The New SAT

1
The New SATImportant Information for High
School Math Students

• Prepare. Inspire. Connect.

2
Why Is the SAT Changing?

• To better reflect todays classroom practices
• To make the test more closely related to the
  skills students will need to succeed in college
• To reinforce the importance of writing skills
• To help colleges make better admissions and
  placement decisions

3
Changes to the SAT and the PSAT/NMSQTAn Overview

• Skills Feedback
• The PSAT/NMSQT provides individualized feedback
  to students through its Score Report Plus.
• The College Board is working toward the addition
  of a similar tool to the SAT.

4
SkillsFeedbackScore Report Plus
5
Skills FeedbackScore Report Plus

• Tells students how their scores compare to 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

6
Skills FeedbackScore Report Plus

• Improve Your SkillsExamples
• Applying rules in algebra and geometry
• How to improve Review algebra rules (such as
  exponents, solving equations and inequalities)
  and geometry rules (such as measures of angles
  associated with parallel lines). Become familiar
  with geometric formulas at the beginning of math
  sections of the test, and practice problems that
  use them.See questions 7, 11, 13
• 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

7
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.

8
Math Changes to the SAT An Overview

• New SAT will include expanded math topics, such
  as exponential growth, absolute value, and
  fractional exponents. Function notation will also
  be introduced. Greater emphasis will be placed on
  other topics such as graphs of linear functions
  and scatter plots.
• Quantitative comparisons will be eliminated

9
Math Changes to the SAT An Overview
Quantitative comparisons will be ELIMINATED

• Column A Column B
• x 0
• x 1
• x 1
• 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

0
10
Time Specifications
11
Test Content and Question Types
Note Algebra II is new!!!
12
Test Scores
13
A Closer Look at the Math Sectionof the New SAT
14
Math Section Measures Problem-Solving Skills

• Emphasis on math reasoning SAT math measures the
  ability to apply math content to real-life
  problems.
• SAT is unique in having some grid-in questions
  requiring student-produced responsesas
  recommended by NCTM (National Council of Teachers
  of Mathematics).
• Approximately 1520 percent of math questions on
  the new SAT and 15 percent of math questions on
  the new PSAT/NMSQT will either cover new topics
  or will cover existing topics in greater depth.

15
Calculator Policy

• Every question on the new SAT can be solved
  without a calculator however, using a calculator
  on some questions may be helpful to students.
• A scientific or graphing calculator will be
  recommended for the new tests.

16
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

17
Enhanced Math Section

• Number and Operations

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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.

t 8
19
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.

20
Enhanced Math Section

• Algebra and Functions

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Enhanced Math SectionAlgebra 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

22
Enhanced Math SectionAlgebra 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.
• There will also be expressions such as m where
  the exponent is a rational number.

3 4
23
Enhanced Math SectionAlgebra and
FunctionsInteger and Rational Exponents sample
problem

• If x -3 64, what is the value of x ?
• 4
• 8
• 16
• Correct Answer B
• Whats 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 .

1 2
1 4
1 2
1 2
24
Enhanced Math SectionAlgebra 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
  be inversely proportional if y for some
  constant k

k x
25
Enhanced Math SectionAlgebra 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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Enhanced Math SectionAlgebra and
FunctionsFunction 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
• Whats 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
27
Enhanced Math SectionAlgebra 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.

28
Enhanced Math SectionAlgebra 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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Enhanced Math SectionAlgebra 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?
• 6
• 7
• 8
• 9
• 10
• Correct Answer B
• Whats new about this question? The use of the
  term y-intercept.

30
Enhanced Math SectionAlgebra 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 2x 2 and y 2(x-1)2.

31
Enhanced Math Section

• Geometry and Measurement

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Enhanced Math SectionGeometry 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.

33
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
34
Enhanced Math SectionGeometry 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.

35
Enhanced Math SectionGeometry 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.

36
Enhanced Math SectionGeometry 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.
• The answer is 4

37
Enhanced Math SectionGeometry 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(x2).

38
Enhanced Math Section

• Data Analysis, Statistics,and Probability

39
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 scatter plot. Students
  would be expected to identify the general
  characteristics of the line of best fit by
  looking at the scatter plot.
• Students would not be expected to use formal
  methods of finding the equation of the line of
  best fit.
• Students will also be expected to interpret data
  displayed in tables, charts, and graphs.

40
Enhanced Math SectionData Analysis, Statistics,
and ProbabilityData 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
  batterys 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
• B
• C
• D
• E
• Correct Answer C
• Whats new about this question? The new SAT will
  have more questions involving scatterplots and
  proportional reasoning, of which this question is
  an example.

41
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.

42
How Students Can Prepare

• Students should
• Challenge themselves throughout high school by
  taking rigorous courses, including at least three
  years of math
• 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 2004the new
  PSAT/NMSQT will be the best preparation for the
  new SAT

43
How Students Can PrepareSample 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 mailing
  will include advanced math sample questions.
• The new version of Taking the SAT, the free
  booklet that includes a full-length practice
  test, will be available in fall 2004.
• Real SATs, the successor to 10 Real SATs, 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.