algebra 2 x - tredyffrin/easttown school district / … · web view... determine whether each data...

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 ASSIGNMENT1 8.2 MULTIPLYING AND DIVIDING

RATIONAL EXPRESSIONSpg. 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 TBA5 Operations Practice #2 TBA6 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, 13-15pg. 573 # 20-23, 31, 40, 41

8 UNIT REVIEW Day #1 Review Worksheet

9 UNIT Review Day #2 TBD

10Unit 8 Test

Enjoy the last day of winter. Spring is almost here.

Please be flexible as assignments may change.

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Warm up: Simplify the following

1) 2) 3) 4)

When simplifying rational expressions…

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

1) 2) 3)

__________ __________ __________

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) 2) 3)

4)

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Day 1: Multiplying and Dividing Rational Expressions

Division is just like multiplication, except:_________________________________________________!

Examples: Divide. Assume that all expressions are defined.

1) 2) 3)

Mixed Practice:

1) 2) 3)

4) 5) 6)

7) * 8)

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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) and 25x 3) and

4) and 5) and

Using example #3 from above, let’s add to rational expressions. Also, state x-values that make the expressions undefined.

1)

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) 3)

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Day 2: Adding and Subtracting Rational Expressions

Try on your own…

4) 5)

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

1) 2)

Mixed Practice:

1. 2.

3. 4.

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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.

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

1. Simplify the following:

2. 3.

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Day 3: Complex Rational Expressions

4. 5.

6. 7.

8.

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

1) Multiplying:

2) Dividing:

3) Adding:

4) Subtracting:

5) Complex:

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Day 4: Classwork – Operations Practice #1

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)

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

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Day 5: Classwork – Operations Practice #2

There are two types of rational equations…

1) 2)

* use either method * Multiply by LCD right away or** Combine into 1 fraction then cross multiply

1. 2.

3.

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Day 6: Solving Rational Equations

4 5.

6.

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 TimeUpstream

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 RateJason 1Lacy 1

Together 1

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Simplify and state the restrictions on x.

1. 2.

Simplify. You do not need to state restrictions.

3. 4.

5. 6.

7. 8.

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Day 7: Unit Review

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

9. 10.

11. 12.

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 hours. How long would it take Melissa to mow the lawn?

Time Work RateJohn 1

Melissa 1Together 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 TimeUpstream 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 RatePipe A 1Pipe B 1

Together 1

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

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

Type of Variation

Equation Form Ratio Form Example

Direct

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 9y 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.

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Day 9: Direct, Inverse, & Joint Variations

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

x y z2 45 52.5 7

1.5 -361.38 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 25y 120 2400 144z 5 15 6

Answers!

1. 4. atmospheres.

2. 5. k = 12

3. miles; hours

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x 2 10 25 2y 120 1800 2400 144z 5 15 8 6

algebra 2 x - tredyffrin/easttown school district / … · web view... determine whether each data...

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