## Midterm Review Chapter 1-4

Chapter 1 : Sequences and Series (1.6 Infinite Geometric Series #13 p. 73)

Chapter 2  : Absolute Value and Radicals (2.5 Solving Radical Equations #11 p. 149)

Chapter 3  : Solving Quadratic Equations (Chapter 3 Review #7a p. 248)

Chapter 4 : Analyzing Quadratic Functions (4.6 Analyzing Quadratic Functions of the Form y = ax^2 + bx + c #8a p. 308)

## What is the best method for Solving Quadratic equations?

A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a is not equal to zero.

The fastest way to solve a quadratic equation is through factoring, which involves inspection of the equation. If, upon inspection, the equation does not factor, you can try adding a value to both sides to complete the square. The quadratic formula is essentailly an already reduced version of competing the square. In my opinion the quadratic formula is consistently the most reliable to solve, but, when possible, I would like to factor first.

## What Darwin Never Knew

Charles Darwin’s findings in South America and the Galapagos islands promted him to think of what has been called the “Greastest Idea of all time”; The theory of evolution. In South America, Darwin found the fossils of a giant sloth, which he was able to trace back to modern, smaller size sloths that were still alive. This was the evidence that put his train of thought in motion. Later, he travelled to the Galapagos islands and made many observations there, as well as collecting samples of different animals, most notably the Galapagos finches. However, Darwin did not fully complete his theory until he returned home. There, he studied his findings and was intruiged by the finches. He noted all the similarities and differences between the finches, such as their different sizes and beaks. Darwin arrived at his theory after studying embryos of different species and noted that they all started out very similar, and that the developmental process was where they began to slowly differentiate. This sparked an idea of a common ancestor. For example, a single species of finch could have journeyed to the Galapagos and, over time, have evolved into many different species. Darwin’s theory was absolutely correct, however, he had no idea how it happened.

What Darwin never knew about was DNA. A species gradually changes over time through random genetic mutations, which can give different characteristics to a member of a species. Should this mutation be beneficial to said member, chances are that they will live long enough to reproduce, and thus pass on the mutation to their offspring. Keeping a specific group of a species isolated long enough, (isolating the gene pool), will broaden the chances of a new species forming, since the two seperated groups will keep different mutations contained within their individual offspring. Given enough time, the single species could easily become two. This is how a single common ancestor could’ve, over many years, become the millions of species that we have on our planet today. In conclusion, DNA was the missing link to Darwin’s theory of evolution, the key to all life on earth.

## Biology Kingdoms

Archaebacteria

Sulfolobus islandicus

growth occurs in volcanic springs, optimally at a temperature of 80 degrees Celsius with a ph of 2-3

Ignicoccus hospitalis

Lives in marine hydrothermal vents temperatures range up to 464 degrees Celsius

Eubacteria

E-coli

Salmonella

Protist

Amobea

Volvox globator

Fungi

Agaricus bisporus

Lichen

Animalia

The common spotted cuscus

Grimpoteuthis

Plants

Rafflesia arnoldii

Baobab

## Pizza Problem

Q: You start eating a half a pizza, then eat the remaining half of the half and continue to eat the pizza this way. Will you ever finish? Explain your reasoning. How is this a sequence?

A: In theory, no, you will never finish the pizza. By continually cutting the remaining pizza in half each time you will become closer and closer to zero each time, however, you will never reach it. This is an infinite sequence with an infinite number of terms, because we are calculating how much of the pie remains. Were we calculating how much of the pie we had eaten, this would be a geometric series.

(In theory you would never finish the pizza, however, were we to actually try this I am sure it would eventually all be devoured)

## Water for Elephants: Book Review

Water for Elephants follows the dog-eat-dog world of the circus in the 1930’s through the eyes of Jacob Jankowski as he learns to made hard choices and to stand up for what is right at all costs. The author tells the story from a timely perspective (for the most part) that is only effective, however, if the reader makes some effort to share that perspective.

For example, the animal cruelty in the book is criminal by today’s standards. Not only are the animals neglected, but also subject to routine beatings. Jacob, as the show’s vet, has a perspective more similar to our own than anyone else because he also harbours a soft spot for them and because he sees the most clearly how damaging it is to their physical and mental health. Back in the 1930’s, the mental health of a person was barely considered an issue and the mental health of an animal was virtually unheard of. The routine beatings that August gave out (the mentally unhealthy person, ironically), were seen by him as just to teach the animals a lesson, he didn’t see how it damaged their overall morale.

Personal mental health was an issue in the plot where the author strayed from her timely perspective. In relation to August’s frequent bouts of insanity and rage, she makes it known that he’s a paranoid schizophrenic. This particular disease wasn’t even diagnosed until the 1970’s, but it gives us perspective and depth to the choices that Jacob and Marlena have to make regarding ho to deal with him and wether or not Marlena can afford to get back together with him.

Overall the plot was very compelling but the prologue left the reader confused when it repeats itself later on in the book. It’s a book that requires on to put oneself in different characters’ shoes to get the most out of the book. I would recommend to fans of Jodi Picoult’s My Sister’s Keeper and to those who agree that a book is only as good as it’s characters.