Solving problems - Bremerton School District / …€¦ · Web viewShow your work using words, numbers, and/or diagrams. Jay earns $16.42 per hour. He earns 1.5 times his hourly wage

Algebra EOC Review and Practice

Solving problems A1.1.A Select and justify functions and equations to model and solve

problems.Where is this in my textbook?

throughout

Example problems

In Pedro’s barn, the number of mice is inversely proportional to the number of cats. When he owned 5 cats, there were 48 mice in the barn. He increased the number of cats to 8.Based on the increased number of cats, how many mice are in the barn?The value of a $6,000 investment is increasing 15% each year.Which equation represents y, the value of the investment in x years?

A. y = 6000(0.15)xB. y = 6000(1.15)xC. y = 6000 + 0.15xD. y = 6000 + 1.15x

Mr. Madison gave his students this pattern of white tiles:

He asked his students to write an equation to represent the number of white tiles, t, for any figure number, n. Which equation represents the number of white tiles in the pattern?A. t 4n 8 B. t 4n 4 C. t n 4 D. t n 2Julie’s grandfather gives her a dollar one day. Each day after that, he gave her twice as many dollars as he had given her on the previous day. Let f ( n )represent the number of dollars Julie’s grandfather gave her on day n.a) Which function models this situation?A. f ( n )=2n−1 B. f ( n )=2n C. f ( n )=2n+1 D. f ( n )=(n−1)2

b) How much will Julie have after 12 days? __________Kesha is planning to rent a van for her trip to Mt. Rainer. Two of her friends each rented the same type of van from the same car rental company last week. This is what they told her:

John: “The cost of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for five days and drove it 200 miles.”

Katie: “The cost of my rental was only $100. I drove it for 100 miles and had it for two days.”

Kesha plans to get the same type of van that John and Katie had from the same car rental company. Kesha estimated her trip would be 250 miles, and she would have the vehicle for four days. Let C = cost, M = miles, and D = daysWhich of the following equations could Kesha use to figure out how

much her rental would cost?A. C= 40.00M + 0.20DB. C= 40.00D + 0.20MC. C= 20.00M + 0.40DD. C= 20.00D + 0.40M

Mike kept track of the number of passengers on his bus, noticing the following:

- At the first stop, several passengers (p) got on the empty bus.- At the second stop, the number of passengers doubled when

more people got on.- At the third stop, 3 passengers got off the bus and no

passengers got on.- At the fourth stop, 2 passengers got on the bus and no

passengers got off.Which expression represents the number of passengers on the bus after the fourth stop?

A. 2p + 5B. 2p – 1C. 2p – 5D. 2p + 1

Self Assessment Still Struggling Getting it Got it

A1.1.BSolve problems that can be represented by linear functions, equations, and inequalities.

Where is this in my textbook?

Chapters 2, 3, 4, and 5.

Example problems

Tricia is reading a 750-page novel for English class.— Tricia has already finished reading part of the novel at school.— She has planned to finish the novel by reading the same number of pages at homeevery day.— After reading 2 days at home, she had finished a total of 210 pages.— After reading 6 days at home, she had finished a total of 330 pages.

a) Write an equation that can be used to determine y, the total number of pages. Tricia has read after reading at home for x days.b) Use the equation to determine the total number of days Tricia needs to read the novel at home to finish it.The Acme Recycling Company has three salary options for its part-- time summer ‐employees.The total money earned is related to the amount of cans recycled and an optional hourly wage.

Option 1: $0.25 a can plus $1.00 an hourOption 2: $0.05 a can plus $5.00 an hourOption 3: $0.40 a can and no hourly wage

Jamal estimates that he can recycle a minimum of 20 cans per hour. Which option will allow Jamal to make the most money? Show your work using words, numbers, and/or diagrams.Jay earns $16.42 per hour. He earns 1.5 times his hourly wage for every hour he works over 40 hours each week. He earns 2 times his hourly wage on Sunday. Jay worked 3

2

hours on Sunday and earned a total of $903.10 for the week. How many total hours did Jay work last week? Show your work using words, numbers, and/or diagrams.

Dorian is saving money to buy a bicycle. Currently he has saved 23 of the money he needs

to buy the bicycle. He earns $14.50 more mowing lawns and now has 45

of the money he

needs to buy the bicycle. Determine the cost of the bicycle.The assistant pizza maker makes 6 pizzas an hour. The master pizza maker makes 10 pizzas an hour but starts baking two hours later than his assistant. Together, they must make 92 pizzas. How many hours from when the assistant starts baking will it take?A swimming pool holds 375,000 liters of water. Two large hoses are used to fill the pool. The first hose fills at the rate of 1,500 liters per hour and the second hose fills at the rate of 2,000 liters per hour. How many hours does it take to fill the pool completely?Radio Shack makes $100 profit on every DVD player it sells and a $60 profit on every CD player it sells. The store manager wants to make a profit of at least $600 a day selling DVD players and CD players.a. Write a linear inequality to determine the number of DVD players x and the number of CD players y that the owner needs to sell to meet his goal.b. Graph the linear inequality.c. List three possible combinations of DVD players and CD players that the owner could sell to meet his goal.


A1.1.CSolve problems that can be represented by a system of two linear equations or inequalities.


Chapter 6

Example problems

Two-hundred items were sold at a snack stand for a total of $130.00. The only items sold were cans of pop for $0.50 and bags of popcorn for $0.75.How many of each item were sold?

A. 120 cans of pop, 80 bags of popcornB. 80 cans of pop, 120 bags of popcornC. 160 cans of pop, 40 bags of popcornD. 40 cans of pop, 160 bags of popcorn

A basic photo package costs $15.00 from Company A and $12.00 from Company B. Additional wallet-sized photos can be purchased for $0.50 each from Company A and $0.75 each from Company B.The same number of wallet-sized photos will be purchased from each company.Determine the number of additional wallet-sized photos that need to be purchased from each company so that the total cost of the basic package and the additional wallet-sized photos from Company A will be equal to the cost from Company B.The admission fee at a small local fair was $1.50 for children and $4.00 for adults. A total of 2,200 people entered the fair and $5,050

3

was collected.Let c = the number of children that attended the fair.Let a= the number of adults that attended the fair. Write two equations that can be used to determine the number of children and adultsthat entered the fair. Solve the system of equations to determine the number of adultsthat entered the fair.


A1.1.ESolve problems that can be represented by exponential functions and equations.


11.2 and 11.3

Example problems

E.coli bacteria reproduce by division. Every 30 minutes one E.coli cell divides into two cells. A new E.coli culture is started with 1 cell.a. Generate a table of values using time for x and cells for y.

b. Write a function that models the number of E.coli cells at the end of each 30-minute interval. View both the graph and the table on the graphing calculator to verify your function.c. State an approximate domain for the model based on the context.d. How many E.coli bacteria will be present after the 10th 30-minute interval?e. After what 30-minute interval will you have at least 600 bacteria?The population of a town in 2003 was estimated to be 35,000 people with an annual rate of increase of about 2.4%.The equation shown represents the growth of the population, where y is the number of people living in the town in t years after 2003.

y=35000 (1.024)t

Determine the approximate population in 2007.Self Assessment Still Struggling Getting it Got it

Numbers, expressions, & operations

A1.2.AKnow the relationship between real numbers and the number line, and compare and order real numbers with and without the number line.


Throughout and 7.2

Example problems

Place the following numbers in order from least to greatest.

π , 103

,−3.34 ,3. 2,0 ,−√9

Order the following numbers from largest to smallest:

4

6.32 x 103, 6.32 x 10-2, 8.32 x 10-4, 7.32 x 10-3

Which numbers are both less than−56 ?

A. −23 and −3

4

B. -2.1 and −65

C. -0.65 and -1.2

D. −23 and -0.8

The distance from Seattle to each of three cities is shown in the table.

Which list shows the three cities in order from nearest to farthest distance from Seattle?

A. Phoenix, Ames, MinneapolisB. Ames, Phoenix, MinneapolisC. Minneapolis, Phoenix, AmesD. Phoenix, Minneapolis, Ames


A1.2.BRecognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.


throughout

Example problems

Determine the value of the expression when x = 2, y = 5 and z = -3.4 y−3|x−z2|

For what values of a is 1a an integer?

A. when a is an integer B. when a is a positive numberC. when a is greater than 0 and less than 1 D. when a is greater than 0For what values of a is –a always positve?Given n is an integer greater than 0 and a is a real number when is always negative?A. when a is negative B. when n is oddC. when a is negative and n is even D. when a is negative and n is oddFor what values of a is√5−a defined (a real number)? A. a<5 B. a>5 C. only 0 D. only 5

5


A1.2.CInterpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.


7.1-7.4 and 11.6

Example problems

Write the expression in simplest radical form.

√ 1825

Simplify the expression. Express your answer using positive exponents.

( x2

x−3 )4

The expression ((x3)−2

x2 x3 )3

simplifies to the form, xm, for all nonzero

values of x.Determine the value of m.


FunctionsA1.3.A Determine whether a relationship is a function and identify the

domain, range, roots, and independent and dependent variables.Where is this in my textbook?

4.1-4.3

Example problems

The equation of a function is shown.f ( x )=|x+1|

What is the domain of f (x)?A. All real numbersB. All real numbers except -1C. All real numbers greater than -1D. All real numbers between -1 and 1

An absolute value function is given:

f ( x )=−2|x−1|+5

a) What is the domain?

b) What is the range?


6

A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.


Chapter 4, 5, and 11

Example problems

Ms. Smith is purchasing a fruit platter. She has received pricing information from three restaurants. Each restaurant uses a different linear function to determine the price of a fruit platter where x is the pounds of fruit purchased.Restaurant #1 Restaurant #2 Restaurant #3

p ( x )=2+2.6 x

a) Determine which restaurant Ms. Smith should choose to receive the best deal when she purchases a 10 –pound fruit platter.

b) Based on your choice, determine the price Ms. Smith will pay for a 10-pound fruit platter.

The table shown gives the total cost of paying an admission fee to a county fair and purchasing ride tickets.a) Plot all the data from the table on the grid provided.

b) Write an equation that can be used to determine c, the total cost, in dollars, for n tickets and admission to the fair.


A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b.

7


4.3, and throughout

Example problems

Given f ( x )=x2+3 x−1, find f (−2).Suppose f is a function.If 10=f (−4), give the coordinates of a point on the graph of f.Determine the value of f (4 ) given the function shown. f (x)=– x2+3


Linear equations & inequalitiesA1.4.A Write and solve linear equations and inequalities in one variable.Where is this in my textbook?

Chapter 2 and 3

Example problems

Solve the following equations. Determine if they have one, none, or infinite solutions.

a. −2 x+4=5−3 x

b. 5 z=12

(10 z+5 )

c. 3 ( x−2 )+2=5 x−7−2 xd. 6 x−1=4 x+8−6 x−3e. 2 ( x−3 )+4 x=15+2 x

The equation 13−2|x+3|=5 has two real solutions. Determine the negative solution of the equation.The equation 2|x−1|−10=−4 has two real solutions. Determine the negative solution of the equation.Which inequality represents all the solutions to 3 ( x−4 ) ≥−8?

A. x ≥−203

B. x≥−43

C. x≥ 43

D. x≥ 283


A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.


Chapter 5, esp. 5.7 and 5.8

8

Example problems

Write an equation for a line with a y-intercept equal to (0,-5) and a

slope equal to 23

.

A. y=5 x+ 23 B. y=2

3x−5 C. y=5 x−2

3 D.

y=−23

x−5

Write an equation for a line with a slope of 2 that goes through the point (1,1). A. y−1=2(x−1) B. y+1=2( x+1) C. y−1=2(x+1) D. y−1=1(x−2)Write an equation for a line (in point-slope form) that goes through the points (6, -2) and (-3, 5).

A. y+3=−79

(x−5) B. y−5=79(x−3)

C. y+3=79

( x−5 )D. y−5=−79

( x+3)

Write an equation for a line passing through the points (-1, 2) and (4, -23).

A. y=−15

x+ 125

B. y=5 x+3 C. y=−5 x−3 D. y=5 x−3

Write an equation in slope intercept form for a line passing through (3, 7) and (7, 4).

A. y=−34

x+ 374 B. y=3

4x+ 37

4 C. y=−43

x+ 374 D.

y=−34

x+ 437

Write the equation 3 x+2 y=5 in slope intercept form.

A. 2 y=−3 x+5B. y=−3 x+5 C. y=−32

x+ 52 D. y=3

2x+ 5

2Write the equation y+3=−4 (x−7 ) in slope intercept form. A. y=−4 x+25 B. y=−4 x−31 C. y=4 x−31 D. y=−4 x+28

Write the equation y−1=23(x−6) in standard form.

A. y=23

x−3 B. 2 x+3 y=9 C. −2 x+ y=−3 D. 2 x−3 y=9

Describe the graph of the equation y=7 x−3. A. gradual increasing line that passes through the point (0, 7) B. steep decreasing line that passes through the point (0, 3) C. gradual decreasing line that passes through the point (0, -3) D. steep increasing line that passes through the point (0, -3)

Describe the graph of the equation y−7=12( x−2) .

A. flat line neither increasing or decreasing that passes through the point (-2, -7) B. gradual decreasing line that passes through the point (2, 7) C. gradual increasing line that passes through the point (2, 7) D. steep increasing line that passes through the point (2, 7)

9


A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.


Chapter 5

Example problems

What is the slope of the line that passes through the points (-3, 2) and (5, -10)?

A. −32

B. −23

C. 23

D. 32

What are the slope and y-intercept of the line that represents 3 x−5 y=1?

A. slope = −35 ; y-intercept = 1

5

B. slope = −35 ; y-intercept = 5

C. slope = 35 ; y-intercept = −5

D. slope = 35 ; y-intercept = −1

5Mary is going to deposit an equal amount of money into a checking account each month until she has saved $500. The amount of money,y, in the account after x months can be modeled by the equation y=25 x+100.What does the slope of the graph of the equation represent?

A. The amount of money deposited monthlyB. The amount of money originally in the accountC. The number of months it would take to earn $100D. The number of months it would take to reach $500

1. Catarina and Laura need to travel to a soccer team meeting located on the far side of town. Laura leaves from her house and Catarina leaves from school. The graph below shows the relationship between time and distance from their school.

10

What can be said about the intersection of the graphs of Laura and Catarina?

A. Laura and Caterina are both still at school.B. Laura and Catarina are the same distance away at school.C. Catarina is farther away from school than Laura.D. Laura is farther away from school than Catarina.

2. What can be said about the relationship between the rate at which Laura travels and the rate at which Catarina travels.

A. Laura and Catarina are traveling at the same rate.B. Laura is traveling at a faster rate than Catarina.C. Originally, Laura was traveling at a faster rate than Catarina.D. Catarina is traveling at a faster rate than Laura.

Given that the figure to the right is a square, find the slope of the perpendicular sides AB and BC. Describe the relationship between the two slopes.

A. AB has a slope of 85 and BC has a slope of −5

8 , which are

negative reciprocal slopes.

B. AB has a slope of 85 and BC has a

slope of 58 which are reciprocal slopes.

C. AB has a slope of 85 and BC has a

slope of 85 which are the same slopes.

D. AB has a slope of 85 and BC has a

slope of −85 which are opposite slopes.

What is the slope of a line perpendicular to the line that represents y=2 x=3?

A. -2

B. −12

C. 12

D. 211


A1.4.D Write and solve systems of two linear equations and inequalities in two variables.


Chapter 6

Example problems

Two lines divide the coordinate plane into the four lettered regions shown.

One region represents the solution set to the system of inequalities given.

{ y≥ 2 x+1

y≤−13

x−3

Which region represents the solution set for the system of inequalities given?

A. Region MB. Region NC. Region PD. Region Q

The graphs of two lines are shown on the coordinate plane.Which region is the solution to the

system of inequalities {y≥ 12

x+1

y ≥ 2 x+1?

A. PB. QC. RD. S

Solve the system of linear equations.

{y=−13

x−2

y=43

x+3

12

A. B.

C. D.

A system of linear equations is given.

{3 x−2 y=6x− y=1

Determine the solution to the system of equations.Self Assessment Still Struggling Getting it Got it

A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.


5.10 and 5.ext

Example problems

Two functions are shown. f ( x )=|x| g ( x )=|x+4|−7How does the graph of g(x ) differ from the graph of f (x)?

A. g(x ) is translated 7 units to the left and 4 units upB. g(x ) is translated 7 units to the right and 4 units upC. g(x ) is translated 4 units to the left and 7 units downD. g(x ) is translated 4 units to the right and 7 units down

1. A student filmmaker has a budget of $5000 to make a film. He begins filming which costs $75 an hour. Determine which function best represents this situation.A. C=5000+75 h B. C=5000 h+75 C. C=5000 h−75 D. C=5000−752. If the cost to film increases to $100 an hour, how will this increase affect the function above?3. How will the graph change if the filming costs increases from $75 an hour to $100 an hour?4. Determine the x and y intercepts for the graph and define the

13

meaning of each if the filming costs are $100 an hour.y intercept:x intercept:5. At the last minute, the student filmmaker discovers he must pay $1500 to rent the building and $100 an hour for filming. At this rate, how many hours will the student be able to spend filming before he runs out of money?A) 3.5 hours B) 30 hours C) 35 hours D) 40 hoursWhich statement best describes the transformation of the graph of y=|x| to the graph of y=|x+2|?

A. The graph shifts up 2 units.B. The graph shifts down 2 units.C. The graph shifts left 2 units.D. The graph shifts right 2 units.


Data & distributionsA1.6.A Use and evaluate the accuracy of summary statistics to describe and

compare data sets.


Chapter 10

Example The hourly wages, in dollars, of the employees at a company are listed in the chart.

14

Determine which measure of central tendency (mean, median, or mode) is most representative of the data in the chart. Support your conclusion using data from the chart.An equal number of Brand Q cell phone batteries and Brand R cell phone batteries were tested in cell phones to determine which battery brand had better battery life between charges. The results

are summarized in the box-and-whisker plots shown.Based on the box-and-whisker plots, which statement must be false?

A. The same number of each brand of batteries lasted more than 8 hours.

B. More Brand Q batteries than Brand R batteries lasted less than 10 hours.

C. More Brand Q batteries than Brand R batteries lasted between 5 and 6 hours.

D. More Brand Q batteries than Brand R batteries lasted between 6 and 12 hours.

There are 17 employees at a company. The employees earn these hourly wages.

8 employees earn $9 per hour. 7 employees earn $12 per hour. 2 employees earn $33 per hour.

Determine and explain mathematically which measure of center best represents thehourly wages of employees at the company.The amounts of Cathy’s last six clothing purchases were $109, $72, $99, $15, $99, and $89.a. Which value describes the average of Cathy’s purchases?b. Which value would Cathy tell her parents to convince them that she is not spending too much money on clothes? Explain.c. Which value would Cathy tell her parents to convince them that she needs an increase in her allowance? Explain.The finishing times of two runners (Jamal and Tim) for several one-

15

problems The finishing times of two runners (Jamal and Tim) for several one-mile races, in minutes, are shown in the box-and-whisker plots.

a. Who has the fastest time? b. Who has the slowest time?c. Make a convincing argument that Jamal is the faster runner.The number of traffic citations given daily by two police departments over a two-week period is shown in the box-and-whisker plots.

a. What is the best estimate of the difference in the greatest number of citations given by each department in one day? A. 10 B. 20 C. 30 D. 35b. What is the difference in the median number of citations between the two departments? A. about 8 B. about 15 C. about 22 D. about 40c. Which statement is NOT true? A. The East department gave the greatest number of citations in one day. B. The East department gave the least number of citations in one day. C. The East department has a greater IQR than the West department. D. The East department has the greater median number of citations in one day.


A1.6.B Make valid inferences and draw conclusions based on data.Where is this in my textbook?

Chapter 10

Example problems

An equal number of people from City A and City B were surveyed about the number of hours of TV they watched last week. The results of the survey are summarized in the box-and-whisker plots shown.

16

Based on the box-and-whisker plots, which statement must be false?

A. There were more people in City A than in City B who watched more than 20 hours of TV.

B. The same number of people in City A as in City B watched between 17 and 20 hours of TV.

C. There were more people in City B than in City A who watched between 5 and 12 hours of TV.

D. Twice the number of people in City B than in City A watched between 12 and 17 hours of TV.

Two classes have an equal number of students. The data in the table summarize the scores the students in these two classes earned on a

unit test.Which statement is a valid conclusion based on these data?

A. More students in Class 1 scored 70 than in Class 2.B. The same number of students in Class 1 scored 80 as in Class

2.C. More scores in Class 1 were closer to the median than in

Class 2.D. The highest score in Class 1 was greater than the highest

score in Class 2.Mr. Shapiro found that the amount of time his students spent doing mathematics homework is positively correlated with test grades in his class. He concluded that doing homework makes students’ test scores higher.Is this conclusion justified? Give evidence to support your answer.Joe found that cities with lots of police officers have higher rates of crime. He concluded that as the number of police officers increase, the amount of crimes committed increase as well. Is his conclusion justified? Give evidence to support your answer.When boat rentals increase, ice cream sales also increase. Therefore, when people rent boats they eat a lot of ice cream. To what extent is this conclusion accurate? Give evidence to support your answer.

Self Still Struggling Getting it Got it17

Assessment

A1.6.C Describe how linear transformations affect the center and spread of univariate data.


Chapter 10

Example problems

The mean score on an exam taken by 20 students was 72. The teacher added 8 points to each student’s score.What effect did the 8-point increase have on the mean and range of the scores?

A. The mean increased and the range increased.B. The mean stayed the same and the range increased.C. The mean increased and the range remained the same.D. The mean stayed the same and the range stayed the same.

At a particular company, every employee receives a 4% cost-of-living increase to their salary.What impact does this cost-of-living increase have on the mean and on the range of employee salaries at the company?

A. The mean increases but the range does not change.B. The mean does not change but the range increases.C. The mean and the range both increase.D. The mean and the range do not change.

Due to budget constraints at a particular company, every employee receives a 2% decrease to their salary.What impact does this salary decrease have on the mean and on the median of employee salaries at the company?

A. The mean and median both decrease.B. The mean and median do not change.C. The mean does not change but the median decreases.D. The mean decreases but the median does not change.


A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.


Chapter 5

18

Example problems

Dario kept track of his gas mileage for 5 weeks. He plotted the number of miles he traveled and the number of gallons of gasoline his car used.

a) Write an equation for the line that fits the data Dario plotted.

b) Use the equation to predict the number of miles Dario’s car would travel using 55 gallons of gasoline.

The graph shows the population of Lincoln, Nebraska in select years since 1960.

Which equation represents the line that best fits the data?

A. y=2 xB. y=2 x+120C. y=2 x+150D. y=120 x+2

A student measured the lengths of the hands and the heights of other students in his class for an assignment. The graph shows the data collected and a line that fits the data.

Which equation is best represented by the line?

A. y=0.75 x+20B. y=0.13 x+20C. y=7.5 x+25D. y=25 x+7.5

Vance graphed the relation between fund-raising profits for the chess club and the number of members.

19

a) Which equations best represents the data displayed on the graph?A. y=29n+180B. y=60 n+180

C. y=23

n+180

D. y=2003

n+180

b) What does the y-intercept represent in this situation?c) What does the slope represent in this situation?d) Predict the profit if the number of members increases to 30.Study the pattern shown in the table.

What is the value of s when r equals 10?Self Assessment Still Struggling Getting it Got it

A1.6.E Describe the correlation of data in scatter plots in terms of strong or weak and positive or negative.


4.5

Example problems

Select the description that best matches data shown in the following graphs.

1. A. strong positive B. strong negative C. weak positive D. weak negative E. no correlation

20




Additional ContentA1.7.A Sketch the graph for an exponential function of the form y = abn

where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.


11.2, 11.3

Example problems

Graph the exponential function y=−4 (2)x. Which of the following is the best match?

A. B.

C. D.

21

Graph A is the graph of y=4 (5)x and graph B is the graph of y=5 (4)x.Which statement about the two graphs is true?

A. Both graphs A and B rise at the same rate.B. Graph A rises at a faster rate than graph B.C. Graph B rises at a faster rate than graph A.D. The y-intercept of graph A is above the y-intercept of graph B.

Self Assessment

Still Struggling Getting it Got it

A1.7.B Find and approximate solutions to exponential equations.Where is this in my textbook?

11.2 and 11.3

Example problems

Estimate the solution to 3x=59,049. Explain how you know you are correct.x=¿

For the function f ( x )=( 12 )

x

determine the value of f ( x )when x=0.

When 2x=165, what is the value of x ?A. 4B. 9C. 20D. 32

An exponential equation is shown. 64=2(4)x

What is the value of x?A. 2.00B. 2.32C. 2.50D. 8.00


A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.


4.6 and 11.1

Example problems

For the geometric sequence shown a1=2. 2 , 6 ,18 , 54 , …What is the explicit formula for the sequence?

A. an=2 ∙3n

B. an=3 ∙2n

C. an=2 ∙3n−1

D. an=3 ∙2n−1

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A sequence is defined by the equation shown.t n=t n−1+2.5; t 1=5Determine the value of t 10 .What is the fifth term in the geometric sequence with a first term of 3 and a second termof 6?

A. 15B. 18C. 32D. 48

Let a1=8 and ak+1=ak+3.Determine a7.


A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others.


2.5

Example problems

The formula for the volume of a cylinder is shown.V=π r2 h

Which equation is equivalent to the volume formula when solved for r?

A. r=√ Vπh

B. r=√Vπh

C. r= V√ πh

D. r=√VπhSolve the following equation for R. IR=V

Solve the following equation for A. W = AL

Solve the following equation for h. A=12

bh

Solve the following equation for y. 2 x−3 y=−12Solve the following equation for x. ax+c=RSolve the following equation for p. 2h=w−3 p


Not counted for official score:

A1.1.D Solve problems that can be represented by quadratic functions and equations.A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection.

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A1.2.E Use algebraic properties to factor and combine like terms in polynomials.A1.2.F Add, subtract, multiply, and divide polynomials.A1.5.A Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose.A1.8.H Use inductive reasoning about algebra and proper ties of numbers to make conjectures, use deductive reasoning to prove or disprove conjectures.

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Solving problems - Bremerton School District / …€¦ · Web viewShow your work using words, numbers, and/or diagrams. Jay earns $16.42 per hour. He earns 1.5 times his hourly wage