The New SAT®
Important
Information for
High School
Math Teachers
The New SAT Focuses on
College 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Time Frame
• October 2004: New PSAT/NMSQT®
• March 2005: New SAT
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The New SAT: Important Information for High School Math Teachers, June 2004
Time Frame
Class 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
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The New SAT: Important Information for High School Math Teachers, June 2004
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 needs
of 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.)
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The New SAT: Important Information for High School Math Teachers, June 2004
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
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The New SAT: Important Information for High School Math Teachers, June 2004
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
The Changes to the SAT and the
PSAT/NMSQT
Quantitative comparisons will be ELIMINATED
Column A
Column B
x=0
x+1
x–1
(A)
(B)
(C)
(D)
0
The quantity in column A is greater
The quantity in column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
Correct Answer: B
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The New SAT: Important Information for High School Math Teachers, June 2004
The Changes to the SAT and the
PSAT/NMSQT
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
The Changes to the SAT and the
PSAT/NMSQT
Skills Feedback
• The PSAT/NMSQT provides individualized
feedback to students through its Score
Report Plus.
• The College Board is developing a similar tool
for the SAT.
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The New SAT: Important Information for High School Math Teachers, June 2004
Skills
Feedback
Score Report Plus
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PSAT/NMSQT
Score 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
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The New SAT: Important Information for High School Math Teachers, June 2004
PSAT/NMSQT Score Report Plus
New 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Skills Feedback
Score 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Time Specifications
PSAT/NMSQT
Current PSAT/NMSQT
Critical
Reading
Math
Writing
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New PSAT/NMSQT
2 hours 10 minutes
2 hours 10 minutes
50 minutes
50 minutes
Two 25-minute sections
Two 25-minute sections
50 minutes
50 minutes
Two 25-minute sections
Two 25-minute sections
30 minutes
30 minutes
One 30-minute
multiple-choice section
One 30-minute
multiple-choice section
The New SAT: Important Information for High School Math Teachers, June 2004
Time Specifications
SAT
Current SAT
Critical Reading
Math
3 hours
3 hours 45 minutes
75 minutes
70 minutes
Two 30-minute sections and
one 15-minute section
Two 25-minute sections and
75 minutes
70 minutes
Two 30-minute sections and
one 15-minute section
Two 25-minute sections and
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one 20-minute section
one 20-minute section
60 minutes
Two multiple-choice sections (one
25-minute section and
one 10-minute section) and
one 25-minute essay
Writing
Variable Section
New SAT
30 minutes
25 minutes
The New SAT: Important Information for High School Math Teachers, June 2004
Test Content and Question Types
Current SAT
Critical
Reading
Sentence Completion
Sentence Completion
Critical Reading: Long reading passages
Critical Reading: short and long reading passages
Analogies
Multiple-choice items, student-produced
responses, and quantitative comparisons
measuring:
Math
New SAT
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.
Multiple-choice items: Improving sentences and
paragraphs, and identifying sentence errors.
Writing
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Student-written essay: Effectively communicate a
point of view on an issue, supporting a position with
reasoning and examples.
The New SAT: Important Information for High School Math Teachers, June 2004
Test Scores
Current SAT
New SAT
Critical Reading
V 200–800
CR 200–800
Math
M 200–800
M 200–800
W 200–800
Will include 2 subscores:
Writing
(Subscores)
Essay
2–12
(1/3 of writing score)
Multiple-choice 20–80
(2/3 of writing score)
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The New SAT: Important Information for High School Math Teachers, June 2004
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
The New SAT Field Trial
Based 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
A Closer Look
at the Math
Section of
the New SAT
Math Section
Measures 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
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 complete
3 years of math and 69% complete 4 or
more years of math
• 92% of minority college-bound students complete
3 years of math
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The New SAT: Important Information for High School Math Teachers, June 2004
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Calculator Policy
The 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
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced
Math Section
Number and
Operations
The Enhanced Math Section
Number 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 andt grows by
doubling every eight years. The expression 100 x 2 8 would give
the population t years after it begins to grow.
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The New SAT: Important Information for High School Math Teachers, June 2004
The Enhanced Math Section
Number 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced
Math Section
Algebra and Functions
Enhanced Math Section
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:
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
Integer and Rational Exponents
• On the current SAT, exponents are restricted
to positive integers. The new SAT will have
expressions such as z-3 involving negative
exponents.
3
4
• There will also be expressions such as m where
the exponent is a rational number.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
Integer and Rational Exponents–Sample Problem
1
2
If x-3=64, what is the value of x ?
(A)
1
4
(B)
1
2
(C)
4
(D)
8
(E) 16
Correct Answer: B
What’s new about this question?
The current SAT has questions involving positive integer exponents. The new SAT will have
1
expressions involving negative exponents, such as x-3, and fractional exponents, such as x 2 .
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
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 to
k
be inversely proportional if y= x for some
constant k
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
Function Notation
• Students should be familiar with both the concept of
a 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
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:
5
2
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
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
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
Linear Functions–Equations and Graphs–
Sample Problem
Note: Figure not drawn to scale
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.”
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Algebra and Functions
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 comparing
the graphs of y=2x2 and y=2(x-1)2.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced
Math Section
Geometry and
Measurement
Enhanced Math Section
Geometry and Measurement
Geometric Notation for Length, Segments,
Lines, Rays, and Congruence
• Geometric notation such as
and
will
be used. The term “congruent” and the
congruence symbol will be used.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Geometry 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
x
trigonometry (sin 30o= 12 . 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Geometry and Measurement
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Geometry and Measurement
Coordinate Geometry
• Some questions on the new SAT may require knowledge
of the properties of the slopes of parallel
or 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Geometry and Measurement
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
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Geometry and Measurement
Transformations and Their Effect on
Graphs 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 graph
of function f(x+2).
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced
Math Section
Data Analysis,
Statistics,
and Probability
Enhanced Math Section
Data 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Data Analysis, Statistics, and Probability
Data Interpretation, Scatterplots, and Matrices–Sample Problem
D.
A.
E.
B.
C
.
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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Enhanced Math Section
Data 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Colleges Requiring a Standardized
Writing Test
• Colleges that accept the SAT will continue to
do 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Additional Research on the New SAT
Survey 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
Additional Research on the New SAT
Survey of Admissions Directors
The findings:
• 74 percent of respondents say they will use the new
SAT 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 for
course placement.
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The New SAT: Important Information for High School Math Teachers, June 2004
Additional Research on the New SAT
Survey of Admissions Directors
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
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The New SAT: Important Information for High School Math Teachers, June 2004
Additional Information about the SAT
Subject Tests
• January 2005: The SAT Subject Test
in Writing will be administered for the
last time
• All other SAT Subject Tests will continue,
including Math I and Math II
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The New SAT: Important Information for High School Math Teachers, June 2004
How Students Can Prepare
Students 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
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The New SAT: Important Information for High School Math Teachers, June 2004
How Students Can Prepare
Availability 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.
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The New SAT: Important Information for High School Math Teachers, June 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.
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The New SAT: Important Information for High School Math Teachers, June 2004
www.collegeboard.com
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The New SAT: Important Information for High School Math Teachers, June 2004
www.collegeboard.com
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The New SAT: Important Information for High School Math Teachers, June 2004