Sample Solutions to Recent Twitter CCSS/SAT Problems

The following is copied from solutions I sent today to my mail list of those who have opted for free solutions for the rest of September...

Yes, I've been giving these away for weeks now. Hard to believe anyone would do this? There must be a catch, right?

I will continue this until the 30th then am considering a low fee subscription for the rest of the school year.

Subscribers will get detailed solutions which include strategies, big ideas, extensions, etc. Further I may include additional problems which will not appear on Twitter or this blog.

To sign up, provide all pertinent info in the Blogger Contact Form in the sidebar.

1. Rectangle has integer sides and area=96
(a) How many possible perimeters?
(b) Greatest perim? Least? L=? W=?

Answers
(a) 6
(b) Greatest perim:194; Least:40

Solution: 96 has 6 pairs of factors ---
1,96:2,48;3,32;4,24;6,16;8,12
Each pair has a different sum so there are 6 possible perimeters.
The greatest and least possible occur in the extreme cases, i.e., when the factors are farthest and closest apart. This is generally true.

Note: If integer condition is removed there would be no greatest perimeter and the least would be 16√6, a square!

2. Data:4,6;mean:5
(a) Avg diff from mean= ((4-5)+(6-5))/2=?
(b) v=((4-5)^2+(6-5)^2)/2=?
(c) √v=?
(d)Repeat for 3,7
Obs,Conj?
Common name for √v?

Answers
(a) 0
Note: This is always true -- the avg difference or deviation from the mean is zero! This is why we square the differences to measure deviation!
(b) v=1
Note: The avg of the squared "deviations" from the mean is called the variance.
(c) √v=1
Note: The square root of the variance is called the standard deviation!
(d) For 3,7 ---
Mean is still 5
v=(4+4)/2=4
√v=2, the stand dev.
√v gives a measure of how dispersed the data is from the mean...

Six more Free Twitter CCSS/SAT questions...

Free Twitter CCSS/SAT Problems with complete solutions sent to your inbox ending in 18 days on 9-30-14. You know what you have to do...

1. List in order the ten 5-digit pos int containing 3 nines & 2 eights?
Explain connection to 5C2.
Is this open-ended?

2. The median of 100 different integers is 100. If the numbers are in increasing order and the 50th # is 83 what is the 51st #? Explain/show...

3. Rectangle has integer sides and area=96
(a) How many possible perimeters?
(b) Greatest perim? Least? L=? W=?

4. Data:4,6;mean:5
Avg diff from mean= ((4-5)+(6-5))/2=?
v=((4-5)^2+(6-5)^2)/2=?
√v=?
Repeat for 3,7
Obs,Conj?
Common name for √v?

5. From the brilliant #xkcd...

Sneeze droplet: 200 million germs. Hand sanitizer kills 99.99%. How many live? No calculator-15 seconds!

6. Least positive odd integer with 8 factors?
Strategy: Make it ____
2 factors:3
4: 15 or 3×5
Generalize!

Seven More CCSS/SAT Twitter Math Challenges

Free solutions sent to your inbox?
Only 3 wks left...
http://mathnotations.blogspot.com/2014/08/free-ccsssatchallenge-math.html

1. Circle has center (0,0), radius 2. Line y=1 intersects circle at P and Q. PQ=?
(A)1 (B)√3 (C)2 (D)2√2 (E)2√3

2.
(a) On a number line, how many positive integers are "closer" to 500 than to 1000?
b) Express the condition in (a) as an inequality using absolute values.

3. If the avg of 2 #'s is n, n>0, and the smaller # is 25% of the larger, the smaller # is what % of n?

4. For how many numbers x is the square of x equal to the opposite of x?

5. For how many integer values of x is |50-x| < 10?

6. A set of integers, T, has the property that if x is in T then x^2-1 is also in T. What is the least possible number of #'s in T?

7. Three-eighths of a candle's material remains after burning for 8 hrs. At this rate how many hrs for the rest to melt?

MathNotations Passionate View of the Common Core Controversy

Despite all the backlash against the Common Core, I am deeply committed to raising the bar for all students. The Common Core is an important step in this direction. I may have deep concerns about implementation and assessment, but I have no significant concerns about the quality, appropriateness and importance of the Core math standards and, in particular, the Eight Mathematical Practices.

Those states that are now defending their pre-CCSS standards are forgetting that the Common Core was developed by these states and approved by these states, not the Federal Government. The Common Core was a response to the fact that our students have been falling behind a majority of industrialized nations, particularly in math and science. The future of our children is at stake.

We need to stop the political rhetoric and do what's right for our children. Raise concerns about assessments and the timetable. You should. But remember this. On every international comparison our students have been performing at a mediocre level. That's reality. If there were no problem we wouldn't need to fix it. But there is a problem...

My commitment to our children and our teachers has been demonstrated by giving away hundreds of free higher-order math problems on this blog and on twitter for years now.

But implementation of CCSS will take the commitment of everyone. Or like every other educational initiative it will fail. But this time, if this fails, we will be failing our children. Hyperbole? Just check our nation's performance on international comparisons...

IMPLEMENTING THE CORE: Twitter SAT/CCSS/COORDINATE GEOMETRY Problem

Circle has center (0,0), radius 2. Line y=1 intersects circle at P and Q. PQ=?

(A)1 (B)√3 (C)2 (D)2√2 (E)2√3

I'm sorry to keep reminding my readers that free detailed solutions to all current Twitter problems can be sent to your inbox if you request it via Blogger Contact Form.

As any of my followers know, I've posted hundred of free problems on my blog and on Twitter for a very long time. However I have omitted answers and solutions to many of these.

For the past month I have offered to send free detailed solutions of these to your inbox if requested.  I will continue to do so until the end of this month. After that I will continue to post problems but solutions will be available only via paid subscription.

NOTE WELL:
In addition to solutions those on the mailing list can confirm that I'm also including alternate methods and specific references to the Mathematical Practices of the Common Core and strategies for implementing CCSS. This is my commitment to our teachers and our children.

Free Twitter CCSS/SAT Problems/Solutions ending on 9-30

Right now it's still free to have these sent to your inbox. Blogger Contact Form must be filled out with all requested info. See http://mathnotations.blogspot.com/2014/08/free-ccsssatchallenge-math.html

After that date by subscription only...

More Recent Twitter Problems (twitter.com/dmarain)

1. Right circ cylinder: base circumf 16π. If greatest distance between bases=20, volume =kπ, k=?
Ans:768
Soln?

2. #ImplementTheCore

Median of 1st 1000 pos even int's?
Name of strategy one could use?

Free soln?

3. If area between 2 concentric circles=area of smaller circle then Larger radius:Smaller radius=?
Ans: √2:1
Free soln to inbox?

4.
2^100-1 must be div by
I. 2^10-1
II. 2^50-1
III. 2^50+1
(A)I (B)II (C)I,II (D)II,III (E)I,II,III
Soln?
http://mathnotations.blogspot.com/2014/08/free-ccsssatchallenge-math.html

Sometimes "free" actually means free!

Update on Free Solutions to Problems

Based on response thus far I am restricting emails to Solutions of the Twitter problems I post @dmarain.

The opportunity to be added to the mail list and have free solutions sent to you is limited.  Pls include all requested info - see link below...

http://mathnotations.blogspot.com/2014/08/free-ccsssatchallenge-math.html

IMPLEMENT THE CORE-SIX Twitter/CCSS/SATPREP Math Questions to Start the Year

From Twitter (@dmarain)...

Want free answers solutions/discussion sent to your inbox?
http://mathnotations.blogspot.com/2014/08/free-ccsssatchallenge-math.html

1. Reg price:$N
40% discount $32 better than successive disc of 20%,20%
N=?
Want ans/soln/details/discussion sent to inbox?

2.
2^100-1 must be div by
I. 2^10-1
II. 2^50-1
III. 2^50+1
(A)I (B)II (C)I,II (D)II,III (E)I,II,III
Soln?

3.
Need  quarters&dimes for 35¢ bus fare. Asked bank for most I could get from $10. How many dimes did I get?
Soln?

4.
(3/a)•(3/(a-12)) = -1
a=?

Relate this equation to a coord problem involving a right angle!

Want answer/solution/details?

5.
Mork's age
O-yrs  46   90  
E-yrs   1     10
When O-age:E-age=5:1, E-age=? (Assume linear)
Soln sent to inbox?

6. Inscribe a circle of rad=1 in a reg hexagon and inscribe a 2nd reg hex in the circle. Show that the avg of the areas of the hex's = (7√3)/4.
What does this have to do with π?