Category Archives: Grade 11

Week 11- Solving Quadratic Inequalities

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This week in math I learned about solving quadratic inequalities.

When solving quadratic inequalities, you always have to remember that if you are dividing by a negative, you have to flip the inequality sign.

Step 1: Find the roots of a quadratic inequality:

Step 2: Insert the roots into a numbe line:

Then you can pick 3 numbers from the 3 sections on the number line and insert them into the original equation.

I picked 0 becuase it is quick and easy:

I got a positive number so, any number below 2 is positive.

Then I did the same with the number 3:

I got a negative number, that means that all numbers between 2 and 7 would result in a negative number.

Then I did the same with 10 and got a positive number, which means all numbers above 7 would result in a positive number. But the equation is asking which number could be inserted into the equation that would result in negative number. Looking back at the number line I see that all numbers beteeen 2 and 7 would result in a negative number. So the answer is 2<x<7.

LOTF Podcast

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5 facts we found online:
1. (https://www.mentalhelp.net/articles/early-childhood-moral-development/) Morality – Why do children misbehave when not around authority?
According to Piaget, children between the ages of 5 and 10 see the world through a Heteronomous Morality. In other words, children think that authority figures such as parents and teachers have rules that young people must follow absolutely.

2. Morality- Murderous children often come from families where they see or experience much violence. (https://mobile.nytimes.com/1983/10/11/science/children-who-kill-personality-patterns-are-identified.html)

3: Morality- How do boys and girls differ in terms of mortality? When boys are confronted with a conflict involving fairness they tend to argue it out or take their ball and go home. females are typically less concerned with justice and more concerned with caring and maintaining relationships, http://www.earlychildhoodnews.com/earlychildhood/article_view.aspx?ArticleID=118

4: Mob Mentality – majority rules when it comes to influencing the opinion of preschoolers (https://www.google.ca/amp/s/www.ndtv.com/offbeat/herd-mentality-even-kids-know-to-agree-with-the-majority-390835%3famp=1&akamai-rum=off)

5. Mob Mentality – herd mentality is strongest around age 8 and it lessens as we age. (https://dyske.com/paper/1039)

Characterization (3D) – Ralph

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These quotes describe Ralph characteristics through direct and indirect characterization. Ralph is a tall boy who has fair hair and attractive appearance. He is physically fit and one of the oldest boys on the island (12 years old). Ralph has wide shoulders, he also has a kind looking, friendly face. He is one of leaders of the boys on the island. Ralph is confident and has good leadership skills, most likely passed down from his father who is a commander in the navy. After a few months on the island Ralph’s physical appearance changed, his hair grew significantly and was covering his eyebrows, Ralph’s skin was also very tanned.

1. “The boy with fair hair lowered himself down the last few feet of rock and began to pick his way toward the lagoon” (Golding 1).
> This quote describes Ralph’s hair colour: fair (likely blond).

2. “He was old enough, twelve years and a few months, to have lost the prominent tummy of childhood and not yet old enough for adolescence to have made him awkward. You could see now that he might make a boxer, as far as width and heaviness of shoulders went, but there was a mildness about his mouth and eyes that proclaimed no devil.” (Golding PDF 11)
> This quote describes Ralph’s age (12) and physical appearance like his wide shoulders and kind looking face

3. “His [Ralph’s] fair hair was plastered over his eyebrows and he pushed it back.” (Golding PDF 90)
> This quote describes that Ralph’s hair has significantly grown since his arrival on the island and it is covering his eyebrows

4. “Something deep in Ralph spoke for him. ‘I’m chief. I’ll go. Don’t argue’” (Golding 155).
> This quote demonstrates the confident, leadership qualities in Ralph.

5. “But there was a stillness about Ralph as he sat that marked him out: there was his size, and attractive appearance; and most obscurely, yet most powerfully, there was the conch.” (Golding PDF 28)
>This quote describes more of Ralph’s physical characteristics, such as his size and attractive appearance. It also shows how the other boys view him as powerful because he has the conch.

6. “Ralph too was fighting to get near, to get a handful of that brown, vulnerable flesh. The desire to squeeze and hurt was over-mastering” (Golding 76).
> Ralph was raised with proper, innocent morals but the primitive savagery of the island is taking over.

7. “And in the middle of them, with filthy body, matted hair, and unwiped nose, Ralph wept for the end of innocence, the darkness of man’s heart, and the fall through the air of the true, wise friend called Piggy” (Golding 248).
> Ralph’s appearance included: a dirty body, matted hair, and a filthy face. Ralph has feelings and empathy, as he was crying for the loss of a close friend.

8. “We can help them to find us. If a ship comes near the island they may not notice us. So we must make smoke on top of the mountain. We must make a fire.”
> Ralph was pretty smart, and thought it was important to focus on a signal fire for rescue.
9. “His mouth was tight and pale. He put back his hair very slowly… He forced his feet to move until they carried him out on to the neck of the island” (Golding 130).

10. “‘I could swim when I was five. Daddy taught me. He’s a commander in the Navy. When he gets leave he’ll come and rescue us.’” (Golding PDF 15)
>This quote shows us that Ralph is physically skilled, and is a good swimmer. His father is also a commander in the Navy which most likely gives Ralph good physical qualities.

 

 

 

Week 10- Sequences and Series Review

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The unit I needed to recall the most was the Sequences and Series unit. Specifically Infinite Geometric Series. These are the types of infinite geometric series:

Diverging series expand each time so its impossible to determine a sum because the numbers grow so much each time they are multipled by the common ratio. In a diverging series the common ratio has to be negative.

Unlike diverging series, converging series do have a sum, converging series converge, and eventually the numbers will be so small that you could determine a sum. The ratio for a converging series needs to be bigger than -1 and smaller than 0.

This is the formula for finding the sum of a converging series .

 

Week 9- Equivalent Forms of the Quadratic Function

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The General Form and Standard Form can be converted to Equivalent Forms. This can be useful if you are trying to find the vertex or y-intercept.

To convert from General Form to Standard Form we complete the square:

Now we know that the vertex is at (-3, -3)

To convert from Standard Form to General Form we expand the equation:

Now we know that the y-intercept is at 15.

Week 8- General and Standard Form

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This week in Math I learned about the General and Standard forms of the Quadratic Function and how to analyze them. Both General Form and Standard Form equations make parabolas. You can identify many characteristics of a parabola just by looking at a Standard Form or General Form Quadratic Function.

General Form look like this:

In the General Form C always tells you the y-intercept. A tells you if the parabola opens up or down (if it is negative the parabola opens down if it is positive the parabola opens up). A also tells you if the parabola stretches or compresses (if a is bigger than 1 the parabola stretches if a is smaller than 1 the parabola compresses). A cannot be 0.

Standard Form looks like this:

In General Form q tells you the vertical translation or the y-axis of the vertex (q is not always the y-int). P tells you the horizontal translation or the x-axis of the vertex. Using p and q you can identify the vertex of a parabola. A tells you if the parabola opens up or down (if it is negative the parabola opens down if it is positive the parabola opens up). A also tells you if the parabola stretches or compresses (if a is bigger than 1 the parabola stretches if a is smaller than 1 the parabola compresses). A cannot be 0.

“Lord of the Flies”- Island Description

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The following are quotes and a photo that describe the island form Lord of the Flies

The scar- “All round him the long scar smashed into the jungle was a bath of heat” (Golding 6) .

The platform/ meeting place- “Here the beach was interrupted abruptly by the square motif of the landscape; a great platform of pink granite thrust up uncompromisingly through forest and terrace and sand and lagoon to make a raised jetty four feet high” (Golding 13).

The beach- “The shore was fledged with palm trees” (Golding 10)

Site where piggy and Ralph find the conch-“Ralph had stopped smiling and was pointing into the lagoon. Something creamy lay among the ferny weeds.” (Golding 18)

The Lagoon- “Out there, perhaps a mile away, the white surf flinked on a coral reef, and
beyond that the open sea was dark blue. Within the irregular arc of coral
the lagoon was still as a mountain lake—blue of all shades and shadowy
green and purple. The beach between the palm terrace and the water
was a thin stick, endless apparently” (Golding 4)

The Stream- “The pink granite of the next cliff was further back from the creepers
and trees so that they could trot up the path. This again led into more
open forest so that they had a glimpse of the spread sea” (Golding 24)

The Mountain-

“It was roughly boat-shaped: humped near this end with behind them
the jumbled descent to the shore. On either side rocks, cliffs, treetops
and a steep slope: forward there, the length of the boat, a tamer descent,
tree-clad, with hints of pink: and then the jungly flat of the island, dense
green, but drawn at the end to a pink tail. There, where the island petered
out in water, was another island; a rock, almost detached, standing
like a fort, facing them across the green with one bold, pink bastion.
The boys surveyed all this, then looked out to sea” (Golding 26)

The jungle- Ralph disentangled himself cautiously and stole away through the branches. In a few seconds the fat boy’s grunts were behind him and he was hurrying toward the screen that still lay between him and the lagoon. He climbed over a broken trunk and was out of the jungle. (10)

 

Week 5- Factoring Polynomials

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This week in math I learned of a simple strategy to Factor Polynomials.

C- Common. Is there anything common amongst the terms? If there yes, then you can simplify the polynomial. If no, go to the next step. Ex: 8p^3-4p^2-4 = 4(2p^3-p^2-1)

D- Diffrence. Is there a diffrence of squares. If yes, then you could factor the polynial easily (This only works for binomials). If no, go to the next step. Ex: x^2-49 = (x-7)(x+7)

P- Pattern. Is there a pattern? (Only for trinomials) If Yes, go to the next step. Ex: (x^2+x+5)

E- Easy. Is the pattern easy? (Is there a coefficient in the front?) If there is no coefficient in the front then the polynomial is easy and you can factor it. If no, go to the next step. Ex: x^2+10x+25 = $latex (x+5)(x+5).

U- Ugly. Is the pattern ugly? (Is there a coefficient in the front) If Yes, then we can use the square strategy. Ex:

Walter Mitty Daydream 6

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The firing squad took their aim, and unanimously pulled their triggers. The guns went bang and time seemed to move in slow motion. Walter bent down to a ninety-degree angle and dodged all the bullets. The firing squad was astonished to see Walter spring back up. Then, Walter leaped forward at the firing squad and pandemonium ensued. Walter knocked out all of them one-by-one. He thought he was done, but then he heard a voice behind him… “Walter what are you doing? Stop play fighting, we have to get going,” said Mrs. Mitty with an insolent tone. Embarrassed, Walter followed his wife out of the alley and onto the street. As they were walking to their car, Walter Mitty overheard a conversation two men were having on a bench, “have you heard of that new gangster Al Capone, from Chicago?” asked one of the men. “Yes, I hear he’s been causing some trouble,” replied the other man…

“Make sure you pay Jim a visit, and don’t forget about Tony. He still hasn’t payed back his debt,” said Walter “The Boss” Mitty to his henchman, while counting a stack of money. “The Boss’s” black fedora hat and suit made him look dangerous and mysterious. Suddenly, the doors to his office swung open and a henchman with a distraught look on his face ran in; “Boss! You have to get out of here! The cops are outside, they’re trying to break in!” Yelled the henchman. Walter “The Boss” Mitty slowly stood up from his expensive tiger skin chair, and calmly walked down stairs and into his garage. He and two of his henchman got into the bullet-proof 1930 Chevrolet Series 40 Lincoln, and Walter stomped on the gas pedal. The car jolted forward and broke through the front gate, the police reacted quickly and were hot on Walter’s heels. They were gaining on him, and started firing at Mitty, one of the bullets shot through the car and almost hit Mitty. “Don’t just sit there! Shoot back!” Ordered Walter “The Boss Mitty”, when suddenly something struck his leg…

“Walter have you forgotten where we live? You missed the turn!” Yelled Mrs. Mitty. Red-faced from embarrassment, Walter made a U-turn and drove home.