Regents Practice TEST 2
Interactive Version - Long Response

Algebra 2 Trigonometry Level

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Directions:  These are the Part II, III, and IV long response questions.  Have paper ready to work out the problems, then check your answers by clicking the ANSWER button.  You may use your graphing calculator.

Part II:

28   Find the roots of  x2 + 7 = 2x  and express the roots in a + bi form.



for all values of x for which the expression is defined and express your answer in simplest form.                      

30  Write the equation of a circle with a center at (-3, -6) and which passes through the point (-4, 8).
31  The arc of a circle is 6 cm. in length and intercepts a central angle of 1.5 radians.  Find the number of centimeters in the radius of the circle.
32  The number of houses in Pleasantville grows every year according to the function   where H represents the number of houses, and t represents the number of years since the start of 1995.  A developer wants to know when the number of houses exceeds 1,000.  During which year will this first happen?                                  
33  If the probability that it will rain on any given day this week is 60%, find the probability it will rain exactly 3 out of 7 days this week.  
34  Simplify the expression   (1 - cos2 x)(csc x)  to a single trigonometric function.            
35  Solve for x:                                     

Part III:

36  A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach.  The chart below shows a random sample of sales and location data.

Write a linear equation that relates the price of the cottage to the distance form the beach.

Use the equation to predict the price of a cottage, to the nearest dollar, located 3 blocks from the beach.

Number of Block
from Beach (x)
Price of
Cottage (y)
5 $132,000
0 $310,000
4 $204,000
2 $238,000
1 $275,000
7 $60,800
37  The measure of the angles between the resultant and two applied forces are 65 and 42, and the magnitude of the resultant is 24 pounds.  Find, to the nearest pound, the magnitude of the larger force.                             


 38  Solve the equation x3 − 5x2 − 4x + 20 = 0 algebraically for all values
       of x.

Part IV:

39    A vertical flagpole 46 feet high is placed on top of a building.  From a point on the ground level with the base of the building, the angle of elevation of the top of the flagpole and the angle of elevation of the bottom of the flagpole are 40 and 32 respectively.  Sketch a diagram to represent the building, the flagpole, and the two angles, and find the height of the building to the nearest foot.


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