Algebra II Second Six Weeks 2014-2015 6 Move the Monster 7 Transformations Using Function Notation 8 Review 3.3 Systems of Inequalities HW: WS 3.3 Systems of Inequalities # 4, 5, 8-18 evens, 22-28 evens, 34, 36, 44 PP13-16 27 Systems of Equations Applications HW: Systems of Equations Applications 2 EVENS ONLY PP 24 Nov. 3 Linear Programming Practice Day CW/HW: Linear Programming Practice WS 3 PP 33-35 20 Quiz 3.1-3.2 13 Holiday HW: Begin Review 14 Section 3.2A Solving Systems by Substitution HW: WS 3.2A PP 5-6 21 Matrix Introduction HW: Matrix Introduction WS PP 17 (Due 10/23) 28 Systems of Equations Applications (Practice Day) CW: Systems of Equations Applications 2 ODDS PP 24 HW: Systems of Equations Applications 3 PP 28-29 4 Quiz Linear Programming HW: Study for Cumulative Test HW: Explore Transformations HW; Review Sheet 15 PSAT HW/CW: Spiral Review WS 2 PP 7-8 22 Review 3.1 - 3.3 No Matrices on Test dW: Review 3.1-3.3 PP 18-20 29 Systems Quiz 16 Section 3.2B Solving Systems by Elimination HW: WS 3.2B PP 9-10 23 HW: Factoring WS 4 PP 21 30 Section 3.4 Linear Programming HW: Linear Programming WS 1 PP 28-29 Oct. 10 Section 3.1 Graphing Systems of Equations HW: WS 3.1 Solving Systems by Graphing PP 1-4 17 Parent Function (Matching Quiz) Solving Systems of Equations Practice HW/CW: Systems of Equations Practice Worksheet PP 11-12 24 Systems of Equations Applications HW: Systems of Equations Applications 1 PP 23 31 Section 3.4 Linear Programming HW: Linear Programming WS 2 PP 30-32 HW: Factoring WS 5 PP 36 6 Graphing Quadratics 7 Graphing Quadratics
Set up a system and solve. Show all work on your own paper,
10, Mrs, Sweet bought some bran muffins at $0,89 each and corn muffins at $0,79 each,
$16,20 for 20 muffins, how many of each type did she buy?
If she paid
11. bulcie's deli sells ham sandwiches for $2,39 and turkey sandwiches for $3,12, Mark buys 50
sandwiches for his office for $126,80, How many of each sandwich did he buy?
12, Mr, Samuels bought candy for his school carnival, He purchased Skittles for $3,90 per pound andM&M's for $4,30 per pound, If he bought a total of 35 pounds of candy for $146.50, how many pounds
of M&M's did he buy?
13. Kellie participated in a fundraiser selling pens and stationery. Pens sold for $1,25 a piece and
stationery was $5.50 a box, If she sold a total of 13 items for $50.25, how many pens did she sell?
14, There are a total of 26 nickels and dimes in a piggy bank, The value of the coins is $1,65, How many
of each coin are in the bank?
15, Brooke bought 5 rolls of film and 2 photo albums for $49,40, The next day, she bought 6 rolls of
film and 3 photo albums for $65,85, How much does one photo album cost?
16, OMIT
17. The sum of two numbers is 77, The difference of the two numbers is 5, Find the numbers,
18, A teacher orders pens and pencils to be used as class prizes. An order of 20 pencils and 10 pens
costs $7,00 and an order of 5 pencils and 12 pens from the same company costs $6,50, How much is
30. Three apples and 2 peaches sell for $1.25, Five apples and 1 peach sell for $1,50, How much does
each cost?
31, A pizza chef made and sold a total of 100 pizzas that were either cheese or pepperoni. The
cheese pizzas sold for $9 each and 'the pepperoni pizzas sold for $11 each, If the total receiptswere $1026, how many of each kind did he sell?
32, A bowl contains 160 coins which are all pennies and nickels, The total value of the coins is $6.08,
How many nickels are in the bowl?
33 Two cellular phone companies offer different billing methods. Company A charges $10 a monthplus $0.18 per minute. Company B charges $30 a month plus $0,10 per minute, Write a system of
equations that could be used to determine the number of minutes for which the companies charge
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i-Y2z=72 +y+ z=8
- z=5
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11
f7, 13x + 2y = 7
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x-y =3
y+z=4X -- Z='3
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o 5y + 4z = 6x+ y+ z=3
4x- y =8
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14. x -2y + z- 1
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15. x-' y + 2z = 5.
x+ y+ 2z= 52x + 4z = 10
Graph the following systems,
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Systems of Equations Test 1 Review
Name,
Date: Period:
,
Name of System
Complete the following table, (Refer to Section 3,1)
Types of Lines Number of Solutions
Slopes of Lines
(Same orDifferent)
Y-Intercepts
(Same, Differentor N/A)
independent
dependent
inconsistent
Classify each system as independent, dependent, or inconsistent. Then state the number of solutions,
4x+6y= -182, 6x+3y -12
4x + 2y = 103, 2x- 5 = -y
6x - 4y = 10
4, ('ix-y 6
Solve the following systems by graphing:
[x+2y=65, (x=10-2y
/x + 2y = 4 7.6. (2x-y 8
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Sx - 6y = 168, 5x+y= 2
4x - 6y = 24.
1 49.ÿ,ÿx_ ÿy-
4 (x + Sz)11, For the system of equations, 4.z + 2 = ] solve for (x, y).
2x+y=15 '
12, Suppose you bought eight apples and one grapefruit for a total of $4,60, Later that day, you
bought six apples and 'three grapefruits for a total of $4.80. Now you want to find the price of
each apple and of each grapefruit, Write an equation for each purchase, Solve the system of
equations,
13. John has 15 coins, all dimes and quarters, worth $2,55. How many dimes and how many quarters
does John have?
14. The sum of two numbers is 89. The difference of the two numbers is 17. Find the numbers.
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15, OMIT
16, Patti participated in a fundraiser selling pens and thank you cards. Pens sold for $1,25 a piece andthank you cards were $5,50 a box, If she sold a total of 27 items for $88,50, how many pens did shesell?
17, Mason and David sold a total of 252 tickets for a benefit concert, David sold 12 few than twice asmany tickets as Mason, How many tickets did David sell?
Solve the following systems of inequalities:
19,{Y < -2]x2-11+ 6yÿx-2
(y > Ix+21- 4.
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Factor each trinomial, if possible. If it cannot be factored, write prime.
1. Cody is taking a vacation and needs some new clothes. He finds several package deals. One
package has two sweaters, three pants, and three shirts for $335. A different package has
three sweaters, two pants, and two shirts for $290. A third package has four sweaters, four
pants, and two shirts for $430. Find the cost of an individual sweater, pants, and shirt.
. The Geometry Sign Company makes signs. Their "Polygon Pack" contains squares, pentagons, and
hexagons. There are 24 signs in the package with a total of 112 sides. If there are 10 more
squares than pentagons, find the quantity of each shape in the package,
, Rufus, owner of the boggy Boutique, groomed 3 Cocker Spaniels, 5 Poodles, and 6 Schnauzers for
$810. The next day, he groomed 4 Cocker Spaniels, 6 Schnauzers and 7 Scotties for $860.. On
the 3rd day, he groomed 7 Poodles, 2 Schnauzers, and 10 Scotties for $920. If the cost of
grooming a Poodle is twenty dollars more than grooming a Scottie, find the price of grooming each
dog,
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-1 Willy the Bookworm likes to burrow thru books, especially the romance novel, the dictionary, and
the Guinness Book of World Records, Willy can only burrow 14 inches a day, which is the thickness
of the three books stacked together. He burrowedÿthru the romance novel twice and discovered
that it was the same distance as going thru the Guinness Book of World Records once. The next
day, he tried burrowing thru the dictionary once and the Guinness Book of World Records twice
and almost dropped dead of exhaustion because it was a total of 17 inches. He needs a new
combination of books, but needs to know that thickness of each book so that he will not exceed
his limits. Find the thickness of each book.
, Next summer, Frenchie Fry is going to Paris and needs to find out some prices. When her parents
(morn and dad) went, they saw the Notre Dame cathedral, the Louvre, Versailles and the Eiffel
Tower for a total of 114 francs. When her Aunt Betty went, she spent 60 francs going to the
Eiffel Tower once and twice to the Louvre, Roman has been to the Eiffel Tower and Notre Dame
with his morn and the spent 78 francs combined, Frenchie's Spanish teacher spent 78 francs to
see the Louvre once and the Eiffel Tower twice, Find the cost of each tour,
, Carl likes to watch Comedy Central. Monday he watches Kids in the Hall twice, Saturday Night1
Live (SNL), three reruns of Vacant Lot, and Whose Line is it Anyway for a total of 8 ] hours.
Tuesday he saw 2 episodes of Kids in the Hall, the Benny Hill Show, 4 episodes of SNL, and TheVacant Lot for a total of 10 hours, Wednesday he caught a marathon of 6 episodes of Benny Hill,
then 2.5 episodes of SNL for a total of ll.5 hours. Thursday, he saw one episode of each show
for a total of 7 hours. Friday he spent 9 hours watching Whose Line three times, Kids in the Hall
once, and The Vacant Lot twice. How long is each show?
Name Date Period
Systems
1,
of Equations Applications WS 2
Derrick invested $10,000 for one year in three different investments, The investments paid simpleannual interest of 5%, 6%, and 7%, respectively, and he received a total of $610 interests for 'theyear, He Invested $3000,more at 5% than at 6%, Find the amount invested at each rate,
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Carmella put her $5000 earnings into three different accounts, The accounts paid simple annualinterest of 8%, 10%, and 7%, respectively, The total Interest at the end of one year was $405, IfCarmella Invested $500 more at 10% than at 8%, find the amount she Invested In each account,
A box of wood contains wood cut Into triangular, square, and pentagonal shapes, There are 80pieces of wood in "the box, and +he pieces have a total of 290 sides, If there are 10 more triangularpieces than square pieces, find the number of pieces of wood of each shape in the box,
A manufacturer of educational supplies makes plastic shapes to hang tn classrooms, A package ofshapes contains squares, pentagons, and hexagons, There are 24 shapes in the package with a totalof 112 sides, If there are 10 more squares than pentagons, find the number of each shape in thepackage,
A change machine contains nickels, dimes, and quarters, There are 75 coins in the machine, and thevalue of the coins is $7,25, If "there are ,5 times as many nickels as dimes, 'find the number of coinsof each type in the machine,
A bin in a grocery store contains 100 Ib, of a mixture of almonds, peanuts, and ratsins, Almonds sellfor $1,89 per Ib,, peanuts for $1,58 per Ib,, and raisins for $1,39 per Ib, If the mixture containstwice as many pounds of peanuts as almonds, and if the total value of the almonds and raisins In themixture Is $93,40, how many pounds of each item does the mixture contain?
The sum of the digits of a three digit number Is 18, Three times the tens digit minus 5 times theunits digit Is 17, If 4 times the units digit Is added to twice the hundreds digit, 'the result is 22,Find the number,
1 The sum of the digits of a 'three digit number is 17, Four times the hundreds digit minus b 'timesthe tens digit is 12, If 7 times 'the units digit is added to 3 times the tens digit, the result is 47,Find the number,
,
10,
A rectangu!ar box is twice as long as i1' ts wide and twice as wide as it is high, The sum of its length,width, and height is 35 inches, What are the dimensions of the box?
The length of a rectangular shed is twice its height, and 'the height of the shed is one foot greaterthan its width, If the base of the shed has a perimeter of 40 feet, find the dimensions of theshed,
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Algebra 2 Systems of Equations Applications WS 3Date Per
, Next spring, Jack is going to Washington DC and needs to find out some prices. When his uncle went
with his 2 sons, they saw the White House, the Capital, the Pentagon and the National Archives for a
total of $135. When his parents (morn and dad) went, they spent $70 going to the White House, the
Capital, and the Pentagon. His best friend went to the White House twice and the Capital once for
$32. Jack's government teacher spent $50 to see the White House and the Capital once and the
Pentagon twice. Find the cost of each tour.
2. A box contains pieces of wood cut into triangular, pentagonal, and hexagonal shapes. There are 32pieces of wood in the box and the pieces total 142 sides. The box contains 2 more hexagons than
pentagons. How many of each shape are in the box?
system { Triangles
Matrix Pentagons
Hexagons
3. Next summer, Crystal is going to London and needs to find out some prices. When her aunt and uncle went, they
visited the Tower of London, Westminster Abbey, Buckingham Palace, and the National Gallery for $150. Whenher cousin went, she spent $65 going to Westminster Abbey twice and the National Gallery once. Her best friendwent to the Tower twice, Westminster Abbey once, and Buckingham Palace once for $80. Her Dad took his 2 sons
to the Tower and Westminster Abbey for $135. Find the cost of each tour.
System:
Tower
Westminster Abbey
Buckingham Palace
Matrix National Gallery.
4. A bank accepts pennies, nickels and dimes. There are 156 coins in the bank and the value of the coins
is $6.93. If there are 12 more dimes than nickels, find the number of each type of coins in the bank.
5. A box contains pieces of wood cut into triangular, pentagonal, and hexagonal shapes. There are 53pieces of wood in the box and the pieces total 253 sides. The box contains 5 more pentagons than
triangles. How many of each shape are in the box?
Solve the following systems of equations:
6, A pizza chef made and sold a total of 100 pizzas that were either cheese or pepperoni, The cheesepizzas sold for $9 each and the peperoni pizzas sold for $11 each, If the total receipts were $1026how many of each did he sell?
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Name, Datem
Linear Programming WS 1f
Period
1, ÿ4
O,yÿO
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Maximize for N = lOOx + 40y
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2, g tray of corn mufflnÿ reÿiulreÿ 4 cupÿ of milk ÿnd a !'rÿy of bran muffins tÿkes ÿ ours o'f milk, #,'[rÿy of corn mufftrls regulres 3 oups of wheÿ't 'iÿlour, ÿlqd a tray of brclrl muffins re,ÿlulres 3 cupÿ ofwheÿ flour, There ÿre ;I,6 ÿ,ups of milk ÿnd [ÿ oupÿ of whÿt flour,available, ÿnd the bÿker mÿkes a ÿ3profl't per 'trÿy of cor'n muffins (ÿnd ÿ per 'l'rqy of br(ÿn muffins, How mqny 'l'rÿys of .qch should 'Fhÿbÿker mÿRÿ In order 1'o mÿxlmlze profits?
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3, Kÿy 9rowÿ 1'omotoÿ8 ÿnd bÿon& ÿ'r ooÿ'rÿ ,$I fo ÿrow ÿ bushÿl of 1'omÿtoeÿ, ÿnd 11' costÿ #3 to 9rowbushel ,of b¢ÿnÿ, ÿt tÿlÿ 1 ÿquÿrÿ yÿpd 9f 19nd, fo grow q bushel tomÿtoeÿ ÿnd 11' l'qkeÿ 6 ÿuqre yÿrdÿof Iÿnd to grow Q bushel of grÿn beÿnÿ, Kÿy'ÿ budgÿl' Is #1ÿ;, ÿnd ÿhÿ hÿs ;ÿ4 squQrÿ yÿrds of Iÿndwtlÿblÿ, :ÿf ÿhe mqkeÿ $:[ profit on cqoh bushel of ÿomo'roÿs ÿnd $4 profit on eqch bu,ÿhÿl of bÿnÿ,
how mÿny bu,ÿhels of eÿah ÿhould ÿhe 9row In order to mÿxlmlze profits?
ObO¢c'l'lv¢ Function
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4, A biolog!st needs al' leÿt 40 fish for her experiment, she eenno'l' use more than ;ÿ perch or mopethÿn ÿ0 bÿsÿ, Eqch peroh co#ts ÿ5, ÿd eÿoh bÿ#ÿ co8!',ÿ $:ÿ, How mÿny of eÿch fish ÿhould he use Inorder to minimize the oo,ÿl'?
obJecl'lve Function,
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b, 4 restaurant provides Indlvlduel servln9ÿ of ketchup and rnustÿrd free to all ¢,ustornerÿ, onelngle-servln9 oontelner of ke!'chup co€Is the res1'eurant 2 cants end one contalnBr of mustard oostÿ 4
cents, A ketchup container tqlieÿ up ÿomR of ÿounter ÿpece and q mustard oont(ÿInÿr tÿkeÿ up ÿ omRof ÿpÿce, only 600 ctnR of counter space Iÿ ÿvqlleble for fheÿe oondlmenfÿ, The restaurÿn'l' must hove(ÿ'ÿ leQst ÿ0 eervlnBs of ketchup ÿnd %ÿ0 servings of must'ÿrd Qvelleble for the cuÿ'l'omerÿ, How manyservlnss of each condlrnent should be provided to mlnlrnlz, e the cost?
ObJ¢clive Function.
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6, AIIle (ÿrrlves ÿt school Iqte becqu#e her car broke down, Boo,use she hod to ÿo pick upn adrn!l' slip she only had 45 rnlnu!'eÿ 1'o finish a mel'h test when she ÿprtves to ClaS,ÿ, Thexem has two ess(ÿys end 30 multiple choice flueÿi'lon,R, Each correct e,ssoy I# wopt'h 20
points and each correct multiple choice Is worth Z points, she knows It usually tÿkes ÿ{ÿminutes !'o answer eqch essay quest'Ion ÿnd only one minute fo answer each multiple choicequasi'Ion, Assuming she reoelveÿ full ored!t for each quell'fen she enÿwerÿ, how mÿny of¢ÿch 'type of question ÿhould she ÿnÿwer i'o receive 1'h¢ maximum poÿslble polntÿ?
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Algebra 2 Linear Programming WS 3
Date Per
Linear Programming: Graph and find the objective function, constraints, and the solution:
1. Juan makes two types of wood clocks to sell at local stores. It takes him 2 h to assemble a pine clock,which requires 1 oz of varnish. It takes 2 h to assemble an oak clock, which takes 4 oz of varnish. Juan
has 16 oz of varnish in stock, and he can work 20 hours. If he makes $3 profit on each pine clock and $4
on each oak clock, how many of each type should he make to maximize his profits?
Objective Function
Constraints:
Pine Clocks
Oak Clocks
Maximum profit
2. The Cougar Stars are having a bake sale. They are baking pies. A pecan pie is made with 2 eggs and ¼
cup of sugar. An apple pie is made with 4 eggs and 1 cup of sugar. They will make a profit of $1.50 oneach pecan pie and $4 on each apple pie. They have at most 16 eggs and 3 cups of sugar. How many ofeach kind of pie should they make to maximize the profit? What is the maximum profit?
Objective Function
Constraints:
Pecan pies
Apple pies
Maximum profit
3. Lois makes banana bread and nut bread to sell at a bazaar, A loaf of banana bread requires 2 c flour
and 2 eggs. A loaf of nut bread takes 3 c flour and I egg, Lois has 12 c flour and 8 eggs on hand. Shemakes $2 profit per loaf of banana bread and $2 per loaf of nut bread, To maximize profits, how manyloaves of each type should she bake?
Constraints: Objective Function
Banana Bread
Nut Bread
MaximumProfit:
4. A tray of cinnamon muffins requires 4 cups of milk and a tray of blueberry muffins takes 2 cups of milk, A trayof cinnamon muffins requires 3 cups of flour and a tray of blueberry muffins requires 3 cups of flour, There areat most 16 cups of milk and 15 cups of flour available. The baker makes $3 profit per tray of cinnamon muffins and$2 per tray of blueberry muffins, How many trays of each should the baker make in order to maximize profits?
