This Blog exists for the collective benefit of all algebra students. While the posts are specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.
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Tuesday, January 25, 2011
hw MT-2 More Mid-Term Madness!!
... and more errors in the packet (thanks Paul W!)
BT2 pg 21:
#25 answer is B
#26 answer is F
#27 answer is A
anywayy i have a question on #13 in benchmark test 2...what is the compliment of set B...
I got 2,6,8,10 but that wasn't a multiple choice option. Did anyone else have trouble w/ this problem?
In the book it says the compliment is what is in the universal set but not set, in this case, B. However the options have no relevance to that whatsoever.
Yup, you must have been napping again in class. We agreed today that BT2 #13 & #16 were both flawed questions... not to mention the wrong answers in the answer key for #25-27. Did anyone find any other mistakes?
If that's your only problem, you are doing very well... now if you can just stay awake in class!
Here's a popular question from the peanut gallery:
Q. Still a little bit confused on direct variations and how to find them.
A.
1) A direct variation is a linear equation that ALWAYS has a y-intercept of the origin - aka (0, 0).
2) It is typically written as y/x = k where k is called the CONSTANT OF VARIATION. Essentially, we know k as the slope of a straight line. Think about it... SLOPE is the rate of change and a CONSTANT OF VARIATION is just another way of saying that the rate of change is constant.
3) It can also be written as y = kx
Read section 5-2 in the book and look at the video tutors. Take a look at some real life examples.
cut-and-paste it to your browser and give it a look-see.
As far as transformations, I hope you still have the graphs that we did during the classroom lesson? That should help.
When we talk about "transforming" y=|x| we are referring to the the general form of an absval function (equation) that we have been working with, which is: y=|x+a| + b
where a & b can be real numbers (we've been keeping it simple by using integers)
You have to know how various values (pos and neg) of 'a' and/or 'b' impact the location of the vertex.
You know how I despise memorization and tricks, but below is a down-and-dirty summary: The summary is: a positive 'a' slides the vertex left 'a' units a negative 'a' slides the vertex right 'a' units a positive 'b' slides the vertex up 'b' units a negative 'b' slides the vertex down 'b' units
I'm doing my test corrections, and trying to correct #20 d. on the test. My equation was y=(3.5/30x)+14.5. And I substituted 170 into "x" and can't get a different answer! when I substituted 170 into the equation I got 595/30, and then simplified to 119/6. A 119/6 ends up to be about 20, then adding 14.5 makes it 34 1/3. (An answer which does not make sense) HELP!!!
Well, at least you recognize that it doesn't make sense... I LIKE THAT!
Your original equation is flawed. You need to assign year-zero to 1980 and the gallons in 1980 (aka zero) were 27.6... THAT'S your y-intercept!
As for slope, graph the scatter plot and draw a trend line. You should see a slope of somewhere in the ballpark of -1/4 (I had -8/35). You have a slope of +3.5/30... the consumption of milk is declining... how can you have a positive slope???
Should I be using the year 10, year 20, year etc. numbers for the coordinates of the trend line? Or should we use the 1980, 1990, 2000 etc. numbers? Because I am using the year 10.... And I'm getting a slope nowhere close to -1/4!
DO NOT USE actual data points... when you draw the trend line, it is possible NOT to touch any data points. The trend line is an ESTIMATE, so you should also ESTIMATE two points on the line (as far apart as possible) and use those to calculate the slope.
For problems like #20, by setting 1980=0 you are re-establishing your x-axis so that 1990=10, 2005=25, etc.
You got a bad slope (I think) cuz you used the first two points, instead of using the trend line.
I answered the direct variation question in the 3rd comment of this post (above). From a mid-term exam eve standpoint, I can't do much better than that.
WHY DON'T YOU GUYS ASK FOR EXTRA HELP SOONER??!! (yes, I'm screaming!)
1980=0 1981=1 1982=2..... ... 1990=10... ..... 2003=23... etc.
But, ya know, maybe the "years-going-by-10 theory" explains why I'm 572 years old... personally, I don't think I look a day over 450!
Seriously, I think you are making a false assumption when looking at the data table. There is no requirement that the data is presented to you in nicely proportioned "clumps"
Many times you do see:
1980 1985 1990 1995 2000 2005
but there is no reason the data points can't be scattered (ahem, hence the term "scatter plot")
As far as a slope of -6.6/65 (NOPE), how are you getting points 65 years apart, when the question only gives you data points that are 26 years apart and only asks you to extrapolate 35 years from year zero?
I still don't know where the 65 is coming from... 65 would be the year 2045... they only give you data until 2006 (26 on your new x-axis) and they only ask you to extrapolate to 2015 (35 on your new x-axis).... why 65??
And I repeat, you should NOT USE ACTUAL ORDERED PAIRS FROM THE DATA TABLE in your slope calculation. The trend line should be drawn as best as you can through the middle of the data... then you pick estimated ordered pairs (use "easy round" coordinates) in order to calculate the slope.
OH how confused can I get.. I just ignored the graph & plotted the points as if they went 1980, 1990, 2000, 2010, 2020... But I did them in the right order :/ Atleast I figured out what's wrong..
Yup... that's close enough to -1/4 right? Remember, trend lines are roughly drawn estimates... if I have 14 algebra students draw 14 trend lines, they will all be slightly different.
...when you multiply distance over time by time over 1, you have the unit of time in BOTH the numerator and denominator... time becomes a BIG FAT ONE and you are left with distance, yes?
- T is the amount of water left in the tank - they give you an equation (function rule) with an explanation - there are 274L of water left in the tank - hmmm... how could you use that equation (function rule)?
wooooaaaaahhhhhh we had 66 comments???????????????????????????????????????????????????????????????????!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!???!!!?!?!?!?!?!?!?!?
I'll be back after 10pm... so help each other with your questions tonight.
ReplyDeletefyi, questies, see your wiki email!
right...questies best and the brightest
ReplyDeleteanywayy i have a question on #13 in benchmark test 2...what is the compliment of set B...
I got 2,6,8,10 but that wasn't a multiple choice option. Did anyone else have trouble w/ this problem?
In the book it says the compliment is what is in the universal set but not set, in this case, B. However the options have no relevance to that whatsoever.
I need help.
Yup, you must have been napping again in class. We agreed today that BT2 #13 & #16 were both flawed questions... not to mention the wrong answers in the answer key for #25-27. Did anyone find any other mistakes?
ReplyDeleteIf that's your only problem, you are doing very well... now if you can just stay awake in class!
Here's a popular question from the peanut gallery:
ReplyDeleteQ. Still a little bit confused on direct variations and how to find them.
A.
1) A direct variation is a linear equation that ALWAYS has a y-intercept of the origin - aka (0, 0).
2) It is typically written as y/x = k where k is called the CONSTANT OF VARIATION. Essentially, we know k as the slope of a straight line. Think about it... SLOPE is the rate of change and a CONSTANT OF VARIATION is just another way of saying that the rate of change is constant.
3) It can also be written as y = kx
Read section 5-2 in the book and look at the video tutors. Take a look at some real life examples.
Thanks for the feedback. I watched the videos and they helped a lot.
ReplyDeleteIN A DIRECT VARIATION THE Y INTERCEPT HAS TO BE 0? I THINK?
ReplyDeleteALSO A LITTLE BIT CONFUSED ON TRANSFORMATIONS AND HOW TO WRITE AN EQUATION FOR THEM. I WATCHED THE VIDEO BUT I'M STILL A BIT SHAKY ON IT.
ReplyDelete26 ob BT2....don't understand how that is F
ReplyDeleteDear Transformer,
ReplyDeleteFirst of all STOP YELLING!! Using CAPITAL LETTERS means that you are SHOUTING in blog-ese. I might be very old, but I still have my hearing.
Read the notes regarding Direct Variations above... and here is a link to a real-life example direct variation:
http://www.khanacademy.org/video/direct-variation-1?playlist=Algebra%20I%20Worked%20Examples
cut-and-paste it to your browser and give it a look-see.
As far as transformations, I hope you still have the graphs that we did during the classroom lesson? That should help.
When we talk about "transforming" y=|x| we are referring to the the general form of an absval function (equation) that we have been working with, which is:
y=|x+a| + b
where a & b can be real numbers (we've been keeping it simple by using integers)
You have to know how various values (pos and neg) of 'a' and/or 'b' impact the location of the vertex.
You know how I despise memorization and tricks, but below is a down-and-dirty summary:
The summary is:
a positive 'a' slides the vertex left 'a' units
a negative 'a' slides the vertex right 'a' units
a positive 'b' slides the vertex up 'b' units
a negative 'b' slides the vertex down 'b' units
lmk if this helped...
Dear 26F,
ReplyDeleteWhat's the slope of that line? (rise -1 run +2 makes for -1/2, right?
What's the y-intercept? (0, 6), right?
Slope-intercept form baby... what else can it be????????
Ca-peesh?
I'm doing my test corrections, and trying to correct #20 d. on the test. My equation was y=(3.5/30x)+14.5. And I substituted 170 into "x" and can't get a different answer! when I substituted 170 into the equation I got 595/30, and then simplified to 119/6. A 119/6 ends up to be about 20, then adding 14.5 makes it 34 1/3. (An answer which does not make sense) HELP!!!
ReplyDeleteWell, at least you recognize that it doesn't make sense... I LIKE THAT!
ReplyDeleteYour original equation is flawed. You need to assign year-zero to 1980 and the gallons in 1980 (aka zero) were 27.6... THAT'S your y-intercept!
As for slope, graph the scatter plot and draw a trend line. You should see a slope of somewhere in the ballpark of -1/4 (I had -8/35). You have a slope of +3.5/30... the consumption of milk is declining... how can you have a positive slope???
Why 170? I don't know where yougo
lmk how you do...
for 15 on benchmark test 3
ReplyDeleteshouldn't the answer be x-y=-2?
But that isn't one of the multiple choice options
I'm working on it..
ReplyDeleteAnd i used 170 for some reason because it was the "year" that 2015 would have been in the year 10, year 20.. etc. sequence.
Thanks for the help! I'll let you know if I find an answer.
Now I see why I got a positive slope.. I made a mistake of 30-60 being 30. How careless.. :(( But the slope is still wrong.
ReplyDeleteNope, Choice 'A' is the correct answer:
ReplyDeletey = -x - 2 (add x to both sides)
x + y = -2 (a one-stepper!!!)
They listed the answer as y + x = -2... technically correct, however when you use standard form the math gods prefer x before y (except after 'c' jk)
I just went back through the problem and I found so much wrong with it!!
ReplyDelete... and we don't want to anger the math gods on Mid-Term Eve!!
ReplyDeleteI hope you are all decorating your FACTOR TREES tonight!!
To get the slope of a trend line, don't you choose 2 points & use the formula for m to figure it out?
ReplyDeleteOr am I doing something wrong..?
If there is a direct variation is the y intercept 0? I think???
ReplyDeleteShould I be using the year 10, year 20, year etc. numbers for the coordinates of the trend line? Or should we use the 1980, 1990, 2000 etc. numbers? Because I am using the year 10.... And I'm getting a slope nowhere close to -1/4!
ReplyDeletePlease help!
ReplyDeleteDear Trendy,
ReplyDeleteDO NOT USE actual data points... when you draw the trend line, it is possible NOT to touch any data points. The trend line is an ESTIMATE, so you should also ESTIMATE two points on the line (as far apart as possible) and use those to calculate the slope.
For problems like #20, by setting 1980=0 you are re-establishing your x-axis so that 1990=10, 2005=25, etc.
You got a bad slope (I think) cuz you used the first two points, instead of using the trend line.
Did this help?
I answered the direct variation question in the 3rd comment of this post (above). From a mid-term exam eve standpoint, I can't do much better than that.
ReplyDeleteWHY DON'T YOU GUYS ASK FOR EXTRA HELP SOONER??!! (yes, I'm screaming!)
Reviewing.. If you divide a number by a negative number in an inequality, the inequality sign flips, right?
ReplyDeleteI'll try again.
ReplyDeleteAnd sorry, have a lot of Mrs. Henke homework to do!
Dear 170,
ReplyDeleteAre you saying that someone born in 1980 will be 170 years old in 2015?
Hmmmm... are you smarter than a fifth grader?
Dear Flipper,
ReplyDeleteYes, If you divide OR multiply, for that matter.
When I tried the 2 farthest points I could find, I got my slope to be -6.6/65. Is this ABOUT correct?
ReplyDeleteI thought the years went by tens.. so 1980 was 10, 1990 was 20.. and 2015 was 170..
ReplyDeleteLast I checked, the years go by one at a time.
ReplyDelete1980=0
1981=1
1982=2.....
...
1990=10...
.....
2003=23... etc.
But, ya know, maybe the "years-going-by-10 theory" explains why I'm 572 years old... personally, I don't think I look a day over 450!
Seriously, I think you are making a false assumption when looking at the data table. There is no requirement that the data is presented to you in nicely proportioned "clumps"
Many times you do see:
1980
1985
1990
1995
2000
2005
but there is no reason the data points can't be scattered (ahem, hence the term "scatter plot")
1980
1987
1992
1998
2001
2002
2009
etc.
Ca-peesh??
As far as a slope of -6.6/65 (NOPE), how are you getting points 65 years apart, when the question only gives you data points that are 26 years apart and only asks you to extrapolate 35 years from year zero?
ReplyDeleteWhy would #27 be graph D on benchmark test 2?
ReplyDeleteI don't know.. my 'x' axis is labeled up to 80.. should my coordinates be written like this? (1980,27.6) or like this (0,27.6)
ReplyDelete(0, 27.6)
ReplyDeleteYour first step was to set 1980=0...
...on your NEW x-axis, 1980 would be the year 3960!
Ca-peesh??
Dear #27,
ReplyDeleteThe answer is 'A'... look up top at the post MT2 for more info!!
I got it.. But what I don't have is the slope. Two points on my trend line are (0,27.6) and (65,21).. Do they sound wrong?
ReplyDeleteI have extra study time in the morning, now that we have a 90 minute-delay!
ReplyDeleteI still don't know where the 65 is coming from... 65 would be the year 2045... they only give you data until 2006 (26 on your new x-axis) and they only ask you to extrapolate to 2015 (35 on your new x-axis).... why 65??
ReplyDeleteAnd I repeat, you should NOT USE ACTUAL ORDERED PAIRS FROM THE DATA TABLE in your slope calculation. The trend line should be drawn as best as you can through the middle of the data... then you pick estimated ordered pairs (use "easy round" coordinates) in order to calculate the slope.
An FMS student excited about extra study time? Sounds like an oxymoron to me!
ReplyDeleteOH how confused can I get.. I just ignored the graph & plotted the points as if they went 1980, 1990, 2000, 2010, 2020... But I did them in the right order :/
ReplyDeleteAtleast I figured out what's wrong..
And I'm not excited, I'm hoping to get an A+!! :)
If you're hoping to get an A+, you better get excited!!!
ReplyDeleteGETTING EXCITED!! :)
ReplyDeleteI tried for the slope again.. Would -2.8/10 be about right?
ReplyDeleteYup... that's close enough to -1/4 right? Remember, trend lines are roughly drawn estimates... if I have 14 algebra students draw 14 trend lines, they will all be slightly different.
ReplyDeleteOkay! Then I'm on the right track! :)
ReplyDeleteWould I then substitute 35 into my equation to figure out the milk consumption?
ReplyDelete(I'm not sure if anything I am thinking is correct, so I'll ask)
Am I STILL doing something wrong? I substituted 35 into my equation of y=-2.8/10x+27.6, and my answer turned out to be 38.4..
ReplyDeleteWHAT IS WRONG WITH THIS?!?!??!
I'll try to figure it out tomorrow morning.. Got to go to bed! :(
ReplyDeleteOOOOOOH nevermind.. FORGOT THE NEGATIVE SIGN!! A little sign can do so much :)
ReplyDeleteThanks for the help Mr.C! See ya tomorrow! (Maybe)
ReplyDelete:))
Heyy wats good my honors it's Tyler
ReplyDeleteWell, if 4/3 of y'all understand, my work is done here!
ReplyDeleteShouldn't the answer to #14 be g, not h?
ReplyDeleteI don't understand #19.. I got 1/4 as an answer.. And that's not there.. The answer key says it should be B, .1875.. ??
ReplyDeleteDear #19 - The answer is 3/16... re-trace your steps and maybe you'll find the answer.
ReplyDeleteFor #5 in BMT2 wouldn't the answer be A, d<264? Because aren't you measuring the distance? Not distance * time?
ReplyDeleteDear #14... Nope... re-read the question... she makes $100 EACH day... she worked sat & sun, yes?
ReplyDeleteOh I see for #14..
ReplyDeleteI have to be careful reading these problems!
Dear #5, No, the answer is D. Based on d=rt, you live (based on rate*time) 10*(264)=2640 away from school. Your friend is closer, so his d<2640, yes?
ReplyDeleteOh I see, but it says distance (in feet) on the paper..
ReplyDeletedistance = rate * time
ReplyDeleterate is distance over time, so think about it...
...when you multiply distance over time by time over 1, you have the unit of time in BOTH the numerator and denominator... time becomes a BIG FAT ONE and you are left with distance, yes?
THEREFORE you have proven:
distance = rate * time
I Gotsk it!!
ReplyDeleteI don't know how to start #30.. A proportion?
ReplyDeleteI think you are getting tired...
ReplyDelete- T is the amount of water left in the tank
- they give you an equation (function rule) with an explanation
- there are 274L of water left in the tank
- hmmm... how could you use that equation (function rule)?
wooooaaaaahhhhhh we had 66 comments???????????????????????????????????????????????????????????????????!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!???!!!?!?!?!?!?!?!?!?
ReplyDelete