Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2014)

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

More Regents problems.

Algebra 2/Trigonometry Regents, January 2014

Part I: Each correct answer will receive 2 credits.


1. What is the common difference in the sequence
2a + 1, 4a + 4, 6a + 7, 8a + 10, ...?

1) 2a + 3
2) -2a - 3
3) 2a + 5
4) -2a + 5

Answer: 1) 2a + 3

Look at the difference in each term of each binomial in each term of the sequence.

The a term has its coefficient increasing by 2. The constant term is increasing by 3.

2. Which expression is equivalent to (3x²)^-1?

1) 1 / 3x²
2) -3x²
3) 1 / 9x²
4) -9x²

Answer: 1) 1 / 3x²

An exponent of -1 means that you want the reciprocal of the expression getting the exponent. In this case, it's everything inside the parentheses.

The exponent of 2 is ONLY applied to the variable next to it, but not the 3 because there are no parentheses around 3x.

3. If g(x) = 1/2 x + 8 and h(x) = 1/2 x - 2, what is the value of g(h(-8))?

1) 0
2) 9
3) 5
4) 4

Answer: 3) 5

Find the value of h(-8). Take that value and use it as the input of g(x).

h(-8) = 1/2 (-8) - 2 = (-4) - 2 = -6

g(-6) = 1/2 (-6) + 8 = (-3) + 8 = 5

4. The expression 1 / (7 - SQRT(11)) is equivalent to
1) (7 + SQRT(11)) / 38
2) (7 - SQRT(11)) / 38
3) (7 + SQRT(11)) / 60
4) (7 - SQRT(11)) / 60

Answer: 1) (7 + SQRT(11)) / 38

To rationalize the denominator, multiply it by the conjugate. And if you multiply the denominator by the conjugate, you have to multiply the numerator by it as well.

1 / (7 - SQRT(11)) * (7 + SQRT(11)) / (7 + SQRT(11))
= (7 + SQRT(11)) / ((7 - SQRT(11))(7 + SQRT(11))
= (7 + SQRT(11)) / (49 - (SQRT(11)²)
= (7 + SQRT(11)) / (49 - 11)
= (7 + SQRT(11)) / 38

5. The expression (a + b/c) / (d - b/c) is equivalent to

1) (c + 1) / (d - 1)
2) (a + b) / (d - b)
3) (ac + b) / (cd - b)
4) (ac + 1) / (cd - 1)

Answer: 3) (ac + b) / (cd - b)

Multiply the fraction by (1 / c) / (1 / c)

(a + b/c) / (d - b/c) * (1 / c) / (1 / c)

= (ca + b) / (cd - b)

Since there is a minus sign in the formula, subtracting -5 is the same as ADDING 5.

More to come. Comments and questions welcome.

More Regents problems.

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