Category Archives: Grade 10

Math 10 – Week 10 – Factoring Ugly trinomials

April 20, 2020 amyt2018 Leave a comment

This week in math 10, we learned how to factor ugly trinomials. What makes a trinomial ugly? The coefficients are big numbers. For this blog post, I will solve this polynomial: 2x²+17x+35

First I must multiply and leading coefficient (2) and the constant together (35), to get the total (2*35=70).

Next, I will list out all of the factors of 70 and see with set can add to 17:

1*70

2*35

5*14

7*10

7+10=17 so I can now put all of these number into the box to do the reverse box method.


	2x²	7x
	10x	35

Note: It dose not matter where you but the xs.

Now I can fill not the box. To find the outside find what is similar between the number in the row or column. 2x² and 7x have x common. 10x and 35 have 5 in common. 2x² and 10x have 2x in common. 7x and 35 have 7 in common

	2x	7
x	2x²	7x
5	10x	35

Now I can take the out side number and put them into an equation.

(x+5)(2x+7)

Math 10, Uncategorized

Week 7 – Math 10 – Factoring Polynomials

March 14, 2020 amyt2018 Leave a comment

This week in math 10 we learned how to Factoring Polynomials. There are several ways to factor polynomials.

Common factors: To make an equation easier to understand, you can find a common factor in the numbers. The example I will be using is: $2x^2$ + 12x + 10

all number in this equation have a common factor of 2, so we have to divide all the hole equation. and this is the result: 2( $x^4$ + 6x + 5)

Trinomials: $x^2$ -11 + 28

In order to factor the example above, we need to find 2 numbers that add or subtract to -11 and multiply to 28. To Start, I will create a list of factors for 28: 1,2,4,7,14,28

7+4=11 so -7-4=-11 and that means our simplified equation is:

(x-7)(x-4)

Binomials: $x^2$ – 25

(x-5)(x+5)

Math 10, Uncategorized

Week 6 – Math 10 – Multiplying polynomials

March 7, 2020 amyt2018 Leave a comment

This week we learned how to multiply polynomials in several different ways. In order to multiply polynomials, you need to understand the distributive property and the multiplication exponent law, but I will explain them when they come up. I this I will explain how to multiply a trinomial (3 terms) by a binomial (2 terms) in 2 ways. The example I will be solving is (5x²-3x+6)(4x+5)

Way 1: algebraically

First I can start with expanding. Each term in the first bracket will multiply into terms in the second, because of the distributive property. This is what the equation would look expanded:

5x²(4x)+5x²(5)-3x(4x)-3x(5)+5(4x)+5(5)

Know I can do the individual multiplication:

20x³+25x²-12x²-15x+20x+20

The reason 5x²(4x)=20x³ is according to the multiplication exponent law. There in an invisible exponent of 1 on the 4x.

Before I combine like terms I like to organize my equation to make things easier for myself. I organize the equation by like terms then I combine. This equation is already organized so I can skip that step.

Like terms combined: 20x³+13x²+5x+20

Way 2: visually

(5x²-3x+6)(4x+5)

You start with making a box with lines separating it to the number of terms

Then you fill in the polynomials to their respective sides. put each term on a line like this

	4x	5
5x²
-3x
6

Then I would do the multiplication in the individual squares

	4x	5
5x²	20x³	25x²
-3x	-13x²	-15x
6	24x	30

Know I can right out the hole equation and combine like terms.

Written out: 20×3+25×2-12×2-15x+20x+20

Like terms combined: 20×3+13×2+5x+20

Math 10

Week 5 – Math 10 – Naming Polynomials

March 1, 2020 amyt2018 Leave a comment

Week 5 – Math 10 – Naming Polynomials

This week in math 10, we learned how to name polynomials based on the number of terms and the degree. This is an example:

2x³ + x²

This this a Binomial because it has two terms. This is a Cubic polynomial because it has a degree of three. The fallowing is a list of the vocabulary with an example of each:

A Monomial has 1 term

X²

A Binomial has 2 terms

2x² – 4x

A Trinomial has 3 terms

3x² – 2x + 3

A Polynomial has multiple terms

4x³ + 5x² + 6x – 7

A Linear polynomial has a degree of 1

4x – 7

A Quadratic polynomial has a degree of 2

6x² – 2x

A Cubic polynomial has a degree of 3

4x³ + 2x² – 8

A Quartic polynomial has a degree of 4

6x⁴ – 7x² + 5

A Quintic polynomial has a degree of 5

2x⁵ + 3x³ – 4x + 3

Math 10

Math 10 – week 4 – solving triangles

February 23, 2020 amyt2018 Leave a comment

This week in math we learned how to solve a triangle. Solving a triangle is much different than solving an equation. When solving an equation, you are trying to find the variable. However, when you are solving a triangle, you are trying to find all of the side lengths and angles.

Tools for solving Triangles:

All angles in triangles add to 180°

Pythagorean Theorem (a²+b²=c²)

SahCahToa (Sin, Cos, Tan)

Here is an example of a triangle that I will solve:

First we can use the Pythagorean Theorem to solve for the hypotenuse (AB)

29²+38²=C²

841+1444=2285

the answer is the square root of 2285

C=47.8

Now we can start to identify angles. We already know that side C is 90°. Lets start finding side B. I have identified all the sides with B as the reference angle. I will use Tan to find B.

TanB=29/38

B=Tan^-129/38

B=Tan^-10.76

B=37°

How we can solve for A.

180-90-37=53

Here is the solved triangle.

Math 10

Week 3 – math 10 – Trigonometric ratios

February 16, 2020 amyt2018 Leave a comment

This week in math we started to learn about trigonometry, the study of triangles. The base of trigonometry are the trigonometric ratios: Sine, Cosine, and Tangent. But in order to understand equations, you need to understand triangles.

This is a right-angle triangle. The corner with the x in it is the reference angle and the hole equation is based around this. The longest side is they hypotenuse marked by a H. The side across from the reference angle is the opposite side, marked with the O. the final side is known as the adjacent side, marked with A, is beside the reference angle.

Here are the equations

Sine = O/Hs

Sine fined the relationship between the percentage of the opposite side to the Hypotenuse.

Cosine = A/H

Sine fined the relationship between the percentage of the adjacent side to the Hypotenuse.

Tangent = O/A

Sine fined the relationship between the percentage of the opposite side to the Adjacent side.

Below is an example of the with all of the equations

Math 10

Week 2 – Math 10 – Negative Exponents

February 9, 2020 amyt2018 Leave a comment

This week in math we learned about negative exponents and how to deal with them

Unlike with positive exponents, the bigger the exponent the larger the number. If you have a negative exponent and number will be smaller than 1.

2⁴ = 16

2³ = 8

2² = 4

2¹ = 2

2⁰ = 1

2^-1 = $\frac{1}{-2}$

2^-2 = $\frac{1}{-4}$

2^-3 = $latex \frac{1}{-8}

To solve for a negative fraction, we need to find the reciprocal fraction. For example $\frac{2}{1}$ is the reciprocal of $\frac{1}{2}$ . When we reciprocate a negative exponent, the exponent because positive and the question becomes easier to solve. Reminder, when you reciprocate, it only applies to the exponent, so a positive 4 will not become negative if you reciprocate it.

3^-2

Reciprocate

$\frac{1}{3^2}$ = $\frac{1}{9}$

A good way to remember this is too think about wanting to make the exponents happy. If a exponent is negative, or unhappy, move it to where it will be positive, or happy.

English 10

Humanity Exposed

February 7, 2020 amyt2018 Leave a comment

The book Wonder, written by R. J. Palacio, follows the story of August (Auggie), a boy with a rare birth defect that makes his face look weird. The story follows his adventures throughout middle school, through the perspectives of Auggie, his friends and his family. At first, his classmates feared him because he looked weird. Eventually, August started to make more friends due to his personality and other people’s kindness. August’s limited number of friends got bullied and isolated due to their association with him. After some rough patches, August and his friends stood up to the bullies. Humans can be very judgmental. This book shows us that if we take the time to get to know people who are different, they can turn out to be amazing people.

Math 10

Week 1 – Math 10 – Prime Factors

February 1, 2020 amyt2018 Leave a comment

This week we learned about Prime Factoring. Prime Factoring is taking a number and finding its Prime Factors. For example the prime factorization of 12 is 2²x 3 or rewritten is 2 x 2 x 3.

In order to find a number’s prime factors, you need to follow divisibility rules.

2 – ends in an even number

3 – add all digits. If the sum is divisible by 3, the number is divisible by 3

4 – the last 2 digits of a number are divisible by 4. Can be cut in half twice

5 – ends in a 5 or 0

6 – if both 2 and 3 apply

7 – there is no rule

8 – can be cut in half 3 times

9 – digit sum is divisible by 9

10 – ends in a 0

Here is a guide to factorization:

Check if your number is divisible by 2 (if there is any larger number that is divisible do that)
1. If yes move on to the next step
2. If no skip to step 4
Divide
Check if your quotient is still divisible by 2
1. If yes, go back to step 2
2. If no, move on the next step
Repeat step 1-3 for the other factorization numbers

Science 10

space wonder question – Amy

January 8, 2020 amyt2018 4 Comments

I have been thinking about animals in space. It interests me. I have wondered about what an animal would need to survive in space. I decided to do my wonder project on this question. What adaptations would an animal need in space?

Simpler organisms seem to do a lot better in space then others. Complex being, like humans, apes and dogs, can live in space for a short amount of time before their lungs expand, their blood releases and their saliva begins to boil.(2) The I decided to dig a little into saliva, but I got nothing.(3)

Smaller and more simple organisms, like water bears and fish, tend to do better in space, with the former being able to survive in space for 10 minutes. Water bears need to have a light coating of water around them indoor in function, but they can turn off this need by entering a state known as cryptobiosis. In cryptobiosis water bears can withstand below freezing temperatures. Water bears are resistant to, or unaffected by, the suns ultraviolet rays, I think it is because of their size. (4) Fish have been sent up into space and been able to correct there swimming to zero gravity. (1)

I wanted to research this question because of how big it was. Know I wonder what a space ecosystem would look like. My conclusion to the questions is that animals would have to be super small unorder to functional in space.(4)