The SAT

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The SATImportant Information aboutthe Math
section
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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 responsesas
  recommended by NCTM (National Council of Teachers
  of Mathematics).

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Content in the SAT and the PSAT/NMSQT

• Math
• Quantitative comparisons has been eliminated
• The content reflects 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 more effectively assess the
  mathematics necessary for student success in
  college.

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Time SpecificationsSAT
SAT
3 hours 45 minutes
Critical Reading 70 minutes Two 25-minute sections and one 20-minute section
Math 70 minutes Two 25-minute sections and one 20-minute section
Writing 60 minutes Two multiple-choice sections (one 25-minute section and one 10-minute section) and one 25-minute essay
Variable Section 25 minutes
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Test Content and Question Types
SAT
Critical Reading Sentence Completion Critical Reading short and long reading passages
Math 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.
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Test Scores
New SAT
Critical Reading CR 200800
Math M 200800
Writing(Subscores) W 200800 2 subscores Essay 212 (1/3 of writing score) Multiple-choice 2080 (2/3 of writing score)
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Calculator Policy
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Calculator Policy

• A scientific or graphing calculator will be
  recommended for the test.
• 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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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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EnhancedMath Section

• Number and Operations

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The 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
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The 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.

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Math Section

• Algebra and Functions

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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

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Math SectionAlgebra and Functions

• Integer and Rational Exponents
• The 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
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Math SectionAlgebra and Functions

• Integer and Rational ExponentsSample Problem
• If x-364, what is the value of x ?
• (A)
• (B)
• (C) 4
• (D) 8
• (E) 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
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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
  tobe inversely proportional if y for
  some constant k

k x
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Math SectionAlgebra and Functions

• 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.

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Math SectionAlgebra and Functions

• Function NotationSample 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

5 2
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Math SectionAlgebra and Functions

• Concepts of Domain and Range
• The 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 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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Math SectionAlgebra and Functions

• Linear FunctionsEquations and Graphs
• The SAT will include questions involving linear
  equations, such as ymxb, where m and b are
  constants.
• Some questions may involve graphs of linear
  functions

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Math SectionAlgebra and Functions

• Linear FunctionsEquations and GraphsSample
  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

Note Figure not drawn to scale
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Math SectionAlgebra and Functions

• Quadratic Functions Equations and Graphs
• Questions involving quadratic equations and/or
  their graphs may appear on the SAT. For example,
  a question might involve comparingthe graphs of
  y2x2 and y2(x-1)2.

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Math Section

• Geometry and Measurement

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Math SectionGeometry 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.

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Math SectionGeometry and Measurement

• Problems in which trigonometry may be used as an
  alternative method of solution
• The 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
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Math SectionGeometry and Measurement

• Properties of Tangent Lines
• Questions on the 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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Math SectionGeometry and Measurement

• Coordinate Geometry
• Some questions on the 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.

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Math SectionGeometry and Measurement

• Qualitative Behavior of Graphs and Functions
• A question on the SAT might show the graphof 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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Math SectionGeometry and Measurement

• Transformations and Their Effect onGraphs of
  Functions
• The SAT will include questions that ask students
  to determine the effect of simple transformations
  on graphs of functions.
• Example Graph of function f(x) could be given
  and students would be asked questions about the
  graphof function f(x2).

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Math Section

• Data Analysis, Statistics,and Probability

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Math SectionData Analysis, Statistics, and
Probability

• Data Interpretation, Scatterplots, and Matrices
• A question on the 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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Math SectionData Analysis, Statistics, and
Probability Data Interpretation, Scatterplots,
and MatricesSample Problem

• 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) A
• (B) B
• (C) C
• (D) D
• (E) E
• Correct Answer C

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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.