Saturday, September 13, 2014

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=?

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

Solution: 96 has 6 pairs of factors ---
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
Common name for √v?

(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=2, the stand dev.
√v gives a measure of how dispersed the data is from the mean...

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