Math

SAT Suite of Assessments Skills Insight Tool

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 and/or solve a linear equation or system of linear equations, or identify the correct coefficients or constants in the equation(s) that represent(s) the situation
Make connections between different representations of linear equations in one variable, linear functions, linear equations in two variables, systems of two linear equations in two variables, and (SAT, PSAT/NMSQT, and PSAT 10 only) linear inequalities when these representations include symbolic representations that may contain variable constants

Example Questions

Example Question 1

If $\frac{x + 6}{3} = \frac{x + 6}{13}$ , the value of $x plus 6$ is between which of the following pairs of values?

$negative 7$ and $negative 3$
$negative 2$ and $2$
$2$ and $7$
$8$ and $13$

Key: B

Key Explanation

Choice B is correct. Multiplying both sides of the given equation by $left parenthesis 3 right parenthesis left parenthesis 13 right parenthesis$ , or $39$ , yields $(39) (\frac{x + 6}{3}) = (39) (\frac{x + 6}{13})$ , or $13 (x + 6) = 3 (x + 6)$ . Subtracting $3 left parenthesis x plus 6 right parenthesis$ from both sides of this equation yields $10 (x + 6) = 0$ . Dividing both sides of this equation by $10$ yields $x + 6 = 0$ . Therefore, if $\frac{x + 6}{3} = \frac{x + 6}{13}$ , then the value of $x plus 6$ is $0$ . It follows that of the given choices, the value of $x plus 6$ is between $negative 2$ and $2$ .

Distractor Explanations

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.

Example Question 2

The cost of renting a backhoe for up to $10$ days is $dollar sign 270$ for the first day and $dollar sign 135$ for each additional day. Which of the following equations gives the cost $y$ , in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x less than or equals 10$ ?

$y = 270 x - 135$
$y = 270 x + 135$
$y = 135 x + 270$
$y = 135 x + 135$

Key: D

Key Explanation

Choice D is correct. It's given that the cost of renting a backhoe for up to $10$ days is $dollar sign 270$ for the first day and $dollar sign 135$ for each additional day. Therefore, the cost $y$ , in dollars, for $x$ days, where $x less than or equals 10$ , is the sum of the cost for the first day, $dollar sign 270$ , and the cost for the additional $x minus 1$ days, $dollar sign 135 left parenthesis x minus 1 right parenthesis$ . It follows that $y = 270 + 135 (x - 1)$ , which is equivalent to $y = 270 + 135 x - 135$ , or $y = 135 x + 135$ .

Distractor Explanations

Choice A is incorrect. This equation represents a situation where the cost of renting a backhoe is $dollar sign 135$ for the first day and $dollar sign 270$ for each additional day.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Reading and Writing

Math

Math

Reading and Writing

Skills

Example Questions

Example Question 1

Key: B

Key Explanation

Distractor Explanations

Example Question 2

Key: D

Key Explanation

Distractor Explanations