The SAT®
Important
Information about
the Math section
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).
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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 Specifications
SAT
SAT
3 hours 45 minutes
70 minutes
Critical Reading
Two 25-minute sections and
one 20-minute section
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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
Test Content and Question Types
SAT
Critical Reading
Sentence Completion
Critical Reading: short and long reading passages
Multiple-choice items and student-produced responses measuring:
Math
Writing
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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.
Student-written essay: Effectively communicate a
point of view on an issue, supporting a position with reasoning and examples.
Test Scores
New SAT
Critical Reading
CR 200–800
Math
M 200–800
W 200–800
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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Calculator Policy
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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Enhanced
Math Section
Number and Operations
The 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 and
grows by
t
doubling every eight years. The expression 100 x 28 would give
the population t years after it begins to grow.
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The 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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Math Section
Algebra and Functions
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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Math Section
Algebra and Functions
Integer and Rational Exponents
• The SAT will have expressions such as z-3 involving
negative exponents.
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4
• There will also be expressions such as m where the
exponent is a rational number.
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Math Section
Algebra and Functions
Integer and Rational Exponents–Sample Problem
If x-3=64, what is the value of x ?
(A)
1
4
(B)
1
2
(C)
4
(D)
8
1
2
(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
expressions involving negative exponents, such as x-3, and fractional exponents, such as x .
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1
2
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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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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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:
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5
2
or 2.5
Math Section
Algebra 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 reallife 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 Section
Algebra and Functions
Linear Functions–Equations and Graphs
• The 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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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)
(B)
(C)
(D)
(E)
6
7
8
9
10
Correct Answer: B
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Math Section
Algebra 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 comparing
the graphs of y=2x2 and y=2(x-1)2.
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Math Section
Geometry and
Measurement
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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Math Section
Geometry 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
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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Math Section
Geometry 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 Section
Geometry and Measurement
Coordinate Geometry
• Some questions on the 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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Math Section
Geometry and Measurement
Qualitative Behavior of Graphs and Functions
• A question on the 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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Math Section
Geometry and Measurement
Transformations and Their Effect on
Graphs 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 graph
of function f(x+2).
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Math Section
Data Analysis, Statistics,
and Probability
Math Section
Data 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 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
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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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