ALGEBRA 2 X - Tredyffrin/Easttown School District



Name__________________________________________

Syllabus

Unit 8: Rational Expressions & Equations

We will most likely have a mini-quiz or two this unit.

LAST UNIT ‘TIL SPRING BREAK

|DAY |TOPIC |ASSIGNMENT |

|1 |8.2 MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS |pg. 580: 1-29 ODDS (skip 17) |

|2 |8.3 ADDING AND SUBTRACTING RATIONAL EXPRESSIONS | pg. 588 # 7, 9, 10, 22, 26, 34, 35 |

|3 |8.3 COMPLEX RATIONAL EXPRESSIONS |pg. 588 # 1, 28-30, 43-45 |

|4 |Operations Practice #1 |TBA |

|5 |Operations Practice #2 |TBA |

|6 |8.5 SOLVING RATIONAL EQUATIONS |pg. 605 # 1-9 odd, 10, 11 |

|7 |8.1 DIRECT, INVERSE & JOINT VARIATIONS (some hw problems done in class) |pg. 573 # 2-8 even, 9-11, 13-15 |

| | |pg. 573 # 20-23, 31, 40, 41 |

|8 |UNIT REVIEW Day #1 |Review Worksheet |

|9 |UNIT Review Day #2 |TBD |

|10 | |Enjoy the last day of winter. Spring is almost |

| |Unit 8 Test |here. |

Please be flexible as assignments may change.

Warm up: Simplify the following

1) [pic] 2) [pic] 3) [pic] 4) [pic]

When simplifying rational expressions…

Examples: Simplify and then state the values for x that make the expression undefined.

1) [pic] 2) [pic] 3) [pic]

[pic]__________ [pic]__________ [pic]__________

Multiplying rational expressions is just like simplifying two at a time.

Any top can cancel with any ___________________ !!

Examples: Multiply. Assume that all expressions are defined.

1) [pic] 2) [pic] 3) [pic]

4) [pic]

Division is just like multiplication, except:_________________________________________________!

Examples: Divide. Assume that all expressions are defined.

1) [pic] 2) [pic] 3) [pic]

Mixed Practice:

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] * 8) [pic]

To add or subtract fractions, you must have a ____________________________________.

Let’s find a LCD (or LCM) for each of the following.

1) 12 and 18 2) [pic] and 25x 3) [pic] and [pic]

4) [pic] and [pic] 5) [pic] and [pic]

Using example #3 from above, let’s add to rational expressions.

Also, state x-values that make the expressions undefined.

1) [pic]

To recap, here are the steps to adding rational expressions…

Step #1: Identify the __________

Step #2: Multiply each fraction by the _____________ ______________.

Step #3: Distribute (or FOIL) on each of the __________

Step #4: Add the tops and keep the bottoms the __________.

Step #5: State the values that make the expressions undefined (think ___________ = ____)

2) [pic] 3) [pic]

Try on your own…

4) [pic] 5) [pic]

Subtracting is the same process, except you must be careful to ___________________ the negative!

1) [pic] 2) [pic]

Mixed Practice:

1. [pic] 2. [pic]

3. [pic] 4. [pic]

Warm up: Simplify the following 4 problems. Be sure to state restrictions on the variables.

1. 2.

Multiply or divide. Write your answer in simplest form. Be sure to state restrictions on the variables.

3. 4. [pic]

[pic]

Complex Fractions: fractions that have a fraction in the numerator, denominator, or BOTH.

1. Simplify the following: [pic]

[pic] [pic]

2. [pic] 3. [pic]

4. [pic] 5. [pic]

6. [pic] 7. [pic]

8. [pic]

Let’s recap all that we have learned so far about rational expressions…

1) Multiplying:

2) Dividing:

3) Adding:

4) Subtracting:

5) Complex:

[pic]

[pic]

[pic]

[pic]

Directions: use the formula sheet below to help you with the practice PSSA test on the following 4 pages.

There are 22 multiple choice questions to help you prepare for the PSSA (coming up mid April)

[pic]

[pic]

[pic]

[pic]

[pic][pic]

[pic]

[pic]

There are two types of rational equations…

[pic] [pic]

1) [pic] 2) [pic]

* use either method * Multiply by LCD right away or

** Combine into 1 fraction then cross multiply

1. [pic] 2. [pic]

3. [pic]

4[pic] 5. [pic]

6. [pic]

Word Problems

7. A kayaker spends an afternoon paddling on a river. She travels 3 miles upstream and 3 miles downstream in a total of 4 hours. In still water, the kayaker can travel at an average speed of 2 miles per hour. Based on this information, what is the average speed of the river’s current?

| |Distance |Rate |Time |

|Upstream | | | |

|Downstream | | | |

8. Jason can clean a large tank at an aquarium in about 6 hours. When Jason and Lacy work together, they can clean the tank in about 3.5 hours. About how long would it take Lacy to clean the tank if she worked alone?

| |Time |Work |Rate |

|Jason | |1 | |

|Lacy | |1 | |

|Together | |1 | |

Simplify and state the restrictions on x.

1. [pic] 2. [pic]

[pic] [pic]

Simplify. You do not need to state restrictions.

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

Solve the following equations. Don’t forget to check!

9. [pic] 10. [pic][pic]

11. [pic] 12. [pic]

Write an equation and solve it to find the solution to each problem.

13. John can mow a lawn in 4 hours. When Melissa helps him, they can mow the lawn in [pic] hours. How long would it take Melissa to mow the lawn?

| |Time |Work |Rate |

|John | |1 | |

|Melissa | |1 | |

|Together | |1 | |

14. A boat travels 6 miles upstream in the same amount of time it can travel 10 miles downstream. In still water the speed of the boat is 5 miles per hour. What is the speed of the current?

| |Distance |Rate |Time |

|Upstream | |5 - x | |

|Downstream | |5 + x | |

Let x = the current of the water.

15. A water tank is filled by pipes from 2 wells. The first pipe can fill the tank in 4 days. The second pipe can fill the tank in 6 days. How long will it take to fill the tank using both pipes?

| |Time |Work |Rate |

|Pipe A | |1 | |

|Pipe B | |1 | |

|Together | |1 | |

Directions: Use your formula sheet (if appropriate) to help you answer the following 11 questions.

[pic]

|Type of Variation |Equation Form |Ratio Form |Example |

| |[pic] |[pic] |[pic] |

|Direct | | | |

| |[pic] |[pic] |[pic] |

|Inverse | | | |

Questions from HW:

2) If y varies directly as x, find an equation when y = 6 and x = 3.

9) If y varies inversely as x, find an equation when y = 2 and x = 7.

13) Determine whether each data set represents a direct variation, an inverse variation or neither.

|x |2 |5 |9 |

|y |3 |6 |4 |

A ______________________ variation is a relationship that contains both direct and inverse variation in one

problem. Directly will be in the ________________ and inversely will be in the _________________.

20) Medicine: The dosage d of a drug that a physician prescribes varies directly as the patient’s mass m, and d = 100 mg when m = 55 kg. Find d to the nearest milligram when m = 70 kg.

22) Agriculture: The number of bags of soybean seeds N that a farmer needs varies jointly as the number of acres a to be planted and the pounds of seed needed per acre p, and N = 980 when a = 700 acres and p = 70 lb/acre. Find N when a = 1000 acres and p = 75 lb/acre.

40) Complete the table if y varies jointly as x and z.

|x |y |z |

|2 | |4 |

|5 |52.5 |7 |

| | | |

|1.5 |-36 | |

| |1.38 |23 |

1. y varies directly with x, and x = 18 when y = 3. Find y when x = 66.

2. y varies jointly with x and z, and y = 200 when x = 4 and z = 20. Find x when y = 500 and z = 25.

3. Speed is inversely proportional to time. If I can reach my destination travelling at 50 mph for 2 hours, how long would it take me at 65 mph?

4. The volume of a gas varies inversely with the pressure of the gas and directly with the temperature of the gas. A certain gas has a volume of 10 L at a temperature of 300 K (“Kelvin,” an important unit of temp. in Chemistry), and a pressure of 1.5 atmospheres (a unit of pressure). If the volume changes to 7.5 L and the temperature increases to 350 K, what will the new pressure be?

5. Fill in the chart, given that y varies jointly with x and z.

|x |2 |10 |25 | |

|y |120 | |2400 |144 |

|z |5 |15 | |6 |

Answers!

1. [pic] 4. [pic] atmospheres.

2. [pic] 5. k = 12

|x |2 |10 |25 |2 |

|y |120 |1800 |2400 |144 |

|z |5 |15 |8 |6 |

3. [pic] miles; [pic] hours

-----------------------

Day 1: Multiplying and Dividing Rational Expressions

Day 8: Homework – PSSA Prep Worksheet #2 (After the Test)

Day 7: Unit Review

Day 9: Direct, Inverse, & Joint Variations

Day 6: Solving Rational Equations

Day 5: Classwork – Operations Practice #2

Day 4: Homework – PSSA Prep Worksheet #1 (Due Monday)

Day 4: Classwork – Operations Practice #1

Day 3: Complex Rational Expressions

Day 2: Adding and Subtracting Rational Expressions

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