Algebra Problems of the Day (Integrated Algebra Regents, June 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, June 2011

Part I: Each correct answer will receive 2 credits.


16. Which set of ordered pairs represents a function?

1) {(0,4), (2,4), (2,5)}
2) {(6,0), (5,0), (4,0)}
3) {(4,1), (6,2), (6,3), (5,0)}
4) {(0,4), (1,4), (0,5), (1,5)}

Answer: 2) {(6,0), (5,0), (4,0)}

Any set of ordered pairs can be a function so long as none of the x values (the inputs) repeat.

In Choice (1), x = 2 repeats. Eliminate Choice (1).

In Choice (2), none of the x value repeat. The y values repeat, but this is allowed. This is the correct answer.

In Choice (3), x = 6 repeats. Eliminate Choice (3).

In Choice (4), x = 0 and x = 1 both repeat. Eliminate Choice (4).

17. A hiker walked 12.8 miles from 9:00 a.m. to noon. He walked an additional 17.2 miles from 1:00 p.m. to 6:00 p.m. What is his average rate for the entire walk, in miles per hour?

1) 3.75
2) 3,85
3) 4.27
4) 7.71

Answer: 1) 3.75

He waled a total of 12.8 + 17.2 = 30 miles. He walked for a total of 3 + 5 = 8 hours.

His average rate of speed was 30/8 = 3.75.

18. Which ordered pair is a solution of the system of equations y = x + 3 and y = x² − x?

1) (6,9)
2) (3,6)
3) (3,-1)
4) (2,5)

Answer: 2) (3,6)

Eliminate Choice (3) immediately because 3 + 3 =/= -1.

You can solve the system of equations or you can just check if the points are solutions to the quadratic equation.

(6)² - 6 = 30 =/= 9. Eliminate Choice (1).

(3)² - 3 = 6. Choice (2) is the correct answer.

(2)² - 2 = 2 =/= 5. Eliminate Choice (4).

19. Which verbal expression can be represented by 2(x − 5)?

1) 5 less than 2 times x
2) 2 multiplied by x less than 5
3) twice the difference of x and 5
4) the product of 2 and x, decreased by 5

Answer: 3) twice the difference of x and 5

The verbal expressions are translated below:

Choice (1) says 2x - 5.

Choice (2) says 5 - 2x. (It doesn't say 2(5 - x), but that isn't correct either.)

Choice (3) says 2(x - 5). This is the answer.

Choice (4) says 2x - 5 with the comma removing any ambiguity.

20. The dimensions of a rectangle are measured to be 12.2 inches by 11.8 inches. The actual dimensions are 12.3 inches by 11.9 inches. What is the relative error, to the nearest ten-thousandth, in calculating the area of the rectangle?

1) 0.0168
2) 0.0167
3) 0.0165
4) 0.0164

Answer: 3) 0.0165

Relative error is the difference between the two values divided by the actual value.

The difference between the two values is (12.3 * 11.9) - (12.2 * 11.8) = 2.41

2.41 / (12.3 * 11.9) = 0.016465... = 0.0165.

You could have done this in your calculator in one step, as long as you were careful with the parentheses. You also could have found the areas of the two rectangles, but if you're using a calculator anyway, there isn't a need since this is a multiple-choice question. Work doesn't need to be shown.

More to come. Comments and questions welcome.

More Regents problems.

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