Algebra II Trig First Semester Final Review Name______


All solutions should be represented by DANGà Descriptively, Analytically, Numerically, and Graphically

1. You are building a walkway of uniform width around a 95 foot by 65 foot swimming pool. After completing the walkway, you want to put a fence along the outer edge of the walkway. You have 450 feet of fencing to enclose the walkway. What is the maximum width of the walkway?

2. A sporting good store receives a shipment of 124 golf bags. The shipment includes two types of bags, full-size and collapsible. The full-size bags cost $38.50 each. The collapsible bags cost $22.50 each. The bill for the shipment is $3430. How many of each type of golf bag are in the shipment?

3. A school board is investigating various ways of composing the faculty for a proposed new elementary school. The can hire teachers and aides. The amount of money the school district will have to spend on salaries each year depends on how many teachers and on how many aides are hired. The Board finds that the average annual salary for teachers is $37,000 and the average aide’s salary is $29,000. The Board find the the following requirements concerning the permissible numbers of teachers and aides: 1. The building can accommodate no more than 50 faculty members total. 2. A minimum of 20 faculty members is needed to staff the school. 3. The school cannot be run entirely by aides, so there must be at least 12 teachers. 4. For a proper teacher to aide ratio, there must be at least 3 teachers for every 5 aides in the school. What is the minimum cost required to hire the faculty at the school, and how many teachers and aides should be hired?

4. Consider an object launched upward from the ground (what is the height of the ground?) With initial velocity 53ft/s. h(t) =

  1. What is the height of the object after 1.2 seconds?
  1. After how much time does the object hit the ground after being thrown?
  1. At what times is the object at a height of 24 feet? Describe in a sentence why there are two solutions to this problem?
  1. What is the maximum height of the ball? At what time does the ball reach its maximum height?
  1. Graph the points in parts a-d and verify that these points form a parabola. Time should be on the x axis and height on the y axis

5 A football kicker tries to make a field goal with the ball on the 27-yard line. (98 feet from the goal posts). If you imagine a coordinate system with the ball being kicked at x-0 and the goal posts at x =98, then the equation of the ball’s path is , where y is the ball’s height in feet.

  1. Graph the function.
  1. What is the maximum height of the ball?
  1. How much will the ball clear the goalpost crossbar that is 10 feet above the ground? Explain.
  1. If a defensemen jumps vertically 8 feet in the air (arms outstretched) 10 feet in front of the kicker will he block the kick? Explain.

Use synthetic division to find the value of y for both x values.

6. x= 2 and x = -2

7. x = -3 and x = 1