t h e r e d e s i g n e d sat ®

These draft test specifications and sample items and other materials are just that — drafts. As such, they will systematically evolve over time. These sample items are meant to illustrate the shifts in the redesigned SAT® and are not a full reflection of what will be tested. Actual items used on the exam are going through extensive reviews and pretesting to help ensure that they are clear and fair, and that they measure what is intended. The test specifications as well as the research foundation defining what is measured on the test will continue to be refined based on ongoing research.

t h e r e d e s i g n e d sat ® » f o c u s o n m at h t h at m att e rs m o st

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Focus on Math that Matters Most

Surveys of postsecondary mathematics faculty and studies of postsecondary mathematics demands have repeatedly supported the conclusion that postsecondary instructors value a strong command of a smaller set of prerequisites over shallow exposure to a wider array of topics. A greater command of an essential set of skills and understandings allows students to build on what they know and apply their knowledge to solve substantive problems, not only in college but also in their careers.1

Heart of Algebra: A strong emphasis on linear equations and functionsAlgebra is the language of much of high school mathematics, and it is also an important prerequisite for advanced mathematics and postsecondary education in many subjects. Mastering linear equations and functions has clear benefits to students. The ability to use linear equations to model scenarios and to represent unknown quantities is powerful across the curriculum in the postsecondary classroom as well as in the workplace. Further, linear equations and functions remain the bedrock upon which much of advanced mathematics is built. (Consider, for example, the way differentiation in calculus is used to determine the best linear approximation of nonlinear functions at a certain input value.) Without a strong foundation in the core of algebra, much of this advanced work remains inaccessible.

The following sample question helps illustrate one way students will be asked to demonstrate their command of algebra on the redesigned sat®.

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EXAMPLE 1

When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77B) p = 0.44d + 14.74C) p = 2.2d – 1.1D) p = 2.2d – 9.9

Working with linear functions to model phenomena has high relevance for postsecondary study and is a core aspect of a rigorous high school curriculum. Understanding that the pressure increases 2.2 pounds per square inch every 5 feet deeper the scientist dives, and being able to cast this fact into the language of algebra, will steer students to the correct answer, choice B. Students who study this material and learn it well will be rewarded for their knowledge on the redesigned sat.

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Problem Solving and Data Analysis: A strong emphasis on quantitative reasoning

Quantitative reasoning is crucial to success in postsecondary education, career training programs, and everyday life. The question below helps illustrate how students are asked to demonstrate their ability to solve real-world problems by analyzing data and using ratios, percentages, and proportional reasoning on the redesigned sat. It also illustrates a feature of the redesigned sat: multipart questions. Asking more than one question about a given scenario allows students taking the redesigned sat to do more sustained thinking and explore situations in greater depth. Students will generally be seeing longer problems in their postsecondary work. By including item sets, the redesigned sat rewards and incentivizes aligned, productive work in classrooms.

EXAMPLE 2

A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results.

Reported Voting by Age (in thousands)

AGE COHORTS VOTED DID NOT VOTE NO RESPONSE TOTAL

18- to 34-year-olds 30,329 23,211 9,468 63,008

35- to 54-year-olds 47,085 17,721 9,476 74,282

55- to 74-year-olds 43,075 10,092 6,831 59,998

People 75 years old and over 12,459 3,508 1,827 17,794

Total 132,948 54,532 27,602 215,082

According to the table, for which age group did the greatest percentage of people report that they had voted?

A) 18- to 34-year-oldsB) 35- to 54-year-oldsC) 55- to 74-year-oldsD) People 75 years old and over

Of the 18- to 34-year-olds who reported voting, 500 people were selected at random to do a follow-up survey where they were asked which

t h e r e d e s i g n e d sat ® » f o c u s o n m at h t h at m att e rs m o st

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candidate they voted for. There were 287 people in this follow-up survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the follow-up survey and the initial survey, which of the following is most likely to be an accurate statement?

A) About 123 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

B) About 76 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

C) About 36 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

D) About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.

To succeed on these questions, students must conceptualize the context and retrieve relevant information from the table, next manipulating it to form or compare relevant quantities. The first question asks students to select the relevant information from the table to compute the percentage of self-reported voters for each age group and then compare the percentages to identify the largest one, choice C. The second question asks students to extrapolate from a random sample to estimate the number of 18- to 34-year-olds who voted for Candidate A, 287500

30 329 000 17, , million, choice D. Students without a clear grasp

of the context and its representation in the table might easily arrive at one of the other answers listed.

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Passport to Advanced Math: A strong emphasis on understanding the structure of expressions and analyzing expressionsLike linear equations and functions, complex equations, inequalities, and functions provide rich opportunities for students to practice and develop the prerequisite skills for careers and postsecondary education. The following question helps illustrate one way students will be asked to extend the concepts of linear equations/functions to more complex applications.

EXAMPLE 3

x yy x

2 2 1534

+ == −

If ( , )x y is a solution to the system of equations above, what is the value of x2?

A) −51 B) 3C) 9D) 144

In this question, students are asked to analyze a system of nonlinear equations, making use of structure where appropriate. Choice C is correct. For example, substituting –4x for y in the first equation leads to x x2 24 153+ −( ) = ., a simple equation for x x2 216 153+ = ,. Simplifying

this equation, we have 17 1532x = so = =x2 15317

9 . Alternatively, a

student could begin by squaring both sides of the second equation to form y2 = 16x2, then substitute 16x2 for y2 in the first equation. This leads to x x2 216 153+ = , as before.

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Additional Topics in Math: An emphasis on essential geometric and trigonometric concepts

The sat will also require the geometric and trigonometric knowledge most relevant to postsecondary education and careers. By connecting algebra and geometry, analytical geometry becomes a powerful method of analysis and problem solving. The trigonometric functions of sine, cosine, and tangent for acute angles are derived from right triangles and similarity. When combined with the Pythagorean Theorem, the trigonometric functions can be used to solve many real-world problems. The following question helps illustrate one way students will be asked to solve geometry problems on the redesigned sat.

The figure above shows a metal hex nut with two regular hexagonal faces and a thickness of 1 cm. The length of each side of a hexagonal face is 2 cm. A hole with a diameter of 2 cm is drilled through the nut. The density of the metal is 7.9 grams per cubic cm. What is the mass of this nut, to the nearest gram? (Density is mass divided by volume.)

The question above asks students to make connections between physical concepts such as mass and density and essential geometric ideas such as the Pythagorean Theorem and volume formulas. There are multiple approaches to solving this problem, but in any of them, the aim is to find the volume of the metal nut and then use the density of the metal to calculate the mass of the nut (57 grams). This is a multistep problem that requires students to devise a multistep strategy and carry out all the algebraic and numerical steps without error.

1 For a more detailed description of the evidence, please see the “Evidentiary Foundation” section of The Redesigned SAT.

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