MATHEMATICS LPS Algebra 1 Pre-test 1 Go On MATHEMATICS 1 3 The height above the base lodge of a ski facility of a person in a chair lift, in meters, is given by the function y= 2.1x + 3, where x is the time in seconds. What does the slope of the function represent in the context of the problem? System B in the table below is created by retaining the first equation from System A and replacing the second equation. The second equation is replaced with the sum of the first equation from System A and the product of 2 and the second equation in System A. A the initial height of the person in meters B the initial time when the person begins to move upward C the vertical speed in meters per second of the person in the chair lift What can be said about the graphs and solutions for the two systems? D the horizontal speed in meters per second of the person in the chair lift 2 A The graphs of System A and System B have the same lines, and the systems have the same solution. Consider the graph of these linear equations. B The graph of System A has one line that differs from the graph of System B, so the systems have different solutions. -2y = -x 2x + 6y – 15 = 0 C The graph of System A has one line that differs from the graph of System B, but the systems have the same solution. D The graph of System A has two lines that differ from the graph of System B, and the systems have different solutions. What is the solution to the system? 5 A (0, 2) 3 B (3,2) C The system has no solution. D The system has many solutions. LPS Algebra 1 Pre-test 2 Go On MATHEMATICS 4 5 Consider this graph of the function f(x). The electrical current flowing through a circuit is measured in milliamps (mA) over 10 milliseconds (ms). The graph represents the relationship between time and electrical current. Which equation describes a line with the same solution set as f(x)? A 3x – 2y = 4 B 𝟐 𝟑 x+y=2 Which is the best estimate of the average rate of change in current from 2 milliseconds to 6 milliseconds? C 2x + 3y = 5 D 𝟑 𝟐 x – 2y = 4 A 1.00 mA B 1.25 mA C 1.50 mA D 1.75 mA LPS Algebra 1 Pre-test 3 Go On MATHEMATICS 8 A new motorcycle loses approximately 20% of its value each year from the time it is purchased. This function represents the value of a new motorcycle, purchased at $30,000, based on the number of years since its purchase. 6 f(x) = 30,000(0.8)x At a national robotics competition, 128 teams competed in the first round. After each round of the competition, half of the teams were eliminated from the competition. The number of teams remaining after r rounds can be determined by the function t(r) = 128 ∙ 0.5 r. How much could the motorcycle be worth after 3 years? A $12,280 B $15,360 C $18,000 D $19,200 Based on the graph, what is a reasonable domain for this function? A all positive integers 7 B all positive real numbers An internet-based company produces environmentally friendly products. The company starts with 105 employees, and hires p new employees each year. If the company continues to expand at this rate, which equation represents the number of employees that work at the company, E, through n years? C positive integers less than or equal to 7 D positive integers less than or equal to 128 A E = pn + 105 B E = 105n + p C E = 105p + n D E = p + n + 105 LPS Algebra 1 Pre-test 4 Go On MATHEMATICS 9 10 In 2000, the student enrollment of a school was 1,000. Since then, enrollment has increased at a constant percent rate. Which table could represent student enrollment of the school at a constant percent rate? Consider this set of inequalities. y–x<1 y+x≥3 Which graph represents the solutions to this set of inequalities? A B C D A B C D LPS Algebra 1 Pre-test 5 Go On MATHEMATICS 11 13 The number of people, a, who have viewed a video on a website after n hours can be modeled initially by an exponential growth function. For instance, if each person to see the video forwarded it to 5 other people who viewed it in the next hour, the number of additional people who have viewed the video would be given by the formula an = 5n. The formula E = mc2gives the amount of energy, E, contained in a body of mass, m. The constant c represents the speed of light. Which statement accurately relates the quantities in the formula? A The energy in a body is proportional to the square of its mass. B The ratio of mass to energy is equal to the speed of light squared. C The graph of energy as a function of mass curves steeply upward. D The energy of an object increases at the same rate as its mass increases. Which recursive formula represents this scenario? A an = a5n-1 B an = 5an-1 C an = an-1 + 5 14 D an = 5an-1 + 5 12 Consider the graph that represents the number of adults, in thousands, who participate in a city’s recycling program each year. Which table represents an exponential function for depreciation? A B C D Which function represents the number of adults who participate in the recycling program in x years? A f(x) = 10x B f(x) = 20x C f(x) = 10x +130 D f(x) = 20x + 140 LPS Algebra 1 Pre-test 6 Go On MATHEMATICS 15 17 The graph of the function f(x) = x2 is a parabola with its vertex at the coordinates (0,0). How would the graph of the function change for f(x) = (x – 5)2 + 4? A student conducted a survey among his friends to find out which types of television shows they most enjoyed watching. Each student could choose more than one type of show. The line plot reflects the results of the survey. A The graph would be shifted 5 units to the left and 4 units up. B The graph would be shifted 5 units to the right and 4 units up. C The graph would be shifted 5 units to the left and 4 units down. D The graph would be shifted 5 units to the right and 4 units down. Which conclusion can be reached based on the results? 16 A banker is comparing two accounts that are invested in different ways over 6 months. The data in the table represent the percent change in value of each account. The data has a strong negative correlation. A The survey was conducted randomly. B Comedy shows represent the mode of the data. C Talk shows had a greater frequency than crime shows. D Sports shows had the greatest frequency in the survey. Which is the most likely value of x? A 0.2 B 1.0 C 2.4 D 3.2 LPS Algebra 1 Pre-test 7 Go On MATHEMATICS 18 19 A health class collected data about the physical condition of ten randomly selected students and compared it with the data collected from the ten top athletes in the school. The tables show the resting heart rates of both groups. Control Group Student A B C D E F G H I J Heart Rate (beats/min) 65 86 73 91 69 72 78 61 82 73 Student K L M N O P Q R S T Heart Rate (beats/min) 60 78 74 63 67 75 77 79 55 73 In 1938 the whooping crane, an endangered species, was placed in a national park with the hope that the population would grow significantly within a protected environment. In 1938 there were 18 birds remaining. In 1993, the population was 150 birds. Jose used these two data points to fit a growth model to the data. Top Athletes Which statement about the data is true? A The mean heart rate for the athletes is 67. B The mean hart rate for the control group is 73. Based on Jose’s model showing the number of cranes as a function of years, what is a reasonable range for this function? C The median heart rate for both groups is the same. D The median heart rate for the athletes is lower than that for the control group. A 20 ≤ y ≤ 60 B 0 ≤ y ≤ 160 C 0 ≤ y ≤ 55 D 18 ≤ y ≤ 150 LPS Algebra 1 Pre-test 8 Go On MATHEMATICS 20 21 An algebra teacher wants to determine the difference in performance between two classes on a given test. A summary of the test scores is shown. The scatter plot shows the relationship between various weights of vehicles in pounds (lbs.) and their fuel economy in miles per gallon (mpg). If a score of 82 or better receives a letter grade of A, which statement is true? A Most students in Class B received an A because their median score is above 82. B Most students in Class A received an A because their median score is above 82. If the line of best fit is y = -0.005x + 45, what is the predicted weight of a vehicle that has a fuel economy of 27 mpg? C Most students in Class B did not receive an A because their mean score is below 82. A 2,500 lbs. D Most students in Class A did not receive an A because their mean score is below 82. B 3,200 lbs. C 3,600 lbs. D 5,700 lbs. LPS Algebra 1 Pre-test 9 Go On MATHEMATICS 22 23 The scatter plot represents the percentage of students enrolled in at least one online course over a 7-year period. The Carters are deciding whether to install new insulation in their home and want to calculate how cost effective it would be and when they could expect a payback on their investment. The graph shows their expected costs (yearly fuel bills plus the cost of any new insulation) over a period of years. Which function represents the line of best fit? A f(x) = 2x + 8 Which statement does not accurately represent the information in the graph? B f(x) = 2x + 12 A The initial cost of installing the insulation will be b dollars. C f(x) = x + 8 D f(x) = x + 12 B The savings from their investment in insulation will show after a years. C The slope of Line A represents the amount they are now paying in fuel bills each year. D The graph shows that if they do not install new insulation, the slope of their yearly fuel bills will rise. LPS Algebra 1 Pre-test 10 Go On MATHEMATICS 26 24 Lisa solves 2x + 7 = 15. Here are the steps to her solution: Natasha and Victor are discussing correlation. Victor states that if there is a strong correlation between two quantities, then there must be a causal relationship. Natasha claims that a strong correlation between two quantities does not necessarily result in a causal relationship. Which two quantities can Natasha use to defend her claim? Which statement explains how Lisa goes from Step 2 to Step 3? A ice cream sales and air-conditioning costs A simplifies both sides B hours worked at an hourly wage and amount earned B rewrites as equivalent fractions C finds least common denominator C interest rate on an account balance and interest earned D divides both sides by the same quantity D amount of liquid in a spray bottle and the number of sprays 25 27 A salesperson sells x premium plans per week and y discount plans per week. To earn a bonus, he must sell more than 30 plans within the week, and at least twice as many premium plans as discount plans. $499, $649, $1299, $649, $789, $1499, $999, $419, $499, $789, $1299 On the next day, the store offered a $50 decrease in price on all computers. Which number of premium plans and discount plans will not earn the salesperson his bonus? Which measure of central tendency is the same for the full retail price of the computers and the discounted price of the computers? A 20 premium plans; 10 discount plans B 30 premium plans; 15 discount plans A B C D C 40 premium plans; 20 discount plans D 46 premium plans; 20 discount plans LPS Algebra 1 Pre-test An electronics store sold 11 computers in one day. The following is the full retail price of each computer sold that day. 11 mean mode range median Go On MATHEMATICS 28 Phosphorus is used in many household and commercial cleaning products. Because it is never completely removed from the water we use, it can return to the water supply and harm fish and plants. The following table shows the concentrations of phosphorus in used water as it enters a water treatment facility, measured by x in milligrams per liter, and leaves the facility, measured by y in milligrams per liter. x y 5.7 7.3 6.7 5.9 6.1 8.3 5.5 7.0 3.3 5.9 4.8 4.5 4.0 7.1 3.6 6.1 Which line of best fit represents the concentration of water contaminated with phosphorus as it enters and leaves the water treatment facility? A B C D LPS Algebra 1 Pre-test 12 Go On MATHEMATICS 30 29 Matthew keeps track of his grocery spending each week and analyzes the receipts. He created this table showing the number of items he bought on each trip and the total cost of the items. The table also shows the residual value for each trip as determined by the line of the best fit. Ming surveyed 25 married couples and asked the age of each husband and wife to the nearest 0.1 year. She plotted the data in the table on a scatter plot, with the husband’s age on the x-axis and the wife’s age on the y-axis, and drew a line of best fit. The equation for the line of best fit is y = 0.9 x + 2, where x = the husband’s age and y = the wife’s age. Which shopping trip would most likely be considered an outlier when trying to predict Matthew’s total cost based on the number of items purchased? Which statement is true? A The residual for Couple B is 0. B The point for Couple D is an outlier. A The shopping trip with 14 items would most likely be considered an outlier because it has the fewest number of items purchased. C The residual for Couple A and Couple D is the same. D A positive residual means the wife is older than the husband. B The shopping trip with 32 items would most likely be considered an outlier because it has the greatest number of items purchased. C The shopping trip with 20 items would most likely be considered an outlier because its residual shows that it is far off from the predicted value of the line of best fit. D The shopping trip with 28 items would most likely be considered an outlier because its residual shows that it is far off from the predicted value of the line of best fit. LPS Algebra 1 Pre-test 13 Go On MATHEMATICS 31 33 At a flea market, Kayla sold 3 identical statues to 3 different people for 3 different prices. The 3 statues sold for a total of $113. The first person paid $4 more than the second person. The third person paid one more than twice the amount of the second person. This formula shows the area, A, of a trapezoid with base lengths b1 and b2 and height h. A = h(b1 + b2) 2 If the area, the height, and base b1 of the trapezoid are given, which equation can be used to determine the length of base b2? Which equation shows the distribution of prices paid by the 3 buyers? A (x + 4) + x + 2(x + 1) = 113 A b2 = B (x + 4) + x + (2x + 1) = 113 C (4 - x) + x + (2x + 1) = 113 B b2 = D (4 - x) + x + 2(x + 1) = 113 C b2 = 32 A research scientist is measuring the growth rate of a population of microorganisms by using the equation T = a(b)n, where a is the initial number, b is the base repeated n days, and T is the total number of microorganisms in the population. D b2 = 34 Suppose the scientist starts with 1,000 microorganisms and notices that the number doubles every day. Which statement is true? A The total number of microorganisms is being increased by a factor of 2. B The total number of microorganisms is being increased by a factor of 2n. 2𝐴 - b1 ℎ 2𝑏1 ℎ -A 2𝐴− 𝑏1 ℎ 2𝐴 ℎ𝑏1 Kenneth has worked out a study program to prepare for end-of-year exams. His program includes x minutes of algebra and y minutes of English studies per week. He wants to spend at least 240 minutes studying these subjects per week, with more than three times as many minutes studying algebra as minutes studying English. Which pair of inequalities represents the constraints? C The total number of microorganisms is being increased by a factor of 2n. A y – 240 ≥ x ; x < 3y B x – 240 ≥ y ; 3x < y D The total number of microorganisms is being increased by a factor of n + 1. C x + y ≤ 240 ; x > 3y D x + y ≥ 240 ; x > 3y LPS Algebra 1 Pre-test 14 Go On MATHEMATICS 35 Tameka works for Organic Farmers of Oregon and is preparing for an upcoming conference. She translates the information from the table into a line graph. She forgets to add the vertical scale for the number of acres. Which list contains the values of the vertical scale, in thousands of acres, Tameka should use? A 20; 30; 40; 50; 70; 80; 90 B 20; 30; 40; 50; 60; 70; 80 C 30; 40; 50; 70; 80; 100 D 30; 50; 70; 90; 110; 130 LPS Algebra 1 Pre-test 15 Go On MATHEMATICS 36 38 The flow rate of a river can be determined by Q = WDV, where Q is the flow rate, W is the width, D is the depth, and V is the velocity. If the flow rate is 427.5 cubic feet per second and the velocity is 10 feet per second, which equation represents depth, D, of the river? A B 427.5 10𝑊 10 Which equation can be used to find the possible amounts of money that were charged to each of Natalia’s credit card? A 0.12a + 0.18b = 650 =𝐷 427.5𝑊 Natalia has two credit cards. One charges 12% annual interest, and the other charges 18% annual interest. She paid $650 in interest this year. B 0.12a – 0.18b = 650 C 650(0.12a) = 650(0.18b) =𝐷 D (0.12 + 0.18)(a + b) = 650 C 10W(427.5) = D D 427.5 – 10W = D 39 Kim plans to spend between $10 and $12 to purchase songs from an online music store. The music store sells downloaded songs for $1.25 each and offers a $2.00 discount. 37 Manuel joins a car share service. He will be charged $120 for an application fee and car rental. He must also pay $0.35 per mile for each mile driven over 150 miles. The compound inequality describes the number of songs, s, Kim can purchase. Which inequality shows the total number of miles Manuel can drive without the charges exceeding $200? 10 < 1.25s – 2 < 12 How many songs can Kim purchase? A 120 + 0.35x ≤ 200 A 8 or 9 B 120 + 0.35 + x ≤ 200 B 9 or 10 C 120 + 0.35x – 150 ≤ 200 C 10 or 11 D 120 + 0.35(x – 150) ≤ 200 D 11 or 12 LPS Algebra 1 Pre-test 16 Go On MATHEMATICS 40 42 Duane buys five movie tickets from a theater’s website. He pays a $6 service charge for using the website. His total cost can be expressed as 5x + 6. A colony of freshwater algae starts with a single cell and doubles every two hours. Which function can be used to find n, the number of algae cells, after t hours? What does the variable represent? A total cost 𝑡 B number of tickets A n= C cost of one ticket B n = 2t D amount of service charge C n = 2t 2 𝑡 D n = 2(2) 41 An airplane can carry a maximum of 150 passengers. Each passenger receives a meal and can choose either vegetarian or beef. The airline’s policy states that each airplane must carry 1 vegetarian meal for every 5 beef meals. The airplane is supplied with x vegetarian meals and y beef meals. 43 The distance (d) an airplane travels is given by the equation d = vt, where v represents the velocity of the airplane and t represents the time the airplane travels. Given the system of inequalities and equations x + y ≤ 150 and y = 5x, what is the value of x, the number of vegetarian meals? If the distance is given in kilometers (km) and the time is given in minutes (min), what is the unit for the velocity? A km A x ≤ 25 B min B x = 25 C min/km C x < 25 D km/min D x ≤ 30 LPS Algebra 1 Pre-test 17 Go On MATHEMATICS 46 44 Consider this equation. Timothy has completed 4 assignments for math class. His mean grade on the 4 assignments is 83. After his next assignment he wants his mean grade to be 85. Ax – 17 = 2x + 3 Solve for x in terms of A. A x= B x= C x= D x= 20 Calculate the grade Timothy needs to earn on his fifth assignment. 𝐴−2 20 A 85 2−𝐴 B 84 2−𝐴 20 C 93 𝐴− 2 D 95 20 45 47 Marcos is a packaging designer. He is designing a box for a food product. Based on his company’s market research, he wants the width of the box to be 0.2 times the length. A population of 75 foxes in a wildlife preserve is quadrupling in number every 15 years. Let y represent the total number of foxes born in the preserve. If x is the number of 15-year periods, which function can be used to find the rate of change in the number of foxes after 45 years? The volume of the box is given by the formula V = 0.2l2h. Marcos needs to analyze how the volume, V, changes when he changes the height, h. If he increases the height by a factor of 1.1, how does the volume change? A f(x) = 75 x 4x A increases by a factor of 1.1 B f(x) = 75 + 4x B increases by a factor of (1.1)2 C f(x) = 75 + 4x + 1 C increases by a factor of 0.2(1.1) D f(x) = 75 x 4x – 1 D increases by a factor of 0.2(1.1)2 LPS Algebra 1 Pre-test 18 Go On MATHEMATICS 48 49 Mark is playing a computer game, Jungle, which requires him to rescue endangered animals. Rescuing an endangered animal earns r points, while being unable to save an endangered animal costs d points. Players earn 10 bonus points for completing each level. At a certain point in time, Mark’s score is given by the expression shown. A company is offering an incentive for employees to join a gym. The gym membership includes a monthly fee and a $60 joining charge. The company will pay $200, which is equal to one-third of the yearly cost for members. The incentive is represented by this equation, where x is the monthly fee. 𝟏 200 = 𝟑 (12x + 60) (9r – 4d) + 10 Which statement describes the steps to determine the monthly fee? Which scenario explains Mark’s score? A Mark rescued 5 endangered animals and completed ten levels. A subtract 60 from each side of the equation, divide each side of the equation by 12, and then multiply each side of the equation by 3 B Mark rescued 19 endangered animals and was unable to save 6 endangered animals. B subtract 60 from each side of the equation, multiply each side of the equation by 12, and then divide each side of the equation by 3 C Mark rescued 9 endangered animals, was unable to save 4 endangered animals, and completed one level. D Mark rescued 9 endangered animals, was unable to save 4 endangered animals, and completed ten levels. C multiply each side of the equation by 3, subtract 60 from each side of the equation, and then divide each side of the equation by 12. D divide each side of the equation by 3, subtract 60 from each side of the equation, and then multiply each side of the equation by 12 LPS Algebra 1 Pre-test 19 Go On MATHEMATICS 50 52 The graph below describes a student’s drive from home to school. Simplify the expression. 2(x – 1)2 – 4 A 2x2 – 4x – 2 B 2x2 – 4x + 2 C x2 – 2x – 3 Four points are labeled on the graph. D 2x2 – 2 Which statement is an accurate description of the indicated point on the graph? A At point D, the student was 15 miles from home. B At point A, the student turned around to head back home. 53 Consider the expression x2 – 4x + 3. C At point B, the student was stopped at a stoplight for 1 minute. What are the zeroes of this function? A x = -1, x = -3 D At point C, the student was driving at a steady speed for 3 minutes. B x = 1, x = 3 C x = - 4, x = 3 D x = 4, x = -3 51 A software company has earned over 1 million dollars selling its smartphone application for $14.50. What is the rate of change for this function? A B C D 1 million $14.50 1 million/$14.50 1 million x $14.50 LPS Algebra 1 Pre-test 20 Go On MATHEMATICS 54 57 Consider the expression x2 + 4x + 1. Solve the equation 2x2 + 3 = 53. What is the minimum of this function? A x = ±50 A (3, 2) B x = ±25 B (-3, -2) C x = ±5 C (-2, -3) D x = ±√50 D (2, 3) 55 Which expression is equivalent to 𝟑 𝟐 58 8x ? Consider the graph below. A (2x3) ½ B (8x3) ½ C (8x ½ )3 D (2x ½ )3 56 Consider the equation x2 + 6x – 7 = 0. Which equation is equivalent? What is the equation of the function? A (x + 3)2 = 16 A y = (x + 2) – 4 B (x + 3)2 = 7 B y = (x – 2) – 4 C x2 + 6x + 9 = 7 C 𝑦 = |𝑥 + 2| − 4 D x2 + 6x = 16 D 𝑦 = |𝑥 − 2| − 4 LPS Algebra 1 Pre-test 21 Go On MATHEMATICS 59 Which graph indicates the solution to - 3x2 + 16x – 5 = 0? 60 A Compare the functions represented below. Function A: f(x) = 3x2 + 13x + 4 Function B: B Which of the following statements is true? C A Function A has a lower minimum than Function B. B Function B has a lower minimum than Function A. C Function A and Function B have the same minimum. D There is not enough information to determine which function has the lower minimum. D LPS Algebra 1 Pre-test 22 Go On MATHEMATICS 62 61 Carrie applied for an after-school job at the local market. Carrie asked for $2 an hour, but the boss proposed giving the $0.10 for the first hour, $0.20 for the second hour, $0.40 for the third hour, $0.80 for the fourth hour and so on. Below is a table of the hours worked per week and the pay for each hour for each of the two pay plans. Hours worked in a week Earnings for Carrie’s plan Consider the graph that represents the number of adults, in thousands, who participate in a city’s recycling program each year. Earnings for Boss’ plan 1 2 0.10 2 4 0.30 3 6 0.70 4 8 1.50 5 10 3.10 If this trend continues, how many thousand adults would be participating in the city’s recycling program after 15 years? A 200 If you worked 10 hours in one week, under whose plan would you earn more money? B 300 C 280 A You would earn more money under Carrie’s plan. D 440 B You would earn more money under the boss’ plan. C You would earn the same amount of money under either Carrie or the boss’ plan. D There is not enough information to determine under whose plan you would earn more money. LPS Algebra 1 Pre-test 23 Go On MATHEMATICS 64 63 The equation y = 0.002x + 4.75 models the total cost in dollars, y, of using a 20-watt compact fluorescent light bulb for x hours. The table models the cost of using a 60-watt incandescent light bulb. Based on the information given in question 63, determine which light bulb will cost the least amount to use. Be sure to include which costs the least for a small number of hours used and which costs the least for a large number of hours used. They cost the same ($6.75) for 1,000 hours of electricity. If you use less than 1,000 hours then the 60-watt incandescent light bulb is cheaper. If you use more than 1,000 hours then then 20-watt fluorescent bulb is cheaper. 65 The table represents the volume of ink remaining in an inkjet printer cartridge. Which solution represents the number of hours of use when the costs of using the two light bulbs are the same? A 600 hours B 688 hours C 1000 hours D 1148 hours What do the x- and y-intercepts of the graph of these data represent? Explain your answer. The x-intercept is the number of pages the printer prints before running out of ink, which is 500 pages. The y-intercept is the starting amount of ink in the printer, which is 25 ml. LPS Algebra 1 Pre-test 24 Go On END