Algebra I Practice Exam

Transcription

1 Algebra I This practice assessment represents selected TEKS student expectations for each reporting category. These questions do not represent all the student expectations eligible for assessment. Copyright 2011 El Paso Independent School District. All rights reserved. Reproduction of all or portions of this work is prohibited without express written permission from EPISD.

2 INSTRUCTIONS: Identify the choice that best completes the statement or answers the question. Name: Date: Period: Teacher: Page 2

3 1. Several basketball teams in EPISD ordered T-shirts to sell for a fundraiser. Each team paid $ for the shirts and will sell them for $10 a piece. The relationship between the number of shirts sold and each team s profit from the sale of the shirts can be represented by the function f(n) = 10n , in which n represents the number of shirts sold. What is the dependent quantity in this functional relationship? A. The number of shirts sold B. The amount the team paid for the shirts C. The team s profit from the sale of the shirts D. The selling price of the shirts 2. A music store gives its customers a free CD for every five used CDs they trade in. However, the store limits the number of CDs that can be traded in during any one month to 25 CDs. The function y = x describes y, the total number of free CDs, in terms of x, the number of used CDs traded in each month. What is a reasonable domain for this function? F. 0 < y < 5 G. 0 < y <25 H. 0 < x < 5 J. 0 < x <25 Page 3

4 3. Some values for two linear equations are shown in the tables below. What is the solution to the system of equations represented by these tables? A. (2, 3) B. (3, 5) C. (-1, 1) D. (5, 11) 4. Carlos is making cookies that contain both peanut butter chips and chocolate chips. He used a total of 16 ounces of chips. There are 8 chocolate chips in each ounce of chocolate chips, and 12 peanut butter chips in each ounce of peanut butter chips. If Carlos used a total of 300 chips in his cookies, which system of linear equations could be used to find the number of ounces of chocolate chips, c, and the number of ounces of peanut butter chips, p, Carlos used? F. c + p = 16 8c + 12p = 300 G. c + p = 300 8c + 12p = 16 H. 16c + 8p = 300 c + p = 16 J. 16c 8p = 12 c + p = 300 Page 4

5 5. The function y = x 2 5x + 2 is graphed below. One of the roots of the equation x 2 5x + 2 = 0 lies between which pair of integers? A. -1 and 0 B. 3 and 4 C. 4 and 5 D. -2 and At a candy store selling gourmet jelly beans, the amount you pay varies directly with the weight of the beans. The cost of 5 pounds of jelly beans is $12. During the past month $7200 worth of jelly beans have been purchased. How many pounds of jelly beans were purchased during the past month? Record your answer and fill in the bubbles on your answer document Page 5

6 7. The amount of time it takes Karla to drive to school in the morning is given by the function t(x) = x, where x is the number of stops that she makes to pick up her friends. Which is the best interpretation of this function? A. The amount of time it takes Karla to drive to school does not depend on the number of stops she makes B. The minimum amount of time that it takes Karla to drive to school is 3 minutes C. Each stop that Karla makes adds 10 minutes to the total time D. Each stop that Karla makes adds 3 minutes to the total time 8. Jonni runs a convenience store during the weekends. Her monthly profit in dollars, P(x), is given by the function P(x) = x + 20, in which x represents the number of items she sells in a month. What is the minimum number of items she must sell next month if she is to have a profit of at least $2,500? F. 12,400 G. 13,500 H. 25,200 J. 30,120 Page 6

7 9. Which of the following relations is a function? I. II. III. IV. A. I and III only B. II and III only C. I, III, and IV only D. III and IV only 10. Which of the following cannot be described by a linear function? F. The amount spent on n shirts that cost $15 each G. The number of miles driven for h hours at a constant speed of 60 miles per hour H. The total amount saved after making an initial deposit of $50 and depositing $15 a month thereafter for n months J. The area of a rectangular garden that is x feet wide and has a length equal to twice its width Page 7

8 11. Which equation describes the same linear function as the one shown in the table below? x y A. y = x + B. y = x 3 C. y = x 3 D. y = - x Tickets to a rock concert cost $4 for students and $6 for adults. A total of $300 worth of tickets was sold. Let x represent the number of student tickets sold and y the number of adult tickets sold. If the equation that represents this relationship is graphed, which of the following would be true? F. The x-intercept would be 50 G. The y-intercept would be 60 H. The y-intercept would be 65 J. The x-intercept would be 75 Page 8

9 13. The equation y = 5x 2 is graphed below. If the value of the slope in the equation is changed to which of the following best describes the effect on the graph? A. The new line would be translated down B. The new line would be perpendicular to the original line C. The new line would be parallel to the original line D. The new line would intersect the original line on the x-axis 14. Anthony had $35 to spend on movie rentals and snacks for the weekend. He spent $12 on popcorn and sodas. If the movie store rents DVDs for $4 each, which inequality models n, the number of DVDs Anthony is able to rent? F. 4n + 12 < 35 G. 4n 12 < 35 H. < 12 J. 35 4n < 12 Page 9

10 15. Mary fills her swimming pool at a rate of 2000 gallons per hour. There were 3000 gallons of water in the pool when she started filling it. The total number of gallons of water in the pool after Mary fills it for x hours can be represented by the equation y = 2000x If Mary adds a second hose, she can fill the pool twice as fast. How will this affect the graph of the equation? A. The line will be translated up B. The line will be translated down C. The line will be steeper D. The line will be less steep 16. The graph below shows the number of gallons of gas used by Bill s car as a function of the number of miles driven. About how many gallons of gas will Bill need for a 170 mile trip? F. 7 gallons G. 8.5 gallons H. 9.5 gallons J. 11 gallons Page 10

11 17. Mariano recently opened a store. The graph below shows the store s weekly sales since it opened. What can be inferred from this graph? A. The store s sales have been increasing since it opened B. The store s sales increased for the first 2 weeks after it opened, but then they began to decrease C. The store s sales increased for the first 5 weeks after it opened, but then they decreased the next 2 weeks D. The store s sales increased for the first 5 weeks after it opened, remained constant the next week, and then decreased the last week shown 18. A personal trainer at a local gym charges the following fees for a one-hour training session for one to four people. Number of Cost ($) People Which equation best represents the relationship between n, the number of people, and c, the cost? F. n = c + 19 G. c = 20n H. c = 4n + 16 J. c = 5n + 14 Page 11

12 19. Ten years ago, Christine bought a car for her birthday. As the age of the car increased, its value decreased. Which scatterplot best represents this relationship? 20. Sharie is four times as old as Marcos. If the sum of their ages is 45, which equation could best be used to find their ages? F. 4m 2 = 45 G. 2m + 4 = 45 H. 5m = 45 J. 4m + 4 = 45 Page 12

13 21. Which of the following expressions is equivalent to 4(n 3)(n + 2)? A. 4n 2 4n 24 B. 4n 2 + 4n + 24 C. 4n 2 24 D. 4n 2 + 4n A new hotel in El Paso opened up last month. The hotel charges a different rate for its large rooms than for its small rooms. When 20 large rooms are occupied, the total amount of money collected from the large rooms is $1800. When 10 large rooms and 21 small rooms are occupied, the hotel collects $2370. How much does the hotel charge for each small room? Record your answer and fill in the bubbles on your answer document. Page 13

14 23. Which graph represents the solution set of the linear inequality 3x 3y > 9? 24. Which is the equation of the line that contains the points (-1, -5) and (2, 1) F. y = 2x 3 G. y = x + H. y = x + J. y = -4x + 9 Page 14

15 25. Kevin joined the math club of a local high school and needs to raise at least $60 for a field trip. To do so, he is selling chocolates for $3 a box and candies for $2 a box. If the inequality 3x + 2y > 60 represents the possible solutions to this problem, which of the following points represents a reasonable number of boxes of chocolates and boxes of candies that Kevin could sell to raise enough money to attend the field trip? A. (11, 12) B. (12, 14) C. (14, 8) D. (10, 14) 26. Which of the following choices describes the effect on the graph of the equation y =2x 2 when it is changed to y = -0.7x 2? F. The graph is wider and opens downward G. The graph is congruent and is translated up H. The graph is congruent and is translated down J. The graph is narrower and opens downward Page 15

16 27. A ball was projected into the air with an initial upward velocity of 72 ft/sec. The quadratic function h = 72t 16t 2 describes the height, h, of the ball t seconds after it was projected into the air. Based on the graph, which of the following is true? A. The ball reached its maximum height in about 3 seconds B. The ball was in the air for less than 4 seconds C. The height 2.5 seconds after the ball was projected was 64 feet D. The height 3.5 seconds after the ball was projected was 56 feet 28. The surface area of a sphere can be found using the formula S= 4 r 2. Which expression represents the surface area of a sphere with a radius of 5x 4 yz 3 units? F. 100 x 8 y 2 z 6 G. 20 x 8 y 2 z 6 H. 100 x 6 y 2 z 5 J. 20 x 6 y 2 z 5 Page 16

17 29. What is the solution set for the equation x = x 2 42? A. {-6, 7} B. {-7, 6} C. {- 42, 42} D. {-6 7, 6 7} 30. Which function is the parent function of the graph shown below? F. y = x G. y = 2x H. y = x 2 J. y = 0.5x Page 17

18 31. Which graph best represents the relationship in the table shown to the right? 32. A new cell phone company is advertising its new service plan. The company is offering customers up to 1000 minutes of calls each month for only $ If the number of minutes used in a month exceeds the 1000 minutes, then the function c = 0.35(m 1000) describes the monthly charge, c, in dollars in terms of m, the total number of minutes used. Which of the following statements best describes this function? F. If the total number of minutes used is more than 1000, then every minute beyond 1000 costs 35 cents G. Every minute used costs 35 cents, regardless of the total number of minutes used H. The first 1000 minutes used costs 35 cents each, after which there is an additional charge of $29.99 J. If the total number of minutes used is more than 1000, then every minute used costs 35 cents Page 18

19 33. The function f(x) = 7x + 3 represents a relationship between x and y. If the value of x increases by 1, what happens to the value of f(x)? A. The value of f(x) increases by 3 B. The value of f(x) increases by 7 C. The value of f(x) increases by 10 D. The value of f(x) increases by In the equation f(x) = 10 (x 5) 13, which is a value of x when f(x) = 0? Record your answer and fill in the bubbles on your answer document. Page 19

20 35. What is the domain of the function graphed below? A. 0 < x < 5 B. 2 < x < 5 C. 0 < x < 4 D. 0 < x < In the quadratic equation x 2 x + c = 0, c represents an unknown constant. If x = 3 is one of the solutions to this equation, what is the value of c? Record your answer and fill in the bubbles on your answer document. Page 20

21 37. Which of the following is not a correct description of the graph of the function y = 3x 10? A. The graph of the function contains the point ( 2, 4), and when the value of x increases by 1 unit, the value of y decreases by 3 units. B. The graph of the function contains the points ( 1, 5), (2, 11), and (4, 15). C. The graph of the function is a line that passes through the point (0, 10) with a slope of 2. D. The graph of the function contains the points (0, 10), (1, 13), and (3, 1). 38. If (k, 2k) and (5k, 14k) are two points on the graph of a line and k is not equal to 0, what is the slope of the line? F. 3 G. 3k H. 12 J. Not here Page 21

22 39. What is the slope of the linear equation 101x + 53y = 12? A B. 12/53 C. D. 40. Which equation best represents the line graphed below? F. 7x + 4y = 35 G. 4x 7y = 35 H. 4x + 7y = -35 J. 7x 4y = -35 Page 22

23 41. Denise can assemble a chair in 0.75 hour and a table in 0.4 hour. Which inequality best represents the number of chairs, c, and the number of tables, t, that Denise can assemble in one day if she works a maximum of 8 hours? A. ( )(c + t) 8 B. 0.75c + 0.4t 8 C. 0.75c + 0.4t 8 D. ( c) + (0.4 + t) A city bus collected $780 in fares on one day. The price of a regular fare was $0.80, and the price of a discount fare was $0.40. If a total of 1200 people paid the fares on this bus, how many people paid the regular fare? Record your answer and fill in the bubbles on your answer document. Page 23

24 43. If the graph of y = 19x is translated up 15 units, which of the following equations will best describe the resulting graph? A. y = 34x B. y = 34x C. y = 19x D. y = 19x Barbara graphs a family of equations of the form y = ax How does each new graph compare to the previous graph as Barbara increases the value of a from 1 to 1.5 and finally to 2? F. Each new graph is above the previous graph G. Each new graph is wider than the previous graph H. Each new graph is narrower than the previous graph J. Each new graph is to the right of the previous graph Page 24

25 45. Mathematicians developed the linear model below to show the relationship between altitude, or elevation above sea level (0 feet), and air temperature. According to the model, what would be the air temperature at an altitude of 0 feet? A. 16 o F B. 45 o F C. 59 o F D. 77 o F 46. The graph of x + 5y = 9 is shown below. Which point represents a solution to this equation? F. (0, 1) G. (2, 1) H. (1, 2) J. (-7, 0) Page 25

26 47. The graph below represents the relationship between the density of water and the temperature of water. According to the graph, which of the following intervals best represents the temperature at which the density of water is greater than kilograms per cubic meter? A. Less than 1 o C B. Between 0 o C and 4 o C C. Between 4 o C and 8 o C D. Between 1 o C and 7 o C 48. Simplify the polynomial below. -3x (7x 4) + 6x (13 24x 2 ) F. 3x x 13 G. -24x 2 15x 17 H. -24x x 17 J. 3x x + 13 Page 26

27 49. The cost of renting a car includes a $30 deposit plus $55 per day. The cost can be represented with the equation C = d. If we were to create a graph using this equation, what would the cost per month represent? A. the xintercept B. the yintercept C. the slope D. the point of intersection 50. The amount a mechanic charges for each job is represented by the function t = 250h + 100, where h represents the number of hours he spends on the job and t represents the total amount he charges in dollars for the job. The mechanic plans to change the amount he charges for each job. The amount he plans to charge is represented by the function t = 250h What will be the effect of this change on the amount he charges for each job? F. The total amount he charges for each job will increase by $20. G. The total amount he charges for each job will decrease by $20. H. The amount he charges per hour will increase by $20. J. The amount he charges per hour will decrease by $20. Page 27

28 51. The graph of a line is shown below. If the slope of this line is multiplied by 4 and the y-intercept increases by 2 units, which linear equation represents these changes? A. y = -8X + 5 B. y = -4x + 2 C. y = -12x + 5 D. y = -2x A restaurant sold a total of 418 large and small hamburgers during one day. Total hamburger sales were $1077. Large hamburgers sold for $3, and small hamburgers sold for $1.50. Which system of linear equations can be used to find l, the number of large hamburgers sold, and s, the number of small hamburgers sold? F. l + s = l s = 418 G. l + s = 418 3l s = 1077 H. 1.50l + 3s = 418 l + s = 1077 J. l + s = l + 3s = 1077 Page 28

29 53. Ms. Rodríguez plans to order from 20 to 26 books for her class. The prices of the books she plans to order range from $4.95 to $12.95 each. If the publisher charges a shipping fee of $0.50 per book ordered, which of the following is not a reasonable price for the books, including shipping? A. $145 B. $245 C. $345 D. $ What is the solution set for the equation 2x 2 16x 96 = 0 F. {4, 12} G. { 4, 12} H. { 4, 12} I. {4, 12} Page 29

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