Math

SAT Suite of Assessments Skills Insight Tool

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Below are the skills and knowledge that students in the content domain and performance score band selected above are typically able to demonstrate as well as examples of the kinds of questions that these students are likely able to answer correctly. To view skill/knowledge statements and example questions in other domains and/or performance score bands, update the selections above and click Go.

Skills

A student in this performance score band can typically demonstrate the following skills in this content domain:

  • With or without a context, create a linear equation or inequality in two variables when given two input-output pairs, a table of values, or details about a translation of a given function
  • With or without a complex context, create one or both of the two linear equations in two variables that model the situation, or find and use the solution to a given system of linear equations

Example Questions

Example Question 1

Which of the following systems of linear equations has no solution?

  1. y = 6 x + 3 y = 6 x + 9

  2. y = 10 y = 10 x + 10

  3. y = 14 x + 14 y = 10 x + 14

  4. x = 3 y = 10

Key: A

Key Explanation

Choice A is correct. A system of two linear equations in two variables, x and y, has no solution if the graphs of the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by equations in slope-intercept form, y=mx+b, where m and b are constants, are parallel if their slopes, m, are the same and are distinct if their y-coordinates of the y-intercepts, b, are different. In the equations y=6x+3 and y=6x+9, the values of m are each 6, and the values of b are 3 and 9, respectively. Since the slopes of these lines are the same and the y-coordinates of the y-intercepts are different, it follows that the system of linear equations in choice A has no solution.

Distractor Explanations

Choice B is incorrect. The two lines represented by these equations are a horizontal line and a line with a slope of 10 that have the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,10, rather than no solution.

Choice C is incorrect. The two lines represented by these equations have different slopes and the same y-coordinate of the y-intercept. Therefore, this system has a solution, 0,14, rather than no solution.

Choice D is incorrect. The two lines represented by these equations are a vertical line and a horizontal line. Therefore, this system has a solution, 3,10, rather than no solution.

Example Question 2

A model estimates that whales from the genus Eschrichtius travel 72 to 77 miles in the ocean each day during their migration. Based on this model, which inequality represents the estimated total number of miles, x , a whale from the genus Eschrichtius could travel in 16 days of its migration?

  1. 72+16≤x≤77+16

  2. 7216≤x≤7716

  3. 72≤16+x≤77

  4. 72≤16x≤77

Key: B

Key Explanation

Choice B is correct. It's given that the model estimates that whales from the genus Eschrichtius travel 72 to 77 miles in the ocean each day during their migration. If one of these whales travels 72 miles each day for 16 days, then the whale travels 7216 miles total. If one of these whales travels 77 miles each day for 16 days, then the whale travels 7716 miles total. Therefore, the model estimates that in 16 days of its migration, a whale from the genus Eschrichtius could travel at least 7216 and at most 7716 miles total. Thus, the inequality 7216≤x≤7716 represents the estimated total number of miles, x, a whale from the genus Eschrichtius could travel in 16 days of its migration.

Distractor Explanations

Choice A is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from conceptual errors.