Type - JMap

Math B Regents Exam Questions by Type - 6 Point Free Response Page 2
www.jmap.org
6. On a monitor, the graphs of two impulses are
recorded on the same screen, where
0°≤ x < 360°
. The impulses are given by the
following equations:
2
y = 2sin
x
y = 1−sinx
Find all values of x, in degrees, for which the
two impulses meet in the interval
0°≤ x < 360°
. [Only an algebraic solution
will be accepted.]
9. Jim is experimenting with a new drawing
program on his computer. He created
quadrilateral TEAM with coordinates T(-2,3),
E(-5,-4), A(2,-1), and M(5,6). Jim believes
that he has created a rhombus but not a
square. Prove that Jim is correct. [The use of
the grid is optional.]
7. The coordinates of quadrilateral JKLM are
J(1,-2), K(13,4), L(6,8), and M(-2,4). Prove
that quadrilateral JKLM is a trapezoid but not
an isosceles trapezoid. [The use of the grid is
optional.]
10. When Joe bowls, he can get a strike (knock
down all the pins) 60% of the time. How
many times more likely is it for Joe to bowl at
least three strikes out of four tries as it is for
him to bowl zero strikes out of four tries?
Round your answer to the nearest whole
number.
8. The accompanying table illustrates the
number of movie theaters showing a popular
film and the film's weekly gross earnings, in
millions of dollars.
Write the linear regression equation for this
set of data, rounding values to five decimal
places.
Using this linear regression equation, find the
approximate gross earnings, in millions of
dollars, generated by 610 theaters. Round
your answer to two decimal places.
Find the minimum number of theaters that
would generate at least 7.65 million dollars in
gross earnings in one week.
11. A ship captain at sea uses a sextant to sight an
angle of elevation of 37° to the top of a
lighthouse. After the ship travels 250 feet
directly toward the lighthouse, another
sighting is made, and the new angle of
elevation is 50°. The ship's charts show that
there are dangerous rocks 100 feet from the
base of the lighthouse. Find, to the nearest
foot, how close to the rocks the ship is at the
time of the second sighting.