Algebra II

Algebra II Project

For this project we had to create a part of our own final exam.  This entailed creating ten questions that had to do with various algebraical methods that we learned in class.  I myself created problems that had to do with factoring, matrices, line graphing, and a single word problem at the end.

A miniproject that we had to do was the mini equation project that we carried out at the beginning of the year.  It had to do with creating a line graph consisting of ten equations.

My main strength in math is that I can pick up concepts fairly quickly.
My main weakness is that sometimes I have trouble retaining them and thus do badly on quizzes and tests.

EXAM PROBLEMS

Grayson Mooney

DO ON SEPARATE SHEET OF PAPER

EASY

1. Solve for x:  4x+9-2=7

1. Factor:  x²-81

1. Graph:  y=5x+5x-20

MEDIUM

1. Multiply the Matrices:  3  1  x  4  1

        4  2      2  2

1. Simplify:  √(9x²)

1. Factor:  4x²-9

HARD

7.  Graph:  y=2x²+4x+4

1. Factor:  12x²-29x+15

1. Simplify:  √-17  x  2

RIDICULOUS

1. Word Problem:  Bill and Bob are picking apples in an orchard when Bob sprains his shoulder and has to go home.  Before leaving he tells Bill to be sure to clear out the entire orchard before he has to leave in three hours.  Bill estimates that there are a total of 1,513 apples left in the orchard.  He has 180 minutes left to pick them and knows that he can pick 10 apples per minute if the weather is perfect.  However the weather isn’t stellar and there is a strong wind blowing for about 40% of the time during which Bill can only pick 6 apples per minute.  How many apples does Bill pick when the wind is blowing, when it is still, and in total?  Also, does Bill clear out the orchard like Bob asked him to?

SOLUTIONS

EASY

1. 4x+9-2=7 → 4x+7=7 → (Subtract seven from both sides) 4x=0 → (Divide four on both sides) x=0

1. x²-81 → (Divide by nine) (x+9)(x-9)

1. y=5x+5x-20 → (Find the x) x=-20/2(5) → x=-2 (Plug it in) → y=5(-2)+5(-2)-20 → y=0 → (Now insert another number into the x coordinate to find your other coordinates) → y=5(0)+5(0)-20 → y=-20

MEDIUM

1. 3  1  x  4  1  =  14  5

     4  2      2  2      20  8

1. √9x² → (Divide nine by its square root) √3²x² → (Simplify) √3²  x  √x² → (Multiply)      3 multiplied by the absolute value of x

1. y=2x+4x-4 → (Find the x) x=-4/2(2) → x=-1 (Plug it in) → y=2(-1)+4(-1)-4 → y=-10 → (Now insert another number into the x coordinate to find your other coordinates) → y=2(0)+4(0)-4 → y=-4

HARD

1. 4x²-9 → (Use the difference of squares) 4x²=(2x)² and 9=3² → 4x²-9=(2x)²-(3x)² or    (a+b)(a-b)=a²-b² → a=2x and b=3 → (2x+3)(2x-3)=(2x)²-(3)²=4x²-9 →                 4x²-9=(2x+3)(2x-3)

1. 12x²-29x+15 (Find two x numbers that add up to -29, in this case -9 and -20) → 12x²-9x-20x+15 → (Multiply to 180) 3(4x-3)-5(4x-3) → (Factor by grouping) (4x-3)

1. √-17  x  2 → √(-17 x 2) (Multiply -17 by 2) → √-34 = i√34

RIDICULOUS 

10.  (Find out how long the wind is blowing for) 180  x  0.4=72 → (Next calculate how many apples Bill can pick with the wind blowing) 72  x  6=432 → (Repeat with how many apples he can pick with calm weather)  108  x  10=1,080 → Altogether Bill can pick 1,512 apples and cannot pick every single apple in the orchard


                                                      5/23/13 DP Update
My second semester of the Junior year was kind of a frantic rush to get my grade back up from its low point of 55% after I foolishly abandoned it while recovering from a drop in my Spanish grade.  The projects this semester helped me a great deal in recovering from my point drop, my favorite was the encyclopedia project which was very informative and taught me a lot about Matrices.

My favorite project from this semester was the encyclopedia project, which taught me quite a bit about Matrices and their uses in the real world.  I ended up focusing on optical matrices, which were used heavily in building the lenses for the Hubble Space Telescope.