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 2012*

Part II: Each correct answer will receive 2 credits. Partial credit is available.

**32.** A blood bank needs twenty people to help with a blood drive. Twenty-five people have
volunteered. Find how many different groups of twenty can be formed from the twenty-five
volunteers.

**Answer: **

Since the order is not important, this is a combination question, not a permutation question. With combinations, the number of ways that 20 could be chosen out of 25 is the same as the number of ways that 5 could NOT be chosen out of 25.

Both of these numbers can be found in the 25th row of Pascal's triangle, but you wouldn't see a triangle that large -- the numbers in the center would be huge!

_{25}C_{20} = _{25}C_{5} =

__25 * 24 * 23 * 22 * 21 __

5 * 4 * 3 * 2 * 1

= 53130

**33.** On the axes below, for -2 __<__ x __<__ 2, graph y = 2^{x + 1} - 3.

**Answer: **

Graph the exponential function.

*DO NOT*go beyond -2 or 2. Only graph the domain that was asked for. No arrows.

You can use your graphing calculator to find the points to plot: (-2,-2.5) (-1,2), (0,-1), (1,1), (2, 5)

**34.** Write an equation of the circle shown in the diagram below.

**Answer: **

Use the distance formula or Pythagorean Theorem to find

**. Note that you don't need to find the exact radius, so you don't have to take any square roots or simplify any radicals.**

*r*^{2}r^{2} = (-8 - -5)^{2} + (4 - 2)^{2} = (-3)^{2} + (2)^{2} = 9 + 4 = 13

The equation for a circle is (x - h)^{2} + (y - k)^{2} = r^{2}, where (h,k) is the center. Note that there are minus signs in the formula so the signs of the coordinates are flipped.

So the equation is **(x + 5) ^{2} + (y - 2)^{2} = 13**.

**35.** Express the exact value of csc 60°, with a rational denominator.

**Answer: **

Coseceant is 1/sine and sine 60 degrees is √(3)/2.

csc = 1/sin 60 = 1/(√(3)/2) = 2/√(3) = **2√(3) / 3 **

More to come. Comments and questions welcome.

More Regents problems.

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