SAT Math Past Paper Questions PDF

Question ID 88e13c8c Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 88e13c8c The total cost , in dollars, to lease...

Question ID 88e13c8c Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 88e13c8c The total cost , in dollars, to lease a car for months from a particular car dealership is given by , where is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is ? A. B. C. D. ID: 88e13c8c Answer Correct Answer: C Rationale Choice C is correct. It's given that 𝑓𝑥 is the total cost, in dollars, to lease a car from this dealership with a monthly payment of 𝑥 dollars. Therefore, the total cost, in dollars, to lease the car when the monthly payment is $ 400 is represented by the value of 𝑓𝑥 when 𝑥 = 400. Substituting 400 for 𝑥 in the equation 𝑓𝑥 = 36𝑥 + 1,000 yields 𝑓400 = 36400 + 1,000, or 𝑓400 = 15,400. Thus, when the monthly payment is $ 400, the total cost to lease a car is $ 15,400. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID 84664a7c Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 84664a7c The front of a roller-coaster car is at the bottom of a hill and is 15 feet above the ground. If the front of the roller-coaster car rises at a constant rate of 8 feet per second, which of the following equations gives the height h, in feet, of the front of the roller-coaster car s seconds after it starts up the hill? A. B. C. D. ID: 84664a7c Answer Correct Answer: A Rationale Choice A is correct. It’s given that the front of the roller-coaster car starts rising when it’s 15 feet above the ground. This initial height of 15 feet can be represented by a constant term, 15, in an equation. Each second, the front of the roller-coaster car rises 8 feet, which can be represented by 8s. Thus, the equation gives the height, in feet, of the front of the roller-coaster car s seconds after it starts up the hill. Choices B and C are incorrect and may result from conceptual errors in creating a linear equation. Choice D is incorrect and may result from switching the rate at which the roller-coaster car rises with its initial height. Question Difficulty: Easy Question ID 06fc1726 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 06fc1726 If f is the function defined by , what is the value of ? A. B. C. 3 D. 9 ID: 06fc1726 Answer Correct Answer: C Rationale Choice C is correct. If , then. Choice A is incorrect and may result from not multiplying x by 2 in the numerator. Choice B is incorrect and may result from dividing 2x by 3 and then subtracting 1. Choice D is incorrect and may result from evaluating only the numerator 2x – 1. Question Difficulty: Easy Question ID 6863c7ce Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 6863c7ce The given equation represents the distance , in inches, where represents the number of seconds since an object started moving. Which of the following is the best interpretation of in this context? A. The object moved a total of inches. B. The object moved a total of inches. C. The object is moving at a rate of inches per second. D. The object is moving at a rate of inches per second. ID: 6863c7ce Answer Correct Answer: C Rationale Choice C is correct. It’s given that in the equation 𝑑 = 16𝑡, 𝑑 represents the distance, in inches, and 𝑡 represents the number of seconds since an object started moving. In this equation, 𝑡 is being multiplied by 16. This means that the object’s distance increases by 16 inches each second. Therefore, the best interpretation of 16 in this context is that the object is moving at a rate of 16 inches per second. Choice A is incorrect and may result from conceptual errors. Choice B is incorrect. This is the best interpretation of 16𝑡, rather than 16, in this context. Choice D is incorrect and may result from conceptual errors. Question Difficulty: Easy Question ID 0b332f00 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 0b332f00 The function is defined by. For what value of is ? ID: 0b332f00 Answer Correct Answer: 9 Rationale The correct answer is 9. It’s given that 𝑔𝑥 = 6𝑥. Substituting 54 for 𝑔𝑥 in the given function yields 54 = 6𝑥. Dividing both sides of this equation by 6 yields 𝑥 = 9. Therefore, the value of 𝑥 when 𝑔𝑥 = 54 is 9. Question Difficulty: Easy Question ID 0eae6be1 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 0eae6be1 The number is less than the number. Which equation represents the relationship between and ? A. B. C. D. ID: 0eae6be1 Answer Correct Answer: D Rationale Choice D is correct. It’s given that the number 𝑦 is 84 less than the number 𝑥. A number that's 84 less than the number 𝑥 is equivalent to 84 subtracted from the number 𝑥, or 𝑥 - 84. Therefore, the equation 𝑦 = 𝑥 - 84 represents the relationship between 𝑥 and 𝑦. Choice A is incorrect and may result from conceptual errors. Choice B is incorrect and may result from conceptual errors. Choice C is incorrect and may result from conceptual errors. Question Difficulty: Easy Question ID 447fa970 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 447fa970 The function is defined by the equation. What is the value of when ? ID: 447fa970 Answer Correct Answer: 30 Rationale The correct answer is 30. The value of 𝑓𝑥 when 𝑥 = 4 can be found by substituting 4 for 𝑥 in the given equation 𝑓𝑥 = 7𝑥 + 2. This yields 𝑓4 = 74 + 2, or 𝑓4 = 30. Therefore, when 𝑥 = 4, the value of 𝑓𝑥 is 30. Question Difficulty: Easy Question ID bf36c815 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: bf36c815 The function g is defined by. What is the value of ? A. B. 0 C. 4 D. 8 ID: bf36c815 Answer Correct Answer: D Rationale Choice D is correct. The value of is found by substituting 0 for x in the function g. This yields , which can be rewritten as. Choice A is incorrect and may result from misinterpreting the equation as instead of. Choice B is incorrect. This is the value of x, not. Choice C is incorrect and may result from calculation errors. Question Difficulty: Easy Question ID 0d391910 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 0d391910 The function is defined by. For what value of does ? ID: 0d391910 Answer Correct Answer: 2 Rationale The correct answer is 2. Substituting 8 for 𝑓𝑥 in the given equation yields 8 = 4𝑥. Dividing the left- and right-hand sides of this equation by 4 yields 𝑥 = 2. Therefore, the value of 𝑥 is 2 when 𝑓𝑥 = 8. Question Difficulty: Easy Question ID 3f5375d9 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 3f5375d9 The line graphed in the xy-plane below models the total cost, in dollars, for a cab ride, y, in a certain city during nonpeak hours based on the number of miles traveled, x. According to the graph, what is the cost for each additional mile traveled, in dollars, of a cab ride? A. $2.00 B. $2.60 C. $3.00 D. $5.00 ID: 3f5375d9 Answer Correct Answer: A Rationale Choice A is correct. The cost of each additional mile traveled is represented by the slope of the given line. The slope of the line can be calculated by identifying two points on the line and then calculating the ratio of the change in y to the change in x between the two points. Using the points and , the slope is equal to , or 2. Therefore, the cost for each additional mile traveled of the cab ride is $2.00. Choice B is incorrect and may result from calculating the slope of the line that passes through the points and. However, does not lie on the line shown. Choice C is incorrect. This is the y-coordinate of the y- intercept of the graph and represents the flat fee for a cab ride before the charge for any miles traveled is added. Choice D is incorrect. This value represents the total cost of a 1-mile cab ride. Question Difficulty: Easy Question ID 13294295 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 13294295 The graph shown models the number of candy bars a certain machine wraps with a label in seconds. According to the graph, what is the estimated number of candy bars the machine wraps with a label per second? A. B. C. D. ID: 13294295 Answer Correct Answer: B Rationale Choice B is correct. For the graph shown, the x-axis represents time, in seconds, and the y-axis represents the number of candy bars wrapped. The slope of a line in the xy-plane is the change in 𝑦 for each 1-unit increase in 𝑥. It follows that the slope of the graph shown represents the estimated number of candy bars the machine wraps with a label per second. The slope, 𝑚, of a line in the xy-plane can be found using any two points, 𝑥1 , 𝑦1 and 𝑥2 , 𝑦2 , on the 𝑦 -𝑦 line and the slope formula 𝑚 = 2 1. The graph shown passes through the points 0, 0 and 2, 80. Substituting these 𝑥2 - 𝑥1 80 - 0 points for 𝑥1 , 𝑦1 and 𝑥2 , 𝑦2 , respectively, in the slope formula yields 𝑚 = 2-0 , which is equivalent to 𝑚 = 802 , or 𝑚 = 40. Therefore, the estimated number of candy bars the machine wraps with a label per second is 40. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID b8cbe394 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: b8cbe394 Sean rents a tent at a cost of per day plus a onetime insurance fee of. Which equation represents the total cost , in dollars, to rent the tent with insurance for days? A. B. C. D. ID: b8cbe394 Answer Correct Answer: C Rationale Choice C is correct. It’s given that the cost of renting a tent is $ 11 per day for 𝑑 days. Multiplying the rental cost by the number of days yields $ 11𝑑, which represents the cost of renting the tent for 𝑑 days before the insurance is added. Adding the onetime insurance fee of $ 10 to the rental cost of $ 11𝑑 gives the total cost 𝑐, in dollars, which can be represented by the equation 𝑐 = 11𝑑 + 10. Choice A is incorrect. This equation represents the total cost to rent the tent if the insurance fee was charged every day. Choice B is incorrect. This equation represents the total cost to rent the tent if the daily fee was $ 𝑑 + 11 for 10 days. Choice D is incorrect. This equation represents the total cost to rent the tent if the daily fee was $ 10 and the onetime fee was $ 11. Question Difficulty: Easy Question ID 12983c1e Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 12983c1e Some values of the linear function f are shown in the table above. Which of the following defines f ? A. B. C. D. ID: 12983c1e Answer Correct Answer: C Rationale Choice C is correct. Because f is a linear function of x, the equation , where m and b are constants, can be used to define the relationship between x and f (x). In this equation, m represents the increase in the value of f (x) for every increase in the value of x by 1. From the table, it can be determined that the value of f (x) increases by 8 for every increase in the value of x by 2. In other words, for the function f the value of m is , or 4. The value of b can be found by substituting the values of x and f (x) from any row of the table and the value of m into the equation and solving for b. For example, using , , and yields. Solving for b yields. Therefore, the equation defining the function f can be written in the form. Choices A, B, and D are incorrect. Any equation defining the linear function f must give values of f (x) for corresponding values of x, as shown in each row of the table. According to the table, if ,. However, substituting into the equation given in choice A gives , or , not 13. Similarly, substituting into the equation given in choice B gives , or , not 13. Lastly, substituting into the equation given in choice D gives , or , not 13. Therefore, the equations in choices A, B, and D cannot define f. Question Difficulty: Easy Question ID 70d9516e Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 70d9516e A bus is traveling at a constant speed along a straight portion of road. The equation gives the distance , in feet from a road marker, that the bus will be seconds after passing the marker. How many feet from the marker will the bus be seconds after passing the marker? A. B. C. D. ID: 70d9516e Answer Correct Answer: C Rationale Choice C is correct. It’s given that 𝑡 represents the number of seconds after the bus passes the marker. Substituting 2 for 𝑡 in the given equation 𝑑 = 30𝑡 yields 𝑑 = 302, or 𝑑 = 60. Therefore, the bus will be 60 feet from the marker 2 seconds after passing it. Choice A is incorrect. This is the distance, in feet, the bus will be from the marker 1 second, not 2 seconds, after passing it. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the distance, in feet, the bus will be from the marker 3 seconds, not 2 seconds, after passing it. Question Difficulty: Easy Question ID 720e51ac Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 720e51ac The cost , in dollars, for a manufacturer to make rings is represented by the line shown. What is the cost, in dollars, for the manufacturer to make rings? A. B. C. D. ID: 720e51ac Answer Correct Answer: C Rationale Choice C is correct. The line shown represents the cost 𝑦, in dollars, for a manufacturer to make 𝑥 rings. For the line shown, the x-axis represents the number of rings made by the manufacturer and the y-axis represents the cost, in dollars. Therefore, the cost, in dollars, for the manufacturer to make 60 rings is represented by the y-coordinate of the point on the line that has an x-coordinate of 60. The point on the line with an x-coordinate of 60 has a y- coordinate of 175. Therefore, the cost, in dollars, for the manufacturer to make 60 rings is 175. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This is the cost, in dollars, for the manufacturer to make 20 rings. Choice D is incorrect. This is the cost, in dollars, for the manufacturer to make 100 rings. Question Difficulty: Easy Question ID f79fffba Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: f79fffba The function is defined by. What is the value of ? A. B. C. D. ID: f79fffba Answer Correct Answer: A Rationale Choice A is correct. The value of ℎ-2 can be found by substituting -2 for 𝑥 in the equation defining ℎ. Substituting -2 for 𝑥 in ℎ𝑥 = 3𝑥 - 7 yields ℎ-2 = 3-2 - 7, or ℎ-2 = - 13. Therefore, the value of ℎ-2 is -13. Choice B is incorrect. This is the value of ℎ-1, not ℎ-2. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID a9039591 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a9039591 For the linear function , the table shows three values of and their corresponding values of. Which equation defines ? A. B. C. D. ID: a9039591 Answer Correct Answer: A Rationale Choice A is correct. An equation that defines a linear function 𝑓 can be written in the form 𝑓𝑥 = 𝑚𝑥 + 𝑏, where 𝑚 and 𝑏 are constants. It's given in the table that when 𝑥 = 0, 𝑓𝑥 = 29. Substituting 0 for 𝑥 and 29 for 𝑓𝑥 in the equation 𝑓𝑥 = 𝑚𝑥 + 𝑏 yields 29 = 𝑚0 + 𝑏, or 29 = 𝑏. Substituting 29 for 𝑏 in the equation 𝑓𝑥 = 𝑚𝑥 + 𝑏 yields 𝑓𝑥 = 𝑚𝑥 + 29. It's also given in the table that when 𝑥 = 1, 𝑓𝑥 = 32. Substituting 1 for 𝑥 and 32 for 𝑓𝑥 in the equation 𝑓𝑥 = 𝑚𝑥 + 29 yields 32 = 𝑚1 + 29, or 32 = 𝑚 + 29. Subtracting 29 from both sides of this equation yields 3 = 𝑚. Substituting 3 for 𝑚 in the equation 𝑓𝑥 = 𝑚𝑥 + 29 yields 𝑓𝑥 = 3𝑥 + 29. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID a396ed75 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a396ed75 For a training program, Juan rides his bike at an average rate of minutes per mile. Which function models the number of minutes it will take Juan to ride miles at this rate? A. B. C. D. ID: a396ed75 Answer Correct Answer: D Rationale Choice D is correct. It′s given that Juan rides his bike at an average rate of 5.7 minutes per mile. The number of minutes it will take Juan to ride 𝑥 miles can be determined by multiplying his average rate by the number of miles, 𝑥, which yields 5.7𝑥. Therefore, the function 𝑚𝑥 = 5.7𝑥 models the number of minutes it will take Juan to ride 𝑥 miles. Choice A is incorrect and may result from conceptual errors. Choice B is incorrect and may result from conceptual errors. Choice C is incorrect and may result from conceptual errors. Question Difficulty: Easy Question ID bf883fde Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: bf883fde For the function , the graph of in the xy-plane has a slope of and passes through the point. Which equation defines ? A. B. C. D. ID: bf883fde Answer Correct Answer: B Rationale Choice B is correct. An equation defining a linear function can be written in the form 𝑓𝑥 = 𝑚𝑥 + 𝑏, where 𝑚 and 𝑏 are constants, 𝑚 is the slope of the graph of 𝑦 = 𝑓𝑥 in the xy-plane, and 0, 𝑏 is the y-intercept of the graph. It's given that for the function 𝑓, the graph of 𝑦 = 𝑓𝑥 in the xy-plane has a slope of 3. Therefore, 𝑚 = 3. It's also given that this graph passes through the point 0, - 8. Therefore, the y-intercept of the graph is 0, - 8, and it follows that 𝑏 = - 8. Substituting 3 for 𝑚 and -8 for 𝑏 in the equation 𝑓𝑥 = 𝑚𝑥 + 𝑏 yields 𝑓𝑥 = 3𝑥 - 8. Thus, the equation that defines 𝑓 is 𝑓𝑥 = 3𝑥 - 8. Choice A is incorrect. For this function, the graph of 𝑦 = 𝑓𝑥 in the xy-plane passes through the point 0, 0, not 0, - 8. Choice C is incorrect. For this function, the graph of 𝑦 = 𝑓𝑥 in the xy-plane passes through the point 0, 5, not 0, - 8. Choice D is incorrect. For this function, the graph of 𝑦 = 𝑓𝑥 in the xy-plane passes through the point 0, 11, not 0, - 8. Question Difficulty: Easy Question ID 3462d850 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 3462d850 Marisol drove 3 hours from City A to City B. The equation below estimates the distance d, in miles, Marisol traveled after driving for t hours. Which of the following does 45 represent in the equation? A. Marisol took 45 trips from City A to City B. B. The distance between City A and City B is 45 miles. C. Marisol drove at an average speed of about 45 miles per hour. D. It took Marisol 45 hours to drive from City A to City B. ID: 3462d850 Answer Correct Answer: C Rationale Choice C is correct. It’s given that d is the distance, in miles, Marisol traveled after driving for t hours. Therefore, 45 represents the distance in miles traveled per hour, which is the speed she drove in miles per hour. Choice A is incorrect and may result from misidentifying speed as the number of trips. Choice B is incorrect and may result from misidentifying speed as the total distance. Choice D is incorrect and may result from misidentifying the speed as the time, in hours. Question Difficulty: Easy Question ID c4d49134 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: c4d49134 The equation gives the speed , in miles per hour, of a certain car seconds after it began to accelerate. What is the speed, in miles per hour, of the car seconds after it began to accelerate? A. B. C. D. ID: c4d49134 Answer Correct Answer: D Rationale Choice D is correct. In the given equation, 𝑠 is the speed, in miles per hour, of a certain car 𝑡 seconds after it began to accelerate. Therefore, the speed of the car, in miles per hour, 5 seconds after it began to accelerate can be found by substituting 5 for 𝑡 in the given equation, which yields 𝑠 = 40 + 35, or 𝑠 = 55. Thus, the speed of the car 5 seconds after it began to accelerate is 55 miles per hour. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID 255996a6 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 255996a6 In the equation above, T represents Brittany’s total take-home pay, in dollars, for her first week of work, where h represents the number of hours she worked that week and 1,000 represents a sign-on bonus. If Brittany’s total take-home pay was $1,576, for how many hours was Brittany paid for her first week of work? A. 16 B. 32 C. 55 D. 88 ID: 255996a6 Answer Correct Answer: B Rationale Choice B is correct. Since Brittany’s total take-home pay was $1,576, the value 1,576 can be substituted for T in the given equation to give. Subtracting 1,000 from both sides of this equation gives. Dividing both sides of this equation by 18 gives. Therefore, Brittany was paid for 32 hours for her first week of work. Choice A is incorrect. This is half the number of hours Brittany was paid for. Choice C is incorrect and may result from dividing 1,000 by 18. Choice D is incorrect and may result from dividing 1,576 by 18. Question Difficulty: Easy Question ID a1696f3e Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a1696f3e The function is defined as , where a is a constant. If , what is the value of a ? A. B. C. D. ID: a1696f3e Answer Correct Answer: C Rationale Choice C is correct. Substituting 4 for x in g(x) = 5x + a gives g(4) = 5(4) + a. Since g(4) = 31, the equation g(4) = 5(4) + a simplifies to 31 = 20 + a. It follows that a = 11. Choices A, B, and D are incorrect and may result from arithmetic errors. Question Difficulty: Easy Question ID 13909d78 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 13909d78 The function is defined by the equation. What is the value of when ? A. B. C. D. ID: 13909d78 Answer Correct Answer: D Rationale Choice D is correct. Substituting 9 for 𝑥 in the given equation yields 𝑓9 = 1009 + 2, or 𝑓9 = 902. Therefore, the value of 𝑓𝑥 when 𝑥 = 9 is 902. Choice A is incorrect. This is the value of 𝑓𝑥 when 𝑥 = 1.09. Choice B is incorrect. This is the value of 𝑓𝑥 when 𝑥 = 1.16. Choice C is incorrect. This is the value of 𝑓𝑥 when 𝑥 = 8.98. Question Difficulty: Easy Question ID de6fe450 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: de6fe450 On January 1, 2015, a city’s minimum hourly wage was $9.25. It will increase by $0.50 on the first day of the year for the next 5 years. Which of the following functions best models the minimum hourly wage, in dollars, x years after January 1, 2015, where ? A. B. C. D. ID: de6fe450 Answer Correct Answer: C Rationale Choice C is correct. It’s given that the city’s minimum hourly wage will increase by $0.50 on the first day of the year for the 5 years after January 1, 2015. Therefore, the total increase, in dollars, in the minimum hourly wage x years after January 1, 2015, is represented by. Since the minimum hourly wage on January 1, 2015, was $9.25, it follows that the minimum hourly wage, in dollars, x years after January 1, 2015, is represented by. Therefore, the function best models this situation. Choices A, B, and D are incorrect. In choice A, the function models a situation where the minimum hourly wage is $9.25 on January 1, 2015, but decreases by $0.50 on the first day of the year for the next 5 years. The functions in choices B and D both model a situation where the minimum hourly wage is increasing by $9.25 on the first day of the year for the 5 years after January 1, 2015. Question Difficulty: Easy Question ID cee5b352 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: cee5b352 The length, , of a white whale was when it was born and increased an average of per month for the first months after it was born. Which equation best represents this situation, where is the number of months after the whale was born and is the length, in , of the whale? A. B. C. D. ID: cee5b352 Answer Correct Answer: D Rationale Choice D is correct. It's given that the length of the whale was 162 cm when it was born and that its length increased an average of 4.8 cm per month for the first 12 months after it was born. Since 𝑥 represents the number of months after the whale was born, the total increase in the whale's length, in cm, is 4.8 times 𝑥, or 4.8𝑥. The length of the whale 𝑦, in cm, can be found by adding the whale's length at birth, 162 cm, to the total increase in length, 4.8𝑥 cm. Therefore, the equation that best represents this situation is 𝑦 = 4.8𝑥 + 162. Choice A is incorrect and may result from conceptual errors. Choice B is incorrect and may result from conceptual errors. Choice C is incorrect and may result from conceptual errors. Question Difficulty: Easy Question ID aad7e1b9 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: aad7e1b9 The function is defined by. What is the y-intercept of the graph of in the xy-plane? A. B. C. D. ID: aad7e1b9 Answer Correct Answer: B Rationale Choice B is correct. The y-intercept of the graph of a function in the xy-plane is the point on the graph where 𝑥 = 0. 1 1 It′s given that 𝑓𝑥 = 𝑥 - 2. Substituting 0 for 𝑥 in this equation yields 𝑓0 = 0 - 2, or 𝑓0 = - 2. Since it′s given that 10 10 𝑦 = 𝑓𝑥, it follows that 𝑦 = - 2 when 𝑥 = 0. Therefore, the y-intercept of the graph of 𝑦 = 𝑓𝑥 in the xy-plane is 0, - 2. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID 6efcc0a3 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 6efcc0a3 In the linear function , and. Which equation defines ? A. B. C. D. ID: 6efcc0a3 Answer Correct Answer: A Rationale Choice A is correct. An equation defining a linear function can be written in the form ℎ𝑥 = 𝑎𝑥 + 𝑏, where 𝑎 and 𝑏 are constants. It’s given that ℎ0 = 41. Substituting 0 for 𝑥 and 41 for ℎ𝑥 in the equation ℎ𝑥 = 𝑎𝑥 + 𝑏 yields 41 = 𝑎0 + 𝑏, or 𝑏 = 41. Substituting 41 for 𝑏 in the equation ℎ𝑥 = 𝑎𝑥 + 𝑏 yields ℎ𝑥 = 𝑎𝑥 + 41. It’s also given that ℎ1 = 40. Substituting 1 for 𝑥 and 40 for ℎ𝑥 in the equation ℎ𝑥 = 𝑎𝑥 + 41 yields 40 = 𝑎1 + 41, or 40 = 𝑎 + 41. Subtracting 41 from the left- and right-hand sides of this equation yields -1 = 𝑎. Substituting -1 for 𝑎 in the equation ℎ𝑥 = 𝑎𝑥 + 41 yields ℎ𝑥 = - 1𝑥 + 41, or ℎ𝑥 = - 𝑥 + 41. Choice B is incorrect. Substituting 0 for 𝑥 and 41 for ℎ𝑥 in this equation yields 41 = - 0, which isn't a true statement. Choice C is incorrect. Substituting 0 for 𝑥 and 41 for ℎ𝑥 in this equation yields 41 = - 410, or 41 = 0, which isn't a true statement. Choice D is incorrect. Substituting 41 for ℎ𝑥 in this equation yields 41 = - 41, which isn't a true statement. Question Difficulty: Easy Question ID 776cfa7c Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 776cfa7c Hana deposited a fixed amount into her bank account each month. The function gives the amount, in dollars, in Hana's bank account after monthly deposits. What is the best interpretation of in this context? A. With each monthly deposit, the amount in Hana's bank account increased by. B. Before Hana made any monthly deposits, the amount in her bank account was. C. After monthly deposit, the amount in Hana's bank account was. D. Hana made a total of monthly deposits. ID: 776cfa7c Answer Correct Answer: A Rationale Choice A is correct. It's given that 𝑡 represents the number of monthly deposits. In the given function 𝑓𝑡 = 100 + 25𝑡, the coefficient of 𝑡 is 25. This means that for every increase in the value of 𝑡 by 1, the value of 𝑓𝑡 increases by 25. It follows that with each monthly deposit, the amount in Hana's bank account increased by $ 25. Choice B is incorrect. Before Hana made any monthly deposits, the amount in her bank account was $ 100. Choice C is incorrect. After 1 monthly deposit, the amount in Hana's bank account was $ 125. Choice D is incorrect and may result from conceptual errors. Question Difficulty: Easy Question ID 73b5f330 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 73b5f330 The function is defined by. For what value of does ? A. B. C. D. ID: 73b5f330 Answer Correct Answer: A Rationale Choice A is correct. It's given that the function 𝑓 is defined by 𝑓𝑥 = 5𝑥 + 8. Substituting 58 for 𝑓𝑥 in this equation yields 58 = 5𝑥 + 8. Subtracting 8 from both sides of this equation yields 50 = 5𝑥. Dividing both sides of this equation by 5 yields 10 = 𝑥. Therefore, the value of 𝑥 when 𝑓𝑥 = 58 is 10. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the value of 𝑓58, not the value of 𝑥 when 𝑓𝑥 = 58. Question Difficulty: Easy Question ID 81390d6c Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 81390d6c The function is defined by. What is the value of ? A. B. C. D. ID: 81390d6c Answer Correct Answer: B Rationale Choice B is correct. Substituting 50 for 𝑥 in the given function yields ℎ50 = 50 + 200, or ℎ50 = 250. Therefore, the value of ℎ50 is 250. Choice A is incorrect. This is the value of ℎ0. Choice C is incorrect. This is the value of ℎ9,800. Choice D is incorrect. This is the value of ℎ50,000. Question Difficulty: Easy Question ID 2eef7e61 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 2eef7e61 The graph of the function f is a line in the xy-plane. If the line has slope and , which of the following defines f? A. B. C. D. ID: 2eef7e61 Answer Correct Answer: B Rationale Choice B is correct. The equation for the function f in the xy-plane can be represented by , where m is the slope and b is the y-coordinate of the y-intercept. Since it’s given that the line has a slope of , it follows that in , which yields. It’s given that. This implies that the graph of the function f in the xy-plane passes through the point. Thus, the y-coordinate of the y-intercept of the graph is 3, so in , which yields. Therefore, the equation defines the function f. Choice A is incorrect and may result from a sign error for the y-intercept. Choice C is incorrect and may result from using the denominator of the given slope as m in , in addition to a sign error for the y-intercept. Choice D is incorrect and may result from using the denominator of the given slope as m in. Question Difficulty: Easy Question ID 0ea7ef01 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 0ea7ef01 Oxygen gas is placed inside a tank with a constant volume. The graph shows the estimated temperature , in kelvins, of the oxygen gas when its pressure is atmospheres. What is the estimated temperature, in kelvins, of the oxygen gas when its pressure is atmospheres? A. B. C. D. ID: 0ea7ef01 Answer Correct Answer: C Rationale Choice C is correct. For the graph shown, the x-axis represents pressure, in atmospheres, and the y-axis represents temperature, in kelvins. Therefore, the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6 atmospheres is represented by the y-coordinate of the point on the graph that has an x-coordinate of 6. The point on the graph with an x-coordinate of 6 has a y-coordinate of approximately 700. Therefore, the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6 atmospheres is 700. Choice A is incorrect. This is the pressure, in atmospheres, not the estimated temperature, in kelvins, of the oxygen gas when its pressure is 6 atmospheres. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID 1ecaa9c0 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 1ecaa9c0 Robert rented a truck to transport materials he purchased from a hardware store. He was charged an initial fee of $20.00 plus an additional $0.70 per mile driven. If the truck was driven 38 miles, what was the total amount Robert was charged? A. $46.60 B. $52.90 C. $66.90 D. $86.50 ID: 1ecaa9c0 Answer Correct Answer: A Rationale Choice A is correct. It’s given that Robert was charged an initial fee of $20.00 to rent the truck plus an additional $0.70 per mile driven. Let m represent the number of miles the truck was driven. Since the rental charge is $0.70 per mile driven, represents the amount Robert was charged for m miles driven. Let c equal the total amount, in dollars, Robert was charged to rent the truck. The total amount can be represented by the equation. It’s given that the truck was driven 38 miles, thus. Substituting 38 into the equation gives. Multiplying gives. Adding these values gives , so the total amount Robert was charged is $46.60. Choices B, C, and D are incorrect and may result from setting up the equation incorrectly or from making calculation errors. Question Difficulty: Easy Question ID 8643d906 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 8643d906 The population of snow leopards in a certain area can be modeled by the function P defined above, where is the population t years after 1990. Of the following, which is the best interpretation of the equation ? A. The snow leopard population in this area is predicted to be 30 in the year 2020. B. The snow leopard population in this area is predicted to be 30 in the year 2030. C. The snow leopard population in this area is predicted to be 550 in the year 2020. D. The snow leopard population in this area is predicted to be 550 in the year 2030. ID: 8643d906 Answer Correct Answer: C Rationale Choice C is correct. It’s given that represents the population of snow leopards t years after 1990. corresponds to and. It follows that corresponds to 30 years after 1990, or 2020. Thus, the best interpretation of is that the snow leopard population in this area is predicted to be 550 in the year 2020. Choices A and B are incorrect and may result from reversing the interpretations of t and. Choice D is incorrect and may result from determining that 30 years after 1990 is 2030, not 2020. Question Difficulty: Easy Question ID a4d6fbec Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a4d6fbec If , what is the value of when ? ID: a4d6fbec Answer Correct Answer: 50 Rationale The correct answer is 50. Substituting 8 for 𝑥 in the given equation yields 𝑦 = 58 + 10, or 𝑦 = 50. Therefore, the value of 𝑦 is 50 when 𝑥 = 8. Question Difficulty: Easy Question ID a73a5c22 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a73a5c22 The function is defined by. What is the value of when ? A. B. C. D. ID: a73a5c22 Answer Correct Answer: D Rationale Choice D is correct. The value of 𝑔𝑥 when 𝑥 = 8 can be found by substituting 8 for 𝑥 in the given equation 𝑔𝑥 = 10𝑥 + 8. This yields 𝑔8 = 108 + 8, or 𝑔8 = 88. Therefore, when 𝑥 = 8, the value of 𝑔𝑥 is 88. Choice A is incorrect. This is the value of 𝑥 when 𝑔𝑥 = 8, rather than the value of 𝑔𝑥 when 𝑥 = 8. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Question Difficulty: Easy Question ID 5ad6bc97 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: 5ad6bc97 The function gives the total number of people on a company retreat with managers. What is the total number of people on a company retreat with managers? ID: 5ad6bc97 Answer Correct Answer: 50 Rationale The correct answer is 50. It's given that the function 𝑓 gives the total number of people on a company retreat with 𝑥 managers. It's also given that 7 managers are on the company retreat. Substituting 7 for 𝑥 in the given function yields 𝑓7 = 77 + 1, or 𝑓7 = 50. Therefore, there are a total of 50 people on a company retreat with 7 managers. Question Difficulty: Easy Question ID a8e6bd75 Assessment Test Domain Skill Difficulty SAT Math Algebra Linear functions ID: a8e6bd75 Which of the following is the graph of the equation in the xy-plane? A. B. C. D. ID: a8e6bd75 Answer Correct Answer: D Rationale Choice D is correct. In the xy-plane, the graph of the equation , where m and b are constants, is a line with slope m and y-intercept. Therefore, the graph of in the xy-plane is a line with slope 2 and a y- intercept. Having a slope of 2 means that for each increase in x by 1, the value of y increases by 2. Only the graph in choice D has a slope of 2 and crosses the y-axis at. Therefore, the graph shown in choice D must be the correct answer. Choices A, B, and C are incorrect. The graph of in the xy-plane is a line with slope 2 and a y-intercept at. The graph in choice A crosses the y-axis at the point , not , and it has a slope of , not 2. The graph in choice B crosses the y-axis at ; however, the slope of this line is , not 2. The graph in choice C has a slope of 2; however, the graph crosses the y-axis at , not. Question Difficulty: Easy