SAT Math Practice: Algebra and Advanced Functions Challenge

Question ID 43e69f94 ID: 43e69f94 The cost of renting a backhoe for up to days is for the first day and for each additional day. Which of the following equations gives the cost , in dollars, of renting the backhoe for days, where is a positive integer and ? A. B. C. D. Assessment SAT Test Math Domain Algebra Skill Linear functions Diﬃculty Hard

Question ID 252d6b8a ID: 252d6b8a In the given pair of equations, and are constants. The graph of this pair of equations in the xy -plane is a pair of perpendicular lines. Which of the following pairs of equations also represents a pair of perpendicular lines? A. B. C. D. Assessment SAT Test Math Domain Algebra Skill Linear equations in two variables Diﬃculty Hard

Question ID 84f5f182 ID: 84f5f182 A salesperson’s total earnings consist of a base salary of dollars per year, plus commission earnings of of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least times and at most times the base salary. Which of the following inequalities represents all possible values of total sales , in dollars, the salesperson can make this year in order to meet that goal? A. B. C. D. Assessment SAT Test Math Domain Algebra Skill Linear inequalities in one or two variables Diﬃculty Hard

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Question ID 2ebd5e5b ID: 2ebd5e5b The solution to the given system of equations is . What is the value of ? Assessment SAT Test Math Domain Algebra Skill Systems of two linear equations in two variables Diﬃculty Hard

Question ID 35978b89 ID: 35978b89 The point with coordinates lies on the line shown. What is the value of ? A. B. C. D. Assessment SAT Test Math Domain Algebra Skill Linear equations in two variables Diﬃculty Hard

Question ID 005e9982 ID: 005e9982 The given function models the number of advertisements a company sent to its clients each year, where represents the number of years since , and . If is graphed in the xy -plane, which of the following is the best interpretation of the y -intercept of the graph in this context? A. The minimum estimated number of advertisements the company sent to its clients during the years was . B. The minimum estimated number of advertisements the company sent to its clients during the years was . C. The estimated number of advertisements the company sent to its clients in was . D. The estimated number of advertisements the company sent to its clients in was . Assessment SAT Test Math Domain Advanced Math Skill Nonlinear functions Diﬃculty Hard

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Question ID 4443355f ID: 4443355f The expression , where is a constant, can be rewritten as , where , , and are integer constants. Which of the following must be an integer? A. B. C. D. Assessment SAT Test Math Domain Advanced Math Skill Equivalent expressions Diﬃculty Hard

Question ID b40b491b ID: b40b491b The given equation relates the distinct positive real numbers , , and . Which equation correctly expresses in terms of and ? A. B. C. D. Assessment SAT Test Math Domain Advanced Math Skill Nonlinear equations in one variable and systems of equations in two variables Diﬃculty Hard msup msup

Question ID 1145bfcc ID: 1145bfcc The given equation relates the variables and . For what value of does the value of reach its minimum? Assessment SAT Test Math Domain Advanced Math Skill Nonlinear functions Diﬃculty Hard

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Question ID 3138e379 ID: 3138e379 For what value of is the given expression equivalent to , where ? Assessment SAT Test Math Domain Advanced Math Skill Equivalent expressions Diﬃculty Hard

Question ID c50fc439 ID: c50fc439 A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected teams at random from all trivia teams in a certain tournament. The table displays the information for the teams in the sample that practiced for at least hours per week. Hours practiced Number of points per round 6 to 13 points 14 or more points Total 3 to 5 hours More than 5 hours Total Which of the following is the largest population to which the results of the study can be generalized? A. All trivia teams in the tournament that scored or more points in the round B. The trivia teams in the sample C. The trivia teams in the sample that practiced for at least hours per week D. All trivia teams in the tournament Assessment SAT Test Math Domain Problem-Solving and Data Analysis Skill Evaluating statistical claims: Observational studies and experiments Diﬃculty Hard

Question ID e03f95ad ID: e03f95ad Data set A consists of the heights of objects and has a mean of meters. Data set B consists of the heights of objects and has a mean of meters. Data set C consists of the heights of the objects from data sets A and B. What is the mean, in meters, of data set C? Assessment SAT Test Math Domain Problem-Solving and Data Analysis Skill One-variable data: Distributions and measures of center and spread Diﬃculty Hard

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Question ID 3ea17fb0 ID: 3ea17fb0 A gift shop buys souvenirs at a wholesale price of dollars each and resells them each at a retail price that is of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is off the retail price. What is the discounted price of each remaining souvenir, in dollars? Assessment SAT Test Math Domain Problem-Solving and Data Analysis Skill Percentages Diﬃculty Hard

Question ID f95c357a ID: f95c357a Two data sets of integers each are summarized in the histograms shown. For each of the histograms, the first interval represents the frequency of integers greater than or equal to , but less than . The second interval represents the frequency of integers greater than or equal to , but less than , and so on. What is the smallest possible difference between the mean of data set A and the mean of data set B? A. B. C. D. Assessment SAT Test Math Domain Problem-Solving and Data Analysis Skill One-variable data: Distributions and measures of center and spread Diﬃculty Hard

Question ID 0a975aa5 ID: 0a975aa5 For , the function is defined as follows: equals of Which of the following could describe this function? A. Decreasing exponential B. Decreasing linear C. Increasing exponential D. Increasing linear Assessment SAT Test Math Domain Problem-Solving and Data Analysis Skill Two-variable data: Models and scatterplots Diﬃculty Hard

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Question ID 3a95868c ID: 3a95868c Point is the center of a circle. The measure of arc on this circle is . What is the measure, in degrees, of its associated angle ? Assessment SAT Test Math Domain Geometry and Trigonometry Skill Circles Diﬃculty Hard

Question ID 8235af09 ID: 8235af09 Triangles and are similar. Each side length of triangle is times the corresponding side length of triangle . The area of triangle is square inches. What is the area, in square inches, of triangle ? Assessment SAT Test Math Domain Geometry and Trigonometry Skill Area and volume Diﬃculty Hard

Question ID db84ccdc ID: db84ccdc A circle in the xy -plane has a diameter with endpoints and . An equation of this circle is , where is a positive constant. What is the value of ? Assessment SAT Test Math Domain Geometry and Trigonometry Skill Circles Diﬃculty Hard

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Question ID 307d7ae0 ID: 307d7ae0 Triangle is similar to triangle , where angle corresponds to angle and angle corresponds to angle . Angles and are right angles. If , what is the value of ? Assessment SAT Test Math Domain Geometry and Trigonometry Skill Right triangles and trigonometry Diﬃculty Hard

Question ID 34eb7da8 ID: 34eb7da8 The equation represents circle A. Circle B is obtained by shifting circle A down units in the xy -plane. Which of the following equations represents circle B? A. B. C. D. Assessment SAT Test Math Domain Geometry and Trigonometry Skill Circles Diﬃculty Hard msup msup msup msup

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