PRE-CALCULUS PERFORMANCE TASK #2
FIRST GRADING, 1st SEMESTER
This is a 30 - point group work. The group will be composed of 5 members (Remember CBL
students group among themselves, same with OBL students.) You may communicate through
whatever is convenient for you.
Instructions:
•
Write your output on clean sheets (3) of short bond paper with half inch margin on all
sides. Write 2 numbers for each sheet of paper.
•
Names of each member should be written below the top margin, on the left hand corner
and on each page. Write the class number, family name first. Write your grade and section after
the names. On the right hand corner, write the course name, Performance Task #, grading period.
Names
Pre - Calculus
12 STEM (section)
Grading Period (1st or 2nd )
Performance Task #
•
Everything should be handwritten with blue or black ink. Illustrations may be drawn using
pencil.
Perfect score will be given for neat and complete solution and correct answer. Outputs with
erasures, untidy and not properly handwritten, and did not follow instructions will be given 2 points
(each) deduction from the final score.
Solve what is asked from the given situations. (6 points each)
Illustrate and label properly the given data (2 points)
then solve showing all pertinent solutions (3 points).
Write your final answer in complete sentence (1 point).
Do not forget to write the units for the final answer where ever possible.
1. A cable of a suspension bridge hangs in the form of a parabola when the load is uniformly
distributed horizontally. The distance between two towers is 150 meters, the point of support of
the cable on the towers are 22 meters above the roadway, and the lowest point on the cable is 7
meters above the roadway. Find the vertical distance to the cable from a point in the roadway 15
meters from the foot of the tower.
2. In order to hear what is said in a football huddle, a listening device is set up on the sideline. It
consists of a parabolic dish with a microphone at its focus. The dish is 4 feet across and 16 inches
deep. Give an equation for the parabola with vertex at the origin and the parabola, opening to the
right. At what point should the microphone be placed? (answer should be in inches)
3. The earth moves in an elliptic orbit about the sun, with the sun at one focus. The least and
greatest distances of the earth from the sun are 91,446,000 miles and 94,560,000 miles
respectively. How long are the major and minor axes?
Challenge yourself: (6 points)
4. Global Positioning System (GPS) is a satellite-based navigation system made up of more than
20 satellites. Each satellite transmits a unique signal and orbital parameters that allow GPS
devices, such as mobile phones, watches and cars, to compute the precise locations of the
devices. A GPS receiver uses this information and trilateration to calculate the distances between
the receiver and several satellites, and determines a user’s position.
There are three base stations that can send and receive signals from your mobile phone P.
Suppose that, in a rectangular coordinate system, the locations of the three base stations A, B
and C are (0,0), (36,0) and (16,32) respectively (1 unit represents 1km). It is found that the
distance between P and the three base stations A, B and C are 29 km, 25 km and 13 km
respectively. Assume that A, B, C and P lie on the same horizontal plane. Find the coordinates of
the point P. (Hint: find the intersection of the 3 circles)
5. A design for a cooling tower project is shown in the figure. Find the equation of the hyperbola
that models the sides of the cooling tower. Assume that the center of the hyperbola—indicated
by the intersection of dashed perpendicular lines in the figure—is the origin of the coordinate
plane. Round final values to four decimal places.