Thursday, November 18, 2021

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.

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 = 2x + 1 - 3.

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.

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.

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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