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Common Core Algebra I, Regents

Get the Math & the Points! Jan 2018 CC Alg I Regents #6

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Look for the point that does not make the equation true.
This is a very accessible question as all the x values in the choices are negative integers (-4, -3, -2, and -1) and will easily be found on the table.
When x = -4, y = -60 check
When x = -3, y = -24 check
When x = -2, y = -6 check
Um, when x = -1…
Most, if not all students, can build understanding of Math and critically think while gaining points to pass the Regents!  This question from January 2018 asks the student to notice the word not and to find the point that does not belong.

2 points :)

brain puzzler

March 2018 Brain Puzzler Solution

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Q: Leaving at 8:00 AM, if Ms. Brown drives at an average speed of 40 miles per hour, she will be late by 3 minutes. If she drives at an average speed of 60 miles per hour, she will be early by 3 minutes.  How many miles per hour does Ms. Brown need to drive to get to work exactly on time?

A: 48 miles per hour

There is a 6 minute difference between the fast (60 mph) speed and the slow (40 mph) speed.  This 6 minutes is 1/10 of an hour.
Distance = rate x time.  The two distances are equal so:
We can figure out how long it would take at 60 mph and go from there.
40 (t + .1) = 60 t
40t  + 4 = 60 t
4 = 20 t
4/20 = t = 1/5 hour
So it will take 1/5 hour at 60 mph which is 12 miles. (1/5 hour = 12 minutes)
It will take abit longer at 40 mph:
1/5 hour + 1/10 hour =
.2 hour + .1 hour = .3 hour at 40 mph  which is also 12 miles. (.3 hour is 18 minutes).
If Ms. Brown was exactly on time it would take her 15 minutes to go the 12 miles.
12 miles in 15 min = 48 mph.

brain puzzler

February 2018 Brain Puzzler Solution

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Q: For a calendar, with two six sided dice make all possible monthly dates using two digits  (from 01 to 31) by writing one digit (from 0, 1, 2, …, 8, 9) on each face of the two dice.
A: It does not seem like it can be done — but…the Eureka part of the answer is:
the 9 is the 6 upside and vice versa!
Dice 1: 0 1 2 4 5 7 and  Dice 2: 0 1 2 3 8 9 (9 is also 6)
or
Dice 1 : 0 1 2 3 4 5 and Dice 2 : 0 1 2 6 7 8 (6 is also 9)

Common Core Algebra I, Regents, test prep

Get the Math and the Points Jan 2018 CC Alg I #2

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Jan 2018 CC Alg I 2
Two questions to ask:
1. Does V(x) grow or decay?
2. When putting 4(0.65)^x vs 4(1.35)^x into the Y= of the TI-83/4, does the table look like the one above?
Hopefully the student will know that the number in parentheses (the growth/decay factor) determines if it is growth or decay but through the graphing calculator, they can figure it out, get the right answer and earn 2 points!

brain puzzler

January 2018 Brain Puzzler Solution

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Q: What is the sum of the digits of the square of $111,111,111$?

A: 81
Using the standard multiplication algorithm, $111,111,111^2=12,345,678,987,654,321,$whose digit sum is 81.

Or by looking at the pattern:

$11^2 = 121 \\ 111^2 = 12321 \\ 1111^2 = 1234321$

$111,111,111^2=12,345,678,987,654,321$ whose digit sum is 81
There is a shortcut to adding these digits
Reading from left to right, we can add the first 8 digits, 1 through 8 by making 4 pairs of 9 (1 + 8, 2 + 7, 3 + 6 and 4 + 5) making 36
Reading from right to left, we can add the last 8 digits (1- 8) the same way making 36.
Leaving the middle digit of 9.

36 + 36 + 9 = 81