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

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

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

Team Assignments for Meet 4

Meet 4 is at St. Thomas on Dec 8.
Heritage will have early dismissal at 2:50
Friendly Hills - meet at south circle at 3:20 - I will come in from our bus we will leave at 3:25

HERITAGE

8	Aiden Jacobs	8	2	38.0
7	Anthony Rocke	10	0	38.0
7	Steve Nickson	0	0	24.5
8	Abbey Dzurilla	0	2	22.0
7	Cullen Sander	0	2	17.5
7	Ben Nickson	0	0	14.5
7	Skylar Janssen			6.5
5	Nik Zeravica	0	0	5.0
6	Angel Hernandez	0	0	3.5
	Victoria Dzrurilla	0	0	0.0

FRIENDLY HILLS

Grade	Name	P4b	P4c	M4r
8	Frank Sullivan	8	4	50.3
6	Noelle Wang	4	4	31.2
5	Oscar Halverson	2	6	28.7
5	Nick Wendt	1	0	21.7
5	Cyrus Martin Risch	0	0	16.0
5	Oslo Martin Risch	2	0	15.0
8	Naomi Spande	2	0	13.7
5	Aidan Dolan	2	0	13.3
6	Lydia Houge	0	0	12.0
5	Dain Dolan	2	4	8.0
6	Emma Stevenson	2	0	5.3
5	Sophia Schomer	0	0	4.0
6	Aiden Lee			3.7
6	Lily Pince			3.7
5	Nicholas Reisig	1	0	3.3
5	Jake Lancaster	1	0	2.7