Week 11 – Graphing Linear Inequalities in Two Variables

This week in Pre-Calculus 11 we reviewed linear graphing (y=mx+b) from Math 10 and expanded on it. So instead of looking for just one answer of y we look for the possibilities of y. Also we use inequalities instead of an equal sign. I will be blogging about Graphing linear inequalities in two variables (x and y). Solutions to linear inequalities in two variables is represented by the boundary lines and shading on one side.

The inequality used decides what the boundary line looks like.

A solid line is greater/less than or equal to…

A broken line is greater/less than…

When you shade you need to test one of point on either side of the line. If the answer is true such as (y<x+2  —>  0<0+2  —>  0<2) then shade on that side of the line. In the example I used (0,0) as my test point. If it isn’t true choose a point on the other side of the line and test that. Try and use (0,0) as your test point it makes it easier and leaves less room for mistakes.

 

Examples

This when y is greater than x+2. So the line is broken and the shading is above.

 

In this graph y is less than x+2. So the line is broken and the shading is on the bottom.

 

This graph is saying y is greater than or equal to x+2. So the boundary line is solid and the shading is above.

 

y is less than or equal to x+2 in this graph. So the boundary line is solid and the shading is below.

 

Week 10 – Discriminant

This week in Pre-Calculus 11 we reviewed for our midterm. So we are suppose to blog about something we haven’t blogged about yet. I chose the discriminant because it was something I struggled with until review this week. The discriminant is how we determine how many solutions there are. Here is how to find the discriminants b^2-4ac. This connects to the quadratic formula, the pink is the discriminant formula.

So you can have 2 solutions, 1 solution, or no solution.

x^2-6x+5=0

a=1, b=-6, c=5

b^2-4ac

Plug in a, b, and c.

(-6)^2-4(1)(5)

36-20

16 gives 2 solutions

This parabola crosses the x-axis twice giving us two solutions.

 

x^2-6x+9=0

a=1, b=-6, c=9

b^2-4ac

Plug in a, b, and c.

-6^2-4(1)(9)

36-36

0 gives one solution

The parabola crosses the x-axis once meaning there is only one solution.

 

x^2-6x+13=0

a=1, b=-6, c=13

b^2-4ac

Plug in a, b, and c.

-6^2-4(1)(13)

36-52

-16 gives no solution

The parabola never crosses the x-axis so there is no solution.

LOTF Podcast

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The podcast above is about herd mentality and morality and how it relates to the novel “Lord of the Flies” by William Golding.

 

Work Cited:

By watching and imitating others, young children learn how to interact socially. They learn acceptable and unacceptable kinds of behaviour.
“Child Development and Early Learning.” Facts for Life – Child Development and Early Learning, www.factsforlifeglobal.org/03/4.html.

The years between 6 and 14—middle childhood and early adolescence—are a time of important developmental advances that establish children’s sense of identity.
Eccles, Jacquelynne S. “The development of children ages 6 to 14.” The future of children (1999): 30-44.

babies, children and teenagers tend to grieve in bursts, and at other times will look for reassurance and comfort in their normal routines and activities
Lissienko, Katherine. “Bereavement Reactions by Age Group.” Kidshealth, Kidshealth, 13 Sept. 2011, www.kidshealth.org.nz/bereavement-reactions-age-group.

Trying to raise a responsible, cooperative child without age-appropriate boundaries is like trying to raise a goldfish outside its fishbowl. Far from squelching the spirit, rules are needed for kids to flourish
“Why Kids Need Rules.” Parenting, 18 Mar. 2014, www.parenting.com/article/why-kids-need-rules.

living in an environment affected by chaos and poverty can lead to changes in the brain’s stress system that increase a child’s vulnerability to chronic diseases later in life.
http://www.urbanchildinstitute.org/sites/all/files/databooks/TUCI_Data_Book_VII_2012.05_family.pdf

Acting out reduces stress. It’s often a child’s attempt to show otherwise hidden emotions.

Attention issues: Children often seek attention from parents, peers, or other authority figures. If they don’t get the positive attention they want, they will act out to get negative attention.

Desire for power: Children often feel powerless. They’re usually unable to control their situations and environment. They act out because it allows them to feel in control of their actions.
https://www.healthline.com/health/acting-out

Mob mentality/ herd mentality
how people are influenced by there peers to be involved in certain behaviours
Contagion theory – uncontrolled wild frenzy – the beast
Convergent theory- choosing the correct answer from said choices
Emergent – norm theory – combination of like minded individuals

The theory adapted this idea in a sociological basis and stated as the transmission of ideas or even irrational behavior collectively displayed by an individual when engaged in a group. It is stated that large number of people are influenced by the contagious behavior of the group and avoids their individual responsibility.

CONTAGION THEORY

 

There are two main strands of convergence theory. One strand focuses on the shared traits of all humanity and argues that explosive crowd behavior is a result of latent tendencies that are often violent. The other strand emphasizes that crowds are homogenous in their makeup and are a result of like-minded individuals coming together to take action collectively.
https://www.enotes.com/research-starters/convergence-theory

Instead, norms emerge through a process of social interaction in which people look to others for cues and signs indicating various possibilities of what they might expect.
https://www.thoughtco.com/emergent-norm-theory-3026305

A natural desire to be part of the ‘in crowd’ could damage our ability to make the right decisions, a new study has shown. – University of Exeter
https://www.sciencedaily.com/releases/2014/12/141216212049.htm

Week 9 – Equivalent Forms of the Quadratic Functions

This week in Pre-Calculus 11 we learned about equivalent forms of the quadratic functions, analyzing ax^2+bc+c, and applying what we learned this unit into word problems. This post I am going to focus in on equivalent forms of the quadratic functions. There are three equivalent forms of the quadratic function the general, standard, and factored form. We are going to look on the general and standard form.

General form —> ax^2+bc+c

Standard form —> y=(x-p)^2+q

When changing between general and standard form you have to use the completing the square method to do so.

 

Week 8 – Translation and Scale

This week in Pre-Calculus 11 we learned about quadratic functions. We learned about the properties, looking at an equation and extracting information for the parabola, and analyzing $latexy=a(x-p)^2+q$. I am going to focus on looking at an equation and extracting information for the parabola. Translations can go up and down or side to side. Scales can either stretch or compress the parabola.

$latexy=x^2+p$ —> The parabola moves up/down because there are no brackets around $latexy=x^2+p$

$latexy=(x-p)^2$ —> The parabola moves left or right because there are brackets around x-p. When p is negative the parabola moves to the right but if p is positive the parabola moves to the left.

$larexy=ax^2$ —> The parabola stretches when is greater than 1. If a is less than one the parabola compresses. Also if a is negative the parabola will open down instead of up.

 

 

“Lord of the Flies”- Island Description

The Island:

“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” (Golding 26)

Scar:

“Behind this was the darkness of the forest proper and the open space of the scar”. (Golding 4).

Lagoon :

“lagoon was still as a mountain lake—blue of all shades and shadowy green and purple” (10)

Shore:

“The shore was fledged with palm trees. These stood or leaned or reclined against the light and their green feathers were a hundred feet up in the air” (4)

Beach:

“The beach between the palm terrace and the water drew to a point at infinity; and always, almost invisible, was the heat” (Golding 4).

 

 

Mountain :

“rock of the cliff was split and the top littered with great lumps that seemed to totter” (Golding 113)

Forest:

“Flower and fruit grew together on the same tree and everywhere was the scent of ripeness and the booming of a million bees at pasture” (Golding 77)

Reef:

“The reef enclosed more than one side of the island, lying perhaps a mile out and parallel to what they now thought of as their beach” (Golding 38)

Platform:

“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. The top of this was covered with a thin layer of soil and coarse grass and shaded with young palm trees.”(Golding 13)

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. (Golding 10)

Week 6 – Perfect Square Trinomials

This week in Pre-Calculus 11 we learned about perfect square trinomials. We learned how to regonize and factor them. How can you identify perfect square trinomials? You need to look at each term.

The first term is a perfect square

The third term is a perfect square that must be positive.

The second term can be positive or negative.

 

Week 5 – Ugly fractions

This week in Pre-Calculus 11 we learned about factoring polynomials.  Ms. Burton gave a very useful acronym Can Divers Pee Easily Underwater.

Common

Difference of squares

Pattern

Easy

Ugly

These are the steps that help break down a polynomial and properly factor it. In this blog post I am going to focus on Ugly polynomials because it was something I struggled with. There are multiply ways to factor ugly polynomials but I prefer the square method. This is my favourite because it looks nice, its easy to understand, and breaks it down right to the answer.

First I identified is there was anything in common, if there was a difference of squares, or a pattern.

I noticed the pattern of a normal polynomial, then asked if it is easy or ugly? You can identify this by looking infront of the squares variable, so if there is no coefficient then it is easy but if there is a coefficient then it is ugly. So this polynomial is ugly.

Walter Mitty Daydream Six

“To hell with the handkerchief,” said Walter Mitty scornfully. He took one last drag on his cigarette and snapped it away. Then, with that faint, fleeting smile playing about his lips, he faced the firing squad; erect and motionless, proud and disdainful, Walter Mitty the Undefeated, inscrutable to the last. The firing squad aimed, Walter Mitty kept his head high waiting to greet death. A woman jumped through the crowd as the firing squad had their fingers on their tiggers, ready to shoot. She opened her mouth to say something, but she was too late and Walter knew it as the he heard the guns go off “Aaaaaah!”…

“What is wrong dear?” Mrs. Mitty asked the young lady who had just screamed for no apparent reason.

“That m-man ju-just took m-my purse,” the lady replied with tears in her eyes threatening to fall. Mrs. Mitty wrapped her arms around the girl and tried her best to comfort her. Telling her that everything is okay, and that someone will get the police.

Once the police arrived Walter and his wife headed home. The drive home was quiet; when they finally arrived home Mrs. Mitty headed to the kitchen to begin dinner.

“Walter, did you eat all the bread?” Mrs. Mitty called rather insinuatingly.

“No, there should be more in the cabinet.” replied Walter as he headed into the living room.

“Where is that dog?” He thought to himself as he checked under the coffee table, that is when he spotted the blonde cocker spaniel coming down the stairs. The little dog came into the living room; her tail began wagging once she spotted Walter. He bent down and reached into his pocket for the puppy biscuit. The spaniel spotted the puppy biscuit and jumped at him…

“Roooaarrrr” he jumped out of the way as the beast lunged for him. When he turned back to face the beast, but the lion jumped again and had Walter pinned. He frantically looked around for anything to hit the her with. The insolent animal bit his arm as he went to strike it in the side, this distracted the beast long enough for Walter to grab a log and hit it in the face. He then reached for some dirt and threw into her face. Walter got up and started running , he needed to find it before this beast kills him. He stopped at a small little pond to clean the bite mark on his arm. He looked in his reflection and saw a haggard looking man. That’s when he saw it out of the corner of his eye, the cave entrance he has been looking for, for three weeks now. As he stepped into the cave he he quietly whispered to himself, “The life of an archeologist was gonna get him killed.”

This was the second time this trip a wild animal has tried to make him a meal. He heard the soft breathing of the lion as she entered the cave stalking her prey. He stepped behind a large rock and noticed there was gap with the slightest bit of light flowing through it. Walter hurriedly stepped into the gap, as the lion stepped around the boulder. He heard a growl and started running as fast as he could through the narrow space. The light getting brighter as he sprinted through. The sun is setting he does not have much time till he looses daylight. As he neared the end of the tunnel he noticed there was a ledge and looked back at the lion which was getting closer. Once he got to the edge he saw his next clue, the waterfall, so he jumped.

 

 

Week 4-Multiplying Radical Expressions

This week in Pre-Calculus 11 we learned about multiplying and dividing radicals. I struggled to understand multiplying radical expressions and thought it would be good for this weeks blog post. When you are multiplying radical expressions you need to make sure to use the distributive property.

 

Equation:

Use the distributive property.