Examination
January 25, 2011Length: 2 hours
(Exam set for 2 hrs. + 1 hr. flex time) /
Name:
Teacher:
School:
Instructions to students:
- This examination booklet is 13 pages long.
- Answer all questions with complete solutions in the spaces provided on the examination paper.
- You may use any school-approved calculator on this examination.
Make sure that your calculator is in DEGREE mode.
Do not share your calculator.
- There is a formula sheet that goes with the examination.
A) Trigonometry
A1)Solve for x.
A2)Solve for x. Answer to 1 decimal place.
A3)The cost of fencing is $8.50 per metre. Determine the cost of fencing the garden shown below.
A4)A video camera is mounted on the top of a 120 m tall building.
When the camera tilts down 36° with the horizontal, it views the bottom of another building.
If it tilts up 47° with the horizontal, it can view the top of the same building.
Determine the height of the building viewed by the camera.
A5)Is it possible to be given some information about a triangle so that both the sine law and the cosine law could be used to solve for a specific measurement? Explore the possibilities. Justify your answer.
B) Analytic Geometry
B1)Two line segments AB and CD are graphed below. Determine the equation of a line that is parallel to segment AB and intersects segment CD.
B2)Joe has two summer jobs.
During the first week he works 18 hours at Andy’s Café and 22 hours at Bob’s Pizza and earns $431.
In the second week he works 26 hours at Andy’s Café and 20 hours at Bob’s Pizza and earns $493.
State the system of equations that could be used to determine his hourly wage at each place. (Remember to define your variables.)
B3)Suppose you are given that A(-3, -2) and B(5, 2) are two vertices of an isosceles right triangle .
a) Determine the possible coordinates of a point C.
b) Discuss how many other possible locations there are for point C.
B4)Consider the line graphed below.
A second line has equation .
a) Choose a value for A and a value for B and determine the number of points of intersection of the two lines.
b) In general, describe how values of A and B affect the number of points of intersection of the two lines.
C) Quadratic Relations
C1)How many zeros does the quadratic relation have? Justify your answer.
C2)Determine an equation of the parabola whose table of values is given below. Show your work.
x / y-1 / 0
1 / -6
3 / -8
5 / -6
7 / 0
C3)A satellite dish has a parabolic cross section.
When the dish is lying flat, the cross section can be modelled by where h is the height of a point on the dish, in metres, and x is the distance, in metres, from one edge.
Determine the maximum height of the dish.
C4)a) Use a variety of ways to show that has one solution.
b) Discuss how changing the constant term (25) in the equation can affect the number of solutions. Justify your answer.
C5)A firefighting plane is descending to release water on a forest fire.
The height of the plane above the ground is given by the equation ,
where t is the number of seconds after the plane begins its descent, and h is the height in metres.
The plane must be less than 150 m above the ground for at least 20 seconds in order to put out the fire.
For safety reasons the plane should never be less than 70 m above the ground.
At what height(s) should the plane begin its descent?
Justify your answer.
Page 1