Algebra Problems of the Day (Integrated Algebra Regents, January 2011)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones. The Integrated Algebra Regents covered most of the same material as the current Algebra Regents, with a few differences.

More Regents problems.

Integrated Algebra Regents, January 2011

Part II: Each correct answer will receive 2 credits. Partial credit is available.


31. Roberta needs ribbon for a craft project. The ribbon sells for $3.75 per yard. Find the cost, in dollars, for 48 inches of the ribbon.

Answer:

Either convert 48 inches to yards, or convert $/yard to $/inch.

There are 36 inches in on 1 yard, so 48 inches is 48/36 or 4/3 yards.

(4/3)(3.75) = $5.00. Yes, you can multiply fractions and decimals.

Doing it the other way:

There are 36 inches in 1 yard, so ribbon sells for $3.75/36 per inch or 0.10416666... per inch. (You only need a few decimals to avoid the rounding error.

(0.104166666)(48) = 4.999999968, which rounds to $5.00.

32. The square dart board shown below has a side that measures 40 inches. The shaded portion in the center is a square whose side is 15 inches. A dart thrown at the board is equally likely to land on any point on the dartboard.

Find the probability that a dart hitting the board will not land in the shaded area.

Answer:

The area that isn't shaded is equal to th area of the entire board minus the area that is shaded.

Area of the board is 40² = 1600. The shaded area is 15² = 225.

The non-shaded area is 1600 - 225 = 1375.

So the probability that the dart will not land in the shaded area is 1375/1600. You can simplify it, but it isn't necessary. To simplify, divide by 25/25 and you'll get 55/64. If you make a mistake, or write a rounded decimal value, you will lose one of the two points, so be careful.

33. As shown in the diagram below, a ladder 5 feet long leans against a wall and makes an angle of 65° with the ground. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.

Answer:

The ladder forms the hypotenuse of the right triangle. The distance from the wall to the base of the ladder is the side adjacent to the angle. Adjacent and hypotenuse mean that we need to use the cosine.

cos 65^o = x / 5

x = 5 * cos 65^o = 2.113... or 2.1 feet.

If you got a negative answer, first you should realize that a negative distance is impossible. Second, you should realize that your calcluator is radians mode. Switch to to Degrees.

End of Part II.

More to come. Comments and questions welcome.

More Regents problems.

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