Algebra Problems of the Day (Integrated Algebra Regents, August 2010)

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, August 2010

Part I: Each correct answer will receive 2 credits.


21. What is the value of the y-coordinate of the solution to the system of equations 2x + y = 8 and x − 3y = −3?

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

Answer: 2) 2

Solve the system of equations.

2x + y = 8
x - 3y = -3
-2x + 6y = 6

7y = 14

y = 2

Choice (2) is the solution.

You could also solve by substitution:

y = -2x + 8

x - 3(-2x + 8) = -3

x + 6x - 24 = -3

7x = 21

x = 3

2(3) + y = 8

y = 2

22. Which set-builder notation describes {-3,-2,-1,0,1,2}?

1) {x|−3 ≤ x < 2, where x is an integer}
2) {x|−3 < x ≤ 2, where x is an integer}
3) {x|−3 < x < 2, where x is an integer}
4) {x|−3 ≤ x ≤ 2, where x is an integer}

Answer: 4) {x|−3 ≤ x ≤ 2, where x is an integer}

Both -3 and 2 are in the set, so "≤" needs to be used both times.

Choice (1) leaves out 2. Choice (2) leaves out -3. Choice (3) leaves out both of them. Choice (4) includes both of them.

23. Corinne calculated the area of a paper plate to be 50.27 square inches. If the actual area of the plate is 55.42 square inches, what is the relative error in calculating the area, to the nearest thousandth?
1) 0.092
2) 0.093
3) 0.102
4) 0.103

Answer: 2) 0.093

Relative error is the difference from the actual value divided by the actual value. Leave it as a decimal. Do NOT change it into a percentage.

(55.42 - 50.27) / 55.42 = 0.09292..., or 0.093.

Round correctly. The answer is Choice (2).

24. The probability that it will snow on Sunday is 3/5.The probability that it will snow on both Sunday and Monday is 3/10. What is the probability that it will snow on Monday, if it snowed on Sunday?

1) 9/50
2) 2
3) 1/2
4) 9/10

Answer: 3) 1/2

Probability cannot be 2. Elimnate Choice (2). (It cannot be greater than 1.)

The compound probability is equal to the product of the two individual probabilities: 3/5 * P = 3/10.

P = 3/10 / (3/5) = 3/10 * 5/3 = 15/30 = 1/2

25. Which graph represents an exponential equation?

Answer: 4) [See Image]

An exponential graph starts nearly horizontally and increases rapidly, or decreases from infinity rapidly and becomes nearly horizontal. This is Choice (4).

Choice (1) is a linear equation.

Choice (2) is an absolute value equation.

Choice (3) is a quadratic equation. (A parabola.)

More to come. Comments and questions welcome.

More Regents problems.

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