Pre-Calculus Lesson Plans Unit 2- 3rd 9-weeks January 21 ...



Pre-Calculus Lesson Plans Unit 9- 3rd term January 20 to February 3, 2012

Rational Functions and Applications, Nonlinear Inequalities

|Date |Topic |Assignment |Did it. |Grade |

|Friday |2.6 Rational Functions |Complete pages 1 to 3 | | |

|1/ 20/12 | | | | |

|Monday |2.6 Rational Functions |Textbook p. 194 | | |

|1/23/12 | |#s 31 – 43 odd | | |

|Tuesday |2.6 Rational Functions |Textbook p. 194 | | |

|1/24/12 |DA spiraling page 4 |#s 32 – 46 even will be collected | | |

|Wednesday |Work problems |page 5 collected at teacher | | |

|1/25/12 |Quiz |discretion | | |

|Thursday |Mixture Problems |page 6 collected at teacher | | |

|1/26/12 | |discretion | | |

|Friday |Distance Problems |page 7 collected at teacher | | |

|1/27/12 | |discretion | | |

|Monday |2.1 Quadratic Application Problems |Textbook pp. 136 – 137 | | |

|1/30/12 | |#s 71 – 84 | | |

|Tuesday |2.7 Nonlinear Inequalities Quiz |Textbook p. 204 | | |

|1/31/12 | |#s 11 – 23 odd, 39 – 47 odd | | |

|Wednesday |2.7 Nonlinear Inequalities |Textbook p. 204 will be collected | | |

|2/1/12 | |#s 12 – 22 even, 40 – 48 even | | |

|Thursday | | | | |

|2/2/12 |Review |Study for test | | |

|Friday | | | | |

|2/3/12 |Test #9 |Print Unit 10 | | |

Jan. 20th : Notes/ homework Find each item and sketch the rational function.

how do you find? 1. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

2. [pic] 3. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA: page 1

4. [pic] 5. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

6. [pic] 7. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

8. [pic] 9. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

page 2

10. [pic] 11. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

12. [pic] 13. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

14. [pic] 15. [pic]

Domain: Domain:

Hole(s): Hole(s):

VA: VA:

HA: HA:

crosses? crosses?

y- int. y- int

x-int. x-int.

SA: SA:

page 3

Jan. 24th DA spiraling questions: Area – Law of Sines and Law of Cosines

1. A parallelogram has adjacent sides measuring 10 inches and 20 inches with an included angle of 40º. Find the area of the parallelogram to the nearest square inch.

A. 75 in2

B. 64 in2

C. 149 in2

D. 129 in2

2. Determine the area of a triangular plot having the following measurements. B= 51° 28´, a = 13 and c = 8. Round your answer to two decimal places.

A. 48.81 square units

B. 36.61 square units

C. 32.54 square units

D. 40.68 square units

3. A parking lot has the shape of a parallelogram. The lengths of two adjacent sides are 70 meters and 100 meters. The angle between the two sides is 70º. What is the area of the parking lot?

A. 7000 square meters

B. 122.1 square meters

C. 6577.8 square meters

D. 3500 square meters

4. A triangular lot whose sides measure 92 ft., 120 ft., and 164 ft. is formed by three adjacent streets. Find the area of the triangular lot.

A. 395.818 ft2

B. 5,427.185 ft2

C. 76,127.401 ft2

D. 2,148,178.235 ft2

5. A businessman wishes to buy a triangular plot of land in a busy downtown location. He labeled a diagram of the plot ∆ABC and found the following measurements: [pic], b = 12 m and c = 33m. Find the area of this triangular plot of land.

A. 33.531 m2

B. 67.062 m2

C. 195.140 m2

D. 390.280 m2

page 4

Jan 25th: For each word problem: (a) Identify variable(s) (b) write equation(s) (c) Write answer in a complete sentence.

Work Problems:

1) A vat can be filled by the hot-water faucet in 8 minutes and by the cold-water faucet in 6 minutes. It can be emptied through the drain in 4 minutes. If the drain is accidentally left open while both faucets are turned on, how long does it take to fill the vat?

2. Jason can clean a large tank at an aquarium in about 6 hours. When Jason and Lucy work together, they can clean the tank in about 3.5 hours. About how long would it take Lucy to clean the tank if she works by herself?

3) An old conveyor belt takes 21 hours to move one day’s coal output from the rail line. A new belt can do it in 15 hours. How long does it take when both are used at the same time?

4) Joe and Bill can retile a roof in 10 hours. Working alone, Joe could do the job 4.5 hours faster than Bill. How long would each man need to do the job alone?

5) At 10:00 A.M. pipe A began to fill an empty storage tank. At noon, pipe A malfunctioned and was closed. Pipe B was used to finish filling the tank. If pipe A needs 6 hours to fill the tank alone and pipe B needs 8 hours, at what time was the tank full?

6) Marcus and Will are painting a barn. Marcus paints twice as fast as Will. On the first day, they have worked for 6 h and completed [pic] of the job when Will gets injured. If Marcus has to complete the rest of the job by himself, how many additional hours will it take him?

7) John can mow the lawn in 4 hours by himself. Mary can mow it in 5 hours by herself. How long will it take them to mow it together?

8. The stopper is in a large tub. It takes nine minutes to fill a tub if only the hot water tap is turned on, and it takes six minutes to fill the tub if only the cold water tap is turned on. Once the tub is filled and the taps are turned off, it takes ten minutes to empty the tub. (Assume that water flows out at a constant rate when the stopper is removed.) How long will it take to fill the tub if

a. the stopper is out and only the cold water tap is turned on?

b. the stopper is out and only the hot water tap is turned on?

c. the stopper is in and both taps are turned on?

d. the stopper is out and both taps are turned on?

9) A glassblower can produce a set of simple glasses in about 2 h. When the glassblower works with an apprentice, the job takes about 1.5 h. How long would it take the apprentice to make a set of glasses when working alone?

10) Two brick layers can brick a house in 9 hours if they work together. Alone, the more experienced bricklayer can brick the same house twice as fast as the other bricklayer. How long do they both take alone?

11) Julian can mulch a garden in 20 minutes. Together, Julian and Remy can mulch the same garden in 11 minutes. How long will it take Remy to mulch the garden when working alone?

12) Each month Leo must make copies of a budget report. When he uses both the large and small copier, the job takes 30 minutes. If the small copier is broken the job takes him 50 minutes. How long will the job take if the large copier is broken?

13) A bathroom tub will fill in 15 minutes with both facets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?

14) Neighbors Tom and Jerry use hoses from both of their houses to fill Tom’s swimming pool. They know it takes 18 hours using both hoses. They also know that Tom’s hose, used alone, takes 20% less time then Jerry’s hose alone. How much time is required to fill the pool by each hose alone?

p. 5

Jan. 26th : For each word problem: (a) Identify variable(s) (b) write equation(s) (c) Write answer in a complete sentence.

Mixture Problems:

1) Misty wishes to obtain 85 ounces of a 40% acid solution by combining a 72% solution with a 25% solution. How much of each solution should Misty use?

2) A chemist has 100 g of 12% saline solution that se want to strengthen to 25%. How much salt should she add to create the 25% solution?

3) Henry had a 45% algaecide and a 70% algaecide solution. How much of each solution should he use to make 100 g. of a 50% solution?

4) Ten liters of a 20% acid solution are mixed with 30 liters of a 30% acid solution. What is the percent of acid in the final mixture?

5) How much antifreeze must be added to 25 liters of a 30% solution to get a 70% solution?

6) How much water should be evaporated from a solution of 65 ml of a 10% acid to get a 14% acid solution?

7) Six quarts of a 20% solution of acid in water are mixed with 4 quarts of a 60% solution of acid in water. What is the acidic strength of the mixture?

8) How many pounds of 70% Columbian coffee must be added to ten pounds of 90% Columbian coffee to have

a. 75% Columbian coffee?

b. 80% Columbian coffee?

c. 85% Columbian coffee?

9) A tub contains 300 liters of a 32% salt solution. How much water must be added to reduce it to a 20% salt solution?

10) A zookeeper needs to mix feed for the prairie dogs so that the feed has the right amount of protein. Feed A has 12% protein. Feed B has 8% protein. How many pounds of each does he need to mix to get 100 lbs of feed that is 10% protein?

11) How much pure acid must be added to 50 ounces of a 35% solution to obtain a 70% acid solution?

12) Mary wants to obtain 85 oz. of a 40 % acid solution by combining a 72% acid solution with a 25% acid solution. How much of each solution should Mary use?

13) How much pure antifreeze must be added to 12 L of a 40% solution of antifreeze to obtain a 60% solution?

14) How much water must be evaporated from a 300 L tank of a 2% salt solution to obtain a 5% solution?

15) A pharmacist wishes to make 1.8 L of a 10% solution of boric acid by mixing 7.5% and 12% solutions. How much of each type of solution should be used? p. 6

Jan 27th: Distance Problems:

1) Pam jogged up a hill at 6 km./hr and then jogged back down the hill at 10 km./hr. How many kilometers did she travel in all if her total jogging time was 1 hour and 20 minutes?

2) Sharon drove for a part of a 150 km. trip at 45 km./hr and the rest of the trip at 75 km./hr. How far did she drive at each speed if the entire trip took her 2 hours and 40 minutes?

3) A plane has a speed of 300 mph in still air. Find the speed of the wind if the plane travels 900 miles with a tailwind in the same amount of time it takes to travel 600 miles into a head wind.

4) Sugar Land and Sealy are 45 miles apart. Chris rode his bike 10 miles from his home in Sugar Land, and then completed the trip to Sealy by car. Assume the average rage of the car is 40 mph faster than the average rate of the bike. Find the bike’s rate if the total time of the trip was 50 minutes.

5) A freight train averages 20 mph traveling to its destination with full cars and 40 mph on the return trip with empty cars. What is the train’s average speed for the entire trip?

6) Emily drove 30 miles to a train station and then completed her trip by train. In all, she traveled 120 miles. The average rate of the train was 20 mph faster then the average rage of the car.

a) How long will the trip take if Emily drives 50 mph?

b) What rate should Emily drive to ensure that the total time for her to complete the trip is less than

2.5 hours?

7) A passenger boat travels 35 km upstream and then back again in 4 h 48 min. If the speed of the boat in still water is 15 km/h, what is the speed of the current?

8) Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes longer will it take him than if he makes the entire trip at 20 kilometers per hour?

9) Elizabeth drove the first half of the trip at 36 mi/h. At what speed should she cover the remaining half of the trip in order to average 45 mi./h for the entire trip?

10) Kyle paddled his kayak 12 km upstream against a 3 km/h current and back again in 5h 20 min. In that time how far

could he have paddled in still water?

13) A kayaker spends an afternoon paddling on a river. She travels 3 mi upstream and 3 mi downstream in a total of 4 h. In still water, the kayaker can travel at a speed of 2 mi/h. Based on this information, what is the speed of the river’s current?

14) A passenger jet travels from Los angles to Bombay, India, in 22 h. The return flight takes 17 h. The difference in flight times is caused by winds over the Pacific Ocean that blow primarily from west to east. If the jet’s speed is 550 m/h, what is the speed of the wind during the round-trip flight?

15) A jet flew from New York to Los Angles, a distance of 4200 km. The speed for the return trip was 100 km/h faster than the outbound speed. If the total trip took 13 hours, what was the speed from New York to Los Angles?

16) Jean averaged 50 km/h for the first 25% of her trip (distance), but she averaged 70 km/h for the entire trip. What was her average speed for the last 75% of her trip (distance)?

17) An elevator went from the bottom to the top of a tower at an average speed of 4 m/s, remained at the top for 90 seconds, and then returned to the bottom at 5 m. /s. If the total elapsed time was 4.5 minutes, how high was the tower?

18) Phil is making a 40-kilometer canoe trip. If he travels at 30 kilometers per hour for the first 10 kilometers, and then at 15 kilometers per hour for the rest of the trip, how many minutes longer will it take him than if he makes the entire trip at 20 kilometers per hour?

19) Sharon drove part of a 150 km trip at 45 km/h and the rest of the trip at 75 km/h. How far did she drive at each speed if the entire trip took 2 h 40 min? p. 7

DA spiraling questions: Area – Law of Sines and Law of Cosines Aplication Problems

6. Two planes leave an airport at the same time. Plane A travels at 750 mph, while Plane B travels at 500 mph. How far

apart will they be after 5 hours if the angle between their paths is 75 ?

A. 3931.875 miles

B. 65.032 miles

C. 683.259 miles

D. 845.839 miles

7. Surveyors measured the three sides of a triangular field and obtained measurements of 110 m, 135 m, and 124 m.

What is the measure of the smallest angle of the triangle?

A. 50.044°

B. 59.779°

C. 39.956°

D. 70.177°

8. A weather balloon B is directly over a 2000 meter airstrip extending from A to C. The angles of elevation to B are

62° and 31°, respectively. Find the equation that can be used to find AB.

A. [pic] B. [pic]

C. [pic] D. [pic]

9. The sides of a triangular plot of land have lengths of 10 yards and 15 yards. They meet at an angle of 75 degrees. Find the approximate length of the third side.

A. 12 yards

B. 14 yards

C. 16 yards

D. 18 yards

10. The lengths of the two adjacent sides of parallelogram parking lot are 18 and 24 yards respectively. If the degree

measure of the included angle is 60º, what is the approximate length of the shorter diagonal of the parallelogram?

A. 12.319 yards

B. 21.633 yards

C. 36.495 yards

D. 40.599 yards

11. Steve found the angle of elevation from a ship to the top of a lighthouse was 20°. When he moved 150 feet closer, the angle of elevation from the ship to the top of the lighthouse was 25°. How tall is the lighthouse?

A. 127.9 feet

B. 248.8 feet

C. 588.6 feet

D. 727.4 feet

12. In navigation, a bearing is the angle of a course, measured in a clockwise direction, from due north. Find the positive angle in standard position for a ship’s bearing of 320º.

A. –140°

B. – 50°

C. 40°

D. 130° p. 8

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