives: September 2018

Week 4 – Pre Calc 11

September 30, 2018Math 11shaylyng2016

One thing that I learned this week in Pre Calc 11 is how to multiply radicals. Multiplying radicals is very similar to multiplying fractions, as Mrs. Burton told us you “just do it.” As long as the radicand is in the simplest form, you can multiply the like terms together. Meaning you multiply the coefficients together and the radicands together. Ex. $(2\sqrt3) (3\sqrt5) = (2)(3)\sqrt(3)(5) = 6\sqrt15$ . Depending on the question you can also use distributive property or FOIL. Ex. $2\sqrt3 (6\sqrt3+5\sqrt3 -7\sqrt3)$ . To FOIL an equation it is easiest to do so when all of the numbers are in their simplest form such as in the example. You can then add or subtract any like terms, meaning terms with the same radicand $(= 2\sqrt3(4\sqrt3))$ and then you can FOIL the equation. For this equation, you would distribute $2\sqrt3$ into the rest of the equation $(=(2)(4)\sqrt(3)(3)) = 8\sqrt9)$ . Once you have distributed, you can check to see if the equation can be simplified anymore or added or subtracted anymore $(=8\sqrt9 = (8)(3) = 24)$ .

I have included an example below that shows the steps I would take to multiply a more challenging equation using radicals and distributive property.

Week 3 – Pre Calc 11

September 22, 2018Math 11shaylyng2016

One thing that I learned this week in Pre Calc 11 is how to solve absolute values. The definition of an absolute value is the principal square root of the square of a number. This definition explains that the number to the power of two, square rooted is equal to the absolute value. Ex. $\sqrt8^2 = |8| = 8$ . The absolute value will always be a positive number also known as the “principal square root”.

You can tell a number is an absolute value when it has absolute value bars around it: $|3|$ . These bars do not mean the same thing as parentheses or brackets. However, if there are absolute value bars with an equation inside, you must solve whats in-between the bars before being able to find the absolute value.

I have included an example below that shows the steps I would take to find the absolute value of an equation, where you must solve what is in-between the bars before finding the final answer.

Week 2 – Pre Calc 11

September 14, 2018Math 11shaylyng2016

One thing that I learned this week in Pre Calc 11 is how to calculate the sum of the terms in a Geometric Series. A Geometric Series is when you find the sum of the terms in a Geometric Sequence. To find the sum, you must find the first term, the common ratio and the number of terms in the series. For instance, if this was my Geometric Series: $-2+8-32+128$ than I would use the equation $S_n=\frac{a(r^n-1)}{r-1}$ to figure out the sum. To input the numbers needed into the equation, I would replace $S_n$ with $S_4$ because there are 4 terms in the series. I would also replace $a$ with $-2$ because that is the first term in the series. Since $r$ represents the common ratio I would replace it with $-4$ and $n$ reprsents the value of the fourth term I would input it as $128$ . From there I will be able to determine the sum of all 4 terms in this Geometric Series.

This week I also learned that I can enter an entire equation into my calculator and it is able to solve it completely, which means that after I have inputed the numbers into the equation, the calculator is able to find the answer, which takes less steps and time to solve the equation.

I have included an example below that shows the steps I would take in further detail and the equations I would use to find the sum of the terms in a Geometric Series.

Week 1 – My Arithmetic Sequence

September 10, 2018Math 11sequencesshaylyng2016

My Arithmetic Sequence: -2, 5, 12, 19, 26…

$t_n=t_1+(n-1)(d)$

$t_{50}=-2+(50-1)(7)$

$t_{50}=-2+(49)(7)$

$t_{50}=-2+343$

$t_{50}=341$

$t_n=t_1+(n-1)(d)$

$t_n=-2+(n-1)(7)$

$t_n=-2+7_n-7$

$t_n=7_n-9$

$S_n=\frac{n}{2}(t_1+t_n)$

$S_{50}=\frac{50}{2}(-2+341)$

$S_{50}=25(339)$

$S_{50}=8475$

Week 1 – Pre Calc 11

September 8, 2018Math 11shaylyng2016

One thing that I learned this week in Pre Calc 11 is how to find the number of terms in an Arithmetic Series, when the number of terms is unknown. An Arithmetic Series is the sum of terms in an Arithmetic Sequence. To find the number of terms in an Arithmetic Series you must use the first and last number of the series and the common difference in the sequence. For instance if this was my Arithmetic Series, 3+7+11+15…+43, then I would use those numbers and the equation $t_n$ = $t_1 + (n-1)(d)$ to fiqure out how many terms are in the series. I would replace $t_1$ with the first number in the series 3, (d) with the number 4 as my common difference and $t_n$ with the final number of the series 43. From there I will be able to solve the equation and figure out what n=? (n= the number of terms). Once I have the number of terms I can then find out the sum of the numbers in the series.

Below is an example showing the steps I would take and the equations I would use to find the number of terms in an Arithmetic Series.

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