import { type PracticeQuestion } from "../../types/lesson";

export const TWO_VAR_DATA_EASY: PracticeQuestion[] = [
  {
    id: "2e511919",
    type: "mcq",
    questionHtml:
      "The line graph shows the estimated number of chipmunks in a state park on April <strong>1</strong> of each year from <strong>1989</strong> to <strong>1999</strong>.<br>The line graph:<br><br>Begins at 1989, 38 chipmunks<br>Remains level to 1990, 38 chipmunks<br>Rises sharply to 1991, 98 chipmunks <br>Rises gradually to 1992, 101 chipmunks<br>Falls sharply to 1993, 53 chipmunks<br>Rises sharply to 1994, 158 chipmunks <br>Falls sharply to 1995, 48 chipmunks <br>Rises sharply to 1996, 98 chipmunks <br>Falls gradually to 1997, 93 chipmunks<br>Falls sharply to 1998, 53 chipmunks <br>Rises sharply to 1999, 113 chipmunks<br><br>Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?",
    choices: [
      { label: "A", text: "<strong>1989</strong>" },
      { label: "B", text: "<strong>1994</strong>" },
      { label: "C", text: "<strong>1995</strong>" },
      { label: "D", text: "<strong>1998</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. For the given line graph, the estimated number of chipmunks is represented on the vertical axis. The greatest estimated number of chipmunks in the state park is indicated by the greatest height in the line graph. This height is achieved when the year is <strong>1994</strong>.<br>Choice A is incorrect and may result from conceptual errors.<br>Choice C is incorrect and may result from conceptual errors.<br>Choice D is incorrect and may result from conceptual errors.",
    hasFigure: true,
    figureUrl: "/practice-images/2e511919_svg1.svg",
  },
  {
    id: "39aa146d",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between <strong>x</strong> and <strong>y</strong>. A line of best fit is also shown.<br>The scatterplot has 6 data points.<br>The data points are in a linear pattern trending up from left to right.<br>A line of best fit is shown:<br><br>The line of best fit slants up from left to right.<br>1 point is touching the line of best fit.<br>2 points are above the line of best fit.<br>3 points are below the lines of best fit.<br>The line of best fit passes through the following approximate coordinates:<br><br>(0 comma 0.2)<br>(4 comma 2)<br><br>Which of the following is closest to the slope of the line of best fit shown?",
    choices: [
      { label: "A", text: "<strong>−2.27</strong>" },
      { label: "B", text: "<strong>−0.44</strong>" },
      { label: "C", text: "<strong>0.44</strong>" },
      { label: "D", text: "<strong>2.27</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. It's given that the scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>, and a line of best fit is shown. For the line of best fit shown, for each increase in the value of <strong>x</strong> by <strong>1</strong>, the corresponding value of <strong>y</strong> increases by a constant rate. It follows that the relationship between the variables <strong>x</strong> and <strong>y</strong> has a positive linear trend. A line in the xy-plane that passes through the points <strong>(a, b)</strong> and <strong>(c, d)</strong> has a slope of <strong>(d − b) / (c − a)</strong>. The line of best fit shown passes approximately through the points <strong>(0, 0.25)</strong> and <strong>(4, 2)</strong>. It follows that the slope of this line is approximately <strong>(2 − 0.25) / (4 − 0)</strong>, which is equivalent to <strong>0.4375</strong>. Therefore, of the given choices, <strong>0.44</strong> is closest to the slope of the line of best fit shown.<br>Choice A is incorrect. This is the slope of a line of best fit for a relationship between <strong>x</strong> and <strong>y</strong> that has a negative, rather than a positive, linear trend.<br>Choice B is incorrect. This is the slope of a line of best fit for a relationship between <strong>x</strong> and <strong>y</strong> that has a negative, rather than a positive, linear trend.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: true,
    figureUrl: "/practice-images/39aa146d_svg1.svg",
  },
  {
    id: "43744269",
    type: "mcq",
    questionHtml:
      "An airplane descends from an altitude of <strong>9, 500</strong> feet to <strong>5, 000</strong> feet at a constant rate of <strong>400</strong> feet per minute. What type of function best models the relationship between the descending airplane's altitude and time?",
    choices: [
      { label: "A", text: "Decreasing exponential" },
      { label: "B", text: "Decreasing linear" },
      { label: "C", text: "Increasing exponential" },
      { label: "D", text: "Increasing linear" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. It′s given that the airplane descends at a constant rate of <strong>400 feet per minute</strong>. Since the altitude decreases by a constant amount during each fixed time period, the relationship between the airplane′s altitude and time is linear. Since the airplane descends from an altitude of <strong>9, 500 feet</strong> to <strong>5, 000 feet</strong>, the airplane′s altitude is decreasing with time. Thus, the relationship is best modeled by a decreasing linear function.<br>Choice A is incorrect and may result from conceptual or calculation errors.<br>Choice C is incorrect and may result from conceptual or calculation errors.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: false,
  },
  {
    id: "4a2264b3",
    type: "mcq",
    questionHtml:
      "The line graph shows the percent of cars for sale at a used car lot on a given day by model year.<br>The line graph:<br><br>Begins at 2010, 12%<br>Remains level to 2011, 12%<br>Remains level to 2012, 12%<br>Falls sharply to 2013, 8%<br>Falls sharply to 2014, 4%<br>Rises sharply to 2015, 9%<br>Rises gradually to 2016, 10%<br>Remains level to 2017, 10%<br>Rises gradually to 2018, 11%<br>Remains level to 2019, 11%<br><br>For what model year is the percent of cars for sale the smallest?",
    choices: [
      { label: "A", text: "<strong>2012</strong>" },
      { label: "B", text: "<strong>2013</strong>" },
      { label: "C", text: "<strong>2014</strong>" },
      { label: "D", text: "<strong>2015</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. For the given line graph, the percent of cars for sale at a used car lot on a given day is represented on the vertical axis. The percent of cars for sale is the smallest when the height of the line graph is the lowest. The lowest height of the line graph occurs for cars with a model year of <strong>2014</strong>.<br>Choice A is incorrect and may result from conceptual errors.<br>Choice B is incorrect and may result from conceptual errors.<br>Choice D is incorrect and may result from conceptual errors.",
    hasFigure: true,
    figureUrl: "/practice-images/4a2264b3_svg1.svg",
  },
  {
    id: "5c24c861",
    type: "mcq",
    questionHtml:
      "According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?",
    choices: [
      { label: "A", text: "25" },
      { label: "B", text: "30" },
      { label: "C", text: "210" },
      { label: "D", text: "250" },
    ],
    correctAnswer: "C",
    explanation:
      "Correct Answer Rationale<br><br>Choice C is correct. According to the model, the stopping distance, in feet, of a vehicle traveling 55 miles per hour is about 200 feet. Of the choices given, the best estimate of the stopping distance for a car traveling 55 miles per hour is 210 feet.Incorrect Answer Rationale<br><br>Choices A, B, and D are incorrect and may be the result of incorrectly reading the given quadratic model. The corresponding x-values to the y-values of 25 and 30 are not part of the model. The corresponding x-value to a y-value of 250 is approximately 60 mph, not 55 mph.",
    hasFigure: true,
    figureUrl: "/practice-images/5c24c861_img1.png",
  },
  {
    id: "5f3ee607",
    type: "mcq",
    questionHtml:
      "The scatterplot has 10 data points.<br>The data points are in a linear pattern trending down from left to right.<br>Select data points have the following approximate coordinates:<br><br>(0.8 comma 8.9)<br>(2.8 comma 5.1)<br>(4.1 comma 2.9)<br><br>Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?",
    choices: [
      { label: "A", text: "<strong>y = − 1.9 x − 10.1</strong>" },
      { label: "B", text: "<strong>y = − 1.9 x + 10.1</strong>" },
      { label: "C", text: "<strong>y = 1.9 x − 10.1</strong>" },
      { label: "D", text: "<strong>y = 1.9 x + 10.1</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The equation representing a linear model can be written in the form <strong>y = a + b x</strong>, or <strong>y = b x + a</strong>, where <strong>b</strong> is the slope of the graph of the model and <strong>(0, a)</strong> is the y-intercept of the graph of the model. The scatterplot shows that as the x-values of the data points increase, the y-values of the data points decrease, which means the graph of an appropriate linear model has a negative slope. Therefore, <strong>b < 0</strong>. The scatterplot also shows that the data points are close to the y-axis at a positive value of <strong>y</strong>. Therefore, the y-intercept of the graph of an appropriate linear model has a positive y-coordinate, which means <strong>a > 0</strong>. Of the given choices, only choice B, <strong>y = − 1.9 x + 10.1</strong>, has a negative value for <strong>b</strong>, the slope, and a positive value for <strong>a</strong>, the y-coordinate of the y-intercept. <br>Choice A is incorrect. The graph of this model has a y-intercept with a negative y-coordinate, not a positive y-coordinate.<br>Choice C is incorrect. The graph of this model has a positive slope, not a negative slope, and a y-intercept with a negative y-coordinate, not a positive y-coordinate.<br>Choice D is incorrect. The graph of this model has a positive slope, not a negative slope.",
    hasFigure: true,
    figureUrl: "/practice-images/5f3ee607_svg1.svg",
  },
  {
    id: "661dfddd",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Temperature and Elevation.” The horizontal axis is labeled “Elevation, in feet, ” and the numbers 6, 000 through 9, 000, in increments of 500, are indicated. The vertical axis is labeled “Temperature, in ° Fahrenheit, ” and the integers 37 through 45 are indicated. There are 8 data points. The data points begin a little below, and to the right of the top of the vertical axis, then trend downward and to the right. A line of best fit is drawn. The data represented by the 8 data points are as follows. Note that all values are approximate. . 1. 6, 350 feet, 42 . 9 ° Fahrenheit. . 2. 6, 750 feet, 43 . 8 ° Fahrenheit. . 3. 6, 750 feet, 42 ° Fahrenheit. . 4. 7, 500 feet, 42 . 2 ° Fahrenheit. . 5. 8, 000 feet, 40 . 5 ° Fahrenheit. . 6. 8, 000 feet, 40 ° Fahrenheit. . 7. 8, 800 feet, 38 . 6 ° Fahrenheit. . 8. 8, 800 feet, 37 . 6 ° Fahrenheit. The line of best fit passes through the data . representing 7, 500 feet, 41 . 1 ° Fahrenheit, and the data . representing 8, 500 feet, 39 ° Fahrenheit</strong>The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. Which of the following statements best describes the association between the elevation and the temperature of locations in the Lake Tahoe Basin?",
    choices: [
      {
        label: "A",
        text: "As the elevation increases, the temperature tends to increase.",
      },
      {
        label: "B",
        text: "As the elevation increases, the temperature tends to decrease.",
      },
      {
        label: "C",
        text: "As the elevation decreases, the temperature tends to decrease.",
      },
      {
        label: "D",
        text: "There is no association between the elevation and the temperature.",
      },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The association between the elevation and the temperature of locations in the Lake Tahoe Basin can be described by looking at the direction of the line of best fit. The line of best fit slopes downward, which corresponds to the temperature decreasing as the elevation increases.Choices A and C are incorrect. Both of these choices would be represented by a line of best fit that slopes from the lower left to the upper right of the graph, which isn’t what’s shown on the graph. Choice D is incorrect. This choice would be represented by a line of best fit that is horizontal or has a slope very close to 0. This is not what’s shown on the graph.",
    hasFigure: true,
    figureUrl: "/practice-images/661dfddd_img1.png",
  },
  {
    id: "74dee52b",
    type: "mcq",
    questionHtml:
      "The line graph shows the number of graduates from the classes of 2001 through 2007 at a certain school who enrolled in college within 24 months of graduation. Of the following, which class had the fewest graduates who enrolled in college within 24 months of graduation?",
    choices: [
      { label: "A", text: "2002" },
      { label: "B", text: "2004" },
      { label: "C", text: "2005" },
      { label: "D", text: "2007" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The year with the fewest graduates who enrolled in college within 24 months of graduation is the point with the lowest value on the vertical axis. This occurs at 2002.Choice B, C, and D are incorrect. The years 2004, 2005, and 2007 each had a greater number of graduates who enrolled in college within 24 months of graduation than did the year 2002.",
    hasFigure: true,
    figureUrl: "/practice-images/74dee52b_img1.png",
  },
  {
    id: "8156d446",
    type: "spr",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Number of Beach Visitors versus Temperature.” The horizontal axis is labeled “Average temperature, in ° Celsius, ” and the numbers 25 through 35, in increments of 2, are indicated. The vertical axis is labeled “Number of people, ” and the numbers 0 through 640, in increments of 80, are indicated. There are 11 data points in the scatterplot that begin near the bottom left portion of the coordinate plane and trend upward and to the right. The line of best fit for the data is also shown. The line of best fit passes through 25, 80 and 32, 480.</strong>Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. According to the line of best fit, what is the number of people, rounded to the nearest 10, predicted to visit this beach on a day with an average temperature of 32°C?",
    choices: [],
    correctAnswer: "",
    explanation:
      "The correct answer is 480. An average temperature of <strong>32 ° Celsius</strong> corresponds to the value 32 on the x-axis. On the line of best fit, an x-value of 32 corresponds to a y-value of 480. The values on the y-axis correspond to the number of people predicted to visit this beach. Therefore, 480 people are predicted to visit this beach on a day with an average temperature of <strong>32 ° Celsius</strong>.",
    hasFigure: true,
    figureUrl: "/practice-images/8156d446_img1.png",
  },
  {
    id: "82aaa0a1",
    type: "mcq",
    questionHtml:
      "Of the following, which is the best model for the data in the scatterplot?",
    choices: [
      { label: "A", text: "<strong>y = 2 x² − 11 x − 20</strong>" },
      { label: "B", text: "<strong>y = 2 x² − 11 x + 20</strong>" },
      { label: "C", text: "<strong>y = 2 x² − 5 x − 3</strong>" },
      { label: "D", text: "<strong>y = 2 x² − 5 x + 3</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The graphical model that most closely fits the data in the scatterplot is a model in which the number of data points above and below the model are approximately balanced. Fitting a graphical model to the data shown results in an upward-facing parabola with a y-intercept near <strong>0, 20</strong> and a vertex with an approximate x-value of 2.5. Of the given choices, only choice B gives an equation of an upward-facing parabola with a y-intercept at <strong>0, 20</strong>. Furthermore, substituting 2.5 for x into the equation in choice B yields <strong>y = 5</strong>. This is approximately the y-value of the vertex of the model.Choices A, C, and D are incorrect. These equations don’t give a graphical model that best fits the data. At <strong>x = 0</strong>, they have y-values of <strong>−20</strong>, <strong>−3</strong>, and 3, respectively. At <strong>x = 2 . 5</strong>, they have y-values of <strong>−35</strong>, <strong>−3</strong>, and 3, respectively.",
    hasFigure: true,
    figureUrl: "/practice-images/82aaa0a1_img1.png",
  },
  {
    id: "83272c51",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Temperature of a Cup of Coffee during an Experiment.” The horizontal axis is labeled “Time since cup was removed from heat source, in minutes, ” and the numbers 0 through 140, in increments of 20, are indicated. The vertical axis is labeled “Temperature, in ° Fahrenheit, ” and the numbers 0 through 220, in increments of 20, are indicated. There are 15 data points in the scatterplot. The data points begin with . 0, 195, and trend downward and to the right, rapidly at first, then more and more slowly, finally leveling off. The last data . is 140, 76. The 15 data points are as follows. The second coordinate of each . is approximate. . 1, 0, 195. . 2, 10, 153. . 3, 20, 136. . 4, 30, 122. . 5, 40, 109. . 6, 50, 100. . 7, 60, 92. . 8, 70, 84. . 9, 80, 82. . 10, 90, 80. . 11, 100, 79. . 12, 110, 77. . 13, 120, 77. . 14, 130, 76. . 15, 140, 76.</strong>In an experiment, a heated cup of coffee is removed from a heat source, and the cup of coffee is then left in a room that is kept at a constant temperature. The graph above shows the temperature, in degrees Fahrenheit (°F), of the coffee immediately after being removed from the heat source and at 10-minute intervals thereafter. During which of the following 10-minute intervals does the temperature of the coffee decrease at the greatest average rate?",
    choices: [
      { label: "A", text: "Between 0 and 10 minutes" },
      { label: "B", text: "Between 30 and 40 minutes" },
      { label: "C", text: "Between 50 and 60 minutes" },
      { label: "D", text: "Between 90 and 100 minutes" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The average rate of change in temperature of the coffee in degrees Fahrenheit per minute is calculated by dividing the difference between two recorded temperatures by the number of minutes in the corresponding interval of time. Since the time intervals given are all 10 minutes, the average rate of change is greatest for the points with the greatest difference in temperature. Of the choices, the greatest difference in temperature occurs between 0 and 10 minutes.Choices B, C, and D are incorrect and may result from misinterpreting the average rate of change from the graph.",
    hasFigure: true,
    figureUrl: "/practice-images/83272c51_img1.png",
  },
  {
    id: "8baf2118",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>. A line of best fit is also shown.<br>The scatterplot has 10 data points.<br>The data points are in a linear pattern trending down from left to right.<br>A line of best fit is shown:<br><br>The line of best slants down from left to right.<br>1 point is touching the line of best fit.<br>4 points are above the line of best fit.<br>5 points are below the line of best fit.<br>The line of best fit passes through the following approximate coordinates:<br><br>(2 comma 12)<br>(8 comma 7)<br>(13 comma 3)<br><br>Which of the following equations best represents the line of best fit shown?",
    choices: [
      { label: "A", text: "<strong>y = 13.5 + 0.8 x</strong>" },
      { label: "B", text: "<strong>y = 13.5 − 0.8 x</strong>" },
      { label: "C", text: "<strong>y = −13.5 + 0.8 x</strong>" },
      { label: "D", text: "<strong>y = −13.5 − 0.8 x</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a negative slope. The graph of an equation of the form <strong>y = a + b x</strong>, where <strong>a</strong> and <strong>b</strong> are constants, intersects the y-axis at a y-value of <strong>a</strong> and has a slope of <strong>b</strong>. Of the given choices, only choice B represents a line that intersects the y-axis at a positive y-value, <strong>13.5</strong>, and has a negative slope, <strong>−0.8</strong>.<br>Choice A is incorrect. This equation represents a line that has a positive slope, not a negative slope.<br>Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a positive slope, not a negative slope.<br>Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.",
    hasFigure: true,
    figureUrl: "/practice-images/8baf2118_svg1.svg",
  },
  {
    id: "9296553d",
    type: "mcq",
    questionHtml:
      "Which of the following could be an equation for a line of best fit for the data in the scatterplot?",
    choices: [
      { label: "A", text: "<strong>y = −x + 6</strong>" },
      { label: "B", text: "<strong>y = −x − 6</strong>" },
      { label: "C", text: "<strong>y = 6 x + 1</strong>" },
      { label: "D", text: "<strong>y = 6 x − 1</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. A line of best fit for the data in a scatterplot is a line that follows the trend of the data with approximately half the data points above and half the data points below the line. Based on the given data, a line of best fit will have a positive y-intercept on or near the point <strong>with coordinates 0, 6</strong> and a negative slope. All of the choices are in slope-intercept form <strong>y = m x + b</strong>, where m is the slope and b is the y-coordinate of the y-intercept. Only choice A is an equation of a line with a positive y-intercept at <strong>0, 6</strong> and a negative slope, <strong>−1</strong>.Choice B is incorrect. This equation is for a line that has a negative y-intercept, not a positive y-intercept. Choices C and D are incorrect and may result from one or more sign errors and from switching the values of the y-intercept and the slope in the equation.",
    hasFigure: true,
    figureUrl: "/practice-images/9296553d_img1.png",
  },
  {
    id: "9d88a3e3",
    type: "mcq",
    questionHtml:
      "Theresa ran on a treadmill for thirty minutes, and her time and speed are shown on the graph above. According to the graph, which of the following statements is NOT true concerning Theresa’s run?",
    choices: [
      { label: "A", text: "Theresa ran at a constant speed for five minutes." },
      {
        label: "B",
        text: "Theresa’s speed was increasing for a longer period of time than it was decreasing.",
      },
      {
        label: "C",
        text: "Theresa’s speed decreased at a constant rate during the last five minutes.",
      },
      {
        label: "D",
        text: "Theresa’s speed reached its maximum during the last ten minutes.",
      },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. Theresa’s speed was increasing from 0 to 5 minutes and from 20 to 25 minutes, which is a total of 10 minutes. Theresa’s speed was decreasing from 10 minutes to 20 minutes and from 25 to 30 minutes, which is a total of 15 minutes. Therefore, Theresa’s speed was NOT increasing for a longer period of time than it was decreasing.Choice A is incorrect. Theresa ran at a constant speed for the 5-minute period from 5 to 10 minutes. Choice C is incorrect. Theresa’s speed decreased at a constant rate during the last 5 minutes, which can be seen since the graph is linear during that time. Choice D is incorrect. Theresa’s speed reached its maximum at 25 minutes, which is within the last 10 minutes.",
    hasFigure: true,
    figureUrl: "/practice-images/9d88a3e3_img1.png",
  },
  {
    id: "a6b2fcce",
    type: "mcq",
    questionHtml:
      "According to the line graph above, between which two consecutive years was there the greatest change in the number of 3‑D movies released?",
    choices: [
      { label: "A", text: "2003–2004" },
      { label: "B", text: "2008–2009" },
      { label: "C", text: "2009–2010" },
      { label: "D", text: "2010–2011" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The change in the number of 3-D movies released between any two consecutive years can be found by first estimating the number of 3-D movies released for each of the two years and then finding the positive difference between these two estimates. Between 2003 and 2004, this change is approximately <strong>2 − 2 = 0</strong> movies; between 2008 and 2009, this change is approximately <strong>20 − 8 = 12</strong> movies; between 2009 and 2010, this change is approximately <strong>26 − 20 = 6</strong> movies; and between 2010 and 2011, this change is approximately <strong>46 − 26 = 20</strong> movies. Therefore, of the pairs of consecutive years in the choices, the greatest increase in the number of 3-D movies released occurred during the time period between 2010 and 2011.Choices A, B, and C are incorrect. Between 2010 and 2011, approximately 20 more 3-D movies were released. The change in the number of 3-D movies released between any of the other pairs of consecutive years is significantly smaller than 20.",
    hasFigure: true,
    figureUrl: "/practice-images/a6b2fcce_img1.png",
  },
  {
    id: "ac5b6558",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Temperature and Elevation.” The horizontal axis is labeled “Elevation, in feet, ” and the numbers 6, 000 through 9, 000, in increments of 500, are indicated. The vertical axis is labeled “Temperature, in ° Fahrenheit, ” and the integers 37 through 45 are indicated. There are 8 data points. The data points begin a little below, and to the right of the top of the vertical axis, then trend downward and to the right. A line of best fit is drawn. The data represented by the 8 data points are as follows. Note that all values are approximate. . 1. 6, 350 feet, 42 . 9 ° Fahrenheit. . 2. 6, 750 feet, 43 . 8 ° Fahrenheit. . 3. 6, 750 feet, 42 ° Fahrenheit. . 4. 7, 500 feet, 42 . 2 ° Fahrenheit. . 5. 8, 000 feet, 40 . 5 ° Fahrenheit. . 6. 8, 000 feet, 40 ° Fahrenheit. . 7. 8, 800 feet, 38 . 6 ° Fahrenheit. . 8. 8, 800 feet, 37 . 6 ° Fahrenheit. The line of best fit passes through the data . representing 7, 500 feet, 41 . 1 ° Fahrenheit, and the data . representing 8, 500 feet, 39 ° Fahrenheit</strong>The scatterplot above shows the high temperature on a certain day and the elevation of 8 different locations in the Lake Tahoe Basin. A line of best fit for the data is also shown. What temperature is predicted by the line of best fit for a location in the Lake Tahoe Basin with an elevation of 8,500 feet?",
    choices: [
      { label: "A", text: "37°F" },
      { label: "B", text: "39°F" },
      { label: "C", text: "41°F" },
      { label: "D", text: "43°F" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The line of best fit passes through the point <strong>with coordinates 8, 500, 39</strong>. Therefore, the line of best fit predicts a temperature of 39°F for a location in Lake Tahoe Basin with an elevation of 8,500 feet.Choice A is incorrect. This is the lowest temperature listed on the scatterplot, and the line of best fit never crosses this value for any of the elevations shown. Choice C is incorrect. According to the line of best fit, the temperature of 41°F is predicted for an elevation of slightly greater than 7,500 feet, not an elevation of 8,500 feet. Choice D is incorrect. According to the line of best fit, the temperature of 43°F is predicted for an elevation of roughly 6,700 feet, not an elevation of 8,500 feet.",
    hasFigure: true,
    figureUrl: "/practice-images/ac5b6558_img1.png",
  },
  {
    id: "c9dd92b1",
    type: "mcq",
    questionHtml:
      "The densities of different concentrations of grape juice are shown in the scatterplot above. According to the trend shown by the data, which of the following is closest to the predicted density, in kilograms per cubic meter (kg/m3), for grape juice with a concentration of 60%?",
    choices: [
      { label: "A", text: "1,200" },
      { label: "B", text: "1,250" },
      { label: "C", text: "1,300" },
      { label: "D", text: "1,350" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. The data in the scatterplot show an increasing linear trend. The density when the juice concentration is 60% will be between the densities shown at about 53% and 67% concentration, or between about 1,255 and 1,340 kg/m3. Of the choices given, only 1,300 falls within this range.Choices A, B, and D are incorrect. These are the approximate densities of grape juice with a concentration of 45%, 55%, and 70%, respectively.",
    hasFigure: true,
    figureUrl: "/practice-images/c9dd92b1_img1.png",
  },
  {
    id: "cf0ae57a",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Distance and Density of Planetoids in the Inner Solar System.” The horizontal axis is labeled “Distance from the Sun, ” in astronomical units (A U), and the numbers zero through 3 . 2, in increments of zero . 4, are indicated. The vertical axis is labeled “Density, ” in grams per cubic centimeter, and the numbers 3 through 6, in increments of zero . 5, are indicated. The graph has 7 data points. Three of the points are grouped in the upper left corner of the graph, below 1 . 2 A U and above 5 grams per cubic centimeter. The remaining points are above 1 . 4 A U and below 4 grams per cubic centimeter, with 3 of the points grouped in the lower right corner above 2 . 2 A U and below 3 . 7 5 grams per cubic centimeter. The line of best fit is also graphed. The line of best fit passes through the following coordinates on the grid. All data are approximate: zero A U, 5 . 7 5 grams per cubic centimeter. Zero . 8 A U; 5 grams per cubic centimeter. 1 . 6 A U; 4 . 2 5 grams per cubic centimeter. 2 . 4 A U; 3 . 5 grams per cubic centimeter. 2 . 9 A U; 3 grams per cubic centimeter.</strong>The scatterplot above shows the densities of 7 planetoids, in grams per cubic centimeter, with respect to their average distances from the Sun in astronomical units (AU). The line of best fit is also shown. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?",
    choices: [
      { label: "A", text: "3.6" },
      { label: "B", text: "4.1" },
      { label: "C", text: "4.6" },
      { label: "D", text: "5.5" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. According to the line of best fit, a planetoid with a distance from the Sun of 1.2 AU has a predicted density between <strong>4 . 5 grams per cubic centimeter</strong> and <strong>4 . 7 5 grams per cubic centimeter</strong>. The only choice in this range is 4.6.Choices A, B, and D are incorrect and may result from misreading the information in the scatterplot.",
    hasFigure: true,
    figureUrl: "/practice-images/cf0ae57a_img1.png",
  },
  {
    id: "d112bc9d",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the temperature <strong>y</strong>, in <strong>° F</strong>, recorded by a meteorologist at various times <strong>x</strong>, in days since June <strong>1</strong>. <br>The scatterplot has 7 data points.<br>The data points are in a linear pattern trending approximately horizontally.<br>The data points have the following coordinates:<br><br>(1 comma 69)<br>(2 comma 60)<br>(3 comma 73)<br>(4 comma 67)<br>(5 comma 64)<br>(6 comma 62)<br>(7 comma 65)<br><br>During which of the following time periods did the greatest increase in recorded temperature take place?",
    choices: [
      {
        label: "A",
        text: "From <strong>x = 6</strong> to <strong>x = 7</strong>",
      },
      {
        label: "B",
        text: "From <strong>x = 5</strong> to <strong>x = 6</strong>",
      },
      {
        label: "C",
        text: "From <strong>x = 2</strong> to <strong>x = 3</strong>",
      },
      {
        label: "D",
        text: "From <strong>x = 1</strong> to <strong>x = 2</strong>",
      },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. The scatterplot shows that there was an increase in recorded temperature from <strong>x = 2</strong> to <strong>x = 3</strong> and from <strong>x = 6</strong> to <strong>x = 7</strong>. When <strong>x = 2</strong>, the recorded temperature was approximately <strong>60 ° F</strong> and when <strong>x = 3</strong>, the recorded temperature was greater than <strong>70 ° F</strong>. This means that the increase in recorded temperature from <strong>x = 2</strong> to <strong>x = 3</strong> was greater than <strong>(70 − 60) ° F</strong>, or <strong>10 ° F</strong>. When <strong>x = 6</strong>, the recorded temperature was greater than <strong>60 ° F</strong> and when <strong>x = 7</strong>, the recorded temperature was less than <strong>70 ° F</strong>. This means that the increase in recorded temperature from <strong>x = 6</strong> to <strong>x = 7</strong> was less than <strong>(70 − 60) ° F</strong>, or <strong>10 ° F</strong>. It follows that the greatest increase in recorded temperature took place from <strong>x = 2</strong> to <strong>x = 3</strong>.<br>Choice A is incorrect. The increase in recorded temperature from <strong>x = 6</strong> to <strong>x = 7</strong> was less than the increase in recorded temperature from <strong>x = 2</strong> to <strong>x = 3</strong>.<br>Choice B is incorrect. From <strong>x = 5</strong> to <strong>x = 6</strong>, a decrease, not an increase, in recorded temperature took place.<br>Choice D is incorrect. From <strong>x = 1</strong> to <strong>x = 2</strong>, a decrease, not an increase, in recorded temperature took place.",
    hasFigure: true,
    figureUrl: "/practice-images/d112bc9d_svg1.svg",
  },
  {
    id: "d230e963",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>. A line of best fit is also shown.<br>The scatterplot has 10 data points.<br>The data points are in a linear pattern trending up from left to right.<br>A line of best fit is shown.<br><br>The line of best fit slants up from left to right.<br>1 point is touching the line of best fit.<br>5 points are above the line of best fit.<br>4 points are below the line of best fit.<br>The line of best fit passes through the following approximate coordinates:<br><br>(0 comma 3)<br>(3 comma 8)<br>(7 comma 15)<br><br>Which of the following equations best represents the line of best fit shown?",
    choices: [
      { label: "A", text: "<strong>y = 2.8 + 1.7 x</strong>" },
      { label: "B", text: "<strong>y = 2.8 − 1.7 x</strong>" },
      { label: "C", text: "<strong>y = −2.8 + 1.7 x</strong>" },
      { label: "D", text: "<strong>y = −2.8 − 1.7 x</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The line of best fit shown intersects the y-axis at a positive y-value and has a positive slope. The graph of an equation of the form <strong>y = a + b x</strong>, where <strong>a</strong> and <strong>b</strong> are constants, intersects the y-axis at a y-value of <strong>a</strong> and has a slope of <strong>b</strong>. Of the given choices, only choice A represents a line that intersects the y-axis at a positive y-value, <strong>2.8</strong>, and has a positive slope, <strong>1.7</strong>.<br>Choice B is incorrect. This equation represents a line that has a negative slope, not a positive slope.<br>Choice C is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value.<br>Choice D is incorrect. This equation represents a line that intersects the y-axis at a negative y-value, not a positive y-value, and has a negative slope, not a positive slope.",
    hasFigure: true,
    figureUrl: "/practice-images/d230e963_svg1.svg",
  },
  {
    id: "d6121490",
    type: "mcq",
    questionHtml:
      "The graph above shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet. Approximately how many feet greater will the car’s braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?",
    choices: [
      { label: "A", text: "75" },
      { label: "B", text: "125" },
      { label: "C", text: "175" },
      { label: "D", text: "250" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. According to the graph, when the car is traveling at 50 miles per hour, the braking distance is approximately 225 feet, and when the car is traveling at 30 miles per hour, the braking distance is approximately 100 feet. The difference between these braking distances is <strong>225 − 100</strong>, or 125 feet.Choice A is incorrect and may result from finding the braking distance for 20 miles per hour, the difference between the given speeds. Choice C is incorrect and may result from subtracting the speed from the braking distance at 50 miles per hour. Choice D is incorrect and may result from finding the difference in the braking distances at 60 and 20 miles per hour.",
    hasFigure: true,
    figureUrl: "/practice-images/d6121490_img1.png",
  },
];

export const TWO_VAR_DATA_MEDIUM: PracticeQuestion[] = [
  {
    id: "03a16790",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>. A line of best fit is also shown.<br>The scatterplot has 10 data points.<br>The data points are in a linear pattern trending down from left to right.<br>A line of best fit is shown:<br><br>The line of best fit slants down from left to right.<br>2 points are touching the line of best fit.<br>3 points are above the line of best fit.<br>5 points are below the line of best fit.<br>The line of best fit passes through the following approximate coordinates:<br><br>(0 comma 12.9)<br>(6 comma 8)<br>(12 comma 3.2)<br><br>Which of the following is closest to the slope of the line of best fit shown?",
    choices: [
      { label: "A", text: "<strong>−2.4</strong>" },
      { label: "B", text: "<strong>−0.8</strong>" },
      { label: "C", text: "<strong>0.8</strong>" },
      { label: "D", text: "<strong>2.4</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. A line of best fit is shown in the scatterplot such that as the value of <strong>x</strong> increases, the value of <strong>y</strong> decreases. Thus, the slope of the line of best fit shown is negative. The slope of a line passing through two points, <strong>(x 1, y 1)</strong> and <strong>(x 2, y 2)</strong>, can be calculated as <strong>(y 2 − y 1) / (x 2 − x 1)</strong>. The line of best fit shown passes approximately through the points <strong>(1, 12)</strong> and <strong>(11, 4)</strong>. Substituting <strong>(1, 12)</strong> and <strong>(11, 4)</strong> for <strong>(x 1, y 1)</strong> and <strong>(x 2, y 2)</strong>, respectively, in <strong>(y 2 − y 1) / (x 2 − x 1)</strong> gives <strong>(4 − 12) / (11 − 1)</strong>, which is equivalent to <strong>−eight tenths</strong>, or <strong>−0.8</strong>. Therefore, of the given choices, <strong>−0.8</strong> is closest to the slope of the line of best fit shown.<br>Choice A is incorrect and may result from conceptual or calculation errors.<br>Choice C is incorrect. The line of best fit shown has a negative slope, not a positive slope.<br>Choice D is incorrect. The line of best fit shown has a negative slope, not a positive slope.",
    hasFigure: true,
    figureUrl: "/practice-images/03a16790_svg1.svg",
  },
  {
    id: "1adb39f0",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following is closest to the difference between the y-coordinate of the data point with <strong>x = 1</strong> and the y-value predicted by the line of best fit at <strong>x = 1</strong> ?<br> <strong>The figure presents a scatterplot in the xy plane. The numbers 0 through 6, in increments of 1, are indicated on the x-axis. The numbers 6 through 12, in increments of 1, are indicated on the y-axis. There are 10 data points in the scatterplot. The data points begin at 0, 12, and trend downward and to the right. The coordinates of the data points are as follows. Note that all values are approximate.<br>. 1. 0, , 12.<br>. 2. 0 . 8, , 11.<br>. 3. 1, , 12.<br>. 4. 1 . 5, , 10 . 3.<br>. 5. 2, , 10.<br>. 6. 2 . 2, , 9 . 2.<br>. 7. 3, , 9.<br>. 8. 3 . 5, , 8.<br>. 9. 3 . 8, , 8 . 3.<br>. 10. 4, , 7. A line of best fit is also drawn. The line slants downward and to the right, passing through the . with approximate coordinates 1, 11, and the . with approximate coordinates 4, 7 . 5.</strong>",
    choices: [
      { label: "A", text: "1" },
      { label: "B", text: "2" },
      { label: "C", text: "5" },
      { label: "D", text: "12" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The data point with <strong>x = 1</strong> has a y-coordinate of 12. The y-value predicted by the line of best fit at <strong>x = 1</strong> is approximately 11. The difference between the y-coordinate of the data point and the y-value predicted by the line of best fit at <strong>x = 1</strong> is <strong>12 − 11</strong>, or 1.Choices B and C are incorrect and may result from incorrectly reading the scatterplot. Choice D is incorrect. This is the y-coordinate of the data point at <strong>x = 1</strong>.",
    hasFigure: true,
    figureUrl: "/practice-images/1adb39f0_img3.png",
  },
  {
    id: "2e74e403",
    type: "mcq",
    questionHtml:
      "In the given scatterplot, a line of best fit for the data is shown.<br>The scatterplot has 10 data points.<br>The data points are in a linear pattern trending down from left to right.<br>A line of best fit is shown:<br>The line of best fit slants down from left to right.<br><br>5 points are touching the line of best fit.<br>2 points are above the line of best fit.<br>3 points are below the line of best fit.<br>The line of best fit passes through the following approximate coordinates:<br><br>(1 comma 7)<br>(4 comma 5)<br>(10 comma 1)<br><br>Which of the following is closest to the slope of this line of best fit?",
    choices: [
      { label: "A", text: "<strong>7</strong>" },
      { label: "B", text: "<strong>0.7</strong>" },
      { label: "C", text: "<strong>−0.7</strong>" },
      { label: "D", text: "<strong>−7</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. A line of best fit is shown in the scatterplot such that as the value of <strong>x</strong> increases, the value of <strong>y</strong> decreases. It follows that the slope of the line of best fit shown is negative. The slope of a line in the xy-plane that passes through the points <strong>(x 1, y 1)</strong> and <strong>(x 2, y 2)</strong> can be calculated as <strong>(y 2 − y 1) / (x 2 − x 1)</strong>. The line of best fit shown passes approximately through the points <strong>(0, 8)</strong> and <strong>(10, 1)</strong>. Substituting <strong>(0, 8)</strong> for <strong>(x 1, y 1)</strong> and <strong>(10, 1)</strong> for <strong>(x 2, y 2)</strong> in <strong>(y 2 − y 1) / (x 2 − x 1)</strong> yields the slope of the line being approximately <strong>(1 − 8) / (10 − 0)</strong>, which is equivalent to <strong>(−7) / (10)</strong>, or <strong>−0.7</strong>. Therefore, of the given choices, <strong>−0.7</strong> is the closest to the slope of this line of best fit.<br>Choice A is incorrect. The line of best fit shown has a negative slope, not a positive slope.<br>Choice B is incorrect. The line of best fit shown has a negative slope, not a positive slope.<br>Choice D is incorrect and may result from conceptual or calculation errors.",
    hasFigure: true,
    figureUrl: "/practice-images/2e74e403_svg1.svg",
  },
  {
    id: "3c5b19ef",
    type: "mcq",
    questionHtml:
      "The scatterplot above shows the number of visitors to a railroad museum in Pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. A line of best fit is also shown. Which of the following could be an equation of the line of best fit shown?",
    choices: [
      { label: "A", text: "<strong>n = 16, 090 + 4, 680, t</strong>" },
      { label: "B", text: "<strong>n = 4, 690 + 16, 090, t</strong>" },
      { label: "C", text: "<strong>n = 16, 090 + 9, 060, t</strong>" },
      { label: "D", text: "<strong>n = 9, 060 + 16, 090, t</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. An equation of a line of best fit can be written in the form <strong>y = a + b x</strong>, where a is the y-intercept of the line and b is the slope. In the scatterplot shown, the line of best fit intersects the y-axis just over halfway between 10,000 and 20,000, or approximately 16,000. The line of best fit also intersects the graph at <strong>5, 40, 000</strong>. Using the slope formula <strong>b = the fraction with numerator y sub 2 − y sub 1, and denominator x sub 2 − x sub 1, end fraction</strong> and two points that lie on the graph such as <strong>5, 40, 000</strong> and <strong>0, 16, 000</strong>, the slope can be approximated as <strong>the fraction with numerator 40, 000 − 16, 000, and denominator 5 − 0, end fraction</strong>, or 4,800. Only choice A has a y-intercept near the estimate of 16,000 and a slope near the estimate of 4,800. Therefore, an equation of the line of best fit could be <strong>n = 16, 090 + 4, 680 t</strong>.Choice B is incorrect because the values for the slope and the y-coordinate of the y-intercept are switched. Choice C is incorrect because the value for the slope is approximately double the actual slope. Choice D is incorrect because the values for the slope and the y-intercept are switched and because the slope is approximately double the actual slope.",
    hasFigure: true,
    figureUrl: "/practice-images/3c5b19ef_img1.png",
  },
  {
    id: "3d985614",
    type: "mcq",
    questionHtml:
      "Each dot in the scatterplot above represents the height x, in feet, in the high jump, and the distance y, in feet, in the long jump, made by each student in a group of twenty students. The graph of which of the following equations is a line that most closely fits the data?",
    choices: [
      { label: "A", text: "<strong>y = 0 . 8 2 x + 3 . 3 0</strong>" },
      { label: "B", text: "<strong>y = 0 . 8 2 x − 0 . 8 2</strong>" },
      { label: "C", text: "<strong>y = 3 . 3 0 x + 0 . 8 2</strong>" },
      { label: "D", text: "<strong>y = 3 . 3 0 x − 3 . 3 0</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. A line that most closely fits the data is a line with an approximately balanced number of data points above and below the line. Fitting a line to the data shown results in a line with an approximate slope of 3 and a y-intercept near the point <strong>with coordinates 0, 1</strong>. An equation for the line can be written in slope-intercept form, <strong>y = m x + b</strong>, where m is the slope and b is the y-coordinate of the y-intercept. The equation <strong>y = 3 . 3 0 x + 0 . 8 2</strong> in choice C fits the data most closely.Choices A and B are incorrect because the slope of the lines of these equations is 0.82, which is a value that is too small to be the slope of the line that fits the data shown. Choice D is incorrect. The graph of this equation has a y-intercept at <strong>0 −3 . 3 0</strong>, not <strong>0, 0 . 8 2</strong>. This line would lie below all of the data points, and therefore would not closely fit the data.",
    hasFigure: true,
    figureUrl: "/practice-images/3d985614_img1.png",
  },
  {
    id: "50b2807e",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>.<br>The scatterplot has 10 data points.<br>The data points are in a linear pattern trending down from left to right.<br>The data points have the following approximate coordinates:<br><br>(0 comma 10)<br>(1.2 comma 9)<br>(2.3 comma 8)<br>(3.1 comma 5)<br>(4.8 comma 5)<br>(5.2 comma 3)<br>(6.5 comma 3)<br>(7.2 comma 3)<br>(9.6 comma 2)<br>(8.8 comma 1)<br><br>Which of the following equations is the most appropriate linear model for the data shown?",
    choices: [
      { label: "A", text: "<strong>y = 0.9 + 9.4 x</strong>" },
      { label: "B", text: "<strong>y = 0.9 − 9.4 x</strong>" },
      { label: "C", text: "<strong>y = 9.4 + 0.9 x</strong>" },
      { label: "D", text: "<strong>y = 9.4 − 0.9 x</strong>" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The data points suggest that as the variable <strong>x</strong> increases, the variable <strong>y</strong> decreases, which implies that an appropriate linear model for the data has a negative slope. The data points also show that when <strong>x</strong> is close to <strong>0</strong>, <strong>y</strong> is greater than <strong>9</strong>. Therefore, the y-intercept of the graph of an appropriate linear model has a y-coordinate greater than <strong>9</strong>. The graph of an equation of the form <strong>y = a + b x</strong>, where <strong>a</strong> and <strong>b</strong> are constants, has a y-intercept with a y-coordinate of <strong>a</strong> and has a slope of <strong>b</strong>. Of the given choices, only choice D represents a graph that has a negative slope, <strong>−0.9</strong>, and a y-intercept with a y-coordinate greater than <strong>9</strong>, <strong>9.4</strong>.<br>Choice A is incorrect. The graph of this equation has a positive slope, not a negative slope, and a y-intercept with a y-coordinate less than <strong>1</strong>, not greater than <strong>9</strong>.<br>Choice B is incorrect. The graph of this equation has a y-intercept with a y-coordinate less than <strong>1</strong>, not greater than <strong>9</strong>.<br>Choice C is incorrect. The graph of this equation has a positive slope, not a negative slope.",
    hasFigure: true,
    figureUrl: "/practice-images/50b2807e_svg1.svg",
  },
  {
    id: "58171b5e",
    type: "mcq",
    questionHtml:
      "Each year, the value of an investment increases by <strong>0.49 % sign</strong> of its value the previous year. Which of the following functions best models how the value of the investment changes over time?",
    choices: [
      { label: "A", text: "Decreasing exponential" },
      { label: "B", text: "Decreasing linear" },
      { label: "C", text: "Increasing exponential" },
      { label: "D", text: "Increasing linear" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. Because the value of the investment increases each year, the function that best models how the value of the investment changes over time is an increasing function. It′s given that each year, the value of the investment increases by <strong>0.49 % sign</strong> of its value the previous year. Since the value of the investment changes by a fixed percentage each year, the function that best models how the value of the investment changes over time is an exponential function. Therefore, the function that best models how the value of the investment changes over time is an increasing exponential function.<br>Choice A is incorrect and may result from conceptual errors.<br>Choice B is incorrect and may result from conceptual errors.<br>Choice D is incorrect and may result from conceptual errors.",
    hasFigure: false,
  },
  {
    id: "7ac5d686",
    type: "mcq",
    questionHtml:
      "An inspector begins a day of work with a large sample of shirts that need to be checked for defects. The inspector works at a constant rate throughout the morning. What type of model is best to model the number of shirts remaining to be checked for defects at any given time throughout the morning?",
    choices: [
      { label: "A", text: "A linear model with a positive slope" },
      { label: "B", text: "A linear model with a negative slope" },
      { label: "C", text: "An exponential growth model" },
      { label: "D", text: "An exponential decay model" },
    ],
    correctAnswer: "",
    explanation:
      "Choice B is correct. Since the work is done at a constant rate, a linear model best models the situation. The number of shirts remaining is dependent on the length of time the inspector has worked; therefore, if the relationship were graphed, time would be the variable of the horizontal axis and the number of remaining shirts would be the variable of the vertical axis. Since the number of shirts decreases as the time worked increases, it follows that the slope of this graph is negative.Choice A is incorrect and may result from incorrectly reasoning about the slope. Choices C and D are incorrect and may result from not identifying the constant rate of work as a characteristic of a linear model.",
    hasFigure: false,
  },
  {
    id: "7fd284ac",
    type: "mcq",
    questionHtml:
      "The scatterplot above shows data for ten charities along with the line of best fit. For the charity with the greatest percent of total expenses spent on programs, which of the following is closest to the difference of the actual percent and the percent predicted by the line of best fit?",
    choices: [
      { label: "A", text: "<strong>10 %</strong>" },
      { label: "B", text: "<strong>7 %</strong>" },
      { label: "C", text: "<strong>4 %</strong>" },
      { label: "D", text: "<strong>1 %</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. The charity with the greatest percent of total expenses spent on programs is represented by the highest point on the scatterplot; this is the point that has a vertical coordinate slightly less than halfway between 90 and 95 and a horizontal coordinate slightly less than halfway between 3,000 and 4,000. Thus, the charity represented by this point has a total income of about $3,400 million and spends about 92% of its total expenses on programs. The percent predicted by the line of best fit is the vertical coordinate of the point on the line of best fit with horizontal coordinate $3,400 million; this vertical coordinate is very slightly more than 85. Thus, the line of best fit predicts that the charity with the greatest percent of total expenses spent on programs will spend slightly more than 85% on programs. Therefore, the difference between the actual percent (92%) and the prediction (slightly more than 85%) is slightly less than 7%.Choice A is incorrect. There is no charity represented in the scatterplot for which the difference between the actual percent of total expenses spent on programs and the percent predicted by the line of best fit is as much as 10%. Choices C and D are incorrect. These choices may result from misidentifying in the scatterplot the point that represents the charity with the greatest percent of total expenses spent on programs.",
    hasFigure: true,
    figureUrl: "/practice-images/7fd284ac_img1.png",
  },
  {
    id: "9a144a01",
    type: "mcq",
    questionHtml:
      "Which of the following is true about the values of <strong>2 to the x power</strong> and <strong>2 x + 2</strong> for <strong>x > 0</strong>?",
    choices: [
      {
        label: "A",
        text: "For all <strong>x > 0</strong>, it is true that <strong>2 to the x power < 2 x + 2</strong>.",
      },
      {
        label: "B",
        text: "For all <strong>x > 0</strong>, it is true that <strong>2 to the x power > 2 x + 2</strong>.",
      },
      {
        label: "C",
        text: "There is a constant c such that if <strong>0 < x, which < c</strong>, then <strong>2 to the x power < 2 x + 2</strong>, but if <strong>x > c</strong>, then <strong>2 to the x power > 2 x + 2</strong>.",
      },
      {
        label: "D",
        text: "There is a constant c such that if <strong>0 < x, which < c</strong>, then <strong>2 to the x power > 2 x + 2</strong>, but if <strong>x > c</strong>, then <strong>2 to the x power < 2 x + 2</strong>.",
      },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. At <strong>x = 0</strong>, the value of <strong>2 raised to the x power</strong> is less than the value of <strong>2 x + 2, where 2 to the 0 power < 2 · 0 + 2</strong>, which is equivalent to <strong>1 < 2</strong>. As the value of x increases, the value of <strong>2 raised to the x power</strong> remains less than the value of <strong>2 x + 2</strong> until <strong>x = 3</strong>, which is when the two values are equal: <strong>2³ = 2 · 3 + 2</strong>, which is equivalent to <strong>8 = 8</strong>. Then, for <strong>x > 3</strong>, the value of <strong>2 raised to the x power</strong> is greater than the value of <strong>2 x + 2</strong>. So there is a constant, 3, such that when <strong>0 < x, which < 3</strong>, then <strong>2 raised to the x power < 2 x + 2</strong>, but when <strong>x > 3</strong>, then <strong>2 raised to the x power > 2 x + 2</strong>.Choice A is incorrect because <strong>2 raised to the x power > 2 x + 2</strong> when <strong>x > 3</strong>. Choice B is incorrect because <strong>2 raised to the x power < 2 x + 2</strong> when <strong>0 < x, which < 3</strong>. Choice D is incorrect because <strong>2 raised to the x power < 2 x + 2</strong> when <strong>0 < x, which < 3</strong> and <strong>2 raised to the x power > 2 x + 2</strong> when <strong>x > 3</strong>.",
    hasFigure: false,
  },
  {
    id: "9bb4107c",
    type: "spr",
    questionHtml:
      "In quadrant 1:<br><br>The curve begins at point (0 comma 1).<br>The curve rises sharply to point (2 comma 6).<br>The curve rises gradually to point (4 comma 7).<br>The curve rises gradually to point (6 comma 8).<br>The curve rises sharply and ends at point (8 comma 10).<br><br>The graph shows the momentum <strong>y</strong>, in newton-seconds, of an object <strong>x</strong> seconds after the object started moving, for <strong>0 < or = x < or = 8</strong>. What is the average rate of change, in newton-seconds per second, in the momentum of the object from <strong>x = 2</strong> to <strong>x = 6</strong>?",
    choices: [],
    correctAnswer: ".5, 1/2",
    explanation:
      "The correct answer is <strong>one half</strong>. For the graph shown, <strong>x</strong> represents time, in seconds, and <strong>y</strong> represents momentum, in newton-seconds. Therefore, the average rate of change, in newton-seconds per second, in the momentum of the object between two x-values is the difference in the corresponding y-values divided by the difference in the x-values. The graph shows that at <strong>x = 2</strong>, the corresponding y-value is <strong>6</strong>. The graph also shows that at <strong>x = 6</strong>, the corresponding y-value is <strong>8</strong>. It follows that the average rate of change, in newton-seconds per second, from <strong>x = 2</strong> to <strong>x = 6</strong> is <strong>(8 − 6) / (6 − 2)</strong>, which is equivalent to <strong>two fourths</strong>, or <strong>one half</strong>. Note that 1/2 and .5 are examples of ways to enter a correct answer.",
    hasFigure: true,
    figureUrl: "/practice-images/9bb4107c_svg1.svg",
  },
  {
    id: "9eb896c5",
    type: "mcq",
    questionHtml:
      "Which of the following could be the equation for a line of best fit for the data shown in the scatterplot above?",
    choices: [
      { label: "A", text: "<strong>y = 3 x + 0 . 8</strong>" },
      { label: "B", text: "<strong>y = 0 . 8 x + 3</strong>" },
      { label: "C", text: "<strong>y = −0 . 8 x + 3</strong>" },
      { label: "D", text: "<strong>y = −3 x + 0 . 8</strong>" },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The data show a strong linear relationship between x and y. The line of best fit for a set of data is a linear equation that minimizes the distances from the data points to the line. An equation for the line of best fit can be written in slope-intercept form, <strong>y = m x + b</strong>, where m is the slope of the graph of the line and b is the y-coordinate of the y-intercept of the graph. Since, for the data shown, the y-values increase as the x-values increase, the slope of a line of best fit must be positive. The data shown lie almost in a line, so the slope can be roughly estimated using the formula for slope, <strong>m = the fraction with numerator y sub 2 − y sub 1, and denominator x sub 2 − x sub 1, end fraction</strong>. The leftmost and rightmost data points have coordinates of about <strong>1, 4</strong> and <strong>8, 26</strong>, so the slope is approximately <strong>the fraction with numerator 26 − 4, and denominator 8 − 1, end fraction = the fraction 22 over 7</strong>, which is a little greater than 3. Extension of the line to the left would intersect the y-axis at about <strong>0, 1</strong>. Only choice A represents a line with a slope close to 3 and a y-intercept close to <strong>0, 1</strong>.Choice B is incorrect and may result from switching the slope and y-intercept. The line with a y-intercept of <strong>0, 3</strong> and a slope of 0.8 is farther from the data points than the line with a slope of 3 and a y-intercept of <strong>0, 0 . 8</strong>. Choices C and D are incorrect. They represent lines with negative slopes, not positive slopes.",
    hasFigure: true,
    figureUrl: "/practice-images/9eb896c5_img1.png",
  },
  {
    id: "ab7740a8",
    type: "mcq",
    questionHtml:
      "In which of the following tables is the relationship between the values of x and their corresponding y-values nonlinear?",
    choices: [
      {
        label: "A",
        text: "<strong>The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x, ” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 11. Column 3. x is 3. y is 14. Column 4. x is 4. y is 17.</strong>",
      },
      {
        label: "B",
        text: "<strong>The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x, ” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 4. Column 2. x is 2. y is 8. Column 3. x is 3. y is 12. Column 4. x is 4. y is 16.</strong>",
      },
      {
        label: "C",
        text: "<strong>The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x, ” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 8. Column 2. x is 2. y is 13. Column 3. x is 3. y is 18. Column 4. x is 4. y is 23.</strong>",
      },
      {
        label: "D",
        text: "<strong>The answer choice presents a 2 row table, with 4 columns of data. The heading for row 1 is “x, ” and the heading for row 2 is “y.” The data in the table are as follows. Column 1. x is 1. y is 6. Column 2. x is 2. y is 12. Column 3. x is 3. y is 24. Column 4. x is 4. y is 48.</strong>",
      },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The relationship between the values of x and their corresponding y-values is nonlinear if the rate of change between these pairs of values isn’t constant. The table for choice D gives four pairs of values: <strong>1, 6</strong>,<strong>2, 12</strong>, <strong>3, 24</strong>, and <strong>4, 48</strong>. Finding the rate of change, or slope, between <strong>1, 6</strong> and <strong>2, 12</strong> by using the slope formula, <strong>the fraction with numerator y sub 2 − y sub 1, and denominator x sub 2 − x sub 1, end fraction</strong>, yields <strong>the fraction with numerator 12 − 6, and denominator 2 − 1, end fraction</strong>, or 6. Finding the rate of change between <strong>2, 12</strong> and <strong>3, 24</strong> yields <strong>the fraction with numerator 24 − 12, and denominator 3 − 2, end fraction</strong>, or 12. Finding the rate of change between <strong>3, 24</strong> and <strong>4, 48</strong> yields <strong>the fraction with numerator 48 − 24, and denominator 4 − 3, end fraction</strong>, or 24. Since the rate of change isn’t constant for these pairs of values, this table shows a nonlinear relationship.Choices A, B, and C are incorrect. The rate of change between the values of x and their corresponding y-values in each of these tables is constant, being 3, 4, and 5, respectively. Therefore, each of these tables shows a linear relationship.",
    hasFigure: true,
    figureUrl: "/practice-images/ab7740a8_img1.png",
  },
  {
    id: "f46139df",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>. A line of best fit for the data is also shown.<br>The scatterplot has 11 data points.<br>The data points are in a linear pattern trending down from left to right.<br>A line of best fit is shown:<br><br>The line of best fit slants down from left to right.<br>6 points are above the line of best fit.<br>5 points are below the line of best fit.<br>The line of best fit goes through the following approximate coordinates:<br><br>(28 comma 6)<br>(33 comma 1.5)<br><br>At <strong>x = 25.5</strong>, which of the following is closest to the y-value predicted by the line of best fit?",
    choices: [
      { label: "A", text: "<strong>6.2</strong>" },
      { label: "B", text: "<strong>7.3</strong>" },
      { label: "C", text: "<strong>8.2</strong>" },
      { label: "D", text: "<strong>9.1</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. On the line of best fit, an x-value of <strong>25.5</strong> corresponds to a y-value between <strong>8</strong> and <strong>8.5</strong>. Therefore, at <strong>x = 25.5</strong>, <strong>8.2</strong> is closest to the y-value predicted by the line of best fit.<br>Choice A is incorrect and may result from conceptual errors.<br>Choice B is incorrect and may result from conceptual errors.<br>Choice D is incorrect and may result from conceptual errors.",
    hasFigure: true,
    figureUrl: "/practice-images/f46139df_svg1.svg",
  },
  {
    id: "fdfc90e4",
    type: "mcq",
    questionHtml:
      "The scatterplot shows the relationship between two variables, <strong>x</strong> and <strong>y</strong>. A line of best fit for the data is also shown.<br>The scatterplot has 11 data points.<br>The data points are in a linear pattern trending down from left to right.<br>A line of best fit is shown:<br><br>The line of best fit slants down from left to right.<br>6 points are above the line of best fit.<br>5 points are below the line of best fit.<br>The line of best fit goes through the following approximate coordinates:<br><br>(28 comma 6)<br>(33 comma 1.5)<br><br>At <strong>x = 32</strong>, which of the following is closest to the y-value predicted by the line of best fit?",
    choices: [
      { label: "A", text: "<strong>0.4</strong>" },
      { label: "B", text: "<strong>1.5</strong>" },
      { label: "C", text: "<strong>2.4</strong>" },
      { label: "D", text: "<strong>3.3</strong>" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. At <strong>x = 32</strong>, the line of best fit has a y-value between <strong>2</strong> and <strong>3</strong>. The only choice with a value between <strong>2</strong> and <strong>3</strong> is choice C.<br>Choice A is incorrect. This is the difference between the y-value predicted by the line of best fit and the actual y-value at <strong>x = 32</strong> rather than the y-value predicted by the line of best fit at <strong>x = 32</strong>.<br>Choice B is incorrect. This is the y-value predicted by the line of best fit at <strong>x = 31</strong> rather than at <strong>x = 32</strong>.<br>Choice D is incorrect. This is the y-value predicted by the line of best fit at <strong>x = 33</strong> rather than at <strong>x = 32</strong>.",
    hasFigure: true,
    figureUrl: "/practice-images/fdfc90e4_svg1.svg",
  },
];

export const TWO_VAR_DATA_HARD: PracticeQuestion[] = [
  {
    id: "1e1027a7",
    type: "mcq",
    questionHtml:
      "The scatterplot above shows a company’s ice cream sales d, in dollars, and the high temperature t, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?",
    choices: [
      { label: "A", text: "<strong>d = 0 . 0 3 t + 402</strong>" },
      { label: "B", text: "<strong>d = 10 t + 402</strong>" },
      { label: "C", text: "<strong>d = 33 t + 300</strong>" },
      { label: "D", text: "<strong>d = 33 t + 84</strong>" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. On the line of best fit, d increases from approximately 480 to 880 between <strong>t = 12</strong> and <strong>t = 24</strong>. The slope of the line of best fit is the difference in d-values divided by the difference in t-values, which gives <strong>the fraction with numerator 880 − 480, and denominator 24 − 12, end fraction = the fraction 400 over 12</strong>, or approximately 33. Writing the equation of the line of best fit in slope-intercept form gives <strong>d = 33 t + b</strong>, where b is the y-coordinate of the y-intercept. This equation is satisfied by all points on the line, so <strong>d = 480</strong> when <strong>t = 12</strong>. Thus, <strong>480 = 33 · 12 + b</strong>, which is equivalent to <strong>480 = 396 + b</strong>. Subtracting 396 from both sides of this equation gives <strong>b = 84</strong>. Therefore, an equation for the line of best fit could be <strong>d = 33 t + 84</strong>.Choice A is incorrect and may result from an error in calculating the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at [] rather than the value of d at <strong>t = 0</strong>. Choice B is incorrect and may result from using the smallest value of t on the graph as the slope and misidentifying the y-coordinate of the y-intercept of the graph as the value of d at <strong>t = 10</strong> rather than the value of d at <strong>t = 0</strong>. Choice C is incorrect and may result from misidentifying the y-coordinate of the y-intercept as the smallest value of d on the graph.",
    hasFigure: true,
    figureUrl: "/practice-images/1e1027a7_img1.png",
  },
  {
    id: "79137c1b",
    type: "mcq",
    questionHtml:
      "The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?",
    choices: [
      { label: "A", text: "<strong>y = 200 x + 100</strong>" },
      { label: "B", text: "<strong>y = 100 x + 100</strong>" },
      { label: "C", text: "<strong>y = 50 x + 100</strong>" },
      { label: "D", text: "<strong>y = 100 x</strong>" },
    ],
    correctAnswer: "B",
    explanation:
      "Choice B is correct. From the shape of the cluster of points, the line of best fit should pass roughly through the points <strong>with coordinates 1, 200</strong> and <strong>2 . 5, 350</strong>. Therefore, these two points can be used to find an approximate equation for the line of best fit. The slope of this line of best fit is therefore <strong>the fraction with numerator y sub 2 − y sub 1, and denominator x sub 2 − x sub 1, end fraction = the fraction with numerator 350 − 200, and denominator 2 . 5 − 1, end fraction</strong>, or 100. The equation for the line of best fit, in slope-intercept form, is <strong>y = 100 x + b</strong> for some value of b. Using the point <strong>with coordinates 1, 200</strong>, 1 can be substituted for x and 200 can be substituted for y: <strong>200 = 100 · 1 + b</strong>, or <strong>b = 100</strong>. Substituting this value into the slope-intercept form of the equation gives <strong>y = 100 x + 100</strong>.Choice A is incorrect. The line defined by <strong>y = 200 x + 100</strong> passes through the points <strong>with coordinates 1, 300</strong> and <strong>2, 500</strong>, both of which are well above the cluster of points, so it cannot be a line of best fit. Choice C is incorrect. The line defined by <strong>y = 50 x + 100</strong> passes through the points <strong>with coordinates 1, 150</strong> and <strong>2, 200</strong>, both of which lie at the bottom of the cluster of points, so it cannot be a line of best fit. Choice D is incorrect and may result from correctly calculating the slope of a line of best fit but incorrectly assuming the y-intercept is at <strong>0, 0</strong>.",
    hasFigure: true,
    figureUrl: "/practice-images/79137c1b_img1.png",
  },
  {
    id: "7b52985c",
    type: "spr",
    questionHtml:
      "The scatterplot shows the relationship between the length of time <strong>y</strong>, in hours, a certain bird spent in flight and the number of days after January <strong>11</strong>, <strong>x</strong>.<br>The scatterplot has 10 data points.<br>The data points are spread out.<br>The data points have the following coordinates:<br><br>(1 comma 14)<br>(2 comma 6)<br>(3 comma 10)<br>(4 comma 15)<br>(5 comma 14.2)<br>(6 comma 7)<br>(7 comma 11)<br>(8 comma 14)<br>(9 comma 13.5)<br>(10 comma 13.2)<br><br>What is the average rate of change, in hours per day, of the length of time the bird spent in flight on January <strong>13</strong> to the length of time the bird spent in flight on January <strong>15</strong>?",
    choices: [],
    correctAnswer: "4.5, 9/2",
    explanation:
      "The correct answer is <strong>nine halves</strong>. It's given that the scatterplot shows the relationship between the length of time <strong>y</strong>, in hours, a certain bird spent in flight and the number of days after January <strong>11</strong>, <strong>x</strong>. Since January <strong>13</strong> is <strong>2</strong> days after January <strong>11</strong>, it follows that January <strong>13</strong> corresponds to an x-value of <strong>2</strong> in the scatterplot. In the scatterplot, when <strong>x = 2</strong>, the corresponding value of <strong>y</strong> is <strong>6</strong>. In other words, on January <strong>13</strong>, the bird spent <strong>6</strong> hours in flight. Since January <strong>15</strong> is <strong>4</strong> days after January <strong>11</strong>, it follows that January <strong>15</strong> corresponds to an x-value of <strong>4</strong> in the scatterplot. In the scatterplot, when <strong>x = 4</strong>, the corresponding value of <strong>y</strong> is <strong>15</strong>. In other words, on January <strong>15</strong>, the bird spent <strong>15</strong> hours in flight. Therefore, the average rate of change, in hours per day, of the length of time the bird spent in flight on January <strong>13</strong> to the length of time the bird spent in flight on January <strong>15</strong> is the difference in the length of time, in hours, the bird spent in flight divided by the difference in the number of days after January <strong>11</strong>, or <strong>(15 − 6) / (4 − 2)</strong>, which is equivalent to <strong>nine halves</strong>. Note that 9/2 and 4.5 are examples of ways to enter a correct answer.",
    hasFigure: true,
    figureUrl: "/practice-images/7b52985c_svg1.svg",
  },
  {
    id: "9b5b23fc",
    type: "mcq",
    questionHtml:
      "For <strong>x > 0</strong>, the function <strong>f</strong> is defined as follows:<br><strong>f (x)</strong> equals <strong>201 % sign</strong> of <strong>x</strong><br>Which of the following could describe this function?",
    choices: [
      { label: "A", text: "Decreasing exponential" },
      { label: "B", text: "Decreasing linear" },
      { label: "C", text: "Increasing exponential" },
      { label: "D", text: "Increasing linear" },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. It's given that for <strong>x > 0</strong>, <strong>f (x)</strong> is equal to <strong>201 % sign</strong> of <strong>x</strong>. This is equivalent to <strong>f (x) = (201) / (100) x</strong>, or <strong>f (x) = 2.01 x</strong>, for <strong>x > 0</strong>. This function indicates that as <strong>x</strong> increases, <strong>f (x)</strong> also increases, which means <strong>f</strong> is an increasing function. Furthermore,  <strong>f (x)</strong> increases at a constant rate of <strong>2.01</strong> for each increase of <strong>x</strong> by <strong>1</strong>. A function with a constant rate of change is linear. Thus, the function <strong>f</strong> can be described as an increasing linear function.<br>Choice A is incorrect and may result from conceptual errors.<br>Choice B is incorrect and may result from conceptual errors.<br>Choice C is incorrect. This could describe the function <strong>f (x) = (2.01)^(x)</strong>, where <strong>f (x)</strong> is equal to <strong>201 % sign</strong> of <strong>f (x − 1)</strong>, not <strong>x</strong>, for <strong>x > 0</strong>.",
    hasFigure: false,
  },
  {
    id: "9d95e7ad",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Total Protein and Total Fat for Eight Sandwiches.” The horizontal axis is labeled “Total protein, ” in grams, and the numbers zero through 50, in increments of 10, are indicated. The vertical axis is labeled “Total fat, ” in grams, and the numbers zero through 80, in increments of 10, are indicated. Eight data points and the line of best fit are shown. The line of best fit touches all 8 data points and extends upward and to the right through the following coordinates. All data are approximate. Protein, 9 grams; Fat, 17 grams.<br>Protein, 20 grams; Fat, 33 grams.<br>Protein, 30 grams; Fat, 48 grams.<br>Protein, 40 grams; Fat, 63 grams.<br>Protein, 48 grams; Fat, 75 grams.</strong>The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?",
    choices: [
      { label: "A", text: "2.5" },
      { label: "B", text: "2.0" },
      { label: "C", text: "1.5" },
      { label: "D", text: "1.0" },
    ],
    correctAnswer: "C",
    explanation:
      "Choice C is correct. The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points <strong>with coordinates 20, 34</strong> and <strong>with coordinates 30, 48</strong> are on the line of best fit, and the slope of the line that passes through them is <strong>the fraction with numerator 48 − 34, and denominator 30 − 20, end fraction = 14 over 10</strong>, or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.Choices A, B, and D are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.",
    hasFigure: true,
    figureUrl: "/practice-images/9d95e7ad_img1.png",
  },
  {
    id: "af142f8d",
    type: "mcq",
    questionHtml:
      "Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?",
    choices: [
      {
        label: "A",
        text: "Account A always earns more money per year than Account B.",
      },
      {
        label: "B",
        text: "Account A always earns less money per year than Account B.",
      },
      {
        label: "C",
        text: "Account A earns more money per year than Account B at first but eventually earns less money per year.",
      },
      {
        label: "D",
        text: "Account A earns less money per year than Account B at first but eventually earns more money per year.",
      },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. Account A starts with $500 and earns interest at 6% per year, so in the first year Account A earns (500)(0.06) = $30, which is greater than the $25 that Account B earns that year. Compounding interest can be modeled by an increasing exponential function, so each year Account A will earn more money than it did the previous year. Therefore, each year Account A earns at least $30 in interest. Since Account B always earns $25 each year, Account A always earns more money per year than Account B.Choices B and D are incorrect. Account A earns $30 in the first year, which is greater than the $25 Account B earns in the first year. Therefore, neither the statement that Account A always earns less money per year than Account B nor the statement that Account A earns less money than Account B at first can be true. Choice C is incorrect. Since compounding interest can be modeled by an increasing exponential function, each year Account A will earn more money than it did the previous year. Therefore, Account A always earns at least $30 per year, which is more than the $25 per year that Account B earns.",
    hasFigure: false,
  },
  {
    id: "d0430601",
    type: "spr",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Number of Beach Visitors versus Temperature.” The horizontal axis is labeled “Average temperature, in ° Celsius, ” and the numbers 25 through 35, in increments of 2, are indicated. The vertical axis is labeled “Number of people, ” and the numbers 0 through 640, in increments of 80, are indicated. There are 11 data points in the scatterplot that begin near the bottom left portion of the coordinate plane and trend upward and to the right. The line of best fit for the data is also shown. The line of best fit passes through 25, 80 and 32, 480.</strong><br> <br><br>Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, on one of eleven different days. The line of best fit for the data is also shown. The line of best fit for the data has a slope of approximately 57. According to this estimate, how many additional people per day are predicted to visit the beach for each 5°C increase in average temperature?",
    choices: [],
    correctAnswer: "",
    explanation:
      "The correct answer is 285. The number of people predicted to visit the beach each day is represented by the y-values of the line of best fit, and the average temperature, in degrees Celsius (<strong>° Celsius</strong>), is represented by the x-values. Since the slope of the line of best fit is approximately 57, the y-value, or the number of people predicted to visit the beach each day, increases by 57 for every x-value increase of 1, or every <strong>1 ° Celsius</strong> increase in average temperature. Therefore, an increase of <strong>5 ° Celsius</strong> in average temperature corresponds to a y-value increase of <strong>57 · 5 = 285</strong> additional people per day predicted to visit the beach.",
    hasFigure: true,
    figureUrl: "/practice-images/d0430601_img1.png",
  },
  {
    id: "d6af3572",
    type: "mcq",
    questionHtml:
      "<strong>The figure presents a scatterplot titled “Minimum Wage.” The x axis is labeled “Years since 1940, ” and the integers 0 through 80, in increments of 10, are indicated. The y axis is labeled “Minimum wage, in dollars per hour, ” and the integers 0 through 8 are indicated. There are 8 data points in the scatterplot, and the line of best fit is drawn. The line of best fit begins at the . representing 0 years since 1940, minimum wage 0 dollars per hour. It slants upward and to the right, and passes through the . representing 40 years since 1940, minimum wage 3 . 3 5 2 dollars, and the . representing 70 years since 1940, minimum wage 6 . 2 3 2 dollars</strong>The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is <strong>y = 0 . 0 9 6 x − 0 . 4 8 8</strong>. What does the line of best fit predict about the increase in the minimum wage over the 70-year period?",
    choices: [
      {
        label: "A",
        text: "Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.",
      },
      {
        label: "B",
        text: "Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars.",
      },
      {
        label: "C",
        text: "Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars.",
      },
      {
        label: "D",
        text: "Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars.",
      },
    ],
    correctAnswer: "A",
    explanation:
      "Choice A is correct. The given equation is in slope-intercept form, or <strong>y = m x + b</strong>, where m is the value of the slope of the line of best fit. Therefore, the slope of the line of best fit is 0.096. From the definition of slope, it follows that an increase of 1 in the x-value corresponds to an increase of 0.096 in the y-value. Therefore, the line of best fit predicts that for each year between 1940 and 2010, the minimum wage will increase by 0.096 dollar per hour.Choice B is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope. Choice C is incorrect and may result from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit. Choice D is incorrect and may result from using the y-coordinate of the y-intercept as the average increase, instead of the slope, and from using the 10-year increments given on the x-axis to incorrectly interpret the slope of the line of best fit.",
    hasFigure: true,
    figureUrl: "/practice-images/d6af3572_img1.png",
  },
  {
    id: "e821a26d",
    type: "mcq",
    questionHtml:
      "Of the following equations, which best models the data in the scatterplot?",
    choices: [
      {
        label: "A",
        text: "<strong>y = 1 . six seven four x² + 19 . seven six x − 745 . seven three</strong>",
      },
      {
        label: "B",
        text: "<strong>y = −1 . six seven four x² − 19 . seven six x − 745 . seven three</strong>",
      },
      {
        label: "C",
        text: "<strong>y = 1 . six seven four x² + 19 . seven six x + 745 . seven three</strong>",
      },
      {
        label: "D",
        text: "<strong>y = −1 . six seven four x² + 19 . seven six x + 745 . seven three</strong>",
      },
    ],
    correctAnswer: "D",
    explanation:
      "Choice D is correct. The data in the scatterplot roughly fall in the shape of a downward-opening parabola; therefore, the coefficient for the <strong>x²</strong> term must be negative. Based on the location of the data points, the y-intercept of the parabola should be somewhere between 740 and 760. Therefore, of the equations given, the best model is <strong>y = −1 . 6 7 4, x² + 19 . 7 6 x + 745 . 7 3</strong>.Choices A and C are incorrect. The positive coefficient of the <strong>x²</strong> term means that these equations each define upward-opening parabolas, whereas a parabola that fits the data in the scatterplot must open downward. Choice B is incorrect because it defines a parabola with a y-intercept that has a negative y-coordinate, whereas a parabola that fits the data in the scatterplot must have a y-intercept with a positive y-coordinate.",
    hasFigure: true,
    figureUrl: "/practice-images/e821a26d_img1.png",
  },
];
