The New SAT ® Important Information for High School Math Teachers

The New SAT®

Important Information forHigh SchoolMath Teachers

3 The New SAT: Important Information for High School Math Teachers, June 2004

The New SAT Focuses onCollege Success™ Skills

• Critical Reading

• Mathematics

• Writing

The SAT® tests students’ reasoning based on knowledge and skills developed through their course work.

It measures their ability to analyze and solve problems by applying what they have learned in school.


Time Frame

•October 2004: New PSAT/NMSQT®

•March 2005: New SAT


Time FrameClass of 2006 will take new SAT

• Class of 2005—current seniors

Current SAT as seniors in fall 2004

New SAT as seniors in March 2005 (if necessary)

• Class of 2006—current juniors

New PSAT/NMSQT as juniors in fall 2004

New SAT as juniors in March 2005 and later

New SAT as seniors


Has the SAT Ever Changed Before? • Yes, the SAT has changed several times since

it was first administered in 1926.

• The SAT evolves to meet the changing needsof students, teachers, and colleges.

• The most recent changes were made in 1994. (Adding writing to the SAT was recommended but not possible in 1994 due to inadequate technology and lack of large number of readers needed.)


Why Is the SAT Changing?• To better reflect today’s classroom practices

and curriculum by replacing analogies with short reading passages and quantitative comparisons with more math problems, some including content from third-year college-preparatory math

• To reinforce the importance of writing skills

• To help colleges make better admissions and placement decisions


Will the New SAT Be Harder?• No, the new SAT will be designed so that a student who could

score a 500 on the math section (for example) of the current SAT could score a 500 on the math section of the new test.

• 97% of college-bound students complete 3 years of math so the test will more closely measure the math they are already studying.

• Extensive field trials confirmed that students are taking more upper level math, which is why the overall difficulty of the test is not affected.

• While the test is longer, field trials also confirmed that the increased length of the test has no impact on the students’ scores.


The Changes to the SAT and the PSAT/NMSQT®

Verbal

• Name will be changed to critical reading.

• Analogies will be eliminated.

• Short reading passages will replace analogies and will measure the kind of reasoning formerly measured by analogies.


The Changes to the SAT and the PSAT/NMSQT

Math

• Quantitative comparisons will be eliminated

• The content is being expanded to reflect the mathematics that college-bound students typically learn during their first three years of high school.

• The reasoning aspects of the test together with the expanded content

will more effectively assess the mathematics necessary for student success in college.

• Math content on the PSAT/NMSQT will also be enhanced, but it will not include Algebra II because most students will not be familiar with that level of math.


0

The Changes to the SAT and the PSAT/NMSQTQuantitative comparisons will be ELIMINATED

Column A Column Bx=0

x+1x–1

(A) The quantity in column A is greater(B) The quantity in column B is greater(C) The two quantities are equal(D) The relationship cannot be determined from the

information givenCorrect Answer: B



Writing

• Multiple-choice grammar and usage questions

• Will measure the student’s understanding of how to use language in a clear, consistent manner, how to revise and edit, and how to recognize an error in a sentence.

• Student-written essay (SAT only)

• Will measure the student’s use of language: logical presentation of ideas, development of a point of view, and clarity of expression under timed conditions.

• Essay practice tool provided AT NO COST to all schools administering the PSAT/NMSQT.



Skills Feedback

• The PSAT/NMSQT provides individualized feedback to students through its ScoreReport Plus.

• The College Board is developing a similar toolfor the SAT.

SkillsFeedbackScore Report Plus

14


PSAT/NMSQTScore Report Plus

• Tells students how their scores compare with those of other sophomores or juniors

• Tells students what SAT score ranges they can expect

• Includes a question-by-question breakdown

• Helps students identify strengths and weaknesses and provides tips on how to improve specific skills


PSAT/NMSQT Score Report PlusNew in 2004

Students will use their Score Report Plus code to access free enhancements online at www.collegeboard.com/psatextra:

• Complete explanations for all answers, including why some answers were wrong.

• Full explanations of answers for additional higher-level math practice SAT questions on the back of the PSAT/NMSQT score report.

• Entire SAT essay scoring guide, plus actual sample essay papers at every score point for the practice essay on the back of the PSAT/NMSQT score report.


Skills FeedbackScore Report Plus

Improve Your Skills—Examples

• Being precise and clear

• How to improve: Learn to recognize sentence elements that are ambiguous and confusing. In your writing, choose words carefully and connect them for clear meaning. See questions 4, 6, 8.

• Understanding geometry and coordinate geometry

• How to improve: Review geometry units in your textbook involving perimeter, area, volume, circumference, angles, lines, slope. Familiarize yourself with the formulas given at the beginning of math sections of the set. See questions 7, 13, 19.


Time SpecificationsPSAT/NMSQT

Current PSAT/NMSQT

New PSAT/NMSQT

2 hours 10 minutes 2 hours 10 minutes

Critical Reading

50 minutes

Two 25-minute sections

50 minutes


Math50 minutes


50 minutes


Writing30 minutes

One 30-minute multiple-choice section

30 minutes

One 30-minutemultiple-choice section


Current SAT New SAT

3 hours 3 hours 45 minutes

Critical Reading

75 minutes

Two 30-minute sections and one 15-minute section

70 minutes

Two 25-minute sections and

one 20-minute section

Math75 minutes

Two 30-minute sections and one 15-minute section

70 minutes

Two 25-minute sections and

one 20-minute section

Writing

60 minutesTwo multiple-choice sections (one 25-minute section and one 10-minute section) and one 25-minute essay

Variable Section

30 minutes 25 minutes

Time SpecificationsSAT


Test Content and Question Types

Current SAT New SAT

Critical Reading

Sentence Completion

Critical Reading: Long reading passages

Analogies

Sentence Completion

Critical Reading: short and long reading passages

Math

Multiple-choice items, student-produced responses, and quantitative comparisons measuring:

Number and Operations;

Algebra I and Functions;

Geometry; and Statistics, Probability,

and Data Analysis.

Multiple-choice items and student-produced responses measuring:

Number and Operations;

Algebra I, II, and Functions;

Geometry; and Statistics, Probability, and Data Analysis.

Writing

Multiple-choice items: Improving sentences and paragraphs, and identifying sentence errors.

Student-written essay: Effectively communicate a point of view on an issue, supporting a position with reasoning and examples.


Current SAT

New SAT

Critical Reading

V 200–800 CR 200–800

Math M 200–800 M 200–800

Writing(Subscores)

W 200–800

Will include 2 subscores:

Essay 2–12

(1/3 of writing score)

Multiple-choice 20–80

(2/3 of writing score)

Test Scores


The New SAT Field Trial

• Field trial was conducted in March 2003 to determine the impact of changes to the SAT and PSAT/NMSQT.

• More than 45,000 students from 680 high schools participated.

• Students were representative of SAT-takers and PSAT/NMSQT-takers.

• Students from underrepresented populations were oversampled.


The New SAT Field TrialBased on field trial results, the College Board expects that:

• Changes to the math and verbal sections will not affect the difficulty or reliability of the test.

• Performance differences by subgroups (by race/ethnicity and gender) on the new SAT will not be exacerbated. The relative differences in scores for underrepresented students will not increase due to any of the changes implemented with the new SAT.

• The score scales for math and critical reading on the new SAT will be comparable to the score scales on the math and verbal sections of the current SAT.

• The longitudinal data will be maintained. For example, a 600 on the new critical reading section will be equivalent to a 600 on the current verbal section, and a 580 on the new math section will be equivalent to a 580 on the current math section.

A Closer Look at the Math Section of the New SAT


Math SectionMeasures problem-solving skills

• Emphasis on math reasoning: SAT math measures the ability to apply math content to real-life problems.

• The SAT is unique in having some “grid-in” questions requiring student-produced responses—as recommended by NCTM (National Council of Teachers of Mathematics).

• Approximately 15–20% of math questions on the new SAT and 15% of math questions on the new PSAT/NMSQT will either cover new topics or will cover existing topics in greater depth.


Most Four-Year Colleges Require 3 Years of Math for Admission• 70% of all high school students finish

Algebra II

• 97% of college-bound students complete3 years of math and 69% complete 4 ormore years of math

• 92% of minority college-bound students complete 3 years of math


Calculator Policy• A scientific or graphing calculator will be

recommended for the new tests.

• Though every question can still be answered without a calculator, calculators are definitely encouraged.

• Previously, a basic 4-function calculator was recommended, but now scientific is the base level recommendation.

• Students should bring a calculator with which they are comfortable and familiar.


Calculator PolicyThe following are not permitted:

• Powerbooks and portable/handheld computers

• Electronic writing pads or pen-input/stylus-driven(e.g., Palm, PDAs, Casio ClassPad 300)

• Pocket organizers

• Models with QWERTY (i.e., typewriter) keyboards(e.g., TI-92 Plus, Voyage 200)

• Models with paper tapes

• Models that make noise or “talk”

• Models that require an electrical outlet

• Cell phone calculators

EnhancedMath Section

Number and Operations


t 8

The Enhanced Math SectionNumber and Operations

Sequences involving exponential growth

• Questions that require knowledge of exponential growth or geometric sequences. Example: 7, 21, 63, 189, … is a geometric sequence that has constant ratio 3 and begins with the term 7. The term obtained after multiplying n times by 3 is 7 x 3n

• Since these sequences have real-life applications, questions might be presented in contexts such as population growth.

• Example: a population that initially numbers 100 and grows by doubling every eight years. The expression 100 x 2 would give the population t years after it begins to grow.


The Enhanced Math SectionNumber and Operations

Sets (union, intersection, elements)

• Questions might ask about the union of two sets(i.e., the set consisting of elements that are in either set or both sets) or the intersection of two sets(i.e., the set of common elements).

• Example: If set X is the set of positive even integers and set Y is the set of positive odd integers, a question might ask students to recognize that the union of the two sets is the set of all positive integers.


Algebra and Functions


Absolute Value

• Students should be familiar with both the concept and notation of absolute value and be able to work with expressions, equations, and functions that involve absolute value.

Rational Equations and Inequalities

• Example: . Equations or inequalities involving such expressions will be included on the new SAT

Radical Equations

• Example:

Enhanced Math SectionAlgebra and Functions


Integer and Rational Exponents

• On the current SAT, exponents are restrictedto positive integers. The new SAT will have expressions such as z-3 involving negative exponents.

• There will also be expressions such as m where the exponent is a rational number.

3 4



Integer and Rational Exponents–Sample Problem

If x-3=64, what is the value of x ?

(A)

(B)

(C) 4

(D) 8

(E) 16Correct Answer: B

What’s new about this question? The current SAT has questions involving positive integer exponents. The new SAT will have expressions involving negative exponents, such as x-3, and fractional exponents, such as x .

12

1 2

14

1 2



Direct and Inverse Variation

• Questions involving quantities that are directly proportional to each other.

• The quantities x and y are directly proportional if y= kx, for some constant k. They are said tobe inversely proportional if y= for some constant k

k x




Function Notation

• Students should be familiar with both the concept ofa function and with function notation.

• Example: If the function f is defined by f(x) = x + 2x, students should know that f(5) = 5 + 25 = 37.


Function Notation–Sample Problem

If f is a linear function and if f(6)=7 and f(8)=12,what is the slope of the graph of f in the xy-plane.

Correct Answer: or 2.5

What’s new about this question?The new element in this question is the use of the notation f(x)to refer to the function.

5 2




Concepts of Domain and Range

• The new SAT will include questions that ask about values of x at which a particular function is not defined (outside the domain), or values that f(x) cannot equal (outside the range).

Functions as Models

• The new SAT will include questions that involve mathematical models of real-life situations.

• A question might present information about the projected sales of a product at various prices and ask for a mathematical model in the form of a graph or equation that represents projected sales as a function of price.



Linear Functions–Equations and Graphs

• The new SAT will include questions involving linear equations, such as y=mx+b, where m and b are constants.

• Some questions may involve graphs of linear functions


Linear Functions–Equations and Graphs–Sample Problem

In the figure above, if line k has a slope of -1,what is the y-intercept of k?

(A) 6(B) 7(C) 8(D) 9(E) 10

Correct Answer: B

What’s new about this question? The use of the term “y-intercept.”


Note: Figure not drawn to scale



Quadratic Functions–Equations and Graphs

• Questions involving quadratic equations and/or their graphs may appear on the new SAT. For example, a question might involve comparingthe graphs of y=2x2 and y=2(x-1)2.


Geometry and Measurement


Geometric Notation for Length, Segments, Lines, Rays, and Congruence

• Geometric notation such as and willbe used. The term “congruent” and the congruence symbol will be used.

Enhanced Math SectionGeometry and Measurement


Problems in which trigonometry may be used as an alternative method of solution

• The new SAT will include more questions that rely on the special properties of 30-60-90 triangles or 45-45-90 triangles.

• Example: In the triangle below, the value of x can be found by using trigonometry (sin 30o= . But the value of x can also be determined with the knowledge that in a 30-60-90 triangle, the leg opposite the 30-degree angle is half as long as the hypotenuse.

x 12



Properties of Tangent Lines

• Questions on the new SAT may require knowledge of the property that a line tangent to a circle is perpendicular to a radius drawn to the point of tangency, as illustrated below.




Coordinate Geometry

• Some questions on the new SAT may require knowledge of the properties of the slopes of parallelor perpendicular lines.

• Some questions may require students to find the equations of lines, midpoints of line segments, or distance between two points in the coordinate plane.


Qualitative Behavior of Graphs and Functions• A question on the new SAT might show the graph

of a function in the xy-coordinate plane and ask students to give (for portion of graph shown)the number of values of x for which f(x)=3.

Correct Answer: 4




Transformations and Their Effect onGraphs of Functions

• The new SAT will include questions that ask students to determine the effect of simple transformation on graphs of functions.

• Example: Graph of function f(x) could be given and students would be asked questions about the graphof function f(x+2).


Data Analysis, Statistics,and Probability


Enhanced Math SectionData Analysis, Statistics, and Probability

Data Interpretation, Scatterplots, and Matrices

• A question on the new SAT might ask about the line of best fit for a scatterplot. Students would be expected to identify the general characteristics of the line of best fit by looking at the scatterplot.

• Students would not be expected to use formal methods of finding the equation of the line of best fit.

• Students will be expected to interpret data displayed in tables, charts, and graphs.


A science class bought 20 different batteries of various brands and prices. They tested each battery’s duration by seeing how long it would keep a motor running before losing power. For each battery, the class plotted the duration against the price, as shown above. Of the 5 labeled points, which one corresponds to the battery that cost the least amount per hour of duration?

(A) A(B) B(C) C(D) D(E) E

Correct Answer: C

What’s new about this question? The new SAT will have more questions involving scatterplots and proportional reasoning, of which this question is an example.

Enhanced Math SectionData Analysis, Statistics, and Probability Data Interpretation, Scatterplots, and Matrices–Sample Problem

A.

B.C.

D.

E.


Enhanced Math SectionData Analysis, Statistics, and Probability

Geometric Probability

• Example: If a point is to be chosen at random from the interior of a region, part of which is shaded, students might be asked to find the probability that the point chosen will be from the shaded portion.


Colleges Requiring a Standardized Writing Test

• Colleges that accept the SAT will continue todo so, and all will receive the writing score.

• Many colleges have announced that they will require or recommend that students taking any college admissions exam must submit a writing score (including an essay) beginning with those entering college in the fall of 2006.


Additional Research on the New SATSurvey of Admissions Directors

• A recent College Board sampling of 774 four-year colleges indicates that 59 percent of the institutions sampled will use the writing score for admissions and another 31 percent are still considering its use.

• The colleges varied by admissions selectivity and size, and represented a good cross-section of higher education institutions.



The findings:

• 74 percent of respondents say they will use the newSAT writing score in admissions decisions.

• 68 percent of respondents plan to download and print applicants’ essays.

• 35 percent of these respondents said they would read all essays and 19 percent said they would read most essays.

• 32 percent of respondents will use the essay forcourse placement.



The reasons most often cited by those respondents saying that they plan to read applicants’ essays were:

• To provide additional information about a candidate’s writing skills

• To compare and verify an application essay

• To use as an additional placement essay


Additional Information about the SAT Subject Tests

• January 2005: The SAT Subject Testin Writing will be administered for thelast time

• All other SAT Subject Tests will continue, including Math I and Math II


How Students Can PrepareStudents should:

• Challenge themselves throughout high school by taking rigorous courses, including at least three years of math

• Read and write as much as possible—both in and outside of school

• Familiarize themselves with the SAT so they know what to expect

on test day

• Familiarize themselves with the different types of questions on the SAT, the directions for each type of question, and how the test is scored

• Take the new PSAT/NMSQT in October 2004–the new PSAT/NMSQT will be the best preparation for the new SAT


How Students Can PrepareAvailability of Sample Questions

• The PSAT/NMSQT Student Bulletin, the free booklet that includes a full-length practice test, will be available early fall 2004.

• The 2004 PSAT/NMSQT Score Report Plus will be sent to schools in December 2004 and will include explanations for every question (available online to any student who takes the PSAT/NMSQT in 2004).

• The 2004 PSAT/NMSQT Score Report Plus mailing will include advanced math sample questions.

• The new SAT Preparation Booklet™, (the successor to Taking the SAT), the free booklet that includes a full-length practice test, will be available in fall 2004.


How Students Can Prepare

Availability of Sample Questions

• The Official SAT Study Guide: For the New SAT ™, will be available in fall 2004.

• The Official SAT Online Course™, the successor to One-on-One with the SAT®, will be available in fall 2004.

• The online SAT Learning Center® at www.collegeboard.com will include new SAT sample questions beginning in fall 2004.


www.collegeboard.com


www.collegeboard.com

Documents

The New SAT ® Important Information for High School Math Teachers