# high school mathematics

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

## Basics

1. 1.

set, union, intersection

2. 2.
3. 3.
4. 4.
5. 5.

equation, inequality

6. 6.

proportion equation, proportionality of numbers

7. 7.

per cent

8. 8.

mathematical induction

9. 9.
10. 10.
11. 11.

## Algebra

1. 1.

opposite number, difference

2. 2.
3. 3.
4. 4.
5. 5.
6. 6.

factorization of integers

7. 7.
8. 8.
9. 9.
10. 10.
11. 11.

factoring a sum or difference of two cubes

12. 12.
13. 13.

http://planetmath.org/ConjugationMnemonicconjugation

14. 14.
15. 15.

completing the square

16. 16.
17. 17.
18. 18.
19. 19.
20. 20.
21. 21.
22. 22.

## Geometry

1. 1.

basic geometric figures:

• points

• lines

• planes

• rays

• angles

• circles

• parts of a ball

2. 2.

basic geometric properties:

• intersections

• http://planetmath.org/Betweennessbetween

• http://planetmath.org/Midpointmidpoints

• http://planetmath.org/Congruencecongruence

3. 3.

acute angles, convex angles, radian

4. 4.
5. 5.
6. 6.
7. 7.

locus

8. 8.
9. 9.

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

10. 10.
• http://planetmath.org/Midpointmidpoint

• dropping the perpendicular from a point to a line

• erecting the perpendicular to a line at a point

• http://planetmath.org/CompassAndStraightedgeConstructionOfAngleBisectorangle bisector

• http://planetmath.org/CompassAndStraightedgeConstructionOfRegularTriangleregular triangle

• http://planetmath.org/CompassAndStraightedgeConstructionOfDuplicatingAnAngleduplicating an angle

• http://planetmath.org/CompassAndStraightedgeConstructionOfCenterOfGivenCirclecenter of a circle

• http://planetmath.org/Circumcentercircle passing through three noncollinear points

• http://planetmath.org/CompassAndStraightedgeConstructionOfParallelLineparallel line

• http://planetmath.org/CompassAndStraightedgeConstructionOfSquaresquare

• http://planetmath.org/NSectionOfLineSegmentWithCompassAndStraightedge$n$-section of line segment

• http://planetmath.org/CompassAndStraightedgeConstructionOfSimilarTrianglessimilar triangles

• http://planetmath.org/CompassAndStraightedgeConstructionOfGeometricMeangeometric mean

• http://planetmath.org/ConstructionOfCentralProportioncentral proportional

• http://planetmath.org/CompassAndStraightedgeConstructionOfInversePointinverse point with respect to a circle

• http://planetmath.org/CompassAndStraightedgeConstructionOfRegularPentagonregular pentagon

• http://planetmath.org/ConstructionOfRegular2nGonFromRegularNGonconstruction of regular $2n$-gon from regular $n$-gon

11. 11.
12. 12.

axiomatic proofs in geometry:

• angles of an isosceles triangle

• determining from angles that a triangle is isosceles

• Pythagorean theorem and its various proofs:

• *

http://planetmath.org/ProofOfPythagoreasTheoremusing four congruent triangles and a square

• *

http://planetmath.org/ProofOfPythagoreanTheoremdropping altitude to form three similar triangles

• *

http://planetmath.org/GarfieldsProofOfPythagoreanTheoremGarfield’s proof

• *

http://planetmath.org/ProofOfPythagoreanTheorem2two dissections of a square with side $a+b$

• construct the center of a given circle

• Thales’ theorem and its http://planetmath.org/ProofOfThalesTheoremproof

• opposing angles in a cyclic quadrilateral are supplementary

## Analytic geometry

1. 1.
2. 2.
3. 3.
4. 4.

slope

5. 5.
6. 6.
7. 7.

http://planetmath.org/AngleBetweenTwoLinesangle between two lines

8. 8.
9. 9.

## Vectors and Matrices

1. 1.

sum of vectors (i.e. parallelogram principle), difference of vectors

2. 2.
3. 3.

mutual positions of vectors

4. 4.
5. 5.

matrices, addition and multiplication of matrices

## Trigonometry

1. 1.
2. 2.

regular triangle

3. 3.

isosceles triangle

4. 4.

altitudes

5. 5.
6. 6.

ASA, SSS, SAS, SSA (triangle solving)

7. 7.
8. 8.
9. 9.
10. 10.
11. 11.
12. 12.
13. 13.

## Functions

1. 1.
2. 2.
3. 3.
4. 4.
5. 5.

functions involving

6. 6.
7. 7.
8. 8.
9. 9.

limit of real number sequence

10. 10.
11. 11.

sequences and series

## Differential calculus

1. 1.

concept of a limit

2. 2.
3. 3.
4. 4.

http://planetmath.org/LimitOfDisplaystyleFracsinXxAsXApproaches0limit of sine divided by angle at 0

5. 5.
6. 6.
7. 7.
8. 8.
9. 9.
10. 10.

minimum and maximum of functions (extrema)

11. 11.

least and greatest value of function

12. 12.

mean value theorem

13. 13.

Rolle’s theorem

## Integral calculus

1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
6. 6.

http://planetmath.org/CompositeTrapezoidalRuletrapezoid rule

7. 7.
8. 8.

1. 1.
2. 2.

## Applications (word problems)

1. 1.

graphing of equations and inequalities

2. 2.

counting and basic probability

3. 3.

length, area, volume

4. 4.

distance, rate, speed, velocity

5. 5.
Title high school mathematics HighSchoolMathematics 2013-03-22 15:16:09 2013-03-22 15:16:09 matte (1858) matte (1858) 93 matte (1858) Topic msc 00A20 IndexOfEntriesOnCompassAndStraightedgeConstructions