SAT II 数学大纲
I. ARITHMETIC
A. Whole numbers
1. Operations—addition, subtraction, multiplication, division
2. Prime and composite numbers
3. Factors and divisors
B. Fractions
1 Types—proper, improper, mixed numbers
2 Operations
C. Decimals
1 Operations
2 Conversions
a) Decimals to fractions 0) Fractions to decimals
3 Rounding and approximation
4 Powers of 10 a) Multiplication 0) Division
c) Scientific notation
D. Percent
1 Conversions
a) Percent to decimal 0) Decimal to percent
2 Percent problems
E Ratio and proportion
F Square roots
G. Averages
H Metric measurement
II ALGEBRA
A Signed numbers
1 absolute value
2 Inequality and order of signed numbers
3 Addition, subtraction, multiplication, division
4 Order of operations
5 Grouping symbols
6 Evaluating algebraic expressions and formulas
B. Properties of operations
1 Commutative properties
2 Associative properties
3 Distributive properties
4 Special properties of zero
5 Special properties of one
6 Additive and multiplicative inverses C Operations with polynomials
1 Exponents and coefficients
2 Addition and subtraction
3 Multiplication
4 Division
D Equations in one variable
1 Methods of solution
2 Literal equations
E Inequalities in one variable
F Systems of equations and inequalities in two variables
G. verbal problems
1 number
2 Consecutive integer
3 Motion
4 Coin
5 Mixture
6 Age
7 Work
3 Variation—direct and inverse H. Special products and factoring
1 Common monomial factors
2 Trinomials of the form ax2 + bx + c
3 Difference of two squares
4 Complete factoring I Algebraic fractions
1 Simplifying fractions
2 Multiplication
3 Division
4. Addition and subtraction
a) Same denominators
b) Different denominators
5 Complex fractions
6 Equations involving fractions
J Radicals and irrational numbers
1 Simplifying radicals
2 Addition and subtraction of radicals
3 Multiplication and division of radicals
4 Rationalizing denominators
5 Radical equations
6 Fractional exponents
K. Solution of quadratic equations
1 Factoring
2 Completing the square
3 Formula L. Graphing
1 Ordered pairs in the plane
2 Methods of graphing linear equations a) Pairs in the solution set
0) Intercepts
c) Slope and slope-intercept method
3 Parallel and perpendicular lines
4 Graphing inequalities
5 Graphical solution of systems of equations
M Solution of simple cubic equations
1 Factor theorem
2 Remainder theorem
3 Synthetic division
4 Irrational and complex roots
5 Solving simple cubic equations III. GEOMETRY
A Angles
1 Types—acute, right, obtuse
2 Complements and supplements
3 Vertical angles B Lines
1 Parallel lines and their angles
2 Perpendicular lines
C. Triangles
1 Sum of the angles
2 Congruent triangles
3 Similar triangles
4 Special triangles a) Isosceles
0) Equilateral
c) Right (Pythagorean Theorem)
5 Vectors
D Polygons 1 Quadrilaterals a) Parallelogram 0) Rectangle
c) Square
d) rhombus
e) Trapezoid
f) Regular Polygons
E. Circles
1 Special lines and their related angles a) Radius and diameter
0) Chord
c) Tangent
d) Secant
2 Angle and arc measurement
3 Polygons inscribed in circles F Perimeter and area
1 Triangles
2 Polygons
3 Circles
a) Circumference and arc length 0) Area of sectors and segments
G Volume
1 Pyramid
2 Prism
3 Cylinder
4 Cone
5 Sphere
6 cube
7 Rectangular solid H Coordinate geometry
1 Coordinate representation of points
2 Distance between two points
3 Midpoint of a line segment
4 Slope of a line
5 Parallel and perpendicular lines I Basic trigonometry
1 Definitions of sine, cosine, tangent
2 Trigonometry in special triangles a) 30°-60°-9u° triangle
0) Isosceles right triangle 3 Trigonometric problems a) Angle of elevation 0) Angle of depression
IV FUNCTIONS AND THEIR GRAPHS A Relations and functions
1 Ordered pairs
2 Function notation
3 Domain and range
4 One-to-one functions
5 Inverse functions
6 combining functions
a) Addition, subtraction, multiplication, division 0) Composition B Graphs
1 Linear a) Slope
0) Intercepts
2 Special functions
a) absolute value function 0) Step functions
3 Polynomial and rational functions a) Quadratic—parabola
i Axis of symmetry
n Vertex
0) cubics
c) hyperbola of the form xy = k
4 Related non-function graphs a) Circle
0) Ellipse
c) hyperbola of the form ax2 - 0y2 = c
5 Graphs of inverse functions
V REAL NUMBER SYSTEM
A sunsets of the real numbers
1 Natural numbers a) Primes
0) Composites—prime factorization
2 Integers
a) Multiples and divisors i Factors
n Divisibility
in Least common multiple iv Greatest common divisor v Perfect squares
b) Odd and even integers
3 Rational and irrational numbers
a) Decimal representations
b) Simplification of radicals and exponents
c) Identifying rational and irrational numbers B Operations and properties
1 Properties of the binary operations
a) Closure
b) Commutative properties
c) Associative properties
d) Distributive properties
2 Absolute value
3 Real number line
a) Order
b) Density
c) Completeness
4 Properties of zero and one
a) Identity elements
b) Additive and multiplicative inverses
c) Division involving zero
d) Zero as an exponent
5 Nature of the roots of quadratic equations
6 Pythagorean triples
VI. LOGIC
A Propositions
1 Simple statements
a) Symbols
b) Quantifiers (all, some)
2 Negation
3 Compound statements
a) Conjunction
b) Disjunction
c) Implication (conditional statements)
i Necessary conditions
n Sufficient conditions
in Equivalence (necessary and sufficient conditions)
d) Derived implications i Converse
n Inverse in Contrapositive B Truth tables C Methods of proof
1 Valid arguments
a) Direct
b) Indirect—contradiction and counterexample
2 Invalid arguments—fallacies
VII SETS
A Meaning and symbols
1 Set notation
2 Set membership
3 Ordered pairs
4 Cardinality of a set B Types of sets
1 Finite
2 Infinite
3 Empty
C. Relationships between sets
1 Equal sets
2 Equivalent sets
3 Subsets
4 Complements
D. Set Operations
1 Union
2 Intersection
3 Cartesian products
4 Laws of set operations
5 Closure
E Venn diagrams
VIII TRIGONOMETRY
A. Trigonometry of the right triangle
1 Definitions of the six functions
2 Relations of the functions of the complementary angles
3 Reciprocal relations among the functions
4 Variations in the functions of acute angles
5 Pythagorean and quotient relations
6 Functions of 30°, 45°, and 60°
7 Applications of the functions to right triangle problems
B. Trigonometric functions of the general angle
1 Generating an angle of any size
2 Radians and degrees
3 Using radians to determine arc length
4 Definitions of the functions of an angle
5 Signs of the functions in the four quadrants
6 Functions of the quadrantal angle
7 Finding the value of functions of any angle C Identities and equations
1 Difference between identities in equations
2 Proving identities
3 Solving linear trigonometric functions
4 Solving trigonometric quadratic equations D Generalized trigonometric relationships
1 Functions of the sum of two angles
2 Functions of the difference of two angles
3 Functions of the double angle
4 Functions of the half angle
E Graphs of trigonometric functions
1 Graphs of the sine, cosine, and tangent curves
2 Properties of the sine, cosine, and tangent curves
3 Definitions of amplitude, period, and frequency
4 Solving trigonometric equations graphically F Solutions of oblique triangles
1 Law of sines
2 Law of cosines
3 Using logarithms to solve oblique triangle problems
4 Vector problems—parallelogram of forces
5 Navigation problems
IX MISCELLANEOUS TOPICS A. Complex numbers
1 Meaning
2 Operations
a) Addition and subtraction
b) Multiplication and division i Powers of i
n Complex conjugate
3 Complex roots of quadratic equations B Number Bases
1 Converting from base 10 to other bases
2 Converting from other bases to base 10
3 Operations in other bases C Exponents and logarithms
1 Meaning of logarithms
2 Computation with exponents and logarithms
3 Equations
4 Graphs of exponential and logarithmic functions D Binary operations
1 Definition of binary operations
2 Properties of binary operations
3 Application to modular arithmetic E Identity and inverse elements
1 Addition
2 Multiplication
3 Other operations
[ 本帖最后由 端木·宇 于 2008-6-28 18:38 编辑 ]
