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2
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- 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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3
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- 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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5
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6
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7
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8
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- 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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- 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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10
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11
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- 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.
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12
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- 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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13
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14
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- 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
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15
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- 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.
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16
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- Integer and Rational Exponents–Sample Problem
- If x-3=64, what is the value of x ?
- (A)
- (B)
- (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 expressions involving negative
exponents, such as x-3, and fractional exponents, such as x .
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17
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- 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
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18
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- 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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- 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
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20
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- 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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21
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- 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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22
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- 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
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23
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- 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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24
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25
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- 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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- 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.
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27
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- 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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28
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- 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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29
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- 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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30
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- 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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31
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- Data Analysis, Statistics,
and Probability
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32
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- 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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33
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- 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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- 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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Notes
