Name: ______Algebra II
Unit 11 Practice Test
In #1 – 2, complete the following for each of the following angles :
(a)Draw a rotation diagram.
(b)State the quadrant the terminal ray of falls within.
(c)State 2 angles that are coterminal with .
(d)State the reference angle of .
(e)Determine the ordered pair that lies on the unit circle for . (Give the exact value if possible, if not, round to the nearest hundredth)
- = 2872. =
3.Consider the curve whose equation is .
(a)Determine the exact period of this sinusoidal function.
(b)What is the amplitude of this sinusoidal function?
(c)What is the midline value of this sinusoidal function?
(d)Sketch the function on the axes for a full period on both sides of the y-axis. Label the scale on your x-axis.
4.For the sinusoidal function , determine the following:
a)State the amplitude.b) Determine the period.
c)State the range.d) Determine the midline.
e)Would the line intersect the function?
5.An athlete was having her blood pressure monitored during a workout. Doctors found that her maximum blood pressure, known as systolic, was 123 and her minimum blood pressure, known as diastolic, was 65. If each heartbeat cycle takes 0.8 seconds, then determine a sinusoidal model, in the form , for her blood pressure as a function of time t in seconds. Show the calculations that lead to your answer.
Graph a sketch of one complete heartbeat. Label all minimum and maximum points with their ordered pairs.
6.For each of the following, find
a)b)
7.Find the solutions to in simplest form.
8. The following graph can be described using an equation of the form. Determine the values of A and C and write the equation of the graph.
9.In the backyard, Fido is attached to a 20 foot leash. With his leash pulled tight, he starts at the garage and sprints to the fence. If the measure of the angle between the fence and the garage is, how far did Fido sprint, to the nearest hundredth of a foot?
10.A liquid has a temperature (in ºF) given by the function , where m is the number of minutes it has been cooling in a particular room.
a) Algebraically, determine the initial temperature of the liquid.
b) Algebraically, determine, to the nearest tenth of a minute, when the temperature reaches 98º F.
11.If and the terminal ray of angle lies in quadrant III, find the exact value of all the remaining trigonometric functions.
12.Write the solution of in q(x) + form, where q(x) is a polynomial and
r is the remainder.
13.For each of the following givens, determine what quadrant that angle must terminate in.
a)and b)and
14.A Ferris wheel is constructed such a person’s vertical position on the wheel in feet, y, can be modeled by the function . If one full cycle of the wheel takes 6 minutes, complete the following:
15. Which of the following is equivalent to 8x9+27?
(1) (2x3 + 3)(4x6 – 6x3 + 9)(3) (2x3 + 3)(2x6 – 6x3 + 9)
(2)(2x3 – 3)(4x6 + 6x3 + 9)(4) (2x3 – 3)(2x6 + 6x3 + 9)
16. Which of the following cannot be the value of the sine of an angle?
(1)(2) (3) (4)
17. The amount of money left on a loan that Paul owes the bank is represented by the function
P(t) = 460(1.27)t where P(t) represents the amount of money left on the loan and t represents the time, in
years.
a)Find P(0) .
b)How many years will it take, to the nearest tenth of a year, for Paul to pay back the loan if he still currently owes $3,500 to the bank?
18. Given: m(x) = 4x3 – 6, find m-1(x).