Type - JMap

Math B Regents Exam Questions by Type - 4 Point Free Response Page 2
www.jmap.org
8. A student attaches one end of a rope to a wall
at a fixed point 3 feet above the ground, as
shown in the accompanying diagram, and
moves the other end of the rope up and down,
producing a wave described by the equation
y = asin
bx+
c. The range of the rope's
height above the ground is between 1 and 5
feet. The period of the wave is 4π . Write
the equation that represents this wave.
9. In the interval 0°≤ A ≤ 360°
, solve for all
values of A in the equation
cos2A=−3sin A−1.
10. Sean invests $10,000 at an annual rate of 5%
compounded continuously, according to the
formula A= Pe rt , where A is the amount, P is
the principal, e = 2.718, r is the rate of
interest, and t is time, in years.
Determine, to the nearest dollar, the amount
of money he will have after 2 years.
Determine how many years, to the nearest
year, it will take for his initial investment to
double.
11. As shown in the accompanying diagram, two
tracking stations, A and B, are on an east-west
line 110 miles apart. A forest fire is located
at F, on a bearing 42° northeast of station A
and 15° northeast of station B. How far, to
the nearest mile, is the fire from station A?
12. An archaeologist can determine the
approximate age of certain ancient specimens
by measuring the amount of carbon-14, a
radioactive substance, contained in the
specimen. The formula used to determine the
5760
age of a specimen is A=
A0
2 , where A is
the amount of carbon-14 that a specimen
contains, A 0
is the original amount of carbon-
14, t is time, in years, and 5760 is the half-life
of carbon-14.
A specimen that originally contained 120
milligrams of carbon-14 now contains 100
milligrams of this substance. What is the age
of the specimen, to the nearest hundred
years?
13. At the local video rental store, José rents two
movies and three games for a total of $15.50.
At the same time, Meg rents three movies and
one game for a total of $12.05. How much
money is needed to rent a combination of one
game and one movie?
14. Two straight roads, Elm Street and Pine
Street, intersect creating a 40° angle, as
shown in the accompanying diagram. John's
house (J) is on Elm Street and is 3.2 miles
from the point of intersection. Mary's house
(M) is on Pine Street and is 5.6 miles from the
intersection. Find, to the nearest tenth of a
mile, the direct distance between the two
houses.
−t