Sat math overview from college board

The SAT®

Important 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 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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SAT

3 hours 45 minutes

Critical Reading70 minutesTwo 25-minute sections and one 20-minute section

Math70 minutesTwo 25-minute sections and one 20-minute section

Writing

60 minutesTwo multiple-choice sections (one 25-minute section and one 10-minute section) and one 25-minute essay

Variable Section 25 minutes

Time SpecificationsSAT

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Test Content and Question Types

SAT

Critical ReadingSentence CompletionCritical 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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New SAT

Critical Reading CR 200–800

Math M 200–800

Writing

(Subscores)

W 200–800

2 subscores:

Essay 2–12 (1/3 of writing score)

Multiple-choice 20–80 (2/3 of writing score)

Test Scores

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 PolicyThe 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

EnhancedMath Section

Number and Operations

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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.

t 8

The Math SectionNumber and Operations

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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.

Math Section

Algebra and Functions

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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

• Example:

Math SectionAlgebra and Functions

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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.

3 4


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Integer and Rational Exponents–Sample ProblemIf x-3=64, what is the value of x ?

(A)

(B)

(C) 4

(D) 8

(E) 16Correct 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

14

1 2


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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 tobe inversely proportional if y= for some constant k k

x


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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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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 5 2


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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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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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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


Note: Figure not drawn to scale

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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 comparingthe graphs of y=2x2 and y=2(x-1)2.

Math Section

Geometry and Measurement

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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.

Math SectionGeometry and Measurement

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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.

x 12


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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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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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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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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(x+2).

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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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

Math SectionData Analysis, Statistics, and Probability Data Interpretation, Scatterplots, and Matrices–Sample Problem

A.

B.C.

D.

E.

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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.

Sat math overview from college board

Education

math reasoning

math multiplechoice

expanded content

comparison of test content

math changes

eliminatedthe content

content areas

high school math teachers