Mathematics Unit 1 - Section 1 (Non-Calculator)

Transcription

1 Unit 1 - Section 1 (Non-alculator) This unit has two sections: a non-calculator and a calculator section. You will now take the first section of this unit in which you may not use a calculator. You will not be allowed to return to the non-calculator section of the test after you have started the calculator section. You will need to finish both sections within the allotted testing time. Once you finish the non-calculator section, read the directions in your test booklet on how to continue.

2 1. The cost to manufacture pairs of sunglasses can be represented by a function, ( ). If it costs $ to manufacture pairs of sunglasses, which of the following is true? Select the correct equation. ( ) =. ( ) = ( ) = (. ) = 1

3 . Which is a graph of the solution set of the inequality y? y y y y

4 . Several points are plotted on the graph. y G F E Which of the plotted points on the graph represent the zeros of the function f( ) = ( + )( )? Select all that apply. E F G (, ) (, ) (, ) (, ) (, ) (, ) (, )

5 . The figure shows a graph of the function of f ( ) in the y-coordinate plane, with the verte at (, 1 ) and the zeros at and. f() The function g is defined by g ( ) = +. Which statements are true? Select all that apply. E f( ) is greater than g( ). f( 1) is less than g( 1). f( ) is greater than g( ). f( 1) is less than g( 1). f( ) is greater than g( ).

6 Use the information provided to answer Part and Part for question. onsider the equation ( + ) + 1 = Part Let u = +. Which equation is equivalent to ( + ) + 1 = 1 + in terms of u? u u u u + 1u + 1 = 1u + 1 = + 1u + 1 = 1u + 1 = Part What are the solutions of the equation ( + ) + 1 = 1 +? Select all that apply. E F G 1

7 . In the y-coordinate plane, the graph of the equation y = 1 has zeros at = a and = b, where a < b. The graph has a minimum at (, c ). What are the values of a, b, and c? a =, b =, c = a =, b =, c = a =, b =, c = a =, b =, c = 11

8 Use the information provided to answer Part and Part for question. Let a represent a non-zero rational number and let b represent an irrational number.. Part Which epression could represent a rational number? b a + b ab b Part onsider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero? The other zero must be rational. The other zero must be irrational. The other zero can be either rational or irrational. The other zero must be non-real. 1

9 . The figure shows the graphs of the functions y = f( ) and y = g( ). The four indicated points all have integer coordinates. y y = f() y = g() If g ( ) = k f ( ), what is the value of k? Enter your answer in the bo. \.\\\\\\.....!!!!!! 1 STOP

10 Unit 1 - Section (alculator) Once you have received your calculator, continue with the calculator section. 1

11 . Elephant Population Estimates Namibia ombined estimates for Etosha National Park and the Northwestern Population Year 1 ase Year Estimated Number of Elephants,1,,1,1 The elephant population in northwestern Namibia and Etosha National Park can be predicted by the epression, ( 1. ) b, where b is the number of years since 1. What does the value, represent? the predicted increase in the number of elephants in the region each year the predicted number of elephants in the region in 1 the year when the elephant population is predicted to stop increasing the percentage the elephant population is predicted to increase each year 1

12 1. Jerome is constructing a table of values that satisfies the definition of a function. Input Output Which number(s) can be placed in the empty cell so that the table of values satisfies the definition of a function? Select all that apply. E F

13 11. random sample of teenagers participated in a taste test. Each teenager sampled four choices of fruit drink (labeled,,, and ), and then were asked to pick a favorite. The table shows the results of this taste test. Total oys 1 Girls 1 1 Total ased on the information given, which of the given statements are true? Select all that apply. % of the participants were girls. % of the participants preferred. 1 1 of the boys preferred. of the participants who preferred were girls. E The proportion of boys who preferred is equal to the proportion of girls who preferred. 1

14 1. The epression 1 can be factored into the form a ( + b)( + c), where a, b, and c are constants, to reveal the zeros of the function defined by the epression. What are the zeros of the function defined by 1? Select all that apply. E F G H Find the equation that is equivalent to the quadratic equation shown. = ( ) = ( ) = ( ) = ( ) = 1

15 1. ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the epression 1t + t +. What is the meaning of the in the epression? The ball took seconds to reach its maimum height. The ball took seconds to reach the ground. The ball was thrown from a height of feet. The ball reached a maimum height of feet. 1. local theater sells admission tickets for $. on Thursday nights. t capacity, the theater holds 1 customers. The function Mn ( ) = n represents the amount of money the theater takes in on Thursday nights, where n is the number of customers. What is the domain of Mn ( ) in this contet? all whole numbers all non-negative rational numbers all non-negative integers that are multiples of all non-negative integers less than or equal to 1

16 1. aroline knows the height and the required volume of a cone-shaped vase she s designing. Which formula can she use to determine the radius of the vase? r = V πh r = V πh r = V πh r V = ± πh 1. n epression is shown. aa ( + b ) + ( a + b) + ba ( + b ) Which epression is equivalent to the epression shown? 11a + b ab + a + b 11a + b ab + a + b a + b ab + a + b a + b ab + a + b 1

17 1. The ordered pairs (,. ), ( 1, 1), and (,. ) are points on the graph of a linear equation. Which of the following graphs shows all of the ordered pairs in the solution set of this linear equation? y y y y

18 1. When the solutions to each of the two equations shown are graphed in the y-coordinate plane, the graphs of the solutions intersect at a point. What is the y-coordinate of the point of intersection? Enter your answer in the bo. y = y = \.\\\\\\.....!!!!!!

19 . certain type of lily plant is growing in a pond in such a way that the number of plants is growing eponentially. The number of plants, N, in the pond at time t is modeled by the function Nt () = ab t, where a and b are constants and t is measured in months. The table shows two values of the function. t N( t) 1 1 Which equation can be used to find the number of plants in the pond at time t? Nt () = 1() 1 Nt () = () 1 Nt () = 1() Nt () = () t t t t

20 1. The function r ( ) represents the radius of a circle for a given area,. graph of the function is shown in the figure. r(). Radius (feet) rea (square feet) ccording to the graph, what is the approimate average rate of change in the radius of the circle as the area increases from square feet to square feet?.1 foot per square foot. foot per square foot. foot per square foot feet per square foot

21 . If f( ) = +, which statement regarding the verte form of f ( ) is true? In verte form, of 1. f ( ) = ( ) + 1 and therefore has a minimum value In verte form, of. f ( ) = ( ) + 1 and therefore has a minimum value In verte form, of.. f ( ) = ( ) +. and therefore has a minimum value In verte form, of. f ( ) = ( ) +. and therefore has a minimum value. In the equations listed, a, b, c, and d are real numbers. Which of the equations could have solutions that are non-real? Select all that apply. a = b a + b = a + b + c = E ( a + b)( c + d) = ab ( + c) = d

22 Mathematics Use the information provided to answer Part and Part for question. uring the 1st day of a canned-goods drive, Jasmine s homeroom teacher collected cans. uring the rd day, the teacher collected cans. Let represent each collection day, and let N represent the number of canned goods collected on that day.. Part ased on the situation, Jasmine claims that the number of canned goods collected can be modeled by an eponential function. What is the number of canned goods collected on the th day based on an eponential model? Enter your answer in the bo..\\\\\\.....! \!!!!!

23 Part Ramon disagrees with Jasmine and claims that the number of canned goods collected can be modeled by a linear function. Which statement is true about the number of cans predicted to be collected on the th day based on the two models? The number of cans predicted to be collected on the th day using a linear model is greater than that predicted using an eponential model. The number of cans predicted to be collected on the th day using a linear model is less than that predicted using an eponential model. The number of cans predicted to be collected on the th day using a linear model is equal to that predicted using an eponential model. There is not enough information to determine the relationship between the number of cans predicted to be collected on the th day using a linear model and that predicted using an eponential model.

24 Use the information provided to answer Part and Part for question. In a basketball game, Marlene made 1 field goals. Each of the field goals were worth either points or points, and Marlene scored a total of points from field goals.. Part Let represent the number of -point field goals and y represent the number of -point field goals. Which equations can be used as a system to model the situation? Select all that apply. E F + y = 1 + y = + y = 1 + y = + y = 1 + y = Part How many -point field goals did Marlene make in the game? Enter your answer in the bo. \.\\\\\\.....!!!!!!

25 Use the information provided to answer Part and Part for question. Rachel manages a souvenir store. popular item at the store is a small drum. The store typically sells 1, of these drums per month for $1 each. Rachel knows that for each $1 increase in the price of the drum, fewer drums would be sold in a month.. Part What is a function for the monthly revenue, in dollars, from sales of the drum, R(), where represents the number of price increases of $1? Monthly revenue equals the number of drums sold times the price of each drum. R ( ) = ( 1, )( 1 + ) R ( ) = ( 1, + )( 1 ) R ( ) = ( 1, + )( 1 ) R ( ) = ( 1, )( 1 + ) Part Which statements are true about R, the monthly revenue from sales of the small drum? Select all that apply. E F To maimize revenue, the drum should be sold for $. To maimize revenue, the drum should be sold for $. To maimize revenue, the drum should have a price increase of $. The revenue is the same for a price increase of $1 and a price increase of $. The amount of revenue from the sales of the drum is % greater with a price increase of $. The maimum revenue is $, more than the revenue from selling the drum with no price increase.

26 Use the information provided to answer Part and Part for question. The function f ( ) = is graphed in the y-coordinate plane as shown.. Part ased on the graph of the function, which statements are true? Select all that apply. E F G H f is increasing on the interval <. f is decreasing on the interval <. f is increasing on the interval < <. f is decreasing on the interval < <. f is increasing on the interval < <. f is decreasing on the interval < <. f is increasing on the interval >. f is decreasing on the interval >. 1

27 Part ased on the graph of the function, which statements are true? Select all that apply. E F G H f ( ) < on the interval <. f ( ) > on the interval <. f ( ) < on the interval < <. f ( ) > on the interval < <. f ( ) < on the interval < <. f ( ) > on the interval < <. f ( ) < on the interval >. f ( ) > on the interval >.

28 Use the information provided to answer Part and Part for question. Members of two cross-country teams ran an obstacle course. The table shows the times, in minutes and seconds, for the members of team R to complete the course. Team R Obstacle ourse Times : : : : : : :1 : :1 : : :1 : :1 : : : : : : The obstacle course times, in minutes and seconds, for team S are summarized in the bo plot shown. Team S Obstacle ourse Times 1

29 . Part Which histogram represents the times from Team R on the obstacle course? Team R Team R Frequency 1 1 Obstacle ourse Times Frequency 1 1 Obstacle ourse Times Team R Team R Frequency 1 1 Obstacle ourse Times Frequency 1 1 Obstacle ourse Times Part Which statements are true about the data for team R and team S? Select all that apply. E F The median time of team R is less than the median time of team S. The median time of team R is greater than the median time of team S. The interquartile range of team R is less than the interquartile range of team S. The interquartile range of team R is equal to the interquartile range of team S. The data for team R is skewed to the left. The data for team S includes an outlier.

30 Use the information provided to answer Part through Part for question. onsider the function function. f ( ), shown in the y-coordinate plane, as the parent y y = f() Part The graph of a transformation of the function f ( ) is shown. y Which epression defines the transformation shown? f ( + ) 1 f ( + ) + 1 f ( 1) + f ( + 1) +

31 Part The graph of a transformation of the function f ( ) is shown. y Which epression defines the transformation shown? 1 f ( + ) + f ( + ) + 1 f ( 1) 1 f ( + 1)

32 Part The graph of a transformation of the function f ( ) is shown. y Which epression defines the transformation shown? f ( ) f ( ) + f ( ) + f ( + ) +

33 Part The graph of a transformation of the function f ( ) is shown. y The transformation shown can be epressed in the form y = p f( + r) + n, where p, r, and n are constants. Which value must be less than? p r n

34 Use the information provided to answer Part through Part for question. The population of a city in was,. y 1, the city s population had grown to, people.. Part ssuming that the population of the city has grown linearly since and continues to grow at the same rate, what will be the population in 1? Enter your answer in the bo. \.\\\\\\.....!!!!!! Part Which epression is an appropriate eponential model for the population of the city? Let t represent the time, in years, since., ( 1. ) t, ( 1. ) t, ( 1. 1) t, ( 1. 1) t

35 Part ssuming that the population of the city has grown eponentially since and continues to grow at the same rate, what will be the population in 1? Give your answer to the nearest whole number. Enter your answer in the bo. \.\\\\\\.....!!!!!! Part nother town s population could be modeled by the function t Pt () =, ( 1. ) 1, where P represents the population and t represents the time, in years, since. ased on the model, by approimately what percent does the population of this town increase each year? 1

36 Use the information provided to answer Part and Part for question 1. The area,, in square feet, of a rectangular storage bin in a warehouse is given by the function ( ) = +, where is the width, in feet, of the storage bin. 1. Part If the function is graphed in a coordinate plane, which statement would be true? The -intercepts of the function are and, which are a lower bound and an upper bound for the possible values of the length of the storage bin. The -intercepts of the function are and, which are a lower bound and an upper bound for the possible values of the width of the storage bin. The -intercepts of the function are and 1, which are a lower bound and an upper bound for the possible values of the length of the storage bin. The -intercepts of the function are and 1, which are a lower bound and an upper bound for the possible values of the width of the storage bin. 1

37 Part The process of completing the square can be used to calculate the width, in feet, of the storage bin that gives a maimum area. What is the missing value? Enter your answer in the bo. = + = + ( )?.\\\\\\.....! \!!!!! Mathematics

38 Use the information provided to answer Part and Part for question. onsider the function f( ) = +.. Part What is the verte form of f ( )? f ( ) = ( ) f ( ) = ( + ) f ( ) = ( 1. ) 1. f ( ) = ( + 1. ) 1. Part What is a factored form of f ( )? f ( ) = ( + 1)( ) f ( ) = ( 1)( + ) f ( ) = ( + )( 1) f ( ) = ( )( + 1)

39 Use the information provided to answer Part through Part for question. Leah would like to earn at least $1 per month. She babysits for $ per hour and works at an ice cream shop for $ per hour. Leah cannot work more than a total of hours per month. Let represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.. Part Which graph shows the set of points that represents the number of hours that Leah can work in order to earn at least $1 and not work more than hours per month? y y Hours Working at Ice ream Shop 1 1 Hours Working at Ice ream Shop Hours abysitting Hours abysitting y y Hours Working at Ice ream Shop 1 1 Hours Working at Ice ream Shop Hours abysitting Hours abysitting

40 Part Which pairs conditions? (, y) represent hours that Leah could work to meet the given Select all that apply. E (, 1) (, 1) ( 1, ) ( 1, ) ( 1, 1) Part If Leah babysits for hours this month, what is the minimum number of hours she would have to work at the ice cream shop to earn at least $1? Give your answer to the nearest whole hour. Enter your answer in the bo. \.\\\\\\.....!!!!!!

41 Part Leah prefers babysitting over working at the ice cream shop. Out of total hours, what is the maimum number of hours she can babysit to be able to earn at least $1 per month? Give your answer to the nearest whole hour. Enter your answer in the bo. Mathematics.\\\\\\.....! \!!!!!

42 Use the information provided to answer Part and Part for question. The diagram shows two cylinders with bases that have the same center and heights of 1 millimeters. 1 mm r 1 mm. Part Which is a function for the volume, V, that is inside the larger cylinder but outside the one with the smaller radius, r? Vr () = 1, π 1πr Vr () = 1π 1πr Vr () = 1πr Vr () = 1π( 1 r) Part Suppose that there is space between the inner and outer cylinders and the radius of the inner cylinder must be an integer greater than or equal to. What is the domain of V? all integers greater than or equal to,,,,,,, or 1,,,,,, or m

43 Use the information provided to answer Part and Part for question. The function f is defined by f ( ) =.. Part If f ( + ) = + k 1, what is the value of k? Enter your answer in the bo. \.\\\\\\.....!!!!!! Part What are the zero(s) of f ( + )? Select all that apply. = = = E F = = = STOP