Monday, January 5, 2015

Team Assignments for Final Meet

NEW INFO

I forgot to teach one thing that might be on the test. So here is in a nutshell.
TRANSFORMATION LESSON - transformation is the changing of a shape in the coordinate plaen. There are four methods of transformation:
TRANSLATION - sliding a geometric shape to the left or right on the coordinate plane
     If you've ever used powerpoint, it's like dragging a figure.
ROTATION - rotating or turning the figure
REFLECTION - flipping a figure over to get a mirror image.
DILATION - making a figure larger or smaller

For a 2.5 minute lesson click HERE 

ANSWERS TO TEST

1. Simplify and write in descending order (that means first the x squared’s then the x’s then the plain numbers)
14 + 3(x2 – 2) – 4(5 + 3x) – (x2 + 3)  (First, let’s use the distributive principle.)
14 + 3x2 – 6 – 20 -12x - x2 – 3 (Remember to distribute the negative sign)
Now combine like terms. How many x squared’s? (3-1=2)
So 2x2 … (now how many x’s?) -12x (and finally add the numbers 14-6-20-3= -15)
Final answer: 2x2 -12x -15

2. In right triangle ABC, BD is an altitude. AC=2” and BC=1”. What’s the length of BD?
Use the Pythagorean theorem to find the length of AB. 22 = 12 +AB2  Thus 4=1+ AB2  or 3 = AB2.   So AB = √3

AC=2”
BC=1”
AB =  √ 3   "
Here’s a trick – let’s compute the area of the triangle two different ways. A=½ bh.  A= ½(AB)(BC)  and A= ½(AC)(BD) The two ways of computing the are should be equal, so  ½(AB)(BC)= ½(AC)(BD) or (multiplying both sides by 2)
(AB)(BC)=(AC)(BD). Let’s plug in the values.
(√3)(1) = 2 (BD)
Therefore BD= √3/2


3. Marc made the basket 16 times and missed the basket 9 times in the basketball game. What is the probability that he will make the basket on his next try?
Probability is always expressed as a fraction between 0 and 1.  The numerator will be the successes and the denominator will be the total chances. He was successful 16 times out of a total of 25 chances. So the probability is 16/25 (or 64%)

4. Sandy decorated her holiday tree with 10 red, 15 silver, and 5 green lass ornaments. Her little brother, Ed, pulled the tree over and only one ornament broke. What is the probability it was red?
Again, probability is always expressed as a fraction between 0 and 1.  The numerator will be the successes and the denominator will be the total chances.
So 10 are red of a total of 30 ornaments. The probability is 10/30 which should be reduced to 1/3. 

5. There are six people in a race. There are trophies for first, second and third place. How many different ways are there for handing out those 3 trophies?

First place can go to any of the six racers. Second place can only go to 5 since the first place person can’t also get the second place trophy. Third place can go to 4 racers since there are two racers who already got a trophy. So the total different ways is 6x5x4=  120.

SCORES and Team Assignments
Practice Group Test 
 Friendly Hills Gold 12
 Friendly Hills Red 7
 Heritage 12

FRIENDLY HILLS 
Grade Name P5b M5r
8 Frank Sullivan 4 46.0
5 Oscar Halverson 4 26.0
6 Noelle Wang 2 20.3
5 Cyrus Martin Risch 2 16.0
5 Nick Wendt 2 16.0
5 Dain Dolan 1 11.7
5 Oslo Martin Risch 3 11.0
8 Naomi Spande 4 9.3
6 Lydia Houge 4 8.0
5 Aidan Dolan 1 6.3
5 Sophia Schomer 2 6.0
5 Nicholas Reisig 0 3.3
6 Aiden Lee 2.0
6 Lily Pince 1.3
5 Jake Lancaster 1 1.0
6 Emma Stevenson 0 0.0
HERITAGE

8 Aiden Jacobs 2 34.7
8 Abbey Dzurilla 2 32.0
7 Anthony Rocke 8 30.0
7 Cullen Sander 2 16.0
7 Steve Nickson 4 14.7
7 Ben Nickson 14.3
6 Angel Hernandez 0 2.7
5 Nik Zeravica 0 2.0
5 Victoria Dzurilla 0 2.0

Monday, December 15, 2014

Test B Problems and Solutions

I should have mentioned that #2 and #5 were the 4 point problems. Sorry.

1. What is the intersection of y = 3x+4 and y=x-2
   Since they are both equal to y, that means that:
   3x+4=x-2
   2x+4 = -2
   2x = -6
    x = -3 and plugging -3 into y=x-2 we get y=-3-2 or y=-5 so the point of intersection is (-3,-5)
Let's check our answer by plugging those x and y values into our original two equations.
 (-5)=3(-3) + 4 and (-5)=(-3) - 2
-5 = -9 +4 and -5 = -5 Well, those are both true so we have found the point that satisfies both equations.

2. Find the two points where y=|x-4| and y=2/3 x - 2 intersect. Leave the coordinates as impro
per fractions or integers.
Either y = x-4 or y= -x + 4  Now let's plug in 2/3 x - 2 for y in each of the two equations.
2/3 x - 2 = x-4  or 2/3 x - 2 = -x +4
-2 = 1/3 x -4    or   5/3 x - 2 = 4
2 = 1/3 x       or      5/3 x= 6
6 = x             or      x= 18/5     Now let's y=2/3x -2 to figure out the y value.
y = 2/3(6) - 2  and y=2/3(18/5) - 2
y = 4 - 2          and y = 36/15 - 2
y = 2              and y = 12/5 -10/5
                      and y = 2/5
The two points are (6,2) and (18/5,2/5)

3.Write as a trinomial in descending order: (2x+7) (9x-4)
 18x2 - 8x + 63x -28 = 18x2 + 55x -28 

4. (x2 - 4)/(x  + 2)
There is no x term in the numerator so the coefficient is zero. So the question is what two numbers add to zero and multiply to negative four? Ans. 2 and -2. 
Hence simplify to ((x+2)(x-2))/(x+2) = x-2 =c

5. What is the length of the diagonal of a square of side length 2√15 m, in simplified radical form. Use the Pythagorean Theorem: (2√15)2 + (2√15)2 = c2
Hence 4x15 + 4x15 = c2 or 60 + 60 = c2 
Hence 120 = c2  or c = √120 = √2x2x2x3x5= 2√30

Meet 5 practice

Problem 2 I thought was not difficult but no one got it right. So here it is:

.  If I would like a line with a slope of  -½  to intersect y = 2x – 5, where x=2, 
what would be the equation of that line in slope-intercept form?

    Let's think about this... we want an equation in the slope-intercept form, so my answer is going to be y=mx+b, (for example y=3x+8) where m is the slope and b is the y-intercept. But I'm going to have to figure out what m and b are. 
    Well, They give me the slope, so y=-½ x + b and all I need to do is figure out b, the y-intercept. Well, let's see ... it must intersect the line y = 2x-5 where x=2. What point is that? Well, x=2, but what is y? When x=2, y = 2x-5 means y = 2(2)-5 that's 4-5 or -1. So the point where it crosses is (2, -1). So my equation was y=-½ x + b and now I have a point, an (x,y), that satisfies my equation - namely (2,-1) So that means (-1)=-½(2) + b. Simplify to -1=-1+b or 0=b. 
So I've figured out both m and b and I can write my equation in slope-intercept form, y=mx+b
My equation is y = -½ x + 0

Grade Name P5a M5r
8 Frank Sullivan 6 39.0
5 Oscar Halverson 4 20.0
6 Noelle Wang 0 18.3
5 Cyrus Martin Risch 14.0
5 Nick Wendt 2 13.0
5 Dain Dolan 4 8.7
5 Oslo Martin Risch 2 7.0
8 Naomi Spande 5.3
5 Aidan Dolan 2 4.3
6 Lydia Houge 4.0
5 Sophia Schomer 2 3.0
5 Nicholas Reisig 2 2.3
6 Aiden Lee 2.0
6 Lily Pince 1.3
6 Emma Stevenson 0.0
5 Jake Lancaster 0.0

Grade TEAM ROSTER P5a P5b M5r
8 Aiden Jacobs     33.3
8 Abbey Dzurilla        ?        ? 30.7
7 Anthony Rocke 6   23.7
7 Ben Nickson 0 0 14.3
7 Cullen Sander 4 6 13.0
7 Steve Nickson 0 0 12.0
6 Angel Hernandez     2.7
5 Nik Zeravica     2.0
5 Victoria Dzurilla 0 0 2.0

Monday, December 8, 2014

Top Mathletes after 4 Meets

There may be a few new people, like Aiden Jacobs, who entered the top tier of whom I am currently unaware.  I will update this when the official results are posted. Looks like Frank Sullivan is going to earn a medal. Abbey Dzurilla has a good shot at the #9 spot, and can Aiden Jacobs make the top 10 after missing Meet 1?

1 Huang SPA 104
2 Polley SPA 98
3 Deneen SSP 96
4 Hlavka SPA 94
5 Chang SPA 88
6 Thakkar SPA 82
7 Bijwadia SPA 72
7 Sullivan FHMS 72
8 Moore SPA 70
9 Curran STA 56
9 Frincu SSP 56
11 Dzurilla Heritage 52
11 Konstan SPA 52
13 Winslow-Brewer SSP 48
13 Burris-Brown SPA 48
15 Lenarz SSP 47
16 Hanson SPA 44

16 Aiden Jacobs Heritage 44

Meet 4 Results

TEAM SCORES

These are sorted by Meet 4 Total

School Name and Team ---- A--B–-C Tot Cum
St Paul Academy Gold . . 76 56 40 172 660
South St Paul Maroon . . 40 20 40 100 459
Heritage . . . . . . . . 40 26 24 090 313
Friendly Hills Gold. . . 22 24 24 070 311
St Paul Academy Blue . . 34 12 20 066 390
St Thomas Academy A7 . . 26 30 08 064 252
St Thomas Academy Z. . . 18 20 24 062 096
Friendly Hills Red . . . 04 02 04 010 074
Humboldt . . . . . . . . 02 00 04 006 042

South St Paul White. . . 04 02 00 006 158

INDIVIDUAL RESULTS

HERITAGE
Heritage passed Friendly Hills by 2 points!
We didn't score as well on the team event as we usually do.

Grade TEAM ROSTER M4A M4B M4T
8 Aiden Jacobs 12 10 22
7 Anthony Rocke 4 6 10
7 Steve Nickson 2 0 2
8 Abbey Dzurilla 14 6 20
7 Cullen Sander 2 0 2
7 Ben Nickson 6 4 10
7 Skylar Janssen 0
5 Nik Zeravica 2 0 2
6 Angel Hernandez 2 0 2
5 Victoria Dzurilla 0 2 2

FRIENDLY HILLS
Heritage passed us by 2 points. We need a good Meet 5 to get back into 4th place.
Good job on the team event! You matched Heritage on event C. 
NOTE: Oscar did not get on the SPA bus. His parents picked him up at St. Thomas Academy.

Grade Name M4A M4B M4T
8 Frank Sullivan 8 10 18
6 Noelle Wang 4 4 8
5 Oscar Halverson 2 8 10
5 Nick Wendt 2 2 4
5 Cyrus Martin Risch 6 0 6
5 Oslo Martin Risch 0 0 0
8 Naomi Spande 0 0 0
5 Aidan Dolan 0 0 0
6 Lydia Houge 0 0 0
5 Dain Dolan 2 2 4
6 Emma Stevenson 0
5 Sophia Schomer 2 0 2
6 Aiden Lee 0 0 0
6 Lily Pince 0 0 0
5 Nicholas Reisig 0 0 0
5 Jake Lancaster 0 0 0

Sunday, December 7, 2014

Individual Stantdings - Top 20


Place Name School Score
1 Huang SPA 76
2 Polley SPA 74
3 Deneen SSP 70
3 Hlavka SPA 70
5 Chang SPA 66
6 Moore SPA 60
7 Thakkar SPA 58
8 Bijwadia SPA 54
8 Sullivan FHMS 54
10 Lenarz SSP 47
11 Konstan SPA 44
11 Hanson SPA 44
11 Winslow-Brewer SSP 44
14 Curran STA 40
15 Burris-Brown SPA 38
15 Frincu SSP 38
17 Dzurilla Heritage 32
18 Wang FHMS 31
19 Valeti SPA 30
19 Path SSP 30
19 Nickson S. Heritage 30