Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2012)

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!

₂₅C₂₀ = ₂₅C₅ =

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 r². 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.

r² = (-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 = r², 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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