Monday, July 26, 2021

Algebra Problems of the Day (Integrated Algebra Regents, August 2012)



Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

August 2012

Part I: Each correct answer will receive 2 credits.


11. Is the equation A 21000(1 - 0.12)t a model of exponential growth or exponential decay, and what is the rate (percent) of change per time period?
1) exponential growth and 12%
2) exponential growth and 88%
3) exponential decay and 12%
4) exponential decay and 88%

Answer: 3) exponential decay and 12%


There is 12% decay, which will leave you with 88% of the original amount.

You know it is decay because of the minus sign, telling you that you will have less than 100% (the full amount) after the first time period.





12. The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used to find the longest possible width?
1) 30 + 2w < 50
2) 30 + 2w < 50
3) 30 + 2w > 50
4) 30 + 2w > 50

Answer: 2) 30 + 2w < 50


We are looking for the longest, meaning that there is a maximum number. All of the possibilities have to be LESS THAN that amount. Eliminate Choices (3) and (4).

The words "at most" 50 tell you that it can equal 50, so you want LESS THAN OR EQUAL TO.





13. Craig sees an advertisement for a car in a newspaper. Which information would not be classified as quantitative?
1) the cost of the car
2) the car's mileage
3) the model of the car
4) the weight of the car

Answer: 3) the model of the car


If you were unsure about quantitative vs qualitative, then this would be a good time to play "One of these things is NOT like the others".

Three of the four choices are numerical data and things that can be measured in dollars, miles and pounds. One of them is an arbitrary name given to the car, which is a description for the car.





14. What are the coordinates of the vertex and the equation of the axis of symmetry of the parabola shown in the graph below?


1) (0,2) and y = 2
2) (0,2) and x = 2
3) (-2, 6) and y = -2
4) (-2, 6) and x = -2

Answer: 4) (-2, 6) and x = -2


The vertex of a parabola is the turning point. It is either the maximum or the minimum point (and a parabola will only have one of those). In this example, the topmost point occurs at (-2, 6).

The axis of symmetry is a vertical line that, if drawn, would cut the parabola in half, creating two mirror images. The axis goes through the vertex.

The equation for all vertical lines is x = a, and every point on that line will be (a, y) for whatever value of y. The x coordinate of the vertex is -2.





15. A correct translation of “six less than twice the value of x” is
1) 2x < 6
2) 2x - 6
3) 6 < 2x
4) 6 - 2x

Answer: 2) 2x - 6


Do NOT confuse "less than" (subtraction) with "IS less than" (inequality).

Eliminate Choices (1) and (3) for using the < symbol instead of subtraction.

If my height is three inches less than your height, and your height is 68 inches, would you find my height by doing 68 - 3 or 3 - 68? The latter choice is ridiculous because it would give me a negative height.

"Six less than" something means "take six away from" something, and the something has to be there first to take something away from it.




More to come. Comments and questions welcome.

More Regents problems.

No comments:

Post a Comment