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Digital SAT practice questions

211 free questions with answers and explanations.

Practice test
  1. 1.A robotics engineer is programming a robot arm. The path of the arm's gripper can be described by the equation y = x^2 - 6x + 8, and a laser sensor detects objects along the line y = 2x - 7. At what x-coordinate(s) will the robot arm's gripper intersect the laser sensor's path?Math: Advanced Math
  2. 2.A biologist is studying a population of insects that grows according to the function P(t) = 2000 / (1 + 4e^(-0.1t)), where P(t) is the population after t days. What is the population of the insects as t approaches infinity?Math: Advanced Math
  3. 3.A satellite dish is designed as a parabolic reflector. The cross-section of the dish can be modeled by the equation y = (1/16)x², where x and y are in meters. What is the focal length of the parabolic dish?Math: Geometry and Trigonometry
  4. 4.A scientist is tracking the population of a certain bacteria. The population doubles every 4 hours. If the initial population is 500 bacteria, how many bacteria will there be after 20 hours?Math: Problem-Solving and Data Analysis
  5. 5.A financial analyst is modeling the value of a stock, V(t), in dollars, after t months, using the function V(t) = 0.5t^2 - 10t + 60. At what time t, in months, does the stock reach its minimum value?Math: Advanced Math
  6. 6.A team of researchers is studying the migratory patterns of monarch butterflies. They observe that monarchs typically travel thousands of miles from cooler northern climates to warmer southern regions for winter. Upon arrival, the butterflies often cluster in specific oyamel fir forests in Mexico. The researchers hypothesize that these forests offer unique microclimates essential for monarch survival during dormancy. Which of the following observations, if true, would most strongly support the researchers' hypothesis?Reading and Writing: Information and Ideas
  7. 7.A scientist is observing the population growth of a certain bacteria culture. The population P(t) after t hours is modeled by P(t) = 1000 / (1 + 9e^(-0.5t)). What is the carrying capacity of this bacteria culture?Math: Advanced Math
  8. 8.A chemist is analyzing a solution where the concentration of a certain chemical, C(t), in milligrams per liter, after t minutes is given by C(t) = (5t + 10) / (t + 2). What is the behavior of the concentration as time (t) approaches infinity?Math: Advanced Math
  9. 9.A biologist is studying a population of insects that grows according to the function P(t) = 120 / (1 + 19e^(-0.4t)), where P(t) is the population after t weeks. What is the carrying capacity of this insect population?Math: Advanced Math
  10. 10.A population of fish in a lake is modeled by the function P(t) = 1000 / (1 + 9e^(-0.5t)), where P(t) is the population after t years. What is the carrying capacity of the lake for this fish population?Math: Advanced Math
  11. 11.A production manager is analyzing the cost of manufacturing a new component. The total cost C(x) in dollars, for producing x units, is given by C(x) = 1000 + 50x + 0.1x^2. The company wants the average cost per unit to be no more than $70. Which inequality represents this situation?Math: Advanced Math
  12. 12.A botanist is studying the growth of a rare plant. The height of the plant, H(t), in centimeters, after t weeks, is given by the function H(t) = 5 * (1.2)^t. What is the height of the plant after 3 weeks?Math: Advanced Math
  13. 13.A civil engineer is designing a curved ramp. The height of the ramp, h(x), in meters, at a horizontal distance x from the start, is given by the function h(x) = sqrt(16 - x^2). What is the domain of this function in the context of the real world?Math: Advanced Math
  14. 14.A biologist is studying a local pond ecosystem. She observes that the ratio of frogs to fish in the pond is 3:5. If there are 120 frogs in the pond, how many fish are there?Math: Problem-Solving and Data Analysis
  15. 15.An engineer is designing a spiral staircase. Each step rises 8 inches and has a tread length of 15 inches. If the staircase forms a continuous slope, what is the angle of elevation of the staircase to the nearest degree?Math: Geometry and Trigonometry
  16. 16.A scientist is modeling the concentration of a certain chemical, C(t), in micrograms per milliliter, in a solution over time t, in minutes. The function is C(t) = (3t^2 - 12) / (t^2 + t - 6). What is the value of C(t) as t approaches infinity?Math: Advanced Math
  17. 17.A botanist is studying the growth of a rare plant. The height of the plant, H(t), in centimeters, after t weeks can be modeled by the function H(t) = 5(1.2)^t. What is the predicted height of the plant after 3 weeks?Math: Advanced Math
  18. 18.A nutritionist is creating a meal plan. She wants to mix two types of grains: Grain X, which has 2 grams of protein per 100 grams, and Grain Y, which has 8 grams of protein per 100 grams. If she wants to create a 600-gram mixture that has a total of 30 grams of protein, how many grams of Grain Y should she use?Math: Problem-Solving and Data Analysis
  19. 19.A city council is debating a proposal to convert a disused railway line into a linear park. Proponents argue it would increase green space, encourage walking and cycling, and boost property values in adjacent neighborhoods. Opponents express concerns about increased traffic congestion from visitors, potential for crime, and the cost of maintenance. A recent independent study, commissioned by the city, analyzed similar 'rail-to-trail' projects in other cities. The study found that while property values did increase by an average of 5-10% within a quarter-mile radius, there was no statistically significant increase in crime rates or traffic congestion directly attributable to the parks. Maintenance costs, however, often exceeded initial projections by 15-20% in the first five years. Which of the following statements best describes the overall impact of the independent study's findings on the city council's debate?Reading and Writing: Information and Ideas
  20. 20.A financial analyst is modeling the value of an investment. The value V(t) of the investment, in thousands of dollars, after t years, is given by V(t) = 50e^(0.06t). What is the instantaneous rate of change of the investment's value with respect to time when t = 2 years?Math: Advanced Math
  21. 21.A scientist is observing the growth of a bacterial colony. The number of bacteria, P(t), after t hours is modeled by the function P(t) = 500 * 2^(t/3). What is the initial number of bacteria in the colony?Math: Advanced Math
  22. 22.A biologist is studying a population of fruit flies. The population, P(t), after t days, can be modeled by the function P(t) = 500 / (1 + 4e^(-0.1t)). What is the maximum population the fruit fly colony can sustain?Math: Advanced Math
  23. 23.A historian is examining primary sources related to the American industrial revolution. One document is a letter from a factory owner to a business partner, discussing the recent implementation of new machinery. The owner expresses concern about the initial cost but anticipates significant increases in production efficiency and eventual cost savings due to reduced labor needs. The owner also mentions a plan to reinvest some of the savings into expanding the factory. Based on this letter, what can most reasonably be inferred about the factory owner's primary economic motivation?Reading and Writing: Information and Ideas
  24. 24.A robotics engineer is programming a robot arm. The path of the arm's gripper can be described by the function h(x) = -0.5x^2 + 4x - 6, where h(x) is the vertical height and x is the horizontal distance, both in meters. At what horizontal distances does the gripper touch the ground (i.e., h(x) = 0)?Math: Advanced Math
  25. 25.A company's monthly profit, P(x), in thousands of dollars, from selling x units of a product is modeled by the function P(x) = -0.5x^2 + 10x - 30. How many units must be sold to achieve the maximum profit?Math: Advanced Math
  26. 26.A scientist is studying a chemical reaction where the rate of reaction R (in mol/s) is given by R(x) = (x^2 - 9) / (x - 3), where x is the concentration of a reactant in M. What is the value of R(x) as x approaches 3?Math: Advanced Math
  27. 27.A botanist is studying the growth of a rare plant. The height of the plant, H(t), in centimeters, after t weeks, is modeled by the function H(t) = 5 * (1.2)^t. What is the predicted height of the plant after 3 weeks?Math: Advanced Math
  28. 28.A city council is reviewing a proposal for a new public park. The proposal states that 35% of the park's area will be dedicated to walking trails, 20% to a playground, and the remaining area to open green space. If the total area of the park is 150 acres, how many acres will be dedicated to open green space?Math: Problem-Solving and Data Analysis
  29. 29.A paleontologist is studying fossilized footprints found in a prehistoric riverbed. The tracks show a bipedal creature with three prominent toes and a stride pattern indicating a relatively slow, deliberate gait. Further analysis reveals that the prints are consistently found alongside impressions of large, oval-shaped leaves, suggesting the creature frequented areas with specific vegetation. The paleontologist initially hypothesizes that the creature was an early omnivore that primarily grazed on these plants. Which of the following findings would most significantly weaken the paleontologist's hypothesis?Reading and Writing: Information and Ideas
  30. 30.A financial analyst is modeling the quarterly profit of a startup using the function P(x) = -2x^2 + 20x - 30, where P(x) is the profit in thousands of dollars and x is the quarter number (x ≥ 1). What is the maximum profit the startup can achieve?Math: Advanced Math
  31. 31.A historian is examining two competing theories about the decline of the Mayan civilization. Theory A posits that prolonged drought led to widespread agricultural collapse and subsequent societal breakdown. Theory B suggests that internal warfare and political instability were the primary drivers of decline, exacerbated by environmental pressures. The historian finds archaeological evidence showing a significant increase in defensive structures and mass graves containing victims of violence during the period of decline. Additionally, analysis of skeletal remains from this era indicates widespread malnutrition, but also a higher proportion of individuals with healed injuries consistent with combat. Which of the following statements best describes how this new evidence relates to the two theories?Reading and Writing: Information and Ideas
  32. 32.A scientist is modeling the population growth of a certain bacteria culture. The population P(t) after t hours is given by P(t) = P_0 * e^(kt), where P_0 is the initial population and k is the growth rate constant. If the initial population is 1,000 bacteria and the population doubles every 3 hours, what is the value of the growth rate constant k?Math: Advanced Math
  33. 33.A market researcher observed that 45% of customers in a store purchased item A, and 30% purchased item B. If 15% of customers purchased both item A and item B, what percentage of customers purchased neither item A nor item B?Math: Problem-Solving and Data Analysis
  34. 34.A scientist is observing the population growth of a certain bacteria culture. The population P(t) after t hours is modeled by the function P(t) = P_0 * e^(kt). If the population doubles every 3 hours, what is the value of the growth rate constant k?Math: Advanced Math
  35. 35.A surveyor is measuring a plot of land. They record an angle of 3π/4 radians. To report this angle to a client who is unfamiliar with radians, what is the equivalent measure in degrees?Math: Geometry and Trigonometry
  36. 36.A biologist is tracking the growth of a bacterial colony. The number of bacteria, N(t), after t hours, is given by N(t) = 100 * 2^(0.5t). How many hours will it take for the colony to reach 1,600 bacteria?Math: Advanced Math
  37. 37.A cylindrical water tank has a diameter of 8 feet and a height of 10 feet. If 1 cubic foot of water is approximately 7.48 gallons, what is the maximum volume of water, in gallons, the tank can hold?Math: Geometry and Trigonometry
  38. 38.A quality control engineer is inspecting a component. The acceptable length L (in millimeters) of the component must satisfy the inequality |2L - 10| ≤ 4. What is the range of acceptable lengths for the component?Math: Advanced Math
  39. 39.A financial analyst is modeling the value of a stock, V(t), in dollars, after t months, using the function V(t) = -t^2 + 10t + 200. After how many months will the stock reach its maximum value?Math: Advanced Math
  40. 40.A historian is researching the impact of the printing press on European society in the 15th and 16th centuries. She observes that the number of universities founded increased significantly, literacy rates rose, and there was a proliferation of religious and scientific texts. However, she also notes that the average cost of books, while decreasing, remained relatively high for the common person throughout much of this period. Which of the following inferences about the printing press's impact is best supported by this information?Reading and Writing: Information and Ideas
  41. 41.A cultural anthropologist is studying the evolution of storytelling in a remote indigenous community. She observes that traditional narratives are primarily passed down orally, often incorporating intricate ritualistic performances and music. These stories frequently feature ancestral spirits and lessons on communal harmony. In recent years, due to increased external contact, younger generations have begun to adapt these stories into digital formats, such as short animated videos or interactive apps, sometimes simplifying narratives or altering characters to appeal to a broader, global audience. Which of the following can be most reasonably inferred about the impact of digital adaptation on the community's traditional storytelling?Reading and Writing: Information and Ideas
  42. 42.A quality control engineer is inspecting a component. The acceptable length L (in millimeters) of the component must satisfy the inequality |L - 10| ≥ 0.2. Which of the following represents the range of acceptable lengths for the component?Math: Advanced Math
  43. 43.A civil engineer is designing a new road that needs to go up a hill. The road will rise 15 meters for every 100 meters of horizontal distance. What is the angle of elevation of the road to the nearest degree?Math: Geometry and Trigonometry
  44. 44.A project manager is tracking the progress of two teams. Team A's progress can be modeled by the equation y = 2x + 5, and Team B's progress by y = -3x + 20, where x is the number of days and y is the percentage of completion. At what number of days will both teams have the same percentage of completion?Math: Advanced Math
  45. 45.A quality control engineer is inspecting a component. The acceptable length L (in millimeters) of the component must satisfy the inequality |L - 15| < 0.5. Which of the following ranges represents the acceptable lengths for the component?Math: Advanced Math
  46. 46.A scientist is testing a new fertilizer on a crop. She records the yield (in kg) for two plots: Plot A with fertilizer and Plot B without. After 10 harvests, the mean yield for Plot A was 50 kg with a standard deviation of 5 kg, and for Plot B was 45 kg with a standard deviation of 2 kg. Which of the following statements is best supported by the data?Math: Problem-Solving and Data Analysis
  47. 47.A landscaper is designing a circular garden with a radius of 6 feet. They plan to install a decorative border around the entire perimeter of the garden. If the border material costs $2.50 per foot, what is the total cost of the border?Math: Geometry and Trigonometry
  48. 48.A sociologist is studying the impact of social media on political engagement among young adults. A survey reveals that 70% of respondents aged 18-25 follow at least three political news accounts on social media, yet only 30% report having voted in the last national election. Of those who follow political news, 60% stated they primarily use social media to 'stay informed' rather than to 'participate in discussions' or 'share opinions.' Which of the following inferences about young adults' political engagement is best supported by the data?Reading and Writing: Information and Ideas
  49. 49.A political scientist is analyzing voter turnout data across different demographics. A study found that in the last election, 65% of registered voters aged 65 and older cast a ballot, compared to 40% of registered voters aged 18-29. Among the younger demographic, 75% reported consuming political news primarily through social media, while 80% of older voters cited traditional television news as their primary source. However, 60% of younger voters also expressed distrust in mainstream media, a sentiment shared by only 20% of older voters. Which of the following is the most plausible inference about the factors influencing voter turnout in this study?Reading and Writing: Information and Ideas
  50. 50.A builder is constructing a ramp for wheelchair access. The ramp needs to rise 3 feet vertically over a horizontal distance of 4 feet. What is the length of the ramp surface?Math: Geometry and Trigonometry