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Math B Regents Exam Questions by Type - 6 Point Free Response Page 4
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16. For a carnival game, John is painting two
circles, V and M, on a square dartboard.
a On the accompanying grid, draw and label
circle V, represented by the equation
2 2
x + y = 25, and circle M, represented by the
2 2
equation ( x− 8) + ( y+ 6)
= 4.
19. Given: A(1,6), B(7,9), C(13,6), and D(3,1)
Prove: ABCD is a trapezoid. [The use of the
accompanying grid is optional.]
b A point, (x,y), is randomly selected such
that −10 ≤ x ≤10
and −10 ≤ y ≤10
. What is
the probability that point (x,y) lies outside
both circle V and circle M?
17. Given circle O with diameter GOAL; secants
HUG and HTAM intersect at point H;
mGM : mML : m LT = 7:3:2; and chord GU ≅
chord UT. Find the ratio of m∠ UGL to
m∠ H.
20. In the accompanying diagram of ABCD,
where a ≠ b, prove ABCD is an isosceles
trapezoid.
21. Given: parallelogram ABCD, diagonal AC,
and ABE
Prove: m∠ 1>
m∠2
18. Prove that the diagonals of a parallelogram
bisect each other.
22. A farmer has determined that a crop of
strawberries yields a yearly profit of $1.50 per
square yard. If strawberries are planted on a
triangular piece of land whose sides are 50
yards, 75 yards, and 100 yards, how much
profit, to the nearest hundred dollars, would
the farmer expect to make from this piece of
land during the next harvest?