Algebra 2 Semester 2 Midterm Review

Transcription

1 Algebra Semester Midterm Review NON-CALCULATOR Using the graph of f ( ) or f ( ) as a guide, describe the transformation, fill in the table, and graph each function. Then, identif the domain and range. f Description: Domain: Range:. Using the graph of f ( ) or f ( ) as a guide, describe the transformation, fill in the table, and graph each function. Then, identif the domain and range. g 4 Description: Domain: Range: 5.8. Solve the following equation:

2 4. Solve the following equation: Solve the following equation: Rewrite the following epression using rational eponents: Rewrite the following epression as a radical: Simplif the following epression: Simplif the following epression:

3 Simplif each epression. Identif an -values for which the epression is undefined. a) b) 4 1 c) Add or subtract. Identif an -values for which the epression is undefined. a) 9 b) 5 71 c)

4 Using the graph of f( ) as a guide, describe the transformation, identif the ke points and asmptotes (fill in the table), graph the function, then identif the domain and range of the function. 1 g 1 Description: Vertical Asmptote: Horizontal Asmptote: Domain: Range: 1 1. Using the graph of f( ) as a guide, describe the transformation, identif the ke points and asmptotes (fill in the table), graph the function, then identif the domain and range of the function. Description: f Vertical Asmptote: Horizontal Asmptote: Domain: Range: Solve the following equation:

5 15. Solve the following equation: Solve the following equation: Using a trig function, determine the eact length of and in each triangle below. a) b) c)

6 Find the eact value of each trigonometric function using reference angles. Support our answer with a labeled diagram. a) 5 cos b) sin150 c) tan For each function, identif the amplitude, period, phase shift and vertical shift. Graph the function. a) h sin( ) b) k cos( ) c) f ( ) sin( ) d) g( ) cos( )

7 CALCULATOR The speed in mph of a tsunami can be modeled b the function s.86 depth in feet of the water over which the tsunami travels. a) Solve this equation for d, depth. d, where d is the average b) Suppose the speed of the tsunami is 150 mph. Use our equation from part a to calculate the depth. Round our answer to the nearest hundredth, if necessar A conveor belt leads from the ground to a barn door 4 feet high. The angle between the belt and the ground is. What is the length of the conveor belt to the nearest foot? Draw a labeled diagram to support our answer.. A surveor stands 186 feet from the base of a cliff and measures the angle of elevation to be His ee level is 5 feet above the ground. What is the height of the cliff to the nearest foot? Draw a labeled diagram to support our answer.

8 . The pilot of a hot air balloon measures the angle of depression to a landing spot to be 6.7. If the pilot s altitude is 175 meters, what is the horizontal distance to the landing spot to the nearest meter? Draw a labeled diagram to support our answer. 4. Kate leans a ladder against her house to get on to the roof. The house is 5 feet tall and the foot of the ladder is 15 feet awa from the side of the house. Which is the angle that the ladder makes with the ground? 10. and Draw an angle with the given measure in standard position. Then find (1) a positive co-terminal angle, () a negative co-terminal angle, and () the reference angle. a) 9 b) 16

9 5. Draw an angle with the given measure in standard position. Then find (1) a positive co-terminal angle, () a negative co-terminal angle, and () the reference angle. c) d) Convert from radians to degrees or degrees to radians. a) 105 b) ,.9 7. Use finite differences to determine the degree of the polnomial function that best models the data

10 7. Use finite differences to determine the degree of the polnomial function that best models the data ,.8,.9, A photographer hiked through the Grand Canon. Each da she filled a photo memor card with images. When she returned from the trip, she deleted some photos, saving onl the best. The table shows the number of photos she kept from all those taken on each memor card. Grand Canon Photos Photos Taken Photos Kept a) Use a graphing calculator to make a scatterplot of the data. b) Write the equation of the line of best fit. Round to the nearest hundredth. c) Find the correlation coefficient. d) Predict the number of photos the photographer will keep if she takes 00 photos on the memor card.

11 9. A variet of spruce trees called No. 1 Common Spruce are often used as support columns in buildings. The maimum load allowance for each column depends on the height of the spruce column. The following table gives some of this data. Height of the Column (ft) Maimum Load (lb) a) Find a quadratic regression model for this data. Round to the nearest hundredth. b) Use the model to predict the load allowed for a 6.5 ft spruce column. c) What is the maimum load a Common Spruce of an height can hold? d) What is the height of the spruce column at that maimum load? 0. The data below shows the number of hummingbirds who visited Mr. Hunt s birdfeeder between 7:00 a.m. and 8:00 a.m. from Januar through June 011. Number of Months Number of Birds a) Find a cubic regression model for this data. Round to the nearest hundredth. b) Use the model to predict the number of hummingbirds in August.