high school mathematics

high school mathematics

The aim of this meta entry is to index entries suitable for
high school students.

Basics

1.

set, union,

intersection

2.

natural numbers

,

rational numbers

,

real numbers

3.

associativity of multiplication

4.

product of negative numbers

5.

equation,

inequality

6.

proportion equation

, proportionality of numbers

7.

per cent

8.

mathematical induction

9.

proof by contradiction

10.

converse

11.

contrapositive

Algebra

1.

opposite number,

difference

2.

inverse number

,

division

3.

multiple

,

product

4.

entries on rational numbers

5.

irrational numbers

6.

factorization of

integers

7.

linear equation

8.

square of sum

9.

difference of squares

10.

grouping method for factoring polynomials

11.

factoring

a sum or difference of two cubes

12.

zero rule of product

13.

http://

planetmath

.org/ConjugationMnemonic

conjugation

14.

even-even-odd rule

15.

completing the square

16.

square roots of rationals

17.

quadratic formula

18.

quadratic inequality

19.

strange root

20.

inequality with absolute values

21.

absolute value inequalities

22.

long division

of

polynomials

Geometry

1.

basic geometric figures:

–

points

–

lines

–

planes

–

line segments

–

rays

–

angles

–

triangles

–

parallelograms

–

rectangles

–

trapezoids

–

polygons

–

regular polygons

–

base and height of triangle

–

circles

–

parts of a ball

–

cylinder

–

solid cone

2.

basic geometric

properties

:

–

intersections

–

http://planetmath.org/Betweenness

between

–

endpoints

–

http://planetmath.org/

Midpoint

midpoints

–

parallelism

–

perpendicularity

–

http://planetmath.org/

Congruence

congruence

–

similarity

–

similar triangles

–

tangent of circle

3.

acute angles

, convex angles, radian

4.

complementary angles

,

supplementary angles

,

explementary angles

5.

angle between two lines

,

angle of view

6.

projection of point

7.

locus

8.

normal line

,

angle bisector

,

angle bisector as locus

,

center normal as locus

9.

measurements (lengths, areas, and volumes) of basic geometric figures

10.

compass and straightedge constructions

:

–

http://planetmath.org/Midpoint

midpoint

–

perpendicular bisector

–

dropping the

perpendicular

from a point to a line

–

erecting the perpendicular to a line at a point

–

http://planetmath.org/CompassAndStraightedgeConstructionOfAngleBisector

angle bisector

–

http://planetmath.org/CompassAndStraightedgeConstructionOfRegularTriangle

regular triangle

–

http://planetmath.org/CompassAndStraightedgeConstructionOfDuplicatingAnAngle

duplicating an angle

–

http://planetmath.org/CompassAndStraightedgeConstructionOfCenterOfGivenCircle

center of a circle

–

construction of tangent

–

http://planetmath.org/

Circumcenter

circle

passing through

three noncollinear points

–

http://planetmath.org/CompassAndStraightedgeConstructionOfParallelLine

parallel line

–

http://planetmath.org/CompassAndStraightedgeConstructionOfSquare

square

–

http://planetmath.org/NSectionOfLineSegmentWithCompassAndStraightedge

n

-

section

of line segment

–

circle with given center and given radius

–

http://planetmath.org/CompassAndStraightedgeConstructionOfSimilarTriangles

similar triangles

–

http://planetmath.org/CompassAndStraightedgeConstructionOfGeometricMean

geometric mean

–

http://planetmath.org/ConstructionOfCentralProportion

central proportional

–

http://planetmath.org/CompassAndStraightedgeConstructionOfInversePoint

inverse point

with respect to a circle

–

http://planetmath.org/CompassAndStraightedgeConstructionOfRegularPentagon

regular pentagon

–

http://planetmath.org/ConstructionOfRegular2nGonFromRegularNGon

construction of

regular

2

⁢

n

-gon from regular

n

-gon

11.

trisection of angle

12.

axiomatic proofs in

geometry

:

–

angles of an

isosceles triangle

–

determining from angles that a triangle is isosceles

–

isosceles triangle theorem

–

converse of isosceles triangle theorem

–

parallelogram theorems

–

regular polygon and circles

–

Pythagorean theorem

and its various proofs:

*

http://planetmath.org/ProofOfPythagoreasTheorem

using four

congruent

triangles and a square

*

http://planetmath.org/ProofOfPythagoreanTheorem

dropping

altitude

to form three similar triangles

*

http://planetmath.org/GarfieldsProofOfPythagoreanTheorem

Garfield’s proof

*

http://planetmath.org/ProofOfPythagoreanTheorem2

two dissections of a square with side

a

+

b

–

construct the center of a given circle

–

Thales’

theorem

and its

http://planetmath.org/ProofOfThalesTheorem

proof

–

opposing angles in a

cyclic quadrilateral

are supplementary

–

mid-segment theorem

Analytic geometry

1.

analytic geometry

2.

Cartesian coordinates

3.

coordinates of midpoint

4.

slope

5.

tangent line

6.

condition of orthogonality

7.

http://planetmath.org/AngleBetweenTwoLines

angle between two lines

8.

conics (

ellipse

,

hyperbola

,

parabola

)

9.

polar coordinates

Vectors and Matrices

1.

sum of vectors

(i.e. parallelogram principle),

difference of vectors

2.

Euclidean vectors

3.

mutual positions of vectors

4.

scalar product

5.

matrices,

addition

and

multiplication

of matrices

Trigonometry

1.

right triangle

2.

regular triangle

3.

isosceles triangle

4.

altitudes

5.

bisectors

6.

ASA, SSS, SAS, SSA (

triangle solving

)

7.

exact trigonometry tables

8.

sohcahtoa

9.

determining signs of trigonometric functions

10.

addition formulas for sine and cosine

11.

addition formula for tangent

12.

goniometric formulae

13.

trigonometric equation

Functions

1.

definitions

and

operations

of

functions

2.

argument

3.

polynomial functions

(including

linear functions

)

4.

rational functions

5.

functions involving

6.

exponential functions

7.

Briggsian logarithms

8.

trigonometric functions

9.

limit of real number sequence

10.

geometric sequence

11.

sequences

and series

Differential calculus

1.

concept

of a limit

2.

limit rules of functions

,

improper limit

3.

continuous

4.

http://planetmath.org/LimitOfDisplaystyleFracsinXxAsXApproaches0

limit of sine divided by angle at 0

5.

intermediate value theorem

6.

derivative

7.

derivatives of sine and cosine

8.

derivative of inverse function

9.

related rates

10.

minimum

and

maximum

of functions (

extrema

)

11.

least and greatest value of function

12.

mean value theorem

13.

Rolle’s theorem

Integral calculus

1.

Riemann sum

2.

integral

3.

left hand rule

4.

right hand rule

5.

midpoint rule

6.

http://planetmath.org/CompositeTrapezoidalRule

trapezoid rule

7.

fundamental theorem of calculus

8.

integration techniques

Complex numbers

1.

complex numbers

2.

complex function

Applications (word problems)

1.

graphing of equations and inequalities

2.

counting and basic probability

3.

length, area, volume

4.

distance

, rate, speed,

velocity

5.

money,

interest

,

compound interest

Title

high school mathematics

Canonical

name

HighSchoolMathematics

Date of creation

2013-03-22 15:16:09

Last modified on

2013-03-22 15:16:09

Owner

matte (1858)

Last modified by

matte (1858)

Numerical id

93

Author

matte (1858)

Entry type

Topic

Classification

msc 00A20

Related topic

IndexOfEntriesOnCompassAndStraightedgeConstructions

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