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)x
B.y = 6000(1.15)x
C.y = 6000 + 0.15x
D.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 2
Julie’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 represent the number of dollars Julie’s grandfather gave her on day .
a) Which function models this situation?
A. B. C. D.
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 = days
Which of the following equations could Kesha use to figure out how much her rental would cost?
  1. C= 40.00M + 0.20D
  2. C= 40.00D + 0.20M
  3. C= 20.00M + 0.40D
  4. 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?
  1. 2p + 5
  2. 2p – 1
  3. 2p – 5
  4. 2p + 1

Self Assessment /  Still Struggling Getting it Got it
A1.1.B / Solve 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 home
every 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 hour
Option 2: $0.05 a can plus $5.00 an hour
Option 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 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 of the money he needs to buy the bicycle. He earns $14.50 more mowing lawns and now has 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.
Self Assessment /  Still Struggling Getting it Got it
A1.1.C / Solve problems that can be represented by a system of two linear equations or inequalities.
Where is this in my textbook? / 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?
  1. 120 cans of pop, 80 bags of popcorn
  2. 80 cans of pop, 120 bags of popcorn
  3. 160 cans of pop, 40 bags of popcorn
  4. 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$1.50for children and$4.00for adults. A total of 2,200people entered the fair and$5,050was 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 adults
that entered the fair.
Solve the system of equations to determine the number of adults
that entered the fair.
Self Assessment /  Still Struggling Getting it Got it
A1.1.E / Solve problems that can be represented by exponential functions and equations.
Where is this in my textbook? / 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 cultureis 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 thegraph 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 yis the number of people living in the town in tyears after 2003.

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

Numbers, expressions, & operations

A1.2.A / Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line.
Where is this in my textbook? / Throughout and 7.2
Example problems / Place the following numbers in order from least to greatest.

Order the following numbers from largest to smallest:
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?
A. and
B. -2.1 and
C. -0.65 and -1.2
D. 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?
  1. Phoenix, Ames, Minneapolis
  2. Ames, Phoenix, Minneapolis
  3. Minneapolis, Phoenix, Ames
  4. Phoenix, Minneapolis, Ames

Self Assessment /  Still Struggling Getting it Got it
A1.2.B / Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.
Where is this in my textbook? / throughout
Example problems / Determine the value of the expression when x = 2, y = 5 and z = -3.

For what values of ais an integer?
A. when a is an integer B. when a is a positive number
C. when a is greater than 0 and less than 1 D. when a is greater than 0
For what values of a is–aalways 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 odd
C. when a is negative and n is even D. when a is negative and n is odd
For what values of isdefined (a real number)?
A. B. C. only 0 D. only 5
Self Assessment /  Still Struggling Getting it Got it
A1.2.C / Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.
Where is this in my textbook? / 7.1-7.4 and 11.6
Example problems / Write the expression in simplest radical form.

Simplify the expression. Express your answer using positive exponents.

The expression simplifies to the form, for all nonzero values of .
Determine the value of .
Self Assessment /  Still Struggling Getting it Got it

Functions

A1.3.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.

What is the domain of ?
  1. All real numbers
  2. All real numbers except -1
  3. All real numbers greater than -1
  4. All real numbers between -1 and 1

An absolute value function is given:

a)What is the domain?
b)What is the range?
Self Assessment /  Still Struggling Getting it Got it
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.
Where is this in my textbook? / 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 is the pounds of fruit purchased.
Restaurant #1 Restaurant #2 Restaurant #3

a)Determine which restaurant Ms. Smith should choose to receive the best deal when she purchases a 10 –poundfruitplatter.
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.
Self Assessment /  Still Struggling Getting it Got it
A1.3.C / Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b.
Where is this in my textbook? / 4.3, and throughout
Example problems / Given , find
Suppose f is a function.
If , give the coordinates of a point on the graph of f.
Determine the value of given the function shown.

Self Assessment /  Still Struggling Getting it Got it

Linear equations & inequalities

A1.4.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.

The equation has two real solutions. Determine the negative solution of the equation.
The equation has two real solutions. Determine the negative solution of the equation.
Which inequality represents all the solutions to ?

Self Assessment /  Still Struggling Getting it Got it
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.
Where is this in my textbook? / Chapter 5, esp. 5.7 and 5.8
Example problems / Write an equation for a line with a y-intercept equal to (0,-5) and a slope equal to
A. B. C. D.
Write an equation for a line with a slope of 2 that goes through the point (1,1)
A. B.
C. D.
Write an equation for a line (in point-slope form) that goes through the points (6, -2) and (-3, 5)
A. B.
C. D
Write an equation for a line passing through the points (-1, 2) and (4, -23)
A. B. C. D.
Write an equation in slope intercept form for a line passing through (3, 7) and (7, 4)
A. B. C. D.
Write the equation in slope intercept form
A. B. C. D.
Write the equation in slope intercept form
A. B. C. D.
Write the equation in standard form
A. B. C. D.
Describe the graph of the equation
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
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)
Self Assessment /  Still Struggling Getting it Got it
A1.4.C / Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.
Where is this in my textbook? / Chapter 5
Example problems / What is the slope of the line that passes through the points (-3, 2) and (5, -10)?

What are the slope and y-intercept of the line that represents ?
  1. slope = ; y-intercept =
  2. slope = ; y-intercept =
  3. slope = ; y-intercept =
  4. slope = ; y-intercept =

Mary is going to deposit an equal amount of money into a checking account each month until she has saved $500. The amount of money,, in the account after months can be modeled by the equation .
What does the slope of the graph of the equation represent?
  1. The amount of money deposited monthly
  2. The amount of money originally in the account
  3. The number of months it would take to earn $100
  4. 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.

What can be said about the intersection of the graphs of Laura and Catarina?
  1. Laura and Caterina are both still at school.
  2. Laura and Catarina are the same distance away at school.
  3. Catarina is farther away from school than Laura.
  4. 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 Catarinatravels.
  1. Laura and Catarina are traveling at the same rate.
  2. Laura is traveling at a faster rate than Catarina.
  3. Originally, Laura was traveling at a faster rate than Catarina.
  4. 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 therelationship between the two slopes.
A. AB has a slope of and BC has a slope of , which are negative reciprocal slopes.
B. AB has a slope of and BC has a slope of which are reciprocal slopes.
C. AB has a slope of and BC has a slope of which are the same slopes.
D. AB has a slope of and BC has a slope of which are opposite slopes.
What is the slope of a line perpendicular to the line that represents ?
  1. -2
  2. 2

Self Assessment /  Still Struggling Getting it Got it
A1.4.D / Write and solve systems of two linear equations and inequalities in two variables.
Where is this in my textbook? / 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.

Which region represents the solution set for the system of inequalities given?
  1. Region M
  2. Region N
  3. Region P
  4. Region Q

The graphs of two lines are shown on the coordinate plane.
Which region is the solution to the system of inequalities ?
  1. P
  2. Q
  3. R
  4. S