Information for Users of Assistive Technology

The Redesigned S A T®

Mathematics Sample Sets

Information for users of assistive technology

The document(s) that accompany these instructions are designed to be accessible to individuals who use screen readers, text readers, or other assistive technology. You may wish to consult the manual or help system of your application software to learn how best to take advantage of the following features implemented in this document.

Headings

Some questions include passages or other material that you may find it useful to return to or skip past. To assist in this kind of navigation, the test documents use headings as follows.

Heading level 3: section titles

Heading level 4: directions for a group of questions or references to material on which one or more questions will be based (for example, “Question 3 is based on the following text:”)

Heading level 5: question numbers, which directly precede the associated questions

Heading level 6: indications of skippable content (For example, you may prefer to skip some sections of this script, such as those that provide figure descriptions or possible answers in context for questions that involve revision. This content is identified at the beginning by the phrase “Begin skippable content” and at the end by the phrase “End skippable content.” These phrases are formatted as level‑6 headings.)

Links

This document includes hyperlinked material. There are two ways to follow a link. One is to move the flashing text cursor, or caret, into the hyperlinked text and press the Enter key; the other is to place the mouse cursor, or pointer, over the hyperlinked text and press Ctrl+left‑click (that is, press and release the left button on the mouse while holding down the Ctrl key on the keyboard). Some application software includes commands for listing links in a document. In JAWS, for example, pressing Insert+F5 provides a list of links. After following a link in Microsoft Word®, you can return to your previous location by pressing Alt+left arrow.

Text attributes

Boldfacing and underlining are used in this document for emphasis and in defined heading styles. Italic type is not used as an emphasis indicator in this document but is used in defined heading styles as well as where standard typographic conventions require them, such as book titles and mathematical variables. Adjust the settings of your screen reader or other application software if you wish to be notified of text attribute changes. Except where stated otherwise, this formatting is not critical to the meaning of the test material.

Text and graphics size

The styles used in this document result in text that is moderately enlarged. To enlarge text further in Microsoft Word, the following is recommended, in order of preference:

1. Adjust the styles to meet your needs. You can adjust both font size and typeface if desired.

2. Manually adjust the font size or typeface as desired.

3. Use Microsoft Word’s zoom function. This is the easiest way to enlarge any figures, but note that some screen readers will not read text that has moved off screen as a result of zooming.

Pronunciation

Some changes to the text have been made to improve the way screen readers pronounce the text where doing so would not inappropriately change test content. For example, we have inserted spaces between the letters of initialisms to ensure that the individual letters are spoken separately. However, please note that pronunciation errors may remain. If unsure of a word, use the spelling or character‑by‑character navigation function of your application software to resolve any uncertainties.

Punctuation

Where punctuation or symbols are critical to the meaning of test material, we either convert the symbol or punctuation mark to words (for example, “it apostrophe s” or “it s apostrophe”) or else include a statement advising you to take note of punctuation for a particular question or portion of a question.

Tables

Some questions may include tables. Use the table‑navigation features of your application software.

Figures

This document may include figures, which appear on screen. Following each figure on screen is text describing that figure. Readers using visual presentations of the figures may choose to skip parts of the text describing the figure that begin with “Begin skippable figure description” and end with “End skippable figure description.”

Your application software may speak unhelpful information when you arrive at the figures, such as the figure’s size. If your application software offers a method of configuring speech for graphics, you may wish to use that to prevent it from speaking the unwanted information.

Mathematical Equations and Expressions

Some of these documents include mathematical equations and expressions. Some of the mathematical equations and expressions are presented as graphics. In cases where a mathematical equation or expression is presented as a graphic, a verbal presentation is also given and the verbal presentation comes directly after the graphic presentation. The verbal presentation is in green font to assist readers in telling the two presentation modes apart. Readers using audio alone can safely ignore the graphical presentations, and readers using visual presentations may ignore the verbal presentations.

The Redesigned S A T®: Mathematics—Calculator Page 1

Mathematics—Calculator

The directions and question numbers below are representative of what students will encounter on test day. Some math sections allow the use of a calculator, while others do not, as indicated in the directions.

Turn to Section 4 of your answer sheet to answer the questions in this section.

For questions 1 through 30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 31 through 38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 31 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.

1. The use of a calculator is permitted.

2. All variables and expressions used represent real numbers unless otherwise indicated.

3. Figures provided in this test are drawn to scale unless otherwise indicated.

4. All figures lie in a plane unless otherwise indicated.

5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f of x is a real number.

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of the problems.

Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.

A equals pi times the square of r.

C equals 2 pi r.

Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.

A equals ℓ w.

Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.

A equals one‑half b h.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.

c squared equals a squared plus b squared.

Special Right Triangles

Reference figure 5 is a right triangle with a 30‑degree angle and a 60‑degree angle. The side opposite the 30‑degree angle is labeled x. The side opposite the 60‑degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.

Reference figure 6 is a right triangle with two 45‑degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.

Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.

V equals ℓ w h.

Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.

V equals pi times the square of r times h.

Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.

V equals four‑thirds pi times the cube of r.

Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.

V equals one‑third times pi times the square of r times h.

Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.

V equals one‑third ℓ w h.

Additional Reference Information

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2 pi.

The sum of the measures in degrees of the angles of a triangle is 180.

End skippable figure descriptions.

The Redesigned S A T®: Mathematics—Calculator Page 1

For student‑produced response questions, students will also see the following directions:

For questions 31 through 38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.

1. Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.

2. Mark no more than one circle in any column.

3. No question has a negative answer.

4. Some problems may have more than one correct answer. In such cases, grid only one answer.

5. Mixed numbers such as three and one‑half must be recorded as three point five or seven slash two. (If three and one‑half is entered into the grid as , three, one, slash, two, it will be interpreted as thirty‑one halves, not three and one‑half).

6. Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.

The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.

Examples 1 and 2

Beging skippable figure description.

Example 1: If your answer is a fraction such as seven‑twelfths, it should be recorded as follows. Enter seven in the first space, the fraction bar (a slash) in the second space, one in the third space, and two in the fourth space. All four spaces would be used in this example.

Example 2: If your answer is a decimal value such as two point five, it could be recorded as follows. Enter two in the second space, the decimal point in the third space, and five in the fourth space. Only three spaces would be used in this example.

End skippable figure description.

Example 3

Beging skippable figure description.

Example 3: Acceptable ways to record two‑thirds are: two slash three, point six six six, and point six six seven.

End skippable figure description.

Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need should be left blank.

Beging skippable figure description.

Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record two in the first space, zero in the second space, and one in the third space. Alternatively, you may record two in the second space, zero in the third space, and one in the fourth space. Spaces not needed should be left blank.

End skippable figure description.

The Redesigned S A T®: Mathematics—Calculator Page 1

Mathematics Sample Questions

Question 1.

The recommended daily calcium intake for a 20‑year‑old is 1,000 milligrams (m g). One cup of milk contains 299 milligrams of calcium and one cup of juice contains 261 milligrams of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20‑year‑old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?

A. 299 m plus 261 j is greater than or equal to 1,000

B. 299 m plus 261 j is greater than 1,000

C. the fraction 299 over m, plus the fraction 261 over j, is greater than or equal to 1,000

D. the fraction 299 over m, plus the fraction 261 over j, is greater than 1,000

Answer and Explanation. (Follow link to explanation of question 1.)

Question 2.

A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology‑degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology‑degree program read per day?

A. 40 randomly selected undergraduate psychology‑degree program students

B. 40 randomly selected undergraduate students from all degree programs at the college

C. 300 randomly selected undergraduate psychology‑degree program students

D. 300 randomly selected undergraduate students from all degree programs at the college

Answer and Explanation. (Follow link to explanation of question 2.)

Questions 3 through 5 refer to the following information and figure.

The first metacarpal bone is located in the wrist. The following scatterplot shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.

Begin skippable figure description.

The figure presents a gridded graph titled “Height of Nine People and Length of Their First Metacarpal Bone” and nine data points. The y‑axis is labeled “Length of first metacarpal bone,” in centimeters, and the x‑axis is labeled “Height,” in centimeters. The values 4, 4.5, and 5 are labeled on the x‑axis with a vertical grid line at every increment of 0.1. The values 155 through 185, in increments of 5, are labeled on the y‑axis with a horizontal grid line at every increment of one.