词汇->知识->读题->常错细节
A.Arithmetic
a.odd & even
b.prime & composite
c.factor & multiple
prime factorization (positive only: the definition of prime number)
number of factors (positive+negative)
d.gcd & lcm
both calculated by factorization
e.consecutive numbers
f.remainder
dividend=quotient*divisor+remainder 0<=remainder<|divisor|
be careful when dividend or divisor is negative
g.decimal
digit:
hundreds digit tens digit units(ones) digit . tenths digit hundredth digit
cardinal number+s+digit ordinal number+s+digit
terminating decimal/repeating decimal
h.fraction
numerator/denominator
proper fraction/improper fraction/mixed number
reciprocal
i.
x is divided by y; y divides x;
ratio; ratio of a to b;
there is twice as much A as B; there is twice A as much as B; A is twice as much as B;
A is 20% more than B; B is 20% less than B;
analyzed by preposition
B.Algebra
a.exponent operation
b.root
square root, cube root, fourth root, ... , nth root
c.equation
linear equation in one variable
linear equation in two variables
quadratic equation in one variable
d.inequality
< less than
>greater than
<=less than or equal to
>=greater than or equal to
e.function
coordinate geometry
xy-cordinate system/xy-plane
quadrant
symmetric /reflection (perpendicular bisector)
distance
linear function y=kx+b
slope k
intercept b (x-intercept is specifically indicated)
parallel
perpendicular
shift
quadratic function
parabola
vertex
Vieta's Theorem
circle
(x-a)^2+(x-b)^2=r^2
f.sequence
arithmetic sequence
geometric sequence
C.Geometry
geometric figures are not necessarily drawn to scale
geometric objects are in the relative positions shown
a.2-D geometry
line
parallel
cross
perpendicular
line segment
angle
opposite angle/vertical angle
alternative angle
corresponding angle
interior angle of the same side
acute/right/obtuse angle
complementary angle supplementary angle
triangle
alpha+beta+gemma=180 degree
a+b>c <-> c-b<a
equilateral triangle isosceles triangle
right triangle
hypotenuse & leg
Pythagorean Theorem a^2+b^2=c^2
special right triangle
acute triangle a^2+b^2>c^2
obtuse triangle a^2+b^2<c^2
congruent triangles
similar triangles
quadrilateral
parallelogram
rectangle
square
rhombus
trapezoid
polygon
triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon
n-sided polygon polygon with n sides polygon with n vertices
interior angle/exterior angle diagonal regular polygon
circle
radius
diameter
chord
circumference
arc (major arc/minor arc)
sector
tangent
b.3-D geometry (solid geometry)
rectangular solids
vertex, edge, face
cubes
cylinders
base, lateral surface
D.Data analysis
a.statics
concepts
Mean (Arithmetic Mean/Weighted Mean) Mean(a*x+b)=a*Mean(x)+b
Median (odd elements/even elements) Median(a*x+b)=a*Median(x)+b
Mode (more than one number-> all are) Mode(a*x+b)=a*Mode(x)+b
Range =max-min Range(a*x+b)=a*Range(x)
Variance sigma^2 Variance(a*x+b)=a^2*Variance(x)
Standard Deviation sigma=sqrt(Variance) SD(a*x+b)=a*SD(x)
Quartile Q1, Q2, Q3
IQR (interquartile range) =Q3-Q1
Boxplot L-Q1-Q2(M)-Q3-G
Percentile
Graphs & Tables
Frequency Distribution/Relative Frequency Distribution
Bar Graph
Circle Graph/Pie Graph
Histogram
Scatterplot
Time Plot
Normal Distribution
3-sigma principle:
P(X-sigma<x<X+sigma)=68%
P(X-2*sigma<x<X+2*sigma)=95%
P(X-3*sigma<x<X+3*sigma)=99%
b.probability
mutually exclusive
independent P(A^B)=P(A)P(B)
conditional probability P(A|B)=P(A^B)/P(B)
Bayes' Rule P(A^B)=P(A|B)*P(B)
c.combination & permutation
d.set
union
intersection
complementary/supplementary set
universal set
empty set
