Name ______Honors Algebra II 2nd Semester Review Sheet
Chapter 3
1)Evaluate.
2)Perform the indicated operation.
- g(x) *f(x)
3)Find the inverse.
- + 1
- – 2
4)Verify that f and g are inverse functions.
5)Solve the equations.
6)The fetch f (in nautical miles) of the wind at sea is the distance over which the wind is blowing. The minimum fetch required to create a fully developed storm can be modeled by where s is the speed (in knots) of the wind. Determine the minimum fetch required to create a fully developed storm if the wind speed is 25 knots. (Round to 2 decimal places.)
7)Graph and give the domain and range.
Chapter 4
8)Tell whether the function represents exponential growth or exponential decay.
9)A house was purchased for $90,000 in 1995. If the value of the home increases by 5% per year what will it be worth in 2020?
10)You buy a new car for $22,000. The value of the car decreases by 12.5% each year. Estimate when the car will have a value of $8000.
11)You deposit $800 in an account that pays 5.5% annual interest compounded continuously. What is the balance after 6 years?
12)You deposit $400 into an account that pays 2% annual interest compounded quarterly. How much money will you have in 3 years?
13)Simplify the expression.
14)Graph and write the equation of the asymptote, the domain, and range.
15)Use to approximate.
16)Condense the expression.
17)Expand the expression
18)Evaluate.
19)Find an exponential function to the form of whose graph passes through the points (4,6) and (7,10).
20)Solve. (Check a and b for extraneous solutions.)
21)Graph and write the equation of the asymptote, domain, and range.
22)Graph . Give the domain, range, equation of the asymptote, and the y-intercept.
23)The spread of a virus through a student population can be modeled by where s is the total number of students infected after t days. Tell when the point of maximum growth in infections is reached.
24)Find a power function of the whose graph passes through the points (2, 3) and (10, 21).
25)Most tornadoes last less than an hour and travel less than 20 miles. The speed s (in miles per hour) near the center of a tornado is related to the distance d (in miles) the tornado travels by this model: . Estimate how far a tornado traveled if the wind speed was about 280 miles per hour.
26)The moment magnitude M of an earthquake that releases energy E (in ergs) can be modeled by . How much energy did a 9.5 magnitude earthquake release?
Chapter 5
27)The variables x and y vary inversely. Write an equation relating x and y, if x = 12 and . Then find y when x = 3.
28)The variable z varies jointly with x and y. Write an equation relating x, y, and z, if , , . Then find z when x = -2 and y = 4.
29)The volume of a geometric figure varies jointly with the square of the radius of the base and the height.
- Write an equation for the volume.
- Estimate the constant of variation in V = 63.33 in3, r= 2.4 in, and h = 10.5 in.
30)The number f of flies eaten by a praying mantis in 8 hours can be modeled by where d is the density of flies available (in flies per cubic centimeter). Approximate the density of flies when a praying mantis eats 15 flies in 8 hours. (Round to 4 decimal places.)
31)Graph and Give the domain, range, vertical asymptotes, holes, and horizontal asymptotes.
- .
32)From 1980 to 1995, the total revenue R (in billions of dollars) from hotels and motels in the U.S. can be modeled by where x is the number of years since 1980. In what year was the total revenue approximately $68 billion?
33)Almost all of the energy generated by a long-distance runner is released in the form of heat. The rate of heat generation and the rate of heat released for a runner of height H can be modeled by and where and are constants and V is the runner’s speed/ Write the ratio of heat generated to heat released. Simplify.
34)Perform the indicated operation. Simplify the results.
35)Simplify.
36)Solve.
Chapter 8
37)Find the distance between the two points, (-8, 3) and (4, 7). Then find the midpoint of the line segment connecting the two points.
38)Use the given distance d between the two points to solve for x.
39)A Street light can be seen on the ground within 30 yd of its center. You are driving and are 10 yd east and 25 yd south of the light. Write an inequality to describe the region on the ground that is lit by the light. Is the street light visible?
40)An amusement park has an elliptical garden at its entrance. The garden is 32 ft long and 14 ft wide. Write an equation of the ellipse. What is the area of the garden if.
41)One focus of the summer solstice hyperbola is 207 inches above the ground. The vertex of the aluminum branch is 266 inches above the ground. If the x-axis is 355 inches above the ground and the center of the hyperbola is at the origin, write an equation for the summer solstice hyperbola.
42)A cellular phone transmission tower located 10 miles west and 5 miles north of your house has a range of 20 miles. A second tower, 5 miles east and 10 miles south of your house, has a range of 15 miles. Write an inequality that describes each tower’s range. Do the two regions covered by the towers overlap?
43)Graph.
44)Write the equation of the given conics.
- Circle:
- Ellipse:
- Hyperbola:
- Parabola:
45)Which direction does the parabola open, up, down, left, or right.
46)Classify the conic section.
47)Find the point of intersection, if any of the graphs in the system.
48)The range of a radio station is bounded by a circle given by the following equation. A straight highway can be modeled by the following equation. Find the length of the highway that lies within the range of the radio station.
49)Graph.
50)The table shows the number c of cranes in Izumi, Japan, from 1950 to 1990 where t represents the number of years since 1950. Use exponential regression to find an exponential model for the data and then estimate the number of cranes in the year 2012.
t / 0 / 5 / 10 / 15 / 20 / 25 / 30 / 35 / 40c / 293 / 299 / 438 / 1573 / 2336 / 3649 / 5602 / 7610 / 9959