Algebra 1 Unit 5 Tentative Syllabus - Weebly



Pre-AP Algebra 1 Unit 8 Tentative Syllabus Name

Sect. 6.7 & Chapter 7

|DATE |TOPIC |Practice Over |

| | |Topic |

|Tuesday |7.1 Solve Systems using tables & graphing |Book Pg. 431 – 432 |

|January 8 | |# 3 – 5, 9 # 15, 19, 21, 23, 25, |

| | |29, 30 & packet pg. 3 - 4 |

| | |Notes pg. 2 – 3 |

| | |Graphs on pkt. Pg. 3 - 4 |

|Wednesday |7.2 Solve systems by substitution |Pg. 439 |

|January 9 | |# 7-27 odds & 30 |

|Thursday |7. 3 Solve systems by elimination |Pgs. 447-448 |

|January 10 | |# 3-21 odds, 25-29 odds |

|Friday |Quiz – Solving Systems |No Homework |

|January 11 |Sections 7.1 – 7.3 | |

|Monday |7.4 Solve systems by elimination |Pg. 454 - 455 |

|January 14 | |# 3-31 odds |

|Tuesday | 7.5 Special Types of Systems |Pg. 462 – 463 |

|January 15 | |# 5,6 ,7, 9, 11, 13, |

| | |# 15 – 21 odds, 24, 25, 27 & 29 |

| | |Graphs on Pg. 4 |

|Wednesday |6.7 Solve inequalities by graphing |Pg. 409 – 410 # 9 – 27 odds, |

|January 16 | |# 31, 32, 39, 41, 43, 45 |

| | |Notes pg. 5 |

| | |Graphs on Pg. 6 |

|Thursday |7.6 Solve systems of inequalities |Pg. 469 – 470 # 3 – 8 all |

|January 17 | |9 – 21 odds, 25-31 odds |

| | |Notes pg. 6 |

| | |Graphs on Pg. 7 |

|Friday |Quiz – Solving Systems |No Homework |

|January 18 |Sections 7.1 – 7.6 | |

|Monday |Holiday |No Homework |

|January 21 | | |

|Tuesday |Sect. 6.7 |Packet Pg. 7 - 8 |

|January 22 |Inequality Word Problems | |

|Wednesday |Chapter 7 |Notes - Packet pg. 9 |

|January 23 |System Word Problems | |

| | |Problems – Packet Pgs. 10 - 11 |

|Thursday |Chapter 7 |Notes - Packet pg. 9 |

|January 24 |System Word Problems | |

| | |Problems – Packet Pgs. 10 - 11 |

|Friday |Test – Systems |No Homework |

|January 25 |Equations, Inequalities and Word Problems | |

Notes: Tuesday January 8 Solve Systems Using Tables & Graphing

A System of Equations: _____________________________________________________________________________.

The solution to a system of equations is: ______________________________________________________________.

There are 3 types of solutions to a system of equations.

1. If the two lines intersect then the solution is the point where they intersect (there is one solution).

2. If the two lines are parallel (never cross) then there is no solution.

3. If the two lines actually turn out to be the same line then you have infinitely many solutions.

Graphing by hand:

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

Solution: __________________ Solution: __________________ Solution: __________________

Graphing using the calculator: Using your calculator, find and graph the solution.

Press: y= and put the equations into [pic] and [pic] Make sure y is by itself in the equation!

To find the intersection: Press: 2nd, trace, intersect…make sure you see the intersection on the graph…then press enter 3 times.

1) [pic] 2) [pic]

Solution: __________________ Solution: __________________

Using a Table to Find a Solution.

Find the solution for [pic]

Strategy: Make a table of values for the two equations using your calculator and find the point they

have in common.

|x |[pic] |[pic] |

|-3 | | |

|-2 | | |

|-1 | | |

|0 | | |

|1 | | |

|2 | | |

|3 | | |

*** Re-write the equations so y is by itself:

[pic] _________________ [pic] ________________

HW: Tuesday January 8 Solve Systems Using Tables & Graphing Work should be shown on your own paper.

# 1 & 2: Use a table to find the solution to the following.

1) [pic] 2) [pic]

3) Greta made the table below for the system of equations [pic] and [pic]. What can Greta conclude from the

table?

|x |[pic] |[pic] |

|-3 |-8 |0 |

|-2 |-5 |-1 |

|-1 |-2 |-2 |

|0 |1 |-3 |

|1 |4 |-4 |

|2 |7 |-5 |

|3 |10 |-6 |

Pg. 431 – 432 Graphs.

Pg. 462 - 463

Notes: Wednesday January 16 Solving Inequalities

Reminders:

1) If [pic] or [pic] solid line 2) Then shade in the region below or above

If < or > dashed line using the inequality( may need a point to test).

EX) [pic] EX) [pic]

Special Cases:

1)[pic] 2)[pic]

Is the ordered pair a solution to the inequality?

Determine Algebraically: Determine graphically:

EX) [pic](8, 3) EX) [pic] (10, 1)

HW: Wednesday January 16 Solving Inequalities Work should be shown on your own paper.

Notes: Thursday January 17 Solve Systems of Inequalities

Solve the system of Inequalities and answer the accompanying questions.

Example 1 Example 2

[pic]

Example 3

[pic]

HW: Thursday January 17 Solve Systems of Inequalities Work should be shown on your own paper.

EXTRA GRAPHS:

HW: Tuesday January 22 Inequality Word Problems Work should be shown on your own paper.

Write an inequality to express the situation given.

1. A grocery store has 20 bottles of spring water in stock. The store orders bottles of spring water in cases of 24. The store wants to order enough cases of water that it has over 500 bottles in stock. Write an inequality to model this situation.

2. Sun is making beaded jewelry to sell at the craft fair. She has 720 beads. She uses half of those beads to make necklaces. She also makes bracelets that use 24 beads each. Write an inequality to represent the number of bracelets that Sun can make with the beads she has left over after making the necklaces?

3. A Store is having a 50% off sale on all items originally priced between $20 and $80. Sales tax is 6%. Which inequality represents the range of the total cost, in dollars, of one sale item, including tax?

a. [pic] b. [pic] c. [pic] d. [pic]

4. An inchworm is crawling up a tree. It begins 18 inches above the round and climbs up 3 inches every minute. Let it t represent the number of minutes since the worm began climbing. Veronica wants to know when the inchworm will be more than 60 inches above the ground. Which inequality should she use?

a. [pic] b. [pic] c. [pic] d. [pic]

5. Mel works as a waiter. He uses the linear expression [pic] to calculate his hourly earnings, in dollars, based on the number of tables, x, that he serves. Write an inequality to express the fewest number of tables he must serve per hour in order to earn more than $25 per hour?

6. An airline rejects pilots whose height is less than 70 inches or greater than or equal to 76 inches. Write an inequality to represent the heights of the pilots who are not rejected based on height.

7. Jonah is making a cardboard rectangle. The length of the rectangle is 6 inches. The width of the rectangle is 3x inches and the area of the rectangle must be greater than or equal to 54 [pic] and less than 108 [pic]. The area of the rectangle is found by multiplying the length and the width. Which inequality shows the possible values of x?

a. [pic] b. [pic] c. [pic] d. [pic]

Use the information for questions 8 & 9.

Katia is buying balloons and streamers for her party. Balloons cost $1 each, and streamers cost $3 a roll. She can spend no more than $30 on the decorations. How many balloons and streamers can she buy?

8. If x represents the number of balloons she can buy, and y represents the number of rolls she can buy, write an inequality to model the situation.

9. Which graph represents the solution to the problem?

Notes: Wednesday January 23 & Thursday January 24 System Word Problems

|PERIMETER OF A RECTANGLE |

|A rectangle’s length is 6 meters more than twice its width. The perimeter is 60 meters. Find the length in meters. |

| |

|Define Variables: __________________ _____________________ |

| |

| |

| |

| |

|TICKETS PROBLEMS |

|Jake bought 10 Astro game tickets for a total of $58. Adult tickets cost $8 each and children’s tickets cost $2.50 each. How many children’s tickets did he buy? |

| |

|Define Variables: __________________ _____________________ |

| |

| |

| |

|COIN PROBLEMS |

|Jane has $1.40 in nickels and dimes. If there are 20 coins, write a system of equations that will determine the number of nickels, n, and the number of dimes, d, she |

|has? |

| |

|Define Variables: __________________ _____________________ |

| |

| |

| |

|VARIETY OF SYSTEMS PROBLEMS |

|Don bought some audio cassettes at $4 each and some video cassettes at $6 each. If he bought a total of 7 tapes and spent a total of $30, how many audio |

|cassettes did he buy? |

|Define Variables: __________________ _____________________ |

| |

| |

| |

| |

|INVESTMENT PROBLEMS |

|3. Karen invested part of $5000 in a certificate of deposit (CD) and the rest in stocks. At the end of one year, |

|the CD yielded 7% interest on the amount invested and the stocks yielded 5%. The total yield of the two |

|investments was $315. How much did Karen invest at each rate? |

| |

|Define Variables: __________________ _____________________ |

| |

| |

| |

| |

|RATIO PROBLEMS |

|4. Amber has both a checking account and a savings account at the bank. She has a total of $850 in both |

|accounts. The ratio of checking to savings is 3 to 7. How much money does Amber have in her checking |

|and savings accounts? |

| |

|Define Variables: __________________ _____________________ |

| |

| |

| |

| |

HW: Wednesday January 23 & Thursday January 24 System Word Problems Work should be shown on your own paper.

1. The perimeter of a rectangle is 36 ft. The length of the rectangle is twice the width. Write a system of

equations that you could use to find the length and width where L is the length and W is the width. Solve the equations for

the length and width.

2. Jill has $3.60 in nickels and quarters. The number of nickels is 6 less than the number of quarters. How

many nickels does she have?

3. The cost of an adult ticket to watch the Bulldogs was $1.75. The cost of a student ticket was $1.25. The

number of student tickets sold was twice the number of adult tickets. The total income from the sale of tickets

was $8.50. How many student tickets were sold?

4. The perimeter of a rectangular garden is 100 feet. The length of the garden is 5 feet longer than 2 times the width. What

is the area of the garden?

a. 450 square feet c. 600 square feet

b. 525 square feet d. 625 square feet

5. The number of nickels that Christine has is 5 times the number of dimes. Their value is $1.05. How many

nickels does she have?

6. The perimeter of a rectangle is 40 ft. The length of the rectangle is 4 ft less than three times the width. Find

the length.

7. The Mendez family is going to see a play. Adult tickets cost $9 and children’s tickets cost $6. There are 6 people in the

family, and they spend a total of $48 on the tickets. Which system of equations can be solved to find a, the number of

adult tickets and c, the number of children’s tickets?

a. [pic] b. [pic] c. [pic] d. [pic]

8. Marie has 24 coins in half-dollars and dimes. Their total value is $3.60. Find the number of dimes.

9. When shopping for school supplies for her children, Mrs. Michaels bought two sets of markers, and 3 binders for a total

cost of $21. Mrs. Laurence bought 5 of the same sets of markers and 2 of the same binders for $25. How much does

each binder cost?

a. $2 b. $3 c. $4 d. $5

10. Students are taking a test worth 100 points containing 40 questions. There are 2-point and 4-point questions

on the test. How many of each type of question are on the test?

11. The ratio of right-handed students to left-handed students is 9 to 2. There are 352 students in the school.

How many students are right-handed and how many are left-handed?

12. Clarence bought 5 rolls of color film and 4 rolls of black-and-white film for his camera for a total of $24. The black-and-

white film costs $1.50 more than the color film. How much does one roll of black-and-white film cost?

a. $2 b. $2.50 c. $3.50 d. $4

13. Michael’s income from two stocks each year totals $280. Stock A pays dividends at the rate of 5% and stock

B at the rate of 6%. If she has invested a total of $5000, how much is invested in each stock?

14. A history test has 30 questions worth a total of 250 points. Every question is either multiple-choice or true-false. The

true-false questions are worth 5 points each and the multiple-choice questions are worth 10 points each. Which system

of equations can be used to determine how many multiple-choice questions, m, and how many true-false questions, t, are

on the test?

a. [pic] b. [pic] c. [pic] d. [pic]

15. At the bulk foods store, cashews cost $5 per pound and pecans cost $7 per pound. Julian bought a 3 lb. mixture of

cashews and pecans for $19. How many pounds each of cashews and pecans were in the mix?

a. 2 lbs. of cashews and 1 pound of pecans c. 1 lb of cashews and 2 lbs of pecans

b. 1.5 lbs. of cashews and 1.5 lbs. of pecans d. .5 lbs. of cashews and 2.5 lbs. of pecans

16. The coach of a high school baseball team bought 6 caps and 8 t-shirts for $140. A few days later at the same price, he

bought 6 t-shirts and 9 caps for $132. Write and solve a system of equations to determine the price of a cap and the

price of a cap and the price of a t-shirt.

17. The perimeter of a rectangular deck is 174 feet. The length of the deck, l, is 6 feet longer than 2 times the width, w.

Which system of equations can be used to determine the length and width, in feet, of the deck?

a. [pic][pic] b. [pic] c. [pic] d. [pic]

18. Manuel has $54 to spend on CD’s and books. Each CD costs $9, and each book costs $6. He wants to buy exactly 7

items and spend all of his money. Write a system of equations that can be used to determine the number of CD’s and

books Manuel buys.

19. A box contains 22 coins, consisting of quarters and dimes. The total value of the coins $3.55. Which system of

equations can be used to determine the number of quarters, q , and the number of dimes, d?

a. [pic] b. [pic] c. [pic] d. [pic]

20. Suppose you bought supplies for a party. Three rolls of streamers and 15 party hats cost $30. Later you

bought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much

did each party hat cost?

21. The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent $135

buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of

juice and two cases of bottled water. How much did a case of juice cost? How much did each case of bottled

water cost?

22. You and your cousin go to Wendy’s for a “big” lunch. You buy 3 burgers and 2 orders of fries for $6.50. Your

cousin buys 2 burgers and order 5 orders of fries for $8.00. How much did each item cost?

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

Equations:

_________________________

Equations:

_________________________

Equations:

_________________________

Equations:

_________________________

Equations:

_________________________

Pg. 6

a) The solution to the system is (-2, -2).

b) The solution to the system is (-1, -2).

c) The system has infinitely many solutions

d) The system has no solution.

Pg. 4

Pg. 7

Pg. 2

[pic]

ahs-pfeiffer.

Equations:

_________________________

Pg. 3

Pg. 7

Pg. 10

Pg. 11

Pg. 4

Pg. 5

a) Is (0,-2) a solution

to the system?

b) Is (3,5) a solution

to the system?

a) Is (-2, -3) a solution to the system?

b) Is (1, 1) a solution to the system?

c) Is (-4, 3) a solution to the system?

Pg. 8

Pg. 9

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