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

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

More Regents problems.

Administered January 2013

Part I: Each correct answer will receive 2 credits.


1. The number of hours spent on math homework during one week and the math exam grades for eleven students in Ms. Smith’s algebra class are plotted below.

Based on the plotted data, what is the correlation between the time spent on homework and the exam grade?

(1) positive
(2) negative
(3) no correlation
(4) cannot be determind

Answer: (1) positive

The data is going up and to the right. If you draw a trend line through the data, it would have a positive slope.

2. A car uses one gallon of gasoline for every 20 miles it travels. If a gallon of gasoline costs $3.98, how much will the gas cost, to the nearest dollar, to travel 180 miles?

(1) 9
(2) 36
(3) 45
(4) 80

Answer: (2) 36

One gallon of gas for every 20 miles, then 180 miles would require 180 / 20 = 9 gallons of gas.

Each gallon is $3.98, which is approximately $4, and 4 * 9 = 36, which is Choice 2.



3. If Angelina’s weekly allowance is d dollars, which expression represents her allowance, in dollars, for x weeks?

(1) dx
(2) 7dx
(3) x + 7d
(4) d / x

Answer: (1) dx

Her allowance is per week and the number 7 (days in a week) plays not part in this problem. She earns d dollars in 1 week, 2d dollars in 2 weeks, and so on until she has xd, or dx, dollars after x weeks.

4. What is the solution of the system of equations shown in the graph below?

(1) (1, 0) and (-3, 0)
(2) (0, -3) and (0, -1)
(3) (-1, -2)
(4) (-2, -1)

Answer: (3) (-1, -2)

Choice (1) are the two x-intercepts. Choice (2) are the two y-intercepts. Choice (3) is the point where the two lines intersect, which is the solution to the system of equations. Choice (4) is the point with the reverse co-ordinates of the solution if you got the x and y order incorrect.



5. The solution of the equation 5 - 2x = -4x - 7 is

(1) 1
(2) 2
(3) -2
(4) -6

Answer: (4) -6

5 - 2x = -4x - 7
-2x = -4x - 12
2x = -12
x = -6

You also could have plug in the values to find the correct one, but in this case, you would have had to have tried all four numbers to get the correct one.

5 - 2(1) = 3, -4(1) - 7 = -11

5 - 2(2) = 1, -4(2) - 7 = -15

5 - 2(-2) = 9, -4(-2) - 7 = 1

5 - 2(-6) = 17, -4(-6) - 7 = 17.






More to come. Comments and questions welcome.

More Regents problems.