Objective 1 TEKS Tracker

Transcription

1 Objective TEKS Tracker As ou complete the review and practice pages for Objective, check off the boes net to the TEKS ou have covered below. Objective The student will describe functional relationships in a variet of was. Pages Tracker TEKS Objective TEKS Tracker A. Foundations for functions. The student understands that a function represents a dependence of one quantit on another and can be described in a variet of was. The student is epected to: h A..A describe independent and dependent quantities in functional relationships h A.. gather and record data and use data sets to determine functional relationships between quantities h A..C describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations h A..D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities h A..E interpret and make decisions, predictions, and critical judgments from functional relationships h Objective Mied Review Grade Test Objective TEKS Tracker

2 Objective TEKS A..A Review Objective TEKS A..A Review A..A Describe independent and dependent quantities in functional relationships. In a function, the input is the independent quantit. The output is the dependent quantit because the value of the output depends on the value of the input. Function Dependent Quantit, Independent Quantit, (Output) (Input) When a function is shown as a graph, the independent variable is shown on the horizontal ais and the dependent variable is shown on the vertical ais. EXAMPLE YOU DO IT On average, a oung tree in Jackie s ard grows four feet a ear. The function h represents the height of the tree in feet after ears. Which quantit is the independent quantit in this relationship? Which is the dependent quantit? feet This is a constant quantit, not a variable one. It is neither independent nor dependent. Time that has passed This is the independent quantit because the number of ears that have passed determines the height of the tree. Height of the tree This is the dependent quantit because the height of the tree depends on how much time has elapsed. feet per ear This epresses the rate of growth, which is constant. It is neither independent nor dependent. Mr. Wu is driving at the constant rate of miles per hour on the epresswa. The function d h represents the number of miles d he has traveled after h hours. Which quantit is the independent quantit in this relationship? Which is the dependent quantit? Which is neither? Write our answers in the blanks.. Miles traveled. Speed. miles. Hours traveled dependent quantit neither neither independent quantit Objective TEKS A..A Review Grade Test

3 Objective TEKS A..A Practice Name Date Objective TEKS A..A Practice. A ramp s height increases feet for ever feet of its base length. The function h. represents the height h of the ramp when its base is feet long. What is the independent quantit in this relationship? A C D The slope of the ramp The height of the ramp feet The length of the ramp s base. What is the dependent variable in the equation? F G H J. What is the dependent variable in the graph? A C D. What is the independent variable in the graph?. A wildfire is consuming acres per hour. The function a h represents the number of acres a consumed during h hours. What is the independent quantit in this relationship? A h C h D a. Maria is burning a stick of incense. Twelve millimeters of the incense burn ever minutes. The function.t represents the length in millimeters of the incense after it has burned t minutes. What is the dependent quantit in this relationship? F G H J mm Millimeters per minute Length of the incense in millimeters Time in minutes that the incense has burned. What is the independent quantit in the function r s? A r s C s D Not here. What is the independent variable in the graph? F G H J F G H J Grade Test h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objective TEKS A..A Practice

4 Objective TEKS A.. Review Objective TEKS A.. Review A.. Gather and record data and use data sets to determine functional relationships between quantities. An equation describes a data set of ordered pairs if substituting the ordered pairs in the equation alwas ields a true statement. EXAMPLE YOU DO IT Which equation, or, describes the three ordered pairs (, ), (, ), and (, )? Substitute each pair of values in, one pair at a time. Ordered Pair Values Substitution Evaluation (, ) and : (true) (, ) and : (true) (, ) and : (true) Substitute each pair of values in, one pair at a time. Ordered Pair Values Substitution Evaluation (, ) and :? (not equal) (, ) and : (true) (, ) and :? (not equal) Substituting each data pair ields a true statement for. However, substituting each data pair does not ield a true statement for. Therefore, the equation describes the data set. Does the equation or the equation describe the three ordered pairs (, ), (, ), and (, )? Substitute each pair of values in, one pair at a time.. (, ) and : ( ) True?. (, ) and : ( ) True?. (, ) and : ( ) True? Subsitute each pair of values in, one pair at a time.. (, ) and : ( ) True?. (, ) and : ( ) True?. (, ) and : ( ) True?. Which equation describes the data? Yes Yes No Yes Yes Yes Objective TEKS A.. Review Grade Test

5 Objective TEKS A.. Practice Name Date Objective TEKS A.. Practice. Which equation describes the four ordered pairs (, ), (, ), (, ), and (, )? A C D. Which equation can be used to generate the values in the table? F G H J. Which rule describes the relationship between and in the table?. A function in which the -coordinate is alwas more than twice the -coordinate describes the relationship between the number of plaers on a soccer team and the number of pairs of socks ordered b the coach. Which ordered pair belongs to this function? A (, ) (, ) C (, ) D (, ). Which function includes the data set (, ), (, ), (, ), and (, )? F f() G f() H f() J f(). Which equation describes the points on the graph? A C D. The table shows how the number of students attending a pla determines the total cost of their tickets. Which equation describes this relationship? F G H J } A C D. Which function can be used to generate the points of the graph? f() F f() G f() H f() J f() h A.. When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A.. Practice

6 Objective TEKS A..C Review Objective TEKS A..C Review A..C Describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. Equations and inequalities can be used to model real-life situations. Variable epressions are used to represent unknown quantities. rittan is ears ounger than twice Jose s age. b j rittan s age is b. Jose s age is j. EXAMPLE YOU DO IT Janice spends d dollars for n boes of breakfast cereal. The cereal costs $ a bo, but Janice has a coupon that gives her a $ discount. What equation describes the relationship between the number of dollars Janice spends and the number of boes of cereal she bus? n This is the number of boes of cereal Janice bus. This is the price in dollars of one bo of cereal. n This is the price in dollars of n boes of cereal. n This is the price of n boes of cereal minus the discount. d This represents the number of dollars Janice spends. The epressions n and d represent the same amount. Therefore, the equation d n describes the relationship between the number of dollars Janice spends and the number of boes of cereal she bus. Arturo owes Charles $. He wants to pa Charles back and also to bu some used CDs from him. Arturo spends m dollars to bu used CDs and pa Charles the mone he owes. The CDs cost $ each. What equation describes the relationship between the number of used CDs Arturo bus and what he pas Charles?. How man CDs does Arturo bu?. What is the price in dollars of CD?. What is the price in dollars of CDs?. How man dollars will it cost Arturo altogether to bu CDs from Charles and to pa him back? m m. What letter represents the amount Arturo spends?. What equation describes the relationship between the number of used CDs Arturo bus and what he pas Charles? Objective TEKS A..C Review Grade Test

7 Objective TEKS A..C Practice Name Date Objective TEKS A..C Practice. The amount A that the Hernandez famil spends in n weeks for groceries at a local food club includes $ for the initial registration fee and $ each week for a bo of groceries. Which equation describes the relationship between A and n? A A (n ) A n C A n D A (n ). The temperature in degrees Fahrenheit F is greater than } of the temperature in degrees Celsius C. Which equation or inequalit can be used to determine F? F F } C G F } (C ) H F > } (C ) J F > } C. The base of a hill is feet below sea level. A path up the hill rises feet for ever feet of horizontal distance it gains. Which equation shows the relationship between the elevation above sea level E at an point on the path and the horizontal distance d of the point from the base of the hill? A E } d E } d C E } d D E } d. The quantit a is alwas less than } of the sum of another quantit b and. Which equation or inequalit represents this relationship? F a < } (b ) G a < } b H b > } (a ) J a } (b ). Kala s height in centimeters is represented b k. Randall s height in centimeters is represented b r. The function k.(r ) describes the relationship between Kala s height and Randall s height. What is the best interpretation of this function? A C D Randall s height is. times the difference of Kala s height and. Kala s height is times Randall s height decreased b.. Kala s height is. times the difference of Randall s height and. Kala s height is centimeters less than. of Randall s height.. Four tenths of the sum of the quantit m and is alwas greater than or equal to the quantit n. What inequalit can be used to determine the possible values of n? F n.(m ) G n.(m ) H n <.(m ) J m.(n ). Jared s weight in pounds j is pounds less than twice Sheila s weight. Sheila weighs s pounds. Which equation or inequalit describes this relationship? A j < s j < s C j (s ) D j s Grade Test h A..C When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objective TEKS A..C Practice

8 Objective TEKS A..D Review Objective TEKS A..D Review A..D Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. The relationship among two or more quantities can be represented in a variet of was, including equations and inequalities, tables, graphs, diagrams, verbal descriptions, and concrete models. Verbal description A satellite movie service costs $ per month plus $. for each movie viewed. Equation c.m Table Movies Cost $. $. $. $. EXAMPLE Jerr has $. Shirts on sale cost $ each. Does the table correctl describe the amount of mone d that Jerr has after buing n shirts? YOU DO IT n d An equation for this situation is d n. $ () $ () $ () $ () Does not check. The values in all the rows ecept the last row are correct. If Jerr bus shirts, he will have $ left, not $. The table does not correctl describe the amount of mone Jerr will have after buing n shirts. Alicia has $ in cash. T-shirts are on sale for $. Does the table correctl represent how much cash c Alicia will have after buing T-shirts? c An equation for this situation is c. $. () $. () $. () $. ( ) Yes. Does the table correctl show how much cash Alicia has left? Objective TEKS A..D Review Grade Test

9 Objective TEKS A..D Practice Name Date Objective TEKS A..D Practice. The Fraser famil is traveling miles for a vacation. The drive miles per hour. Which equation describes how man miles m remain after h hours of driving? A m h h m C m h D m h. A plane climbs meters per minute after takeoff from an airport meters above sea level. Which statement best describes the plane s altitude above sea level minutes after takeoff? F Its altitude in meters is the sum of times and.. Ashle has $. Apples cost $. apiece at a Mini Market. Which table shows how much mone m Ashle will have left after buing a apples? G H Its altitude in meters is the sum of times and. Its altitude in meters is the sum of and and. F H a m $. $. $. a m $. $. $. G J a m $. $. $. a m $. $. $.. Heidi bus some pencils, then uses up the same amount each week. The graph below shows how man pencils p Heidi has left after w weeks. Which equation describes the relationship between w and p in the graph? p A p w p w C p w D p w w J Its altitude in meters is the difference of times and.. Rod opens a savings account and puts $ in the account. He will put $ in the account each month afterwards. Assume that Rod does not withdraw an mone from the account. Which equation best describes the total amount s that Rod has deposited after eactl m months? A s m m s C m s D s m. A new skscraper is being built downtown. One stor goes up the first week and stories go up each week after that. Each week Todd tries to guess how man stories the building will have when completed. Which equation or inequalit best describes the number of stories s Todd might guess after n weeks of construction? F s n G s n H s < n J s n h A..D When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..D Practice

10 Objective TEKS A..E Review Objective TEKS A..E Review A..E Interpret and make decisions, predictions, and critical judgments from functional relationships. You can use tables, graphs, and equations to organize and summarize data so ou can make decisions and predictions from the data. A greeting card compan models its income and its epenses with linear functions. The compan knows that income will equal epenses at the point where the graphs of the two lines intersect. Dollars Income Epenses Income Epenses Number of cards sold EXAMPLE The table shows falling temperatures during the earl afternoon. What do ou predict the temperature will be at : in the evening? YOU DO IT Time F : : : : The temperature falls degrees in hours, or degrees per hour on average. If the temperature continues to fall at this rate, it will drop, or more degrees during the net hours. A good prediction, based on this rate, is that the temperature will be, or F at : P.M. Remember, however, that this is onl a prediction. This table shows rising temperatures during the morning hours. What do ou predict the temperature will be at : P.M.? Time F : : : :. The temperature rises degrees in hours.. That is, or degrees per hour.. The temperature will rise, or, more degrees during the net hours if it continues rising at the same rate.. At this rate, the temperature would be F at : P.M.. Do ou think the actual temperature might be different? Eplain. Yes; the actual temperature might be different because the temperature ma not increase at a constant rate. (Eplanations will var.) Objective TEKS A..E Review Grade Test

11 Objective TEKS A..E Practice Name Date Objective TEKS A..E Practice. Which equation might represent the relationship between altitude a in miles and elapsed time t in minutes of a space ship taking off from Earth at sea level? A a t a t C a t D a t. Which graph best represents a likel relationship between stud time h in hours and a student s score s on a test? F s G s. ased on the chart, which value is the best prediction of b when a? a b.... F G H J. The graph shows both the income and the epenses for a compan that manufactures treadmills. Which statement is not true? H s h J s h $ Income (, ) Epenses h. ased on the chart, which value is the best prediction of when?... A C D h A C D No. of treadmills manufactured Epenses are greater than income when treadmills are manufactured. Income is greater than epenses when more than treadmills are manufactured. The compan does not make a profit if it manufactures fewer than treadmills. Income is greater than epenses when treadmills are manufactured. h A..E When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..E Practice

12 Objective Mied Review Objective Mied Review. For a bab girl less than one ear old, the function } m represents the bab s length in inches at the end of m months. What is the independent quantit in this relationship? (A..A) A C D The rate of growth The length in inches The number of months since birth Not here. Which equation can be used to generate the values in the table? (A..) F G H J. Which function includes the data set (, ), (, ), (, ), and (, )? (A..) A f() f() C f() D f(). The weight of Henr s cat c is. times the difference of his dog s weight d and. What equation or inequalit describes this relationship? (A..C) F c <.(d ) G c.(d ) H c.(d ) J c.d. What is the dependent variable in the equation q p? (A..A) A p q. Jake has $ to spend on lunch. The total cost of his lunch will include an % meals ta. Jake also wants to leave a % tip. Which inequalit describes the total cost of his lunch if m represents the cost of his meal? (A..D) F m.m.m G m.m.m H m.() J.m. ased on the table, what would ou predict the value of n to be when m? (A..E) m n.... A C D. Anna has $. She spends $ for lunch each da. Which equation shows how man dollars s Anna still has after d das? (A..D) F s d G s d H d s J s d. Which graph best shows the relationship between time worked t and total pa s? (A..E) A C s s t D s s t C p D t t h When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objective Mied Review Grade Test

13 Objective TEKS Tracker As ou complete the review and practice pages for Objective, check off the boes net to the TEKS ou have covered below. Objective The student will demonstrate an understanding of the properties and attributes of functions. Pages Tracker TEKS A. Foundations for functions. The student uses the properties and attributes of functions. The student is epected to: h A..A identif and sketch the general forms of linear ( ) and quadratic ( ) parent functions h A.. identif mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete h A..C interpret situations in terms of given graphs or create situations that fit given graphs Objective TEKS Tracker h A..D collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approimating linear situations), and model, predict, and make decisions and critical judgments in problem situations A. Foundations for functions. The student understands how algebra can be used to epress generalizations and recognizes and uses the power of smbols to represent situations. The student is epected to: h A..A use smbols to represent unknowns and variables h A.. look for patterns and represent generalizations algebraicall A. Foundations for functions. The student understands the importance of the skills required to manipulate smbols in order to solve problems and uses the necessar algebraic skills required to simplif algebraic epressions and solve equations and inequalities in problem situations. The student is epected to: h A..A find specific function values, simplif polnomial epressions, transform and solve equations, and factor as necessar in problem situations h A.. use the commutative, associative, and distributive properties to simplif algebraic epressions h Objective Mied Review Grade Test Objective TEKS Tracker

14 Objective TEKS A..A Review A..A Identif and sketch the general forms of linear ( ) and quadratic ( ) parent functions. A parent function is alwas the simplest function in its famil. Tpe of parent function Equation Graph Characteristics of graph Objective TEKS A..A Review Linear Straight line Passes through (, ) Slope Quadratic Parabola Passes through (, ) Has vertical line of smmetr through (, ) Minimum point at (, ) EXAMPLE Does the graph show the linear parent function or the quadratic parent function? The graph is a straight line that passes through the origin and has slope. The value of appears to be equal to the value of for ever point on the line. The graph is not a parabola. YOU DO IT The graph shows the linear parent function,. Does the graph show the linear parent function or the quadratic parent function? Is the graph a straight line that passes through the origin and has slope? Is the value of equal to the value of for ever point on the graph? Is the graph a parabola that passes through (, )? Yes Does the graph have a vertical line of smmetr through the origin? Does for ever point on the graph? Which parent function does the graph show? quadratic parent function, No Yes No Yes The graph shows the. Objective TEKS A..A Review Grade Test

15 Objective TEKS A..A Practice Name Date Objective TEKS A..A Practice. Which function does the graph represent?. Which statement is true? F For ever point (, ) on the graph of, the point (, ) is also on the graph. G If (, ) is a point on the graph of, then (, ) is also a point on the graph. A Linear parent function H The graph of shows a constant rate of decrease. C Quadratic parent function oth A and J The domain of the function includes onl the positive real numbers. D Not here. Which function does the graph represent?. Which function does the graph represent? F for G for H for J for. Which statement does not describe the quadratic parent function? A C For ever point (, ) on the graph of the function, there is a corresponding point (, ). The graph of the function shows a constant rate of increase. The range of the function includes onl nonnegative real numbers. A C D Linear parent function Quadratic parent function oth A and Not here. The graph of which function passes through (, ), (, ), (, ), and (, )? F G H J. The graph of which function passes through Ï }, Ï }, },}, (, ), and (p, p)? A C D D The domain of the function includes all real numbers. h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..A Practice

16 Objective TEKS A.. Review A.. Identif mathematical domains and ranges and determine reasonable domain and range values for given situations, both contiguous and discrete. The set of all the first numbers in a set of ordered pairs is called the domain. The set of all the second numbers in the set is called the range. The -coordinates of the points in the graph shown at the right can be an real number. Therefore, the domain of the graphed function is {real numbers}. The -coordinate of ever point is either or, so the range of the function is {, }. Objective TEKS A.. Review EXAMPLE YOU DO IT Walter gets paid an hourl wage. The table shows the amount that Walter earned each of the four das he worked last week. What are the domain and range of the ordered pairs? Eplain wh it is not possible for to be in the domain of this relation? (hours worked) (amount earned) $ $. $ $ The -coordinates are,., and, so the domain is {,., }. The -coordinates are,, and, so the range is {,, }. Since it is not possible for Walter to work hours, cannot be in the domain of this relation.. Determine whether is in the domain of the function }. a. If ou substitute in the equation, what is the value of No; ecause division b is undefined, } is not a possible value for No the denominator of the fraction? b. Is } a possible value for? Eplain our answer. c. Is in the domain of }?. Determine whether is in the range of the function. a. If ou substitute for in the equation, then. b. What is the solution of the equation? c. Is in the range of? Yes. Objective TEKS A.. Review Grade Test

17 Objective TEKS A.. Practice Name Date Objective TEKS A.. Practice. Which value is not in the domain of the function }? A C D. Which value is not in the range of the function? F G H J. What is the range of the function represented b the ordered pairs in the table? A {,,, } {,,, } C D. Contestants in a game select a number from a list of numbers. The table shows that the number the select determines how man chances the have to win a prize. Which number is in the range of this function? Numbers in list Number of chances to win A C D. The graph of is shown below. What is the domain of the function? F G H J {real numbers} {positive real numbers} {negative real numbers} {nonpositive real numbers}. The scatter plot shows the height h of a plant d das after April. Which set describes the most reasonable range of the function for the first das? Height (in.) Flower Height h d Time (da) F {,,,,..., } G {,,,,,,, } H {real numbers less than } J {,,,,..., }. Li is ears old and is inches tall. What is the domain of the function relating Li s age on each birthda to her height in inches that da? A Positive integers less than or equal to Integers greater than zero C Real numbers less than or equal to D Integers between and, inclusive Grade Test h A.. When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objective TEKS A.. Practice

18 Objective TEKS A..C Review A..C Interpret situations in terms of given graphs or create situations that fit given graphs. Objective TEKS A..C Review Graphs can be used to model real-world situations. For eample, the function t } r models the time it will take ou to travel miles at different rates of speed. The graph of this function is shown. EXAMPLE YOU DO IT Time (hours) t r Rate (miles per hour) The graph represents the cost of gasoline at a local gas station. What is the price per gallon of gasoline at this station? What is the cost of gallons of gasoline at this gas station? Cost ($) Cost of Gasoline Amount (gal) The horizontal ais represents the number of gallons of gasoline purchased. The vertical ais represents the cost in dollars of those gallons of gasoline. One gallon of gasoline costs $ at this station, so gallons of gasoline cost $, or $ at the station. This graph represents the price of diesel fuel at the same gas station. What is the price per gallon of diesel fuel at this station? What is the cost of gallons of diesel fuel at this gas station? Cost ($) Cost of Diesel Fuel Amount (gal) One gallon of diesel fuel costs fuel cost $ What does the horizontal ais represent? What does the vertical ais represent? at this station. The horizontal ais represents the number of gallons of diesel fuel purchased. The vertical ais represents the cost in dollars of the gallons of diesel fuel purchased. $ at this station, so gallons of diesel Objective TEKS A..C Review Grade Test

19 Objective TEKS A..C Practice Name Date Objective TEKS A..C Practice. The graph shows the altitude h of an airplane t minutes after it begins its descent. Which information can ou determine from the graph? A C D Altitude (ft) Airplane s Height h t Time (min) The airplane descends feet ever minutes. The airplane starts its descent at feet. The airplane is at feet after minutes. The airplane will land after minutes.. ased on the graph, which statement is true? F G H J Altitude (ft) Altitude of Hot Air alloon Time (min) The balloon reaches a maimum altitude of feet. The balloon is at feet after minutes. The balloon begins falling after minutes. The balloon reaches feet after minutes.. Maggie s weekl salar is $ plus a % commission on her sales. What is the slope of the graph that models her weekl salar as a function of her weekl sales? F } G H } J }. ased on the graph, which statement is true? A Amount Maria s Income $ $ $ $ $ $ Time worked (hr) Maria does not get paid if she works onl minutes. If she works hours, Maria earns $. C D After hours, Maria s rate doubles. Maria s hourl rate increases with each additional hour she works.. Which graph could best model the path of an Olmpic diver s -meter platform dive? A C D A parabola that opens up A parabola that opens down A line with positive slope A line with negative slope. Which graph best models the relationship between the number of gallons of water used in the shower room at an athletic club and the number of people taking a shower? F G H J A line with a positive slope A line with a negative slope A parabola that opens up A parabola that opens down h A..C When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..C Practice

20 Objective TEKS A..D Review A..D Collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approimating linear situations), and model, predict, and make decisions and critical judgments in problem situations. A scatterplot can show whether a negative correlation, a positive correlation, or no correlation eists between the variables in a data set. Objective TEKS A..D Review Negative correlation Positive correlation No correlation EXAMPLE YOU DO IT What does the scatter plot tell ou about the relationship between age and the maimum pulse rate reached? Pulse rate Maimum Pulse Rate Age As age increases, the maimum pulse rate reached b the adults generall decreases. Thus, there is a negative correlation between age and the maimum pulse rate reached for this group of adults. This scatterplot compares age and average weight in a population of mice. Average Weight of Mice. What does the general pattern of the scatterplot tell ou about the relationship between age and weight? Weight (g) Age (wk) The average mouse weight increases as age increases.. What kind of correlation is there between age and weight? There is a positive correlation.. Would ou epect the average weight to continue increasing as the age of the mice increases? Wh or wh not? No, I would not epect the weight to continue increasing because mice do not continue growing indefinitel. Objective TEKS A..D Review Grade Test

21 Objective TEKS A..D Practice Name Date Objective TEKS A..D Practice. Which relationship most likel shows a positive correlation? A C D Ran s age and how man cousins he has Ran s age and his sister s age Ran s age and how man ears of school he has left Ran s age and his rate of growth. ased on the scatterplot, which is the most likel value of when?. Which relationship most likel shows no correlation? A C D Eam grade and hours studied Class size and number of desks Age and number of pets Teacher age and ears until retirement. renda s scatterplot compares temperature when it starts to rain with total rainfall. At C, how man millimeters of rain fell? F G H J. Which equation might represent a line of best fit for this scatterplot? A } } C D }. If a data set can be modeled b the equation }, what is the value of when is? F G H J Rainfall (mm) Temperature and Rainfall Temperature (C) Record our answer and fill in the bubbles in the grid below. e sure to use the correct place value. h A..D When ou finish this page, ou can check off a bo on our TEKS Tracker, page.. Grade Test Objective TEKS A..D Practice

22 Objective TEKS A..A Review A..A Use smbols to represent unknowns and variables. When ou use algebra to model real-life situations, variable epressions can represent unknown or variable quantities in the situation. For eample, suppose ou want to represent the perimeter and area of a square whose side length can var. The chart shows how ou can use the length of the side of the square to represent its perimeter and area. Objective TEKS A..A Review Unknown or variable quantit Length of side of a square Perimeter of the square Variable epression Area of the square s EXAMPLE YOU DO IT In a group of hikers, each hiker is carring an average of pounds. In another group of hikers, each hiker is carring an average of pounds. What epression represents the average weight carried b all the hikers? Each hiker in the first group carries an average of pounds, so the hikers carr a total of pounds. Each hiker in the second group carries an average of pounds, so the hikers carr a total of pounds. The hikers together carr pounds. This is an average of per hiker. Therefore, } represents the average weight that each hiker carries. s s } pounds The average height of the freshmen on the varsit basketball team is u inches. The average height of the freshman on the junior varsit basketball team is v inches. What epression represents the average height in inches of the freshman plaers? The freshmen on the varsit team have an average height of u inches. These freshmen have a combined height of inches. These freshmen on the junior varsit team have an average height of v inches. These freshmen have a combined height of The freshmen plaers have a combined height of The average height of the freshman plaers is u v u v u v } inches. inches. inches. Objective TEKS A..A Review Grade Test

23 Objective TEKS A..A Practice Name Date Objective TEKS A..A Practice. There are dogs and cats living in Richard s neighborhood. Richard calculates that } of the dogs and } of the cats are black. Which epression represents how man more black dogs than black cats are in the neighborhood?. In a game of softball, the bos get an average of hits each and the girls get an average of hits each. Which epression represents the average number of hits for all plaers? A } } A } } } } ( ) C D } }. In Wilma s class, the girls collect an average of m dollars each for disaster relief. The bos collect an average of n dollars each. Which epression represents the total amount of mone collected b Wilma s class? F m n G m n H m n } J m n }. In a chess tournament, sophomores compete against some freshmen. The sophomores win an average of games each. The freshmen win games altogether. Which epression represents how man more games the sophomores won? A C D. The area of a parallelogram is square units and the base is units. Which epression describes the parallelogram s height? F units G units H units J } units C } } D }. If n represents an integer, which epression will produce an odd integer? F n G n H n J n. A jacket that normall sells for n dollars is discounted %. You bu the jacket at the discounted price and also pa a % sales ta. Which epression represents the total cost of the jacket including the sales ta? A.(n.).(.n) C.(.n) D..n. You have a $ gift certificate to bu online music. Each song costs $.. Which epression represents the balance of our gift certificate after ou bu n songs? F (n.) G (n.) H.n J.n. A rectangular prism has a square base with sides of length and a height. Which epression represents the total surface area of the prism? A C D h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..A Practice

24 Objective TEKS A.. Review A.. Look for patterns and represent generalizations algebraicall. A number pattern is also called a sequence. Each number in a sequence is a term of the sequence. The chart shows how ou can use algebraic epressions to describe the nth term of a sequence. Sequence Description n th term,,,,... The terms are consecutive multiples of. n,,,,... The terms are consecutive powers of. n Objective TEKS A.. Review EXAMPLE YOU DO IT What algebraic epression describes the sequence,,,,,...? What will be the th term in the sequence? Since the difference between an two consecutive terms of the sequence is alwas, ou can determine the value of the nth term in the sequence. Term Value ( ) ( ) ( ) ( ) ( ) ( ) n ( n) n The algebraic epression n describes the nth term in the sequence. Therefore, the th term in the sequence is ( ), or. What algebraic epression describes the sequence,,,,,...? What will be the th term in the sequence?. What is the difference between an two consecutive terms in the sequence?. Using this difference, how can ou complete the following? a. ( ) ( ) b. ( ) c. ( ) d. ( ) e. ( ). What algebraic epression describes the nth term in the sequence?. What is the th term in the sequence? n Objective TEKS A.. Review Grade Test

25 Objective TEKS A.. Practice Name Date Objective TEKS A.. Practice. Which epression describes the nth term of the sequence of odd numbers that are greater than or equal to? A n n C n D n. What is the net number in the sequence,,,,,...? Record our answer and fill in the bubbles in the grid below. e sure to use the correct place value... In the chart below, Robi has indicated the number of triangles that can be drawn from one verte of each polgon. How man triangles can be drawn from one verte of a -sided polgon? Number of sides in the polgon Number of triangles F G H J. The first four triangular numbers are shown below.. Paul, Cam, and Liz wrote epressions that will generate integers that are more than a multiple of. Eric s epression does not generate these values. Which epression is Eric s if n is a positive integer? A n n C n D n. Which is the th term in the sequence,,,,,...? F G H J. Which epression will generate the nth term of the sequence,,,,,...? A n n C n D n What is the net triangular number? Record our answer and fill in the bubbles in the grid below. e sure to use the correct place value. h A.. When ou finish this page, ou can check off a bo on our TEKS Tracker, page.. Grade Test Objective TEKS A.. Practice

26 Objective TEKS A..A Review Objective TEKS A..A Review A..A Find specific function values, simplif polnomial epressions, transform and solve equations, and factor as necessar in problem situations. You can multipl two binomials, a b and c d, using the acronm FOIL, which stands for First terms, Outer terms, Inner terms, and Last terms. To use FOIL, multipl the pairs of first, outer, inner, and last terms. Then combine an similar terms. EXAMPLE YOU DO IT F L F L First Outer Inner Last ( )( ) ( ) ( ) ( ) ( ) O I I O A rectangular garden has an area of square feet and a length of feet. What binomial represents the width of the garden? ( )(c d) Area of a rectangle length width ( )( ) You know c because c must equal. You also know d because d must equal. Check the middle term of the polnomial: () Since ( )( ), the garden is feet wide.. A rectangular panel has an area of square meters and a width of meters. What binomial represents the length of the panel? a. (a b)( ) What is the panel s length? b. Since, the value of a is. c. Since ()(), the value of b is. d. Does ( )( )? e. What binomial represents the length of the panel?. What are the solutions of? a. ( )( ) Factor the trinomial. Yes b. ( )( ) Substitute. c. or ( ) Set each factor equal to zero. d. } } or Solve each equation. } and } e. The solutions are. Objective TEKS A..A Review Grade Test

27 Objective TEKS A..A Practice Name Date Objective TEKS A..A Practice. When, what is the value of f() if f()? Record our answer and fill in the bubbles in the grid below. e sure to use the correct place value.. What are the solutions of? A and } and } C } and } D } and }.. A rectangular mirror has an area of square inches. Which polnomials represent possible dimensions of the mirror? F G H in. and in. in. and in. in. and in. J in. and in.. Which equation is equivalent to? F ( )( ) G ( )( ). When, what is the value of if? Record our answer and fill in the bubbles in the grid below. e sure to use the correct place value. H ( )( ) J ( )( ). The height of a triangular sail on Jenn s sailboat is feet longer than twice the length of the sail s base. The area of the sail is square feet. What are the dimensions of the sail? A ft and ft ft and ft C ft and ft D ft and ft. A rectangle has an area of square centimeters. One side measures centimeters. Which epression describes the measure of the other side? F cm G cm H cm J cm. Which epression is equivalent to ab a b ab ab a b? F G H J ab a b ab ab a b ab ab a b ab ab a b. h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..A Practice

28 Objective TEKS A.. Review A.. Use the commutative, associative, and distributive properties to simplif algebraic epressions. The properties listed below are true for all real numbers a, b, and c. Stud the eamples in the table to see how ou can use the properties to write equivalent algebraic epressions. Propert name Propert statement Eample Objective TEKS A.. Review Commutative Propert Of addition: a b b a Of multiplication: ab ba Associative Propert Of addition: (a b) c a (b c) Of multiplication: (ab)c a(bc) Distributive Propert EXAMPLE YOU DO IT a(b c) ab bc a(b c) ab ac What is the simplified epression for (a ) ( a)? Epression Propert () () (a ) ( a) a a Distributive propert The simplified epression is a. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) a a Commutative propert of addition (a a) ( ) Associative propert of addition ( )a ( ) Distributive propert a Simplified epression What are the missing epressions or properties that allow ou to simplif ( c) c? Epression ( c) c c c c c c c c Propert ( ) Distributive propert Simplif. Distributive propert Commutative propert of addition Simplified epression Objective TEKS A.. Review Grade Test

29 Objective TEKS A.. Practice Name Date Objective TEKS A.. Practice. Which is the simplified epression for ( ) ( )? A C D. Four students simplified the epression (n ) ( n) ( n). Which student simplified the epression correctl? Simplified Student Epression Amber n Gloria n Liam n Josh n. Which statement can be justified using the distributive propert? F G H J The cost of bagels and bottles of juice is equal to the times the cost of one bagel and one bottle of juice. The cost of bagels and bottles of juice is equal to the cost of bottles of juice and bagels. The cost of bagels, bottles of juice, and tubs of peanut butter is equal to the cost of tubs of peanut butter, bottles of juice, and bagels. The cost of bagels and bottles of juice is equal to the cost of one bottle of juice and one bagel plus $. F Amber G Gloria H Liam J Josh. Which propert of real numbers justifies the statement (n n) (n n)? A C D Associative propert of addition Distributive propert Commutative propert of addition Associative propert of multiplication. Ricardo has s dollar bills in his pocket. Leda has s dollar bills in her wallet. Which epression represents the total number of dollar bills that Ricardo and Leda have? F s G s H s J s. The epression ( ) ( ) represents the total number of calories renda burned during her workout. What is a simplified form of this epression? A C D. Angela is scheduled to work (q ) hours this week. She worked q hours on Monda and q hours on Frida. How man hours does she have left to work this week? A q q C D. Nuria has completed miles of her run. She plans to run a total of miles. Which epression represents the number of miles she has left to run? F G H J. What is the simplified epression for (a ) (a )? A a a C a D a h A.. When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A.. Practice

30 Objective Mied Review. Which statement does not describe the quadratic parent function? (A..A). ased on the scatterplot, which statement is true? (A..D) A Its graph is a parabola with verte at (, ). Its graph is a parabola with line of smmetr. Objective Mied Review C If (, ) is a point on the graph of the function, then (, ) is also a point on the graph of the function. D An equation of the function is f().. Which numerical value is not in the domain of the function }? (A..) F G H J. ased on the graph, which statement is true? (A..C) A C D Height (ft) ird s Descent Time (sec) The bird starts its descent at feet. The bird descends feet in seconds. The bird lands after descending for } minutes. The bird descends feet ever seconds.. What is the net number in the sequence,,,,,...? (A..) F G H J A There is a positive correlation between and. There is a negative correlation between and. C The dependent variable is. D There is no correlation between and.. On a math quiz, the bos in the class scored an average of points each and the girls scored an average of points each. Which epression shows the average number of points that each student scored? (A..A) F } G } H } J } }. A rectangle has an area of square feet. Its length is feet. Which epression describes its width? (A..A) A ft ft C ft D ft. Which epression is equivalent to (g ) ( g) ( g)? (A..) F g G g H g J g h When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Objective Mied Review Grade Test

31 Objective TEKS Tracker As ou complete the review and practice pages for Objective, check off the boes net to the TEKS ou have covered below. Objective The student will demonstrate an understanding of linear functions. Pages Tracker TEKS A. Linear functions. The student understands that linear functions can be represented in different was and translates among their various representations. The student is epected to: h A..A determine whether or not given situations can be represented b linear functions h A..C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions A. Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is epected to: h A..A develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations h A.. interpret the meaning of slope and intercepts in situations using data, smbolic representations, or graphs h A..C investigate, describe, and predict the effects of changes in m and b on the graph of m b h A..D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and -intercept h A..E determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations h A..F interpret and predict the effects of changing slope and -intercept in applied situations h A..G relate direct variation to linear functions and solve problems involving proportional change h Objective Mied Review Objective TEKS Tracker Grade Test Objective TEKS Tracker

32 Objective TEKS A..A Review A..A Determine whether or not given situations can be represented b linear functions. The graph of a linear function is a straight line. A linear function increases or decreases at a constant rate. Line p shows a constant rate of increase. q p Line q shows a constant rate of decrease. EXAMPLE Is distance a linear function of time in each situation? Wh or wh not? Situation Tina rides her biccle at miles per hour for several hours. A flower pot falls from Jud s third-floor balcon. Response The distance Tina rides is a linear function of time. The distance Tina rides increases at a constant rate over time. The distance the pot falls is not a linear function of time. ecause of gravit, the rate at which the pot falls increases over time. YOU DO IT Is distance a linear function of time in each situation? Wh or wh not? Objective TEKS A..A Review. A ball is rolled up a ramp until it stops and then rolls back down. a. The the ball rolls is not a linear function of time. b. ecause of gravit, the rate at which the ball rolls as the ball rolls up the ramp and then back down the ramp. as the ball rolls. The table shows the relationship between the time t that a flock of geese flies and the distance d it travels. Time in flight, t Distance traveled, d hours miles hours miles hours miles hours miles a. How man miles does the flock fl in one hour? b. The is a linear function of at a distance distance the flock flies time constant rate because the distance the flock of geese flies increases over time. increases decreases miles Objective TEKS A..A Review Grade Test

33 Objective TEKS A..A Practice Name Date Objective TEKS A..A Practice. Which situation can be represented b a linear function?. Which situation can be represented b a linear function? A Some das the temperature is higher than it was the da before, but other das it is lower than it was the da before. F Louis plots the height of a football in feet against time in seconds as a quarterback passes to his wide receiver. C D A ball is tossed high into the air and then falls back to the ground. The rabbit population in the count where Michael lives is doubling ever months. It rains one inch per hour for hours. G H Some das Jamie practices her flute for minutes. Other das she practices for minutes. Marsha tpes words per minute on the first part of her eam. She tpes words per minute on the second part of the eam.. Which situation can be described b a linear function? F G H J Last ear Sandra doubled her savings ever month. Mr. Mendez drives his car at miles per hour for hours until he reaches his destination. Each da for das it rains onl half as much as it did the da before. A parachutist jumps from a plane, falls freel for seconds, opens her chute, and then floats gentl down to earth.. Which situation can be represented b a linear function? A C D Enriqueta earns $ a week selling newspapers. She keeps a table recording her total income. And plots the number of runs his favorite baseball team scores in each game over a period of two weeks. Patricia runs miles ever morning during the week and miles each morning during the weekend. Kevin s stamp collection is growing b % ever month. J During National Librar Week, the students in Ms. ernier s class read an average of. books each.. Which situation cannot be described as a linear function? A C D A submarine descends at a rate of feet per minute. As it runs, a rabbit maintains a constant speed of meters per second. Human hair has periods of growth followed b periods of no growth. During an mile kaak race, Tamara averages. mi/h.. Which graph models a linear function? F A V shaped graph with a verte at (, ) G H A parabola that opens up and has a verte at (, ) A parabola that opens down and has a verte at (, ) J A line that passes through (, ) h A..A When ou finish this page, ou can check off a bo on our TEKS Tracker, page. Grade Test Objective TEKS A..A Practice

34 Objective TEKS A..C Review A..C Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. Equations, tables, graphs, words, and sets of ordered pairs can all represent linear functions. The graph displas all the solutions of the linear function. The table displas some discrete data that fit the model. EXAMPLE Are the points (, ), (, ), (, ), and (, ) on the graph of? Determine which points are solutions of. If, then (). Therefore (, ) is a point on the graph. If, then (). Therefore (, ) is not a point on the graph. If, then (). Therefore, (, ) is a point on the graph. If, then (). Therefore (, ) is a point on the graph. Objective TEKS A..C Review YOU DO IT Onl the points (, ), (, ), and (, ) are on the graph of.. Do ou think that each point in the set {(, ), (, ), (, ), (, )} is or is not on the graph of? a. If, then. Therefore (, ) is on the graph. b. If, then. Therefore, is not on the graph. c. If, then. Therefore, (, ) on the graph. d. If, then. Therefore (, ) on the graph. e. Which of the four points are on the graph of?. In a linear function, f() is alwas more than times. What is the value of f() when? a. Which equation describes the relationship between f () and? b. If, then f() ( ). c. When, f(). (, ) is is The points (, ), (, ), and (, ) are on the graph. f () Objective TEKS A..C Review Grade Test