Monday, May 24, 2021

Algebra Problems of the Day (Integrated Algebra Regents, June 2013)

And now for something completely different.

While I'm waiting for new Regents exams to come along, I revisiting some of the older NY Regents exams.

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


1. Which expression represents “5 less than twice x”?

(1) 2x - 5
(2) 5 - 2x
(3) 2(5 - x)
(4) 2(x - 5)

Answer: (1) 2x - 5
If you have "5 less than" something, then you are taking 5 away from that something.
If I have "5 less dollars" than you, and you have $20, then I would have 20 - 5 = 15.





2. Gabriella has 20 quarters, 15 dimes, 7 nickels, and 8 pennies in a jar. After taking 6 quarters out of the jar, what will be the probability of Gabriella randomly selecting a quarter from the coins left in the jar?

(1) 14/44
(2) 30/44
(3) 14/50
(4) 20/50

Answer: (1) 14/44
There were originally 50 coins in the jar and 20 of them were quarters. However, 6 coins were removed from the jar, meaning that there are only 44 coins remaining. All of the coins that were removed were quarters, so the number of quarters has dropped from 20 to 14.

That means the probability is 14/44.



3.Based on the line of best fit drawn below, which value could be expected for the data in June 2015?



(1) 230
(2) 310
(3) 480
(4) 540

Answer: (3) 480
If you go to June 2015 on the graph and go up to the line, you will reach a point that is just below the 500 level. This makes 480 the best choice.





4.If the point (5,k) lies on the line represented by the equation 2x + y = 9, the value of k is

(1) 1
(2) 2
(3) -1
(4) -2

Answer: (3) -1
Substitute 5 and k in for x and y in the equation. Then solve for k.

2(5) + k = 9
10 + k = 9
k = -1




5. A soda container holds 5 1/2 gallons of soda. How many ounces of soda does this container hold?
1 quart = 32 ounces
1 gallon = 4 quarts


(1) 44
(2) 176
(3) 640
(4) 704

Answer: (4) 704
Convert the units
5.5 gallons = 5.5 (4 quarts) = 5.5 (4) (32 ounces) = 704



More to come. Comments and questions welcome.

More STAAR problems.

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