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

More Regents problems.

*Integrated Algebra Regents, January 2012*

Part I: Each correct answer will receive 2 credits.

**1.** Which expression is equivalent to 64 - x^{2}?

1) (8 - x)(8 - x)

2) (8 - x)(8 + x)

3) (x - 8)(x - 8)

4) (x - 8)(x + 8)

**Answer: 2) (8 - x)(8 + x) **

The Difference of Two Perfect Squares factors into their

**conjugates**.

Choice (1) is 64 - 16x + x^{2}

Choice (3) is x^{2} - 16x + 64

Choice (4) is x^{2} - 64, which is the inverse of what we want.

**2.** Mr. Smith invested $2,500 in a savings account that earns 3% interest
compounded annually. He made no additional deposits or withdrawals.
Which expression can be used to determine the number of dollars
in this account at the end of 4 years?

1) 2500(1 + 0.03)^{4}

2) 2500(1 + 0.3)^{4}

3) 2500(1 + 0.04)^{3}

4) 2500(1 + 0.04)^{3}

**Answer: 1) 2500(1 + 0.03) ^{4} **

The formula is A = P(1 + r)

^{t}, where r is the rate as a decimal and t is the time in years. In this example, 3% means r = 0.03 and t = 4 years.

Choice (2) has 30% interest for 4 years, which is great if you can find it.

Choice (3) has 4% interest for 3 years.

Choice (4) has 40% interest for 3 years.

**3.** What is 2√(45) expressed in simplest radical form?

1) 3√(5)

2) 5√(5)

3) 6√(5)

4) 18√(5)

**Answer: 3) 6√(5) **

Factor 45 into 9 * 5. Since 9 is a perfect square, √(9) = 3, and 2 * 3 = 6. This leaves only the factor of 5 under the radical sign.

**4.** Which graph does not represent a function?

**Answer: 3) (see image) **

Choice (3) fails the Vertical Line Test. There are values of x that have two distinct y values for outputs. You cannot have that in a function.

For example, the points (1, 1) and (1, -1) are both on the graph in Choice (3).

Choice (4) may be a piecewise graph, but it is still a function.

**5.** Timmy bought a skateboard and two helmets for a total of
d dollars. If each helmet cost h dollars, the cost of the skateboard
could be represented by

1) 2dh

2) dh/2

3) d - 2h

4) d - h/2

**Answer: 3) d - 2h **

He spent d dollars for eaverything. He spent 2h for the two helmets (they were h each). Whatever is left over must be the cost of the skateboard. So subtract d - 2h to find the skateboard.

More to come. Comments and questions welcome.

More Regents problems.

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