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

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

More Regents problems.

Administered June 2013

Part I: Each correct answer will receive 2 credits.


11. The solutions of x² = 16x - 28 are

(1) -2 and -14
(2) 2 and 14
(3) -4 and -7
(4) 4 and 7

Answer: (2) 2 and 147
Rewrite x² = 16x - 28 with all the terms on one side and solve the equation by factoring.

x² = 16x - 28
x² - 16x + 28 = 0
(x - 2)(x - 14) = 0
x - 2 = 0 and x - 14 = 0
x = 2 and x = 14

Notice that -28 would have factored into -2 and 14 or 2 and -14. Luckily, neither of those were choices if you had made that mistake with the sign.

12. If the expression (2y^a)⁴ is equivalent to 16y⁸, what is the value of a?

(1) 12
(2) 2
(3) 32
(4) 4

Answer: (2) 2
If (2y^a)⁴ = 16y⁸ then 16y^4a = 16y⁸. That means that 4a = 8, and a = 2.

Remember that the exponent of 4 is applied to everything inside the parentheses, and that the rule for raising a power to a power is to multiply the exponents.



13. Which table shows bivariate data?

Answer: (2)
Bivariate means that you are measuring two kinds of data. In choice (1), only Age is being measured and the frequency of each number is listed. In choices (3) and (4), Type of Car and Day are qualitative, and cannot be measured. You could make bar graphs from these but you couldn't make a histogram out of it.

14. The box-and-whisker plot below represents the results of test scores in a math class.

What do the scores 65, 85, and 100 represent?

(1) Q1, median, Q3
(2) Q1, Q3, maximum
(3) median, Q1, maximum
(4) minimum, median, maximum

Answer: (2) Q1, Q3, maximum
According to the graph, the minimum is 20, Q1 is about 65, the median is about 72, Q3 is about 85, and the maximum is 100. Since the questions asks about 65 and 85, we can assume these are Q1 and Q3. We can't tell exactly what value the median has, but it's in the low 70s, and it isn't put of the question.



15. The expression (x - 3) / (x + 2) is undefined when the value of x is

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

Answer: (1) -2, only
The denominator of a fraction cannot have a value equal to 0. The numerator is allowed to be 0. This is because you can divide 0 by any number -- if you split 0 four ways, each person gets 0. However, you cannot divide by 0. You cannot divide 4 zero ways.

So x + 2 =/= 0. Therefor x =/= -2.



More to come. Comments and questions welcome.

More STAAR problems.